Thesis-Contribution to the management of the drywood termite

Universidade dos Açores
Contribution to the management of
the drywood termite Cryptotermes
brevis in the Azorean Archipelago
ORLANDO MANUEL LABRUSCO FÉLIX GUERREIRO
Diploma Thesis
in order to obtain the degree of
Magister
on the Mestrado em Gestão e Conservação da Natureza
Supervisors:
Prof. Dr. Miguel Ferreira
Prof. Dr. Paulo Borges
Departamento de Ciências Agrárias, Universidade dos Açores
2009
Dedicated to my family, friends
and supervisors for their special
encouragement and support.
Thanks to all that were on the rock with me.
Dedicated especially to you Cláudia for being so patient with me
With special thanks to: Angra do Heroísmo
City Hall for financial support; To Mr. Caiado,
Mr. Gonçalves, Mr. Ernesto and Mr. Valentim
of EDA – Electricidade dos Açores for the
technical support during the field survey
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ABSTRACT
The spread dynamics of an exotic and invasive species is currently an important and
emergent area of research, being the use of computational tools to address this issue highly
relevant. These studies mainly consider the spread of species in natural environments, while
this thesis investigates the spread of an exotic species in the urban environment. In the
Azores archipelago, this environment is significantly infested with the exotic species
Cryptotermes brevis that is causing significant economical and patrimonial losses.
This work aims to provide scientifically based information to understand the potential spread
of the exotic species Cryptotermes brevis in the Azores archipelago at local and regional
scales. At a local scale we aim to determine its flight capability in the specific urban
environment of Angra do Heroísmo and then use that crucial information to build a Cellular
Automata model to reproduce and forecast the species spread in time and space. At a
regional scale, we aim to build a map with the potential occurrence of this species for each
island. These two approaches seek to be helpful tools to the local authorities to manage this
insect pest.
The methods used in the field survey were the door to door interviews, interviews to the pestcontrol companies and to the local City Hall, and application of light traps at the periphery of
the previously known infested area. The light traps provided an estimate of the maximum
flight distances of the winged individuals that was used to calibrate one parameter of the
Cellular Automata based model developed to reproduce, as far has possible, the local
spread pattern.
At the regional scale, a maximum entropy ecological base model was applied in order to
determine the species potential occurrence on each archipelago island. Different scenarios
were constructed using local and world incidence data.
The field data allowed us to update and improve our knowledge of the infestation in the city
buildings since the 2004 survey. We were also able to estimate the flight capacity of the
termite to be of the order of 100m.
The Cellular Automata model was successfully applied to Angra do Heroísmo showing that it
is possible to import the urban environment to the virtual environment of the model. The
stochastic characteristic of the model was unable to generate a strongly asymmetric spatial
distribution of the infestation with only one initial focus of infestation. Unless the probability
of infestation is very small, the evolution of the pest is almost deterministic. The model,
together with some of the field results, suggests that the infestation has spread to areas of
the city with previously unknown occurrence of the pest.
Using the maximum entropy ecological model we constructed several maps showing the
probability of occurrence of this termite on each island. All projections are consistent with a
ii
significant probability of occurrence in all islands. In general, this probability is higher near
the coast line, where the majority of the towns and villages are located.
These results contribute to a better understanding of this species and its presence in the
Azores. The tools developed and applied here are an important starting point for future
applications to study the same species in other cities of the archipelago, or even of other
species. The Cellular Automata model, although in its infancy, clearly has a lot of potential to
help us understand the spatial- temporal evolution of this or other infestation. The results
obtained concerning the probability of occurrence of this species in the archipelago can be
improved once more complete climate information becomes available. These results indicate
that, without appropriate measures, the present situation can become a silent earthquake
slowly spreading to all the Azorean islands.
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RESUMO
A dispersão de espécies exóticas e invasoras é actualmente um emergente e importante
campo de investigação, nomeadamente através do uso de ferramentas computacionais. A
grande maioria destes estudos considera a dispersão de espécies invasoras no ambiente
natural enquanto esta tese investiga a dispersão de uma espécie exótica em ambiente
urbano. No arquipélago dos Açores, este ambiente é significativamente infestado com a
espécie exótica Cryptotermes brevis que tem causado graves danos económicos e
patrimoniais.
Este trabalho ambiciona providenciar informação cientificamente fundamentada para
entender o potencial de distribuição da espécie exótica Cryptotermes brevis no arquipélago
dos Açores à escala local e regional. À escala local procurou-se determinar a capacidade de
voo no ambiente urbano específico de Angra do Heroísmo e utilizar esta importante
informação para construir um modelo de Autómatos Celulares (CA) para reproduzir e prever
a dispersão da espécie espacialmente ao longo do tempo. Ao nível regional, ambicionamos
a construção de um mapa com os potenciais locais de ocorrência da espécie em foco, para
cada ilha. Estas duas abordagens procuram ser importantes ferramentas para as
autoridades locais poderem realizar uma gestão eficaz para o controlo da praga provocada
por este insecto.
Os métodos utilizados na pesquisa de campo foram as entrevistas porta a porta, entrevistas
às companhias de controlo de pragas e à Câmara Municipal de Angra do Heroísmo, e
aplicação de armadilhas luminosas na periferia da área da cidade afectada pela praga. As
armadilhas foram colocadas a várias distâncias de casas e ruas, onde era já sabido a
presença da espécie, permitindo assim estimar um valor provável de distância de voo e
possível fundação de novas colónias. Desta forma foi possível calibrar um importante
parâmetro do modelo de autómatos celulares desenvolvido para reproduzir, tanto quanto
possível, o padrão de dispersão da cidade de Angra do Heroísmo.
Foi utilizado um modelo ecológico, que utiliza a máxima entropia, para determinar o
potencial de ocorrência da espécie em cada ilha do arquipélago. Foram realizadas diversas
simulações utilizando diferentes grupos de variáveis ambientais e dois grupos de
amostragem de presenças da espécie C. brevis. Diferentes cenários foram realizados
utilizando uma amostragem mundial e uma segunda apenas com as presenças regionais.
O trabalho de campo permitiu-nos actualizar e melhorar o nosso conhecimento acerca da
infestação existente nos edifícios da cidade desde 2004. Foi-nos também possível estimar a
capacidade de voo da térmita C. brevis como sendo na ordem dos 100m.
O modelo de autómatos celulares foi aplicado de forma eficaz à cidade de Angra do
Heroísmo demonstrando que é possível importar o ambiente urbano para o ambiente virtual
iv
do modelo. A característica estocástica do modelo não permitiu gerar uma dispersão
espacial assimétrica da praga, apenas utilizando um foco inicial de infestação. Desde que a
probabilidade de infestação não seja muito baixa, a evolução da praga é quase
determinística. O modelo, em conjunto com alguns dados de campo, sugere que a
infestação terá dispersado para áreas da cidade onde ainda não foi confirmada a presença
da espécie.
A utilização do modelo ecológico de máxima entropia permitiu a construção de diversos
mapas que demonstram a probabilidade de ocorrência desta térmita em cada ilha. Todas as
projecções são consistentes com uma significativa probabilidade de ocorrência da espécie
em todas as ilhas. No geral, esta probabilidade é mais elevada perto das zonas costeiras,
mais baixas, onde estão localizadas as principais localidades.
Os resultados apresentados contribuem para um melhor entendimento acerca da espécie
Cryptotermes brevis no arquipélago dos Açores. As ferramentas desenvolvidas e aplicadas
neste trabalho são um importante ponto de partida para futuras aplicações para estudar a
mesma espécie em outras cidades do arquipélago, ou mesmo para simular a dispersão de
outras espécies. O modelo com autómatos celulares, apesar do seu estado inicial,
demonstrou claramente que tem potencial para nos ajudar a entender a evolução espacial e
temporal da dispersão desta praga, ou mesmo de outras espécies. Os resultados obtidos
relativamente à probabilidade de ocorrência da espécie no arquipélago poderão ser
melhorados, desde que, seja disponibilizada informação climática mais completa. Estes
resultados indicam-nos que, sem medidas apropriadas, a situação actual poderá tornar-se
um sismo que silenciosamente afectará todas as ilhas Açorianas.
v
vi
List of Contents
ABSTRACT......................................................................................................................... ii
RESUMO ........................................................................................................................... iv
Chapter I ...............................................................................................................................1
1.1
INTRODUCTION.......................................................................................................1
1.2 TERMITES ................................................................................................................2
1.2.2 C. BREVIS AND OTHER TERMITES IN THE AZORES ...................................................2
1.2.3 CRYPTOTERMES BREVIS BIOLOGY .........................................................................3
1.2.4 URBAN PEST MANAGEMENT ..................................................................................6
1.3
ECOLOGICAL MODELS ...........................................................................................9
1.4
THESIS OUTLINE...................................................................................................12
Chapter II ............................................................................................................................14
2.1 INTRODUCTION.....................................................................................................14
2.1.1 SPREAD AND COLONIZATION ...............................................................................14
2.1.2 CELLULAR AUTOMATA .........................................................................................18
2.1.2.1 General Properties.........................................................................................18
2.1.2.2 NetLogo .........................................................................................................21
2.2 METHODOLOGY ....................................................................................................23
2.2.1 FIELD METHODOLOGY .........................................................................................23
2.2.1.1 Interviews ......................................................................................................23
2.2.1.2 Light Traps.....................................................................................................24
2.2.2 COMPUTATIONAL METHODOLOGY ........................................................................27
2.3 RESULTS................................................................................................................33
2.3.1 FIELD RESULTS ..................................................................................................33
2.3.1.1 Interviews ......................................................................................................33
2.3.1.2 Light Traps.....................................................................................................38
2.3.2 COMPUTATIONAL RESULTS..................................................................................46
2.3.2.1 Cellular Automata ..........................................................................................46
a. How the pest may have begun ................................................................................53
2.4
DISCUSSION ..........................................................................................................57
Chapter III ...........................................................................................................................61
3.1 INTRODUCTION.....................................................................................................61
3.1.1 ECOLOGICAL NICHE MODELS...............................................................................62
3.2
METHODOLOGY ....................................................................................................64
3.3 RESULTS................................................................................................................68
3.3.2 WORLD SAMPLE PROJECTION .............................................................................68
3.3.3 LOCAL SAMPLES PROJECTION .............................................................................74
3.3.3.1 Islands Results ..............................................................................................80
Corvo Island ..................................................................................................................80
Flores Island ..................................................................................................................81
Faial Island ....................................................................................................................82
Pico Island .....................................................................................................................83
S. Jorge Island...............................................................................................................84
Graciosa Island..............................................................................................................85
vii
Terceira Island ...............................................................................................................86
S. Miguel Island .............................................................................................................87
Santa Maria Island.........................................................................................................88
3.3.4 VALIDATION TEST ................................................................................................89
3.4
DISCUSSION ..........................................................................................................93
3.5
CONCLUSION ........................................................................................................97
Chapter IV ...........................................................................................................................98
4.5
GENERAL CONCLUSIONS ....................................................................................98
4.6
FUTURE PERSPECTIVES......................................................................................99
BIBLIOGRAPHIC REFERENCES ...................................................................................101
APPENDIXES .................................................................................................................110
APPENDIX A ..................................................................................................................111
APPENDIX B ..................................................................................................................112
viii
List of Figures
Figure 1.1: World map and affected spots by Cryptotermes brevis (Scheffrahn, et al. 2009)...................2
Figure 1.2: Azores archipelago map, where the named islands are the ones were the affected by
termites (Borges et al. 2005; Myles et al., 2006b). ..........................................................................................3
Figure 1.3: Cryptotermes brevis life cycle (After Scheffrahn & Su, 1999). ...................................................4
Figure 1.4: Several castes of C. brevis and their development. a) Female reproductor; b) Eggs; c)
Young larvae; d) Soldier; e) Group of workers; f) Pseudergate; g) Nymph; h) Young alate. Source:
Borges et al., 2006................................................................................................................................................4
Figure 1.5: Map of Angra do Heroísmo. The colours indicate the degree of infestation of the different
area of the city. The buildings coloured green indicate that either they are not infested or that there is
no data about them implying that further surveillance is required (Adapted from Borges et al., 2004). ..7
Figure 1.6: Pest evolution with time, consequent damages and some alternative measurements (see
also Borges et al., 2007). .....................................................................................................................................8
Figure 1.7: Integrate Pest Management triangle with the three principal concerns: education,
surveillance and control. The circle represents where the computational models are helpful. Adapted
from: Department of the army, Us Army Centre for Health Promotion and Preventive Medicine (1998).
.................................................................................................................................................................................9
Figure 1.8: The best way to review methods of insect population modelling is to analyze their
"phylogeny"(Sharov, 1996)................................................................................................................................10
Figure 2.1: Mating and colonization sequence: a) pairing b) penetrating to substrate c) sealing the
nuptial chamber d) start a new colony (After Guerreiro et al., 2006) ..........................................................15
Figure 2.2: Drywood C. brevis damage in wood structures. (a) - tunnels and galleries in timber; (b) –
normally affected structures in houses. Source: (a) Borges et al., (2004); (b) from:
http://insects.tamu.edu/extension/bulletins/l-1782.html.................................................................................16
Figure 2.3: Conway’s game of life is the best-known example of a cellular automaton. Source:
www.wikipedia.com.............................................................................................................................................19
Figure 2.4: I- Low density ( 0.03 cars per site) simulation result; II- High density ( 0.1 cars per site)
simulation result; and III- Space-time-lines for cars from aerial photography, where each line
represents the movement of one vehicle in the space-time-domain (from Nagel & Schreckenberg,
1992) .....................................................................................................................................................................20
Figure 2.5: I- Traffic flow (in cars per time step) vs. Density (in cars per site) from simulation results (L
= 104). Dots are averages over 100 time steps, the line represents averages over 106 time steps; and
II- Traffic flow (in cars per hour) vs. occupancy is the percentage of the road which is covered by
vehicles (from Nagel & Schreckenberg, 1992) ...............................................................................................21
Figure 2.6: NetLogo window, for a fire forest model......................................................................................22
Figure 2.7: Angra do Heroísmo infested area and places where the interviews occurred. .....................24
Figure 2.8: Light trap ..........................................................................................................................................25
Figure 2.9: EDA car crane and functionaries during the Trap attachment a); EDA official electrician
connecting the Light Trap cable to the public illumination net b). ................................................................25
ix
Figure 2.10: Infested buildings, buffer distance from 50, 100 and 150 meters and light traps initial
placement.............................................................................................................................................................26
Figure 2.11: Ultraviolet light trap on the public illumination post..................................................................26
Figure 2.12: Indoor light trap. ............................................................................................................................27
Figure 2.13: Cell conditions and its evolution along time on the proposed model. ...................................28
Figure 2.14: NetLogo interface view with some of the several possibilities of buttons, sliders, monitor,
etc..........................................................................................................................................................................31
Figure 2.15: Angra do Heroísmo infested area and places where the interviews occurred. ...................33
Figure 2.16: S. Pedro surveyed area. The green houses show the inspected houses............................34
Figure 2.17: Sta. Luzia inspected area. The green houses and the ones on the red circle are the
houses that were inspected...............................................................................................................................34
Figure 2.18: Conceição inspected area. The green houses and the ones on the red circle are the
houses that were inspected...............................................................................................................................35
Figure 2.19: Guarita inspected area. The green houses are the houses that were inspected................35
Figure 2.20: S. Bento inspected area. The green houses are the houses that were inspected. The
orange houses were already infested in 2004 (Borges 2004)......................................................................36
Figure 2.21: Monte Brasil inspected area. The green houses are the houses that were inspected. The
orange and yellow houses were already infested in 2004 Borges (2004)..................................................36
Figure 2.22: Angra do Heroísmo infested area and places where the interviews occurred. ...................37
Figure 2.23: Probable distance to the only mentioned infested house on Rua Dr. Henrique Brás,
according to the Pest control Enterprises........................................................................................................38
Figure 2.24: Light traps positions and displacement during the survey period. ........................................39
Figure 2.25: Appearance of one trap when the glued cardboard was collected for sampling.................39
Figure 2.26: Winged (a) and (b); wings of an alate (c); three individuals who have freed themselves
from the wings and took refuge in the back of the glued cardboard (d). ....................................................40
Figure 2.27: Traps positioning and surveyed areas.......................................................................................41
Figure 2.28: Indoor sticky trap (a); and container underneath to collect some of the alates that were
not glued to the trap (b)......................................................................................................................................42
Figure 2.29: Number of alates captured outdoors with the UV light traps (a); and number of alates
captured indoor (b)..............................................................................................................................................43
Figure 2.30: Number of alates per day captured outdoor on the UV light traps (a); and number of
alates captured indoor per day (b). ..................................................................................................................43
Figure 2.31: Map of Angra do Heroísmo with actual infested areas and pest distance spread from the
centre to the furthermost places. ......................................................................................................................44
Figure 2.32: Kalotermes flavicolis.....................................................................................................................45
x
Figure 2.33: Images from the first tested model at different time steps. Time steps: 0 (a); 1 (b); 6 (c);
11 (d); and 21 (e). Used parameters: radius 8 and probability 1 (upper), 0.2 (middle) and 0.01 (inferior).
Yellow cells – recently infested cells, red cells – cells sources of infestation. ...........................................47
Figure 2.34: Average values of several interactions using the same parameters that were use on the
Figure 2.33 (red, blue and black circles). ........................................................................................................48
Figure 2.35: Average number of infested cells (red cells) as a function of probability and radius..........48
Figure 2.36: Coefficient of variation of the red cells as a function of probability and radius....................49
Figure 2.37: Maximum and minimum values of infested cells for different radius (1, 5 and 10) at
different probability values (0.01 and 0.1). ......................................................................................................49
Figure 2.38: Average number of recently infested cells (yellow cells) as a function of probability and
radius. ...................................................................................................................................................................50
Figure 2.39: Healthy fraction as a function of probability and radius. .........................................................50
Figure 2.40: Average values of the minimum distance as a function of probability and radius. .............51
Figure 2.41: Average values of the maximum distance as a function of probability and radius. ............52
Figure 2.42: Minimum and maximum asymmetry values for radius 10. .....................................................52
Figure 2.43: Simulation of Cryptotermes brevis in Angra do Heroísmo at different time steps. Time
step 0 (a); at time step 10 (b); 20 (c); and 30 (d). ..........................................................................................54
Figure 2.44: Simulation of Cryptotermes brevis in Angra do Heroísmo after 40 time steps....................54
Figure 2.45: Second simulation of Cryptotermes brevis on Angra do Heroísmo at different time steps.
Time step 0 (a); at time step 10 (b); 20 (c); and 30 (d)..................................................................................55
Figure 2.46: Second simulation of the Cryptotermes brevis species in Angra do Heroísmo after 40 time
steps......................................................................................................................................................................56
Figure 2.47: Simulation of Angra do Heroísmo after 40 time steps overlapped with the infested map. 56
Figure 3.1 The two different model approaches (see text for further explanations and for variables
names. ..................................................................................................................................................................65
Figure 3.2: Schematic presentation of Maxent’s procedure .........................................................................67
Figure 3.3: MAXENT software window ............................................................................................................67
Figure 3.4 World Map model prediction using the first set of features, which includes altimetry (set 1),
with used sample spots (white squares), world predicted occurrence probability and world presence
spots not used to model (red squares). ...........................................................................................................68
Figure 3.5: World map model prediction using only three environmental variables (Annual Rain,
Minimum Annual temperature and Maximum Annual temperature) including the used sample spots
(white squares) and world presence spots not used to model (red squares); The probability of
occurrence increases from the coldest colours (dark blue), to the warmer colours (orange-red). .........68
Figure 3.6: Comparison between the results of the MAXENT prediction model for the two sets of
variables in the South East Asia Region. Using altimetry (A); and not using it (B). ..................................70
Figure 3.7: Comparison between the results of the model for the two sets of variables in the south
west of Europe. Using altimetry a); and not using it b).................................................................................70
xi
Figure 3.8: Comparison between the results obtained with the two sets of variables in the Azores.
Using altimetry (A); and not using it (B) ...........................................................................................................71
Figure 3.9: Comparison between the results of the model for the two sets of variables in Terceira
island. Using altimetry (A); and not using it (B) ..............................................................................................72
Figure 3.10: Comparison between the results of the model for the two sets of variables in Pico island.
Using altimetry (A); and not using it (B) ...........................................................................................................73
Figure 3.11: Local model prediction for the Azores. ......................................................................................74
Figure 3.12: Terceira Island set 1 image preview. .........................................................................................76
Figure 3.13: Terceira Island set 2 image preview. .........................................................................................76
Figure 3.14: Terceira Island set 3 image preview. .........................................................................................77
Figure 3.15: Probability of occurrence of C. brevis for Terceira Island using both sets of variables
(using altimetry – set 1, and not using altimetry – set 3)...............................................................................78
Figure 3.16: Pico Island Maxent picture modelling for both variables set. .................................................78
Figure 3.17: Model prediction for Corvo Island. .............................................................................................80
Figure 3.18: Model prediction for Flores Island. .............................................................................................81
Figure 3.19: Model prediction for Faial Island. ...............................................................................................82
Figure 3.20: Model prediction for Pico Island. ................................................................................................83
Figure 3.21: Model prediction for S. Jorge Island. .........................................................................................84
Figure 3.22: Graciosa Island pictures preview from two different model sets. ..........................................85
Figure 3.23: Terceira Island pictures preview from two different model sets.............................................86
Figure 3.24: S. Miguel pictures preview from two different model sets. .....................................................87
Figure 3.25: S. Maria pictures preview from two different model sets. .......................................................88
Figure 3.26: Terceira image (Set3 variable set) using the Island samples ................................................89
Figure 3.27: Terceira image (Set3 variable set) using all the Archipelago samples.................................89
Figure 3.28: Terceira picture simulation using the available occurrence samples from all the islands,
except from Terceira...........................................................................................................................................90
Figure 3.29: Model prediction for Terceira using a sample of nine (a) and three (b) spots from each of
the infested islands. ............................................................................................................................................90
Figure 3.30: Model predictions for Faial using different samples. All available samples on the
archipelago (a); only the Faial local presence samples (b); nine samples from each one of all infested
islands (c); three samples from each one of all infested islands (d); all available samples on the
archipelago with exception of Faial samples (e); and, using the world samples (f)..................................91
Figure 3.31: Model predictions for Flores using samples with different origins. World samples (a); All
available samples on the archipelago (b); Santa Maria spots (c); S. Miguel spots (d); Terceira spots (e);
and, only the Faial spots (f). ..............................................................................................................................92
xii
List of Tables
Table 1.1: Mean annual rainfall (cm), temperatures and dew points (ºC) in cities where Cryptotermes
brevis is established (Scheffrahn, 2009). .................................................................................................5
Table 1.2: Different model types based on the input, data source and output type. (Adapted from
Higgins & Richardson, 1995) .................................................................................................................11
Table 2.1: Locations and approximate number of houses searched in each area ................................34
Table 2.2: Place of interview and date on the presence of termite these locations...............................37
Table 2.3: Streets where the pest control enterprises have been operate. ...........................................38
Table 2.4: Number of winged caught by trap and the distance from the likely area of origin ................40
Table 2.5: Traps and their respective confidence ..................................................................................41
Table 2.6: Different distances and number of alates captured at each distance ...................................42
Table 2.7: Number of Kalotermes flavicolis captured alates..................................................................45
Table 3.1: World spots sample places and number...............................................................................66
Table 3.2: Known locations in the Azores infested with C. brevis .........................................................66
Table 3.3: Contribution value of each environmental variable to the MAXENT models. .......................69
Table 3.4: Altitude data in some sites with confirmed presence of C. brevis
(source:http://www.weatherbase.com/)..................................................................................................73
Table 3.5: Variables used in each set and their percentage contribution to the model. The grey box is
the categorical variable. The blue boxes correspond to the most significant environmental variable...75
xiii
Chapter I
The drywood Cryptotermes brevis pest on the
archipelago of the Azores
1.1 INTRODUCTION
Alien species management is an important issue towards an environmental and economical
impact reduction (Llorent et al., 2008). This is a growing problem because it was never
before possible to exchange an amount of goods around the world as quickly as it is now.
This fact facilitates the spread of invasive species, and consequently it is necessary to apply
control and prevention actions trough the inspection to each type of cargo material, based on
their origin or destination. The invading species, when introduced, are initially ignored and
their proliferation occurs discretely without any control or study. Normally the invasive
species presence is only noticed and given an intruder status when serious problems appear
from its presence and impact in the local ecosystems or directly in the human population
(Mooney & Hobbs, 2000; Shirley & Kark, 2006; Meyerson & Mooney, 2007; EU, 2007).
The species in focus in this thesis is the currently widespread drywood termite Cryptotermes
brevis (Walker, 1953), recently confirmed as native of the South American countries of Chile
and Peru (Scheffrahn et al., 2009). This species is a drywood termite and outside its endemic
range lives inside houses, in their wood structures and furniture. Hence, it is responsible for a
huge damage causing enormous economic investments in restoration and substitution of
structures and in the prevention of new infestations and pest combats (IOMC, 2000; Milano &
Fontes, 2002; Scheffrahn & Su, 2005; Scheffrahn et al., 2009). Presently, it has a world-wide
distribution and is considered one of the termites with the biggest urban pest status causing
seriously economic damages worldwide, specially in the U.S.A. (Hawaii and Florida)
(Scheffrahn & Su, 1999; Haverty, 2003), Australia (Queensland) and South Africa (Heater,
1970). This serious economic impact is already a reality on the major cities of the Azorean
Archipelago (Myles, 2004; Borges et al., 2004, 2006, 2007).
1
1.2 TERMITES
1.2.2 C. BREVIS AND OTHER TERMITES IN THE AZORES
Termites belong to order Isoptera, one of the 32 known insect orders and are parentally
related with grasshoppers and cockroaches ancestors. There are three main groups of
termites: subterranean, living wood and drywood (Milano & Fontes, 2002). Among the 3000
known species in the planet only some of them are baleful to human structures. Most of them
are beneficial to the oxygenation of soils and the decomposition of dead trees. Some of the
termites are arboreal, building the nests in the trees-top, others live in the soil and others live
inside of dead dry lumber. However, some species create tremendous damage to human
habitations, buildings structures and furniture. In some countries like U.S.A., Canada, Brazil,
Australia and South Africa, there is already a traditional fight system with the most
problematic species. This species causes an important economic impact in those countries,
with significant investments into monitoring and preventing new infestations (Heater, 1970;
Scheffrahn et al.1988; Scheffrahn & Su, 1999; IOMC, 2000; Milano & Fontes, 2002; Haverty,
2003).
One of the most harmful species is the West Indies drywood termite Cryptotermes brevis that
was until recently thought to originate from the Caribbean. This species has already spread
into several parts of the world (see Figure 1.1): U.S.A., México, Central America and north
part of South America, Pacific Islands including Galapagos, Fiji, Hawaii, Midway, New
Caledonia e Easter Island and in the Atlantic Islands of Ascension, Bermuda, Canaries,
Madeira and St. Helena. The species was also introduced in other continental regions like:
Australia, Madagascar, Gambia, Ghana, Nigeria, Senegal, Sierra Lion, South Africa, Uganda
and Zaire (Gay & Watson, 1982). The C. brevis origin was only recently discovered to be
from South American Pacific coast of Chile (see Table 1.1) (Scheffrahn et al., 2009).
Figure 1.1: World map and affected spots by Cryptotermes brevis (Scheffrahn, et al. 2009)
The Figure 1.1 shows the widespread distribution of C. brevis around the world. Also, the
extreme northern location of the Azores archipelago, in comparison with the other spots, is
2
easily perceptive. Somehow, this might induce one to think that Azores are in the limit of the
climatic conditions necessary to the species existence. However, the Atlantic Ocean
influence on the climate conditions of the islands provides reasonable conditions to the
species establishments has will be showed further in Table 1.1 and in detail in Chapter III.
Regionally, the species is already known to be present in four of the nine islands of the
Azores archipelago. It has also been determined the presence of two more species: the
Reticulitermes grassei, a subterranean termite also considered a dangerous urban pest, and
the live wood termite Kalotermes flavicolis.
The situation in the remaining islands is still unknown and an evaluation of C. brevis species
potential occurrence in all the islands is an important part of this work.
The present knowledge about the termite presence in the Azores can be seen in Figure 1.2.
Cryptotermes brevis
Kalotermes flavicolis
Reticulitermes grassei
Figure 1.2: Azores archipelago map, where the named islands are the ones were the affected
by termites (Borges et al. 2005; Myles et al., 2006b).
This map is not based on a complete survey on all the islands, so that the problem could be
even more serious. The most spread species is the Cryptotermes brevis (Borges, et al., 2004,
2005, 2006, 2007; Borges & Myles, 2005; Borges & Myles, 2007). It constitutes currently one
of the most serious urban problems in the Azores region.
1.2.3 CRYPTOTERMES BREVIS BIOLOGY
Like the other termite species, C. brevis has a complex life cycle with several castes (see
Figure 1.3). In this species a female and a male normally colonize a wood structure or wood
furniture putting eggs that evolve to form plurypotents or pseudergate (i.e. capable of
transforming into any cast). The casts are divided into workers, soldiers and reproducers
3
(queens and kings). In the first stage of the colony development only workers and soldiers
are produced by a queen and a king. Soldiers and workers are blind and communicate only
through chemical compounds. Soldiers have to protect the workers in the food chase and the
nest from foraging attacks from ants, spiders and other natural predators (Heater, 1970;
Scheffrahn et al.1988; Scheffrahn & Su, 1999; Haverty, 2003; Guerreiro, 2006, 2007).
Figure 1.3: Cryptotermes brevis life cycle (After Scheffrahn & Su, 1999).
The workers are characterized for executing every colony routine procedures, like dead or
sick individuals elimination, eggs maintenance and obtain food and feeding the other casts.
The workers ingest wood rich in cellulose that is digested through a symbiotic protozoon that
lives in the C. brevis digestive system. After this digestive process, the pre-digested cellulose
is then regurgitated to feed the other casts. The small larvae are fed by the workers that also
pass the symbiotic protozoa necessary to their digestive process.
Figure 1.4: Several castes of C. brevis and their development. a) Female reproductor; b) Eggs;
c) Young larvae; d) Soldier; e) Group of workers; f) Pseudergate; g) Nymph; h) Young alate.
Source: Borges et al., 2006
This is a well organized species as prove its global distribution. In a recent article about C.
brevis endemic origin and vast anthropogenic dispersal, Scheffrahn et al. (2009) presented a
table listing considerable number of places where the species occurs. Here, it is possible to
4
compare some environmental variables from a large number of places and, in particular,
from Ponta Delgada in the Azores (see Table 1.1).
1
Table 1.1: Mean annual rainfall (cm), temperatures and dew points (ºC) in cities where
Cryptotermes brevis is established (Scheffrahn, 2009).
City
Country
C. brevis
Rain
Mean T
High T
Low T
Dew pt.
Bluefields
Port-of-Spain
Nicaragua
Trinidad
Rep.
Dominican
Belize
Mexico
Puerto Rico
Jamaica
Puerto Rico
Jamaica
Grand
Turks and
Caicos Isl.
USA
Senegal
Venezuela
USA
Gambia
Reunion
Hawaii
Costa Rica
Honduras
South
Africa
Peru
USA
Bermuda
USA
Brazil
Egypt
Chile
Spain
Australia
Portugal
Chile
Chile
Argentina
Chile
Intr.
Intr.
443
177
26
26
28
30
24
22
23
22
Intr.
138
25
28
22
22
Intr.
Intr.
Intr.
Intr.
Intr.
Intr.
191
173
134
130
201
89
26
25
26
27
27
28
28
29
30
30
30
31
23
21
23
23
23
25
22
21
21
21
21
21
Intr.
60
27
28
25
21
Intr.
Intr.
Intr.
Intr.
Intr.
Intr.
Intr.
Intr.
Intr.
101
50
83
148
121
103
54
187
92
25
24
23
24
26
25
25
20
22
28
26
26
28
30
26
28
25
27
22
21
19
20
22
22
21
15
17
20
19
18
18
18
18
17
16
16
Intr.
105
21
24
17
16
Endemic
Intr.
Intr.
Intr.
Intr.
Intr.
Endemic
Intr.
Intr.
Intr.
Endemic
Intr.
Intr.
Endemic?
0
116
140
156
135
8
0
27
119
80
0
0
97
50
20
23
22
20
20
21
19
21
20
17
17
18
16
14
22
27
24
25
24
23
22
24
25
18
19
20
21
17
17
18
20
15
16
18
16
18
15
15
14
15
11
12
16
16
16
15
15
15
14
14
13
13
12
12
11
10
Santo Domingo
Belize
Veracruz
San Juan
Montego Bay
San Juan
Kingston
Grand Turks and Caicos
Isl.
Key West – Florida
Dakar
Caracas
Miami – Florida
Banjul
St.-Pierre
Honolulu
San José
Tegucigalpa
Durban
Lima
St.Petersburg - Flo.
Hamilton
New Orleans
Sao Paulo
Port Said
Arica
Tenerife – Canary Isl.
Brisbane – Queensland
Ponta Delgada – Azores
Antofagasta
Iquique
Buenos Aires
Valparaiso
Blue colour: Rainiest places; Orange: Warmer places; Light Blue: Coldest places; Grey: high and low dew points;
Yellow; Driest places; Bold: Endemic regions; Green: Azores, Portugal
According to the table above it is easy to realize that the species is established in places with
very diverse environmental conditions. The extreme high temperatures (orange colour) are in
the Caribbean islands of Jamaica with 28, 31 and 25 Cº of mean, high and low temperatures
respectively and Grand Turks and Caicos Islands with an extremely elevated low
temperature of 25 Cº. The lowest temperature value (light blue) occurs on a possible
(Valparaiso) endemic region in Chile (14Cº mean temp.; 17Cº high temp.) and Buenos Aires
in Argentina (11Cº). The spots with less rain are in the C. brevis endemic region in Chile and
Peru with no precipitation (0 cm). The spot with the highest precipitation is in Nicaragua with
443 cm. Also other important climate parameter considered on this table is the dew point.
1
Climatic data from: http://www.weatherbase.com and http://www.worldclimate.com
5
The highest dew point is in Nicaragua (23) and the lowest is on Valparaiso in Chile (10).
Again the Azores region, with a 13 dew point value, it is not on an extreme value.
The vast distribution of C. brevis suggests that it possesses physiological or behavioural
adaptations which enable individuals to withstand considerable seasonal variation in
microclimate. Stewart (1982) compared C. brevis with other drywood termites and found that
this species survives equally well in both hot-dry and cold-humid conditions and its wide
distribution on the planet can be linked to its ability to acclimation and to feed at effectively
both average relative humidity (about 60%) and high relative humidity (about 90%).
The Azores environmental values, represented in the table by Ponta Delgada (green row),
are not in any extreme variable value, so that the environmental conditions in the Azores
appear to be suitable to C. brevis establishment.
1.2.4 URBAN PEST MANAGEMENT
Cryptotermes brevis is a major urban pest management problem as it is extremely
destructive with large economic impact. It is very difficult to perform an appropriate
management of urban spaces that could lead to the control or elimination of this pest. One of
the Cryptotermes brevis worst cases on the Azorean Archipelago is in Angra do Heroísmo
city (Myles, 2004; Borges et al., 2004, 2006, 2007).
The city has an architectonic construction typical of the colonial period with connected
buildings along small streets in the shore of Monte Brazil sheltered bay. Those houses were
build with thick basaltic rock walls and wood roofs and floors with a variety of local and
exotics timbers brought from the colonies. These wood structures are important not only for
its structural properties but also because they have an artistic and patrimonial significance.
This patrimony is seriously threatened by the drywood termite Cryptotermes brevis, first
identified in Azores in 2002 (Borges et al., 2004, Myles 2004).
According to Borges et al. (2004), approximately 50% of the city buildings are affected with
this species and, of this part, about 50% is already with a severe or destructive infestation in
the main wood structures of the habitations as shown by the red and dark red colours in the
map of Figure 1.5 (Borges et al., 2004). Also, some buildings with historical and patrimonial
important value are affected by the C. brevis pest. Some of those buildings are the Edificio
dos Coches in the Angra do Heroísmo museum and the Secretaria Regional da Educação e
Ciência in the Rua da Carreira dos Cavalos also in Angra do Heroísmo and the Conceição
Palace in Ponta Delgada.
6
Figure 1.5: Map of Angra do Heroísmo. The colours indicate the degree of infestation of the
different area of the city. The buildings coloured green indicate that either they are not infested
or that there is no data about them implying that further surveillance is required (Adapted from
Borges et al., 2004).
The image in Figure 1.5 is related to information collected in 2004 and since then no other
surveys were made. Besides this 2004 survey other studies were made locally concerning
the species wood consumption and preference (Ferreira et al., 2006), colony development
(Guerreiro et al., 2006), curative and preventive treatments (Myles et al., 2006a, 2007a;
Brantley et al., 2006; Lopes et al., 2006; Borges, A. et al., 2006) and light traps to capture
alates . Although there are a significant number of studies about this species, some aspects
are yet not well known. In particular, it is largely unknown how the infestation in a city
progresses in time. The local spread capacity, i.e., how far away an alate can colonise a new
building, is an important unknown parameter fundamental to this purpose.
As an urban insect pest, it is extremely important to understand how the spread pattern of
the species is and how the pest increases with time. In the regional context it is necessary to
understand how real the pest threat is to other islands on the archipelago. More precisely,
one should determine where specific environmental conditions for the species occurrence
and settlement are available.
This information is crucial to support the authorities’ management decisions. This would
control the species extent and reduce the spread in the already infested spots to other parts
of the island or to the other islands, through human goods or furniture transport between
islands, and with that reduce the damage and its economic costs.
The present situation is already difficult and expensive to control, but without appropriate
measures it will become worst and more expensive to solve. It is possible to understand the
7
evolution of the pest scenario and the associate damage, necessary interventions, costs and
prevention measures in the Figure 1.6.
TIME
Not infested
Prevention Measurements
•Treatment in structures
•Treatment in furnitures
•Monitorization
Low Cost
Light to Moderate
infestation
Destructive and Severe
infestation
Treatment Wood Damage
Replace Damaged Wood
•Injection treatment in
structures
•Bubble treatment to
furnitures
Reasonable Cost
•Same wood
•Treated wood
•Metallic or concrete
solution
Expensive Cost
Figure 1.6: Pest evolution with time, consequent damages and some alternative measurements
(see also Borges et al., 2007).
These economic costs are imperatively related to the species control. The most common
way to control the invasion of people’s houses is through the expensive application of
chemicals that are extremely persistent in the environment, toxic and constitute a threat to
human health. The control methods can be classified as cultural, physical, chemical and
biological (NAVFAC, 1992; Lind P., 1997; Myles, 2004).
The cultural method is based on the attitude of the local people to the pest, because there
are several simple ways to prevent the pest spread like the simple application of light traps or
through the collocation of nets in the windows during the swarming period in order to protect
the houses from the young alates. In this method it is necessary to distribute an educative
leaflet that provides the necessary information in a non-technical way to the local residents.
The physical control method could be through high temperature treatment, which is not very
practical to big infested structures, being more suitable to furniture treatment (Borges et al.,
2006a, b).
The biological method it is not quite so well developed but fungus and nematodes are one of
the known organisms capable of fighting the termites (Rosengaus et al., 2003). Other
organisms like flies, beetles and virus are also potential enemies.
The chemical control method was for a long time been the only response to control this
insect pest. However, the effects are terrible to the environmental and to the human health,
as the majority of those chemicals are Persistent Organic Pollutants (POPs). As the objective
of pest management is the effective control with minimal use of the least toxic product
8
available, it is necessary to manage other ways of control other than the chemical (IOMC,
2000).
Besides the mentioned control methods, it is necessary to implement an integrate pest
management program (Figure 1.7) in order to obtain positive results in the pest control.
ati
on
Su
uc
rv
eil
lan
ce
Ed
Integrated Pest
Management
Control
Figure 1.7: Integrate Pest Management triangle with the three principal concerns: education,
surveillance and control. The circle represents where the computational models are helpful.
Adapted from: Department of the army, Us Army Centre for Health Promotion and Preventive
Medicine (1998).
The main concerns when implementing an Integrated Pest Management (IPM) plan are a
constant surveillance of the pest spread situation, a continuous application of the several
control methods and a permanent educational attitude to maintain people aware of the
possibility of pest dissemination to other places and to maintain a proactive approach to the
problem.
The use of computational models is a helpful and important tool to define an appropriate IPM
plan. This is due to the fact that models can forecast the most probable places where the
pest might surge or spread to (control and surveillance). The model can also predict future
scenarios and so, be an extremely useful instrument. Although models per se do not solve
the pest problem, they are an important, useful and cheap way to determine the most
appropriate solution.
1.3 ECOLOGICAL MODELS
Several kinds of mathematical models are applied in ecology and therefore a previous
understanding of the available models is necessary in order to choose the best and most
adequate to the problem in hand. According to several authors, the use of mathematic
models is essential to pest management and research, so it is also important to understand
the existing models (Sharov, 1996; Murray, 2002). Here, I present the different types of
models that are used in ecology and discuss their advantages and disadvantages. Which is
9
the best model to each situation? This issue is addressed in Higgins & Richardson (1995)
where a review of models of alien plant spread is presented. It is important to mention that
there are great similarities between the plant and animal spread models, once the principal
ecological features are the same. Sharov (1996) makes another interesting review of
mathematic models addressing forest insect pests, by analysing the methods according to
their simplicity or complexity.
Figure 1.8: The best way to review methods of insect population modelling is to analyze their
"phylogeny"(Sharov, 1996).
Higgins & Richardson (1995) review a number of diverse mathematical models and perform
an analysis of the different capacities of each of the models. We integrate in the list of
models reviewed by these authors a new group of models, which are somewhat related with
the previously existing models, as some mathematical principles are common among them.
This new group is integrated with the others due to its importance in the species occurrence
prediction.
10
Table 1.2: Different model types based on the input, data source and output type. (Adapted
from Higgins & Richardson, 1995)
Model Type
Model
Type of input
Data source
type
Exponential
Simple –
demographic
Spatial –
Logistical
Logistic –
difference
Stochastic
Density
Lower
hierarchical level
Time
No ecological
meaning
Historical
Area
Markov
Influence birth
and death
Same
hierarchical level
Time
Reaction-diffusion
Ecologically
Population
dynamic
meaningful
Cellular automata
Ecological niche
models
Influence birth
and death
Population
Independent
Regression
phenomenological
Spatial mechanistic
Ecologically
meaningful
Type of output
Maximum Entropy
Model
Genetic Algorithm
for Rule-set
Production
(GARP)
Independent
Area
Influence birth,
Lower
death, dispersal
hierarchical level
Environmental
data
Ecologically
meaningful
Population
Historical data
Time
Geographic
distribution
Area
Presence
concurrency
Domain
The selection of models that are presented in Table 1.2, are applicable to different situation
according to the study matter and goal. A brief introduction to the more important models to
our aim, following closely Higgins & Richardson (1996), is now presented.
The Simple – Demographic Models which include the Exponential, Logistic, Logistic –
difference and Stochastic models have as output the population density as a function of time
with no spatial information. These are useful and quite realistic models, however they have
no spatial information which makes them inappropriate to the current purpose.
Spatial – phenomenological models embrace the Regression, Geometrical and Markov
models and have as output the time and area. These models predict the necessary time for
an organism to cover a study area. They are based on independent estimates of ecological
parameters as these represent ecological processes. The predictions are a function of the
ecological interactions and the model’s assumptions.
The Individual-based cellular automata models (CA) are particularly applicable for
conservation, biological and environmental management problems. They are based on local
rules of interactions and are appropriate to problems where the environmental conditions
11
experienced by each individual member of the population are important, or when a presence
of a single individual can influence invasions patterns. A general CA model can be describe
as consisting of a discrete array of cells capable of taking on a finite number of states
(0,1,…..,N). To obtain the value of the ith cell at time t+1 (Ci(t+1)) a transition rule is
developed which depends on the previous state of the cell and the state of other cells in the
array,
Ci(t+1) = F(Ci(t), Cj( j))
where Cj(t) represents the states of other cells in the array denoted by the index j at the
earlier time t .
The Ecological Niche models are different from the ones presented before, as they have
different purposes. It is not the goal of this geographic distribution models to determine the
population density, or understand the competition between species or other population
feature (Philips, et al., 2004, 2006; Elith, et al., 2006). These models are used to predict
species distribution based on environmental data, like climate, topography, vegetation, soil,
site moisture, disturbance and species presence data. This information is crucial to
conservation plans that usually require accurate estimates of the spatial distributions of
species that need to be protected. Such information allows conservationists to predict how a
species’ distribution will respond to landscape alteration and environmental change
(Hernandez, et al., 2006; Sérgio, et al., 2006).
1.4 THESIS OUTLINE
In the context of this thesis the use of scientific tools is required in order to support strategic
decisions and adequate planning policies. Computer tools, like ecological models, are
imperative to an actual approach to the study of the spread of invasive species. These
computer models advance scenario predictions, hence a possible evolution of the focused
situation, leading to a better understanding of the problem and a more correct decision
making. The application of computer models in ecology is currently of great importance for
the advance of the discipline, and “alien species spread models” are amongst of the most
promising (Cannas et al., 1999; Evans & Pritchard, 2000; Bulla & Rácz, 2004; Bendor &
Metcalf, 2006; Elith et al., 2006). The present thesis uses two models in order to understand
the dispersion of an urban invasive alien species in the Azores archipelago.
One first model, presented in Chapter II, is a cellular automata model (CA) that is used to
foresee the spatial-temporal characteristics of its dispersion at a local level in the city of
Angra do Heroísmo in Terceira Island. The CA model is a discrete model in time and allows
space visualization in real time of the pest development in the city from a hypothetical
12
beginning until the present. The confrontation of the simulations with the current pest state
information allows the calibration of the model and allows us to predict how the pest will
develop in the study area. In the future, this model could be applied to other islands where
the pest occurs or where it may occur in the future. It may even be adapted to study other
invasive species in the Azores.
To understand the aspects mentioned above we use information from the bibliography
concerning the species in focus together with information obtained from our own experiments.
In these experiments traps are used to capture young winged reproductive individuals that
abandon the ancestors’ nests in search of a new place for reproduction and establishment of
a new colony. Ultra-Violet (UV) light traps were placed in the city infested zone periphery,
according to a sense carried out by the Universidade dos Açores and Angra do Heroísmo
City Hall in 2004 (Borges et al., 2004). The experiment was carried out during the swarming
season, from late May to September. The objective of these traps is to estimate the
maximum flight distance capability of the young winged termites and thus determine the
probability of infestation of houses neighbouring infested areas.
A new sampling was carried out for an update of the present information, with inspections to
previously visited houses and to houses not visited before, according to the report of Borges
et al. (2004).
The second model uses the principle of maximum entropy to foresee the potential
occurrence places of the focused termite species and will be applied at regional and local
levels. With this model we compare the climatic data of the locations where this species is
known to occur with the climate data of the remaining archipelago. These results are
analysed to determine the spots in each island with the highest probability of being invaded
by Cryptotermes brevis. This result allows a spatial visualization of the species potential
occurrence and will provide support for appropriate prevention measurements in order to
control the dispersion of this termite in each island.
The use of the above described models will allow us to understand the species spread true
potential dimension and, in this way, give support to political decisions of nature
management to each place, island or region. This work is also an important and new
approach to the pest problem that, as far as we know, has never been made before
concerning the C. brevis dispersion.
13
Chapter II
Dispersal of Cryptotermes brevis alates at a local
scale
2.1
INTRODUCTION
In this chapter a model is developed to simulate the spatial-temporal dispersion of the species
Cryptotermes brevis at a local scale. This model is applied to the city of Angra do Heroísmo
(Terceira, Azores), one of the three areas in the Azores with the heaviest infestation of C. brevis.
This model is developed on the platform NetLogo through the creation of a Cellular Automata
(CA) model. The use of a CA model as a tool to support management of exotic species has
already been applied in different environments (Cannas et al., 1999; Bone & Dragicevic, 2005;
Bendor & Metcalf, 2006). However, the application of a CA model to an exotic species in an
urban environment is an original approach to the problem.
In order to obtain the essential parameters to the model it was necessary to have a good
understanding about the dispersal dynamics of the species and a good knowledge of its
habitat. To achieve this, a field survey was accomplished in order to obtain the necessary
information.
2.1.1 SPREAD AND COLONIZATION
The drywood termite individuals live their entire life in colonies inside wood structures in
houses and furniture. However, as in the other termite species a swarming or short-term
dispersal period occurs as part of its life-cycle. This swarming period involves a natural
sequence: 1) leaving the colony; 2) short-term dispersal flight (positive phototaxis 2 ); 3)
negative phototaxis; 4) search for an adequate substrate; 5) dealation; 6) pairing (which
includes tandem and/or calling behaviour; 7) penetration to a substrate to form a
copulatorium (Wilkinson, 1962; Minnick, 1973; Guerreiro et al., 2006, 2007). In this part of
the life cycle, that usually occurs in the summer/warmer season3, the young alates leave the
2
3
Phototaxis is called positive, if the movement is in the direction of light, and negative if in the opposite direction
In some places, like the Hawaiian islands, this stage occurs during the entire year
14
parents nest and fly in search for a partner to start a new colony. Normally about 25% of the
individuals in the colony leave the colony in this period (Tim Myles et al., unpublished data
(2004)).
The leaving period happens in the crepuscule, about half an hour before the sunrise and half
an hour after the sunset. They are attracted by light and fly in its direction. According to a
study (Minnick, 1973), they are more attracted to sun light, UV lights and incandescent lights
respectively. The swarming period is also related with some environmental aspects like
temperature, humidity and barometric pressure.
Figure 2.1: Mating and colonization sequence: a) pairing b) penetrating to substrate c) sealing
the nuptial chamber d) start a new colony (After Guerreiro et al., 2006)
The sexual individuals tend to be weak fliers and the swarm breaks up as the sexual
individuals spread out (Haverty, 2003). The sexual individuals release their wings as soon as
they hit the ground. The females (Queens to be) then either stand still and emit a pheromone
to attract males (Kings) or run around all over the place until they meet one. Courtship
involves the male making some advances towards the female who strikes him with her head.
This is followed by mutual antennal caressing and then by the male making more advances
and the female striking him with her head again followed by more mutual antennal caressing.
This cycle may go round 4 or 5 times before the female makes up her mind whether or not to
accept the male. If she does, she runs away with him in close contact behind her. This is
called 'tandem running' (Figure 2.1b). When they find a place to mate the King and Queen
become very repelled by light and attracted by wood. When they find a suitable piece they
take turns excavating a tunnel with a nuptial chamber or enter in a small wood fissure. In the
end they seal themselves inside and begin the nest construction (Figure 2.1c, d). After a few
weeks, depending on the environmental conditions and the wood colonized, the couple starts
producing eggs and starts building galleries and tunnels trough the wood interior (Figure 2.2).
15
a)
b)
Figure 2.2: Drywood C. brevis damage in wood structures. (a) - tunnels and galleries in timber;
(b) – normally affected structures in houses. Source: (a) Borges et al., (2004); (b) from:
http://insects.tamu.edu/extension/bulletins/l-1782.html
The colony size increases with time without almost any infestation symptoms. Only when the
infestation is spread to several places and has a numerous number of colonies, is that some
warning signs are noted. This makes it very difficult to detect and solve the infestation
problem on its early stages.
Besides, the ecology and patterns of spatial spread of this species are not particularly well
known. In fact, the majority of studies concerning the Cryptotermes brevis are related to
preventing and control methods.
There are studies concerning the termites spread or swarming period, but not especially of
this species. For instance, Martius (2003) narrates the swarming of one species of
Kalotermitidae (also belonging to the genus Cryptotermes) in the Amazon with the air
humidity and rainfall.
Some authors have studied the flight capacity of Reticulitermes flavipes (Kollar, 1837) a
subterranean termite that recorded 458.3 m flight distance (Shelton et al., 2006) and
Coptotermes formosanus (Shiraki, 1909) that recordes 892 m flight distance (Messenger et
al., 2004). Both species belong to the family Rhinotermitidae. A survey of the infestation by
Incisitermes minor (Hagen, 1858) in Wakayama City Hall, Japan, was conducted in 19
buildings. This is a very similar species to C. brevis and on this study approximately 90% of
the surveyed buildings were infested by I. minor. The infested buildings were located in one
area within a 5-15 m distance of each other. This suggests that the infestation proceeded by
natural spread via alate flight (Indrayani et al., 2005). Also, Heather (1970) led a survey
concerning the presence of Cryptotermes brevis in Queensland. Initially, the survey
concerned all buildings within 400 m of the house where the species had been identified.
This was subsequently extended to an area of 1 sq Km, including all houses within a
minimum distance of 400 m of each finding of C. brevis. The distribution of C. brevis within
the surveyed area appeared to be consistent with natural dispersal by flight. The 9
infestations occurred as three groups of infestations, consisting of 5 and 3 adjacent houses
16
and 1 single isolated house. The originally reported infestation of C. brevis was one of the
group of five houses; one isolated additional occurrence was found outside of the surveyed
area.
The survey of buildings is an important method to study the termites spread and understands
the species interaction with the urban ecosystem (Heather, 1970; Scheffrahn et al., 1988;
Eleotério & Filho, 2000; Milano & Fontes, 2002; Borges et al., 2004; Indrayani et al., 2005).
This is also useful to understand the dynamics of the spread for each specific infestation
case in order to be able to choose the right control strategy.
17
2.1.2 CELLULAR AUTOMATA
Cellular Automata (CA) models are a very powerful and recent scientific approach to the
study of complex systems (they have even been considered by some as a new science field
(Wolfram, 2002)). Cellular Automata consist in the implementation of a particular kind of
mathematical models in computers to simulate through simple rules the development of
complex systems with a wide variety of applications in natural and social sciences.
2.1.2.1 General Properties
The CA approach is based on Stanislaw Ulam’s idea when, in the forty’s, he studied systems
in a set up that it is still characteristic of present CA models:
Space and time are discrete: There is a (often two-dimensional) grid of cells that is only
viewed at distinct (equidistant) timesteps.
At each timestep, each cell has one (and only one) state taken from a limited number
of possible ones.
There are simple but universal deterministic update rules: The state of a cell at a given
timestep depends only on its own state and the cell states in its neighbourhood, all taken at
the previous step. These rules are the same for all cells and timesteps.
Like many recent models, Ulam’s first model had only two possible cell states – on and off.
This simple possibility is already capable of producing complex self-reproducing patterns,
somehow imitating the complex behaviour of nature emerging from simple rules (Wolfram,
2002).
Later on, Von Neumann used the CA principles to investigate the complex question of the
origin of life, by trying to design a self-reproducing automaton (Von Neumann and Burks,
1966).
Dilão (1993) makes an interesting analogy between the CA models performance and some
natural systems behaviour like the neurone cells and the human brain function.
There are several possibilities to change the rules mentioned above. While the discreteness
of space and time is one of the foundations of the CA approach, the actual geometry can, in
principle, be defined arbitrarily. Also, the boundary conditions have to be specified and can
take several different forms: open, closed, periodic, antiperiodic, etc. The number of possible
cell states may vary within a wide range. There are interesting models with only two states,
but, for example, many epidemiological models use three or four states, and models with a
much larger number of states (up to a quasi-continuum) are possible.
18
The core part of a CA model, however, is the definition of the neighbourhood and especially
the update rules. These rules can be deterministic or probabilistic, allowing the study of
stochastic models.
One interesting and famous application of CA is the game of life, created by Horton Conway
(Callahan, 2007). In this game there are no players, which mean that the initial conditions
determine the evolution of the game. The player interacts with the game only through the
creation of the initial configuration and then watches its evolution. Despite its simplicity, the
system can achieve an impressive diversity of behaviours from apparent randomness to
order. One of the features of the Game of Life is the frequent occurrence of gliders,
arrangements of cells that essentially move themselves across the grid as illustrated in the
Figure 2.3.
Figure 2.3: Conway’s game of life is the best-known example of a cellular automaton. Source:
www.wikipedia.com
Conway’s model showed the great potentiality of CA models but it was just the beginning of
the vast possibility and wide universe of CA models and its applications.
Nowadays, Cellular Automata are trustworthy tools of spatiotemporal modelling and widely
used in several study issues like Physics (Svozil, 1986; Ladd & Frenkel, 1990; Meyer, 1996;
Weimar, 1997), Astrophysics (Vicsek et al., 1987), Biology (1996; Sharov, 1996; Cannas et
al., 1999; Martins et al., 2000; Lichtenegger, 2004; Bone & Dragicevic, 2005; Bendor &
Metcalf, 2006), Medicine (Evans & Pritchard, 2000; Rush et al., 2003; Milne & Fu, 2003;
Laperriére; 2006), Urban Management (Gaylord & Wellin, 1995; Vanbergue, 2000; Alkheder
& Shan, 2005), Social Sciences (Huberman & Glance, 1993; Hegselmann & Flache, 1998;
Lightfoot & Milne, 2003) and Chemistry (Troisi et al., 2004).
The CA philosophy is easily understood with an example. An interesting stochastic discrete
model was presented by Kai Nagel and Michael Schreckenberg in 1992 to simulate the
freeway traffic4. Their computational model is defined on a one-dimensional array of L sites
and with open periodic boundary conditions. Each site can either be occupied by one vehicle
or empty. Each vehicle has an integer velocity with values between zero and maximum
4
The classical approach to traffic flow models is through the use of fluid-dynamic equations (see Lighthill & Whitham, 1955)
19
velocity (vmax). For an arbitrary configuration, one update of the system consists of the
following four consecutive steps, which are performed in parallel to all vehicles:
Acceleration: if the velocity is lower than vmax and if the distance to the next car ahead is
larger than v+1, the speed is advanced by one [v → v +1].
Slowing down (due to other cars): if a vehicle at site i sees the next vehicle at site i + j
(with j ≤ v) it reduces its speed to j- 1 [v → j -1].
Randomization: with probability p, the velocity of each vehicle (if greater than zero) is
decreased by one [v → v - 1].
Car motion: each vehicle is advanced v sites.
The step 3 is crucial to introduce realistic traffic flow behaviour to the simulations. This takes
into account the velocities fluctuations natural to human behaviour or due to external
conditions. Several simulations were carried out in different conditions and with interesting
results which are important to understand the model behaviour. One first simple simulation is
made in a closed system – traffic on a circle – like a car race single track. The constant
system density is defined by
r= N/L = number of cars in the circle/number of sites of the circle
The simulations start with a random initial configuration of cars with density r and velocity 0
and begin the collection of data after the first t0 time steps, where a t0 = 10 × L. The model
behave is very different with low and high density and a comparison between the high
density result and the real car trajectories in the freeway is very interesting.
I
II
III
Figure 2.4: I- Low density ( 0.03 cars per site) simulation result; II- High density ( 0.1 cars per
site) simulation result; and III- Space-time-lines for cars from aerial photography, where each
line represents the movement of one vehicle in the space-time-domain (from Nagel &
Schreckenberg, 1992)
The models represents quite well the behaviour of freeway drivers; in the low density (I) the
occurrence of traffic jams does not happen; but when the density is higher (II) the cars start
to stop randomly and the formation of clusters occurs suggesting a characteristic freeway
20
start-stop-wave traffic jam. If compared, the high density simulation diagram (II) and the cars
trajectories from aerial photography (III), show appealing similarities.
Due to the stochastic nature of the model it is necessary to perform several simulations to
obtain trustful results. A fundamental diagram of this model represents the average results of
several simulations, where the line indicates the averaging over 106 time steps result, and
the dots represent the averages over 100 time steps. Also a traffic flow vs. occupation
diagram is presented for comparison between the simulations results and the freeway real
traffic flow.
I
II
Figure 2.5: I- Traffic flow (in cars per time step) vs. Density (in cars per site) from simulation
results (L = 104). Dots are averages over 100 time steps, the line represents averages over 106
time steps; and II- Traffic flow (in cars per hour) vs. occupancy is the percentage of the road
which is covered by vehicles (from Nagel & Schreckenberg, 1992)
The similarity of the simulation model diagram and the real traffic diagram is quite
remarkable. It is also evident a change–over at r =0.08. Below this critical density, the flow
increases as the car density increases. But above this critical value the opposite happens,
originating traffic jams. The authors performed other simulations and understood that this
change-over position is dependent with the system size and this dependency only occurs in
simulations with randomization. Other situations were also studied using the same model
with some changes, like the traffic in a bottleneck situation using an open system.
This model is a simple application of CA to the problem of freeway traffic flow. Many other
more complex and detailed models have been developed since, but always keeping the main
aspects presented in Nagel and Schreckenberg (1992) freeway traffic model (e.g. Wahle et
al., 2001).
2.1.2.2 NetLogo
NetLogo5 is a user-friendly programmable modelling environment for simulating natural and
social phenomena. It was created by Uri Wilensky in 1999 and continues in constant
5
Available at http://ccl.northwestern.edu/netlogo/
21
development at the Center for Connected Learning and Computer-Based Modelling. NetLogo
is particularly well suited for modelling complex systems developing over time. This
environment allows modellers to give instructions to hundreds or thousands of "agents" all
operating independently. This makes it possible to explore the connection between the
micro-level behaviour of individuals and the macro-level patterns that emerge from the
interaction of many individuals. NetLogo is simple enough that users can easily run existing
models or even build their own. Also, it is advanced enough to serve as a powerful tool for
researchers in many fields. There is also an extensive documentation and tutorials and a
large collection of pre-written simulations that address many areas in the natural and social
sciences, including biology and medicine, physics and chemistry, mathematics and computer
science, and economics and social psychology.
Figure 2.6: NetLogo window, for a fire forest model.
The NetLogo environment allows the modeller to build the necessary interface providing the
possibility to have buttons, sliders, switches monitors, plots and several other options to the
model. There are three tabs, the interface, the information and the procedures. On the first
tab the user put the necessary wanted elements, like buttons and others mentioned before,
that the user uses to control the model. On the second path, the information one, the
modeller explains the model details. The procedures tab is where the modeller inputs the
program script. The NetLogo platform has one simple vocabulary code that is essential to
help the programmer. The NetLogo is free and easy to obtain on the internet.
22
2.2
METHODOLOGY
2.2.1 FIELD METHODOLOGY
Different methodologies were applied during and after the Cryptotermes brevis swarming
period in order to obtain the maximum information concerning the spread of the species. We
made several light traps that were collocated on the surroundings of the already known
infested area of Angra do Heroísmo. This step was important to understand the flight
distance of the species on the Azores environment, specifically at Angra do Heroísmo. We
made door to door interviews on the infested boundary area and to the owners of the
primordial infested houses6. We also contacted the Angra do Heroísmo City Hall and the
most important pest control enterprises on the Archipelago to know where they had applied
C. brevis treatments.
2.2.1.1 Interviews
The interviews had a social character once we made contact with several agents intervenient
on the termite pest. The interview methodology seeks to obtain more information about the
pest. It was also published on the local newspaper a short article describing some of this
work in order to alert the city inhabitants to the possible visit to their houses.
(i)
House interviews
The interviews had an informal approach and were made through a simple conversation with
the houses owners following a script of interview with a short questionnaire (see Appendix A).
It was also shown a collection of materials and information on the species. This collection
was composed of faecal pellets (of different woods types), wings, sexual individuals (King or
Keens) and a photo of mature sexual winged termites.
With these house visits and interviews we look to verify, on the boundary of the infested area,
the initial period of infestation and the pest evolution in time and space. Once the most
recent data concerning the infested buildings was from 2004, there was a necessity to know
if the infested area was still the same or if it had advanced. Also, we investigated how the
pest might have started. For this purpose, we interviewed the first persons to be affected by
the pest.
6
According to BORGES, P.A.V., LOPES, D.H., SIMÕES, A.M.A., RODRIGUES, A.C., BETTENCOURT, S.C.X. & MYLES, T.
(2004).
23
#
#
#
#
#
#
#
#
#
#
Entreview areas
Light traps
Initial infestation
Moderate infestation
Severe infestation
Figure 2.7: Angra do Heroísmo infested area and places where the interviews occurred.
On the image there are two different interview areas, one related to the boundary issue (light
green larger circle) and the other related to the first infested houses (green smaller circle).
We interviewed the owners of the oldest known complains about the species, according to
the report of Borges et al (2004). There is another question that these interviews look to
answer. This is whether the area between the major infested area on the city centre and the
small infested area on S. Bento (represented in Figure 2.7 by the red arrow) is indeed
uninfested.
(ii) Pest Control Enterprises and City Hall
The contact with the Pest Control Enterprises and Angra do Heroísmo City Hall was made
because they are important intervenient agents on the pest issue. We contacted all the major
Pest Control enterprises and the Angra do Heroísmo City Hall to obtain information on where
they had received complains concerning the focused species. The contact with the
enterprises was made through telephone and email, once personal contact was not possible.
We contacted personally the person in charge of this issue in the City Hall, Mr. Cosme
Picanço.
2.2.1.2 Light Traps
The light traps structures were made with timber and metal joins. On this structure we fixed a
light box, to connect one Ultra Violet light, and a plastic box protecting the security switch
where an electric wire was connected. Below the UV light we placed a clinging yellow plastic
(phototropic trap) or cardboard with the intention to capture the young winged C. brevis
individuals. The Ultra Violet lights have 70 watts power and are the ones normally used in
solariums.
24
Ten light traps were made and placed surrounding some of the infested areas in Angra do
Heroísmo. The main reason to use this traps is to determine how far an infested house can
infest other house. So one needs to know how far the young sexual mature alates can fly to
form a new colony. This information is very important to understand how rapidly the outbreak
progresses.
UV light
Security
switch box
Glued
cardboard
Electric
cable
Figure 2.8: Light trap
We obtained permission to place the traps and to use the necessary energy from the local
city council and the “Secretaria Regional de Habitação e Equipamentos”. We also obtained
the permission and collaboration on this project of EDA – “Electricidade dos Açores”. Without
EDA collaboration this project would not had been possible to complete once a special
technical support was needed to install and connect the traps to the municipal and regional
illumination net.
a)
b)
Figure 2.9: EDA car crane and functionaries during the Trap attachment a); EDA official
electrician connecting the Light Trap cable to the public illumination net b).
The positioning of the light traps was determined according to the infestation map from the
2004 field survey performed by the Universidade dos Açores Termite investigation group
(see Borges et al., 2004) and the available illumination posts where the trap allocation was
possible. The distance of the traps to the infested buildings varied from 50 meters up to more
than 150 meters, has it is shown on Figure 2.10.
25
#
#
#
#
#
#
#
#
#
50, 100 and 150
meters distance buffer
Light traps
Initial infestation
Moderate infestation
Severe infestation
#
Figure 2.10: Infested buildings, buffer distance from 50, 100 and 150 meters and light traps
initial placement.
Some traps were relocated according to the number of C. brevis alates captured and with the
door to door inquire survey. According to this survey, some traps were relocated to other
places at longer distances. This field survey started on the 29th of May and ended on the
12th of November 2008. The data collection was done during all this season and the glued
cardboard was substituted whenever possible. This substitution was done according to the
availability of the crane car and of the employees of EDA. The longest time interval was 72
days and the shortest was 10 days. The light traps were turned on and off at the same time
as the public illumination.
Figure 2.11: Ultraviolet light trap on the public illumination post.
During the same period and intervals, we monitored the swarming period intensity in the
interior of one severely infested building. This was done using one simple light trap tested by
Guerreiro et al (2006). This light trap used the same material as the outside traps, but a
different and less intense light bulb (60 watts fluorescent bulb). This allowed us to know the
swarming intensity on one indoor environment versus (Figure 2.12) the captured alates on
the outside traps.
26
Figure 2.12: Indoor light trap.
Below the indoor light trap we put one plastic box to capture some of the alates that were not
fixed to the glued trap.
2.2.2 COMPUTATIONAL METHODOLOGY
The computational methodology was all completed within the NetLogo environment. We
started to explore some models available on the program library. Then, we proceeded to
build our own simple model. This is a 2 dimensional model that follow some mathematic
rules that correspond as close as possible to the natural and real characteristics of the
species and pest development in Angra do Heroísmo. These important assumptions are:
All cells are equal: All the cells are treated equally in determining the probability value of
being infested. Once one cannot have the entire city information in detail, we start with the
simplest possible scenario.
Radius: The radius is the model parameter that is directly associated with the flight capability
of the alate individuals. This value was obtained through a qualitative analyses of the winged
individuals flight distance captured with the light traps.
Probability of a house being infested: All infested neighbours inside the region defined by
the parameter radius from a given cell have the same probability of infesting it. This
probability is unknown and is a parameter of the model.
Number of Infested Neighbours and computation of probability: Each cell has a
probability of being infested according to the probability parameter and the number of
infested neighbours inside the region defined by the parameter radius. The probability of a
cell becoming infested increases with the number of infested neighbours according to the
rules of probability. For computational reasons, the increase in probability with the number of
infested neighbours is taken into account up to 20 infested neighbours and remains constant
thereafter. As one can easily check, this assumption has no influence in the computation of
the total probability if the probability parameter is not very low because for 20 or more
infested neighbours the total probability will be very close to 1. However, for very low
probability values ( p << 0.1 ) this assumption can in principle lead to a less severe
propagation of the infestation. In practice, for very low probability values, and the values of
radius used in the simulations, the number of infested neighbours rarely exceeds 20.
27
Possible states of a cell: We considered three states:
Not infested – Houses not yet affected by the drywood termite pest yet;
Recently infested – When the house has only recent colonies and it is not an
infestation source. This cells only remain on this state for 4 time steps (years), becoming
source of infestation on the next time step (infested);
Infested – Infested houses that are source of infestation to other houses.
These cell stages are related with the Angra do Heroísmo possible stages. Which are: not
being infested, recently infested and infested7. One should consider the recently infested as
the initial period that a C. brevis colony is already present but it is not yet a source of
infestation. This is a period of 4 years until the colony starts to produce new sexual
individuals and start to be a source of infestation on the next time step – Infested cell.
These two conditions are strictly related with one important detail, which is the:
Time –Our aim is to produce a model discrete in time. In this model, each time step
represents 1 year. Normally, on CA models, the choice of time step is related to the issue to
be modelled. If one aims to model other matters, other time scale could be use. The ecology
of this species makes it imperative to have in this model the scale 1 time step – 1 year.
4 time step
1 time step
Not Infested Cell
Recently Infested Cell
Infested Cell – Source
of New Infestations
on next time step
Figure 2.13: Cell conditions and its evolution along time on the proposed model.
All these situations and conditions are directly related to the factor “time”. Therefore it is
necessary to "inform" our model of the situation step by step. That means that it is necessary
to know the situation in the previous step to take the next step and act. Then, it is necessary
to define global variables in our model.
These global variables are the first to be inserted in the model script:
globals [
7
number-previous
;; number of houses infested in previous iteration
total-houses
;; number of houses (a fraction of the total number of patches)
probability-1
;; probability of becoming infested with only one infested neighbour, setup by slider
probability-2
;; probability of becoming infested with two infested neighbours
probability-3
;; probability of becoming infested with three infested neighbours
Further on, more complex cases will be considered for which the cells can be in a fourth state, the state of immunity.
28
probability-max ;; probability for more than 3 infested neighbours , setup by slider
]
The number of probabilities is shown above and only one detail of the final script that is far
more complex. The example shown above is a simple example and not the final script that is
far more complex. The calculus of the probability follows the normal theory of probabilities:
Prob1 = Prob1
Prob2 = 2*Prob1-(Prob1)2
Prob3 = (Prob1+ Prob2 – Prob2*Prob1)
…
Prob20 = (Prob1+ Prob19 – Prob19*Prob1)
Then we need to insert in the script the characteristics of each cell, defined as patches on
the NetLogo environment:
patches-own [
infested-neighbours
;; number of infested neighbours
years-source-infestation ;; tracks times the house is source of infestation
years-infested
;; tracks number of years the house has become infested
Then one should include the setup procedures:
to setup-behaviour
ca
set tempo 0
ask patches [ set pcolor black
]
set origin patch 0 0
set xorigin 0
set yorigin 0
ask origin [ set pcolor red
set years-infested 0]
set total-houses count patches with [pcolor = black]
end
to setup-houses
ca
set tempo 0
ask patches [
let probability random 100
ifelse (probability < percentagem-de-casas-criadas)
[ set pcolor black ]
[ set pcolor white ]
]
set total-houses count patches with [pcolor = black]
end
And the probability setup:
to go
setup-probability
ask patches
[ set infested-neighbors count neighbors with [pcolor = red] ]
ask patches [
let prob 0
if pcolor = red [ set years-source-infestation years-source-infestation + 1]
if (pcolor = yellow and years-infested <= 3) [set years-infested years-infested + 1]
if (pcolor = yellow and years-infested = 4) [
29
]
set years-source-infestation 1
set pcolor red
]
if (pcolor = black and infested-neighbors = 1) [set prob probability-1]
if (pcolor = black and infested-neighbors = 2) [set prob probability-2]
if (pcolor = black and infested-neighbors = 3) [set prob probability-3]
if (pcolor = black and infested-neighbors > 3) [set prob probability-max]
if prob != 0 [
let probability random-float 1
if (probability < prob ) [ set pcolor yellow set years-infested 1]
]
]
tick
end
The presented script is just a small demonstration of the necessary programming input to
have a functioning model. Also, other script information is necessary to have a more
complete and realistic model. The complete script is presented in Appendix BAPPENDIX .
We present a coloured script to show the primitive programming words that are part of the
large vocabulary of built-in language primitives. Those are direct words proper of the
NetLogo simple language structure. All words, numbers and mathematic symbols, that are
coloured, are representative of different primitives common to all scripts of all models made
in the NetLogo environment.
The model also requires one to set the boundary and neighbourhood conditions. In this case
we chose to define a closed boundary. The program provides several options for the
definition of the neighbourhood such as the Moore neighbourhood (8 cells neighbourhood)
and Van Newman (4 cells neighbourhood) that are designated as environmental NetLogo
neighbours and neighbours4, respectively. There are other types of neighbourhood and in
our model we define it as all the cells in a given radius (in-radius).
30
Figure 2.14: NetLogo interface view with some of the several possibilities of buttons, sliders,
monitor, etc.
The interface of NetLogo is an important structure in the model developing. There is also, an
obvious relationship between the script and the various set elements of interface. These
various elements of interface make it easy to change the parameters and elements of the
model. These elements make the models more attractive and user-friendly.
In addition, we have developed simple tools that allow us to characterise the results of the
model.
These are:
− The maximum distance between the infected cell in the centre of pest and the more
distant cell infested;
− The minimum distance between the infected cell in the centre of pest and the closest
uninfected cell;
− The maximum distance between the two most distant infected cells (diameter of area);
− The number of recently infested cells (houses);
− The number of infested cells (houses) that are source of infestation;
− The healthy fraction that is the proportion of healthy cells (not infested).
31
These results were obtained with a very useful tool of NetLogo, “the behaviour space”. This
tool allows the modellers to learn how changes in certain parameters affect the results
obtained in their models. Usually the models have many parameters, each of which may
have a wide range of values. Together, they form what in mathematics is called the
parameter space of the model, whose dimensions are the number of possible configurations,
in which each point is a specific combination of values. Running a model with different
configurations (and even the same in the stochastic case) can lead to drastically different
results. Therefore, this tool is ideal to our objective, which is to understand how the model
behaves according to the variation of the parameters. These results will be important for the
determination of a more reliable and realistic pest spread model.
After a detailed study concerning the model behaviour, it has become necessary to include
an environment similar to the study area, the city of Angra do Heroísmo. Thus, through the
use of a GIS, the urban net of Angra do Heroísmo area (shape file) was transformed into a
grid file. This process also requires the choice of the size desired for each cell of the grid. We
chose to create a grid with cells of 10 meters by 10 meters. This grid was then saved in CSV
format and later imported into the environment NetLogo. This step aims to apply the model to
a specific problem and therefore provide a practical significance to this work. In particular, it
aims to improve our understanding of the behaviour of the model taking into account the
existing information. The available information is based on local scientific studies, reports of
residents and present status of this pest
These simulations can be used to understand the present situation as well as to predict the
future evolution of the termite infestation in the city of Angra do Heroísmo. Also, the model
can be applied to study the evolution of the infestation in other cities in the Azores.
In the future, other features could be included in the model. These include a greater number
of stages of infestation (early, moderate and severe); pest evolution on each home/cell
(including a clock for a change of infestation in each cell); enabling each infested house to
continue to be subject to infestation of new colonies; different probabilities of infestation for
each house (according to its building materials, prevention, etc.); and allow the inclusion of
treated houses/cells to verify their behaviour in the evolution of the insect pest. All these
suggested improvements are likely to bring more realism to the model and are a strong
reason for further studies.
32
2.3
RESULTS
The results are presented in two different subsections according to their methodology.
Obviously, the results are interconnected. However, the option to separate the results is due
to the specificity of the methods applied. This form makes it much simpler to analyse each
result separately and also both results as a whole.
2.3.1 FIELD RESULTS
2.3.1.1 Interviews
The interviews yielded relevant information to the understanding of the evolution of the C.
brevis pest.
(i)
House Interviews
These results were obtained in the border area of the pest. The different areas and number
of houses surveyed in each area can be seen in Figure 2.15.
#
#
#
5
3
#
#
4
2
#
1
#
#
#
6
#
Entreview areas
Light traps
Initial infestation
Moderate infestation
Severe infestation
Figure 2.15: Angra do Heroísmo infested area and places where the interviews occurred.
The table 2.1 gives the number of places visited in each numbered area shown in the picture
above. In all of these places, on just a few we were able to perform a precise and accurate
survey (in situ confirmation of the presence or not of the species). However, once we showed
in all the houses elucidative materials about the species and a description of their most
prominent vestiges and the majority of the people was concerned about the issue, had a
good receptivity and cooperated enthusiastically, we are confident about the results.
33
Table 2.1: Locations and approximate number of houses searched in each area
Area/Locality
1- S. Pedro
2- Sta. Luzia
3-Conceição
4- Guarita
5-S. Bento
6- Monte Brasil
Number of
surveyed
houses
7
9
8
15
7
5
We now show in detail the houses that were inspected and the information obtained
concerning their infestation.
1- S. Pedro
Infested
Not infested
Light trap
Figure 2.16: S. Pedro surveyed area. The green houses show the inspected houses.
Of all the surveyed houses none showed signs of infestation of the pest.
2- Sta. Luzia
Not infested
Recently infested
Infested
Highly infested
Not mentioned in
2004
Light trap
Figure 2.17: Sta. Luzia inspected area. The green houses and the ones on the red circle are the
houses that were inspected.
During the research conducted in this area some houses showed traces of the presence of
termites. These houses were in an advanced process of degradation by Cryptotermes brevis.
This implies that the infestation has been present for several years and that it already existed
in 2004.
34
3- Conceição
Not infested
Recently Infested
Not mentioned in
2004
50 meters
distance
Light trap
Figure 2.18: Conceição inspected area. The green houses and the ones on the red circle are
the houses that were inspected.
So far this is the most interesting result. By the research done in this house, marked with the
red circle, we find out that the pest has progressed so far. The red circle in the image
indicates a house with an initial infection (yellow house). According to what was observed
and the details supplied by the owners of this house, there were no signs of termites
swarming (wings) present, until this year. The roof structure material is recent and there was
no evidence of infestation in any other room or furniture in the house, which suggests that
the termites have flown in a house infested from the neighbourhoods. The colonized area is
around the skylight in the roof and there were only an estimated number of 3 to 5 colonies.
This suggests that the colonies exist at least for 5 years. This is a most interesting result and
is very likely indicating the progression of the pest.
The nearest infested house is 50 meters away. This was the minimum necessary distance
that the young alates had to fly.
4- Guarita
Not infested
Figure 2.19: Guarita inspected area. The green houses are the houses that were inspected.
The area of Guarita is an important area because it is between the highest spot of infestation
in the city of Angra do Heroísmo and the small infestation region in S. Bento.
In all the surveyed houses there were no traces of the presence of termites found. Many of
those houses do not have wooden structures favourable to C. brevis colonization.
35
5- S. Bento
Not infested
Infested
Light trap
Figure 2.20: S. Bento inspected area. The green houses are the houses that were inspected.
The orange houses were already infested in 2004 (Borges 2004).
In the small infestation area in S. Bento, besides those previously reported in Borges et al.
(2004), none of the inspected houses were infected. There are two old and unoccupied
buildings that were not possible to inspect. However the houses adjacent to them were
inspected and had no traces of termites.
6- Monte Brasil
Not infested
Infested
Not mentioned in
2004
150 meters
distance
Light trap
Figure 2.21: Monte Brasil inspected area. The green houses are the houses that were inspected.
The orange and yellow houses were already infested in 2004 Borges (2004).
Several houses were inspected in the Monte Brasil area, and many of them in the army
barracks on the fortress of S. João Baptista. The most interesting finding was that of an
isolated house that had a moderate infestation and was located about 150 meters (red arrow)
from the nearest infested area. This makes us believe that a couple of termites may have
flown 150 meters and formed a new colony. But we are not as confident in this result as in
the case described previously in the Conceição area, where it was clear that the termites
have been attracted by light from inside the house through the skylight. In the Monte Brasil
case this infestation might have been caused by the transport of furniture. Unfortunately, it is
almost impossible to determine accurately how the pest arrived here.
In addition to the interviews conducted in the border of the pest area, we did some other
interviews to the house owners who reported, during the survey conducted by Borges et al
36
(2004), the earliest dates concerning the presence of the pest. These people were contacted
again to try to determine, with the best possible accuracy, the original date of entry of the
species as well as the primordial infested houses in Angra do Heroísmo.
Table 2.2: Place of interview and date on the presence of termite these locations
Place of Interview
Mentioned date
R. Palha 13 (Sé)………………………............
R. Baixo Sta. Lúzia 38 (Sta. Lúzia)................
R. S. Pedro 126 (S.Pedro).............................
R. António dos Capuchos 5 (S. Bento).......
Before 1972
1980
1996
1999
As you can see in the image in Figure 2.22 the locations were selected by the oldest date
also corresponds also to areas of moderate to severe infestation.
#
#
#
#
#
#
#
#
#
#
Entreview Spots
Light traps
Initial infestation
Moderate infestation
Severe infestation
Figure 2.22: Angra do Heroísmo infested area and places where the interviews occurred.
(ii) Pest Control Enterprises
The interviews made to the two largest pest-control enterprises (Pest Kill and Pest Control)
provided information about the streets that they were aware of the presence of termites. For
reasons of confidentiality, it was only requested to these companies the names of the streets
where they had intervened. The results are presented in the following table:
37
Table 2.3: Streets where the pest control enterprises have been operate.
ANGRA DO HEROÍSMO
Rua da Sé
Rua Direita
Rua do Palácio
Rua do Rego
Alto das Covas
Rua da Garoupinha
Rua da Palha
Travessa de S. Pedro
Caminho Novo – S. Pedro
Rua de S. Pedro
Rua de S. João
Rua de Baixo de S. Pedro
Rua Dr. Henrique Brás
Rua do Morrão
Ladeira de S. Francisco
Of all the mentioned streets only Rua Dr. Henrique Brás was not known to contain infested
houses. Several inspections to houses on this street were made, but no traces of infestation
by C. brevis were found.
500m
380m
280m
Not infested
Moderately Infested
Not mentioned in
2004
Distance from
infested neighbor
Dr. Henrique Brás
Street
Figure 2.23: Probable distance to the only mentioned infested house on Rua Dr. Henrique Brás,
according to the Pest control Enterprises.
According to what was possible to determine from the companies that sent us this
information, only one house was treated for termites in that street.
This means that either this house was infested through the transport of furniture or through
winged flight from a house nearby. This raises some perplexity because the closest known
infested houses distant more than 280 meters. This issue deserves further attention in the
future.
2.3.1.2 Light Traps
The light traps were placed at different distances according to Borges et al. (2004) data. All
traps were initially placed at distances greater than 50 meters, and some more than 150
meters, from the closest known infested houses. According to the research conducted with
38
the interviews to the inhabitants of Angra do Heroísmo, some traps were moved to other
locations. The traps location at different times is shown in the 2.24.
#
#
#
#
#
#3
4
2
#
#5
6#
#
#
#
7
8#
#
#
9
#1
#
Traps Movements
Light traps
Initial infestation
Moderate infestation
Severe infestation
10 #
Figure 2.24: Light traps positions and displacement during the survey period.
The changes in the light trap locations over the survey period produced different results
concerning the number of individuals captured and the estimated minimum distances
covered by them.
Figure 2.25: Appearance of one trap when the glued cardboard was collected for sampling.
39
a)
c)
b)
d)
Figure 2.26: Winged (a) and (b); wings of an alate (c); three individuals who have freed
themselves from the wings and took refuge in the back of the glued cardboard (d).
There are two main reasons that lead us to move the light traps. On the one hand it allows us
to obtain a better estimate of their flight capabilities; on the other hand it is a simple way to
detect the presence of the species in previously unknown areas.
The table 2.4 shows the number of winged individuals caught and the estimated minimum
distance travelled by them.
Table 2.4: Number of winged caught by trap and the distance from the likely area of origin
Cb Dist Cb Dist Cb Dist Cb Dist Cb Dist Cb Dist
Cb
Trap
1
170
170
170
170
170
170
1
1
4
0
1
0
0
Trap
2
196
196
196
196
196
196
0
0
1
nd
0
0
0
Trap
70
70
70
70
70
70
3
0
0
1
0
0
0
0
Trap
4
100
100
170
170
170
170
0
4
1
0
0
0
0
Trap
5
30
30
30
30
30
30
0
0
3
0
1
0
0
Trap
60
60
60
60
60
100
6
0
0
4
6
3
0
0
Trap
7
30
30
30
30
120
600
1
8
5
6
1
0
0
Trap
8
160
160
160
160
160
160
0
nd
4
1
0
0
0
Trap
9
80
80
80
80
130
130
0
0
7
2
5
0
0
Trap
10
100
100
100
100
100
100
0
0
3
0
2
0
0
Total
2
13
33
15
13
0
0
Cb: Cryptotermes brevis alates; Dist: Distance in meters; Nd: no data; PU: Pico da Urze;
SC: São Carlos. Note: on some occasions we only caught the wings
8
Dist
435
348
70
170
30
100
600
PU
SC
100
In the situations where only wings were caught and no individuals were present, we counted
the wings as caught individuals.
8
The large distances that some of the light traps were placed from infested houses, aimed to find out whether the infestation
had progressed to unknown areas. This was unsuccessful once no alates were captured during this period.
40
However, we must note that the trustworthiness of the data presented is not the same for
every light trap. This is due to the difficulty in surveying all the houses on the infested area
periphery. Therefore, we present in Figure 2.27 the light traps location and the inspected
areas to an easy understanding of our judgement.
3#
4#
2#
5#
6
#
7#
8
#
9#
1#
#
10
Entreview areas
Light traps
Initial infestation
Moderate infestation
Severe infestation
Figure 2.27: Traps positioning and surveyed areas.
Despite the great effort made to cover the entire periphery of the infested area, it was not
possible to carry out interviews and surveys in all locations required. Thus, the results
obtained with the different traps have different degrees of certainty. The trap number, its
reliability and the reasons to include or exclude the collected data are presented in Table 2.5.
Table 2.5: Traps and their respective confidence
Trap number
Trap 1
Trap 2
Trap 3
Trap 4
Trap 5
Trap 6
Trap 7
Trap 8
Trap 9
Trap 10
Reasons
This area was not target of a proper survey. The collected samples could have being
originated from closer buildings.
This area was surveyed properly.
This area was surveyed properly.
This area was not surveyed properly. However, the buildings in this area are of
relatively recent construction and no structural wood is used.
This area was surveyed properly.
This area was not target of a proper survey. The collected samples could have being
originated from closer buildings.
This area was surveyed properly.
This area was surveyed properly.
This area was not surveyed properly. However, the buildings in this area are of
relatively recent construction and no structural wood is used.
This area was surveyed properly.
Reliability
Not trustful
Very trustful
Very trustful
Trustful
Very trustful
Not trustful
Very trustful
Very trustful
Trustful
Most trustful
Table 2.6 presents similar results to Table 2.4 but concerning only the data from the trustful
and very trustful traps to a reliable determination of the different distances crossed by the
winged.
41
Table 2.6: Different distances and number of alates captured at each distance
Number of captured
alates/Distance (meters)
30
70
80
100
120
130
160
170
196
Very trustful
24
1
0
5
1
0
5
0
1
Trustful
0
0
9
4
0
5
0
1
0
Trustful and Very trustful
24
1
9
9
1
5
5
1
1
From data in Table 2.6 we infer that this termite can disperse up to a distance of at least 196
meters. However, the probability of dispersion is higher for shorter distances such as 100
and 160 meters where most catches were obtained (and even higher for the closer distance
of 30 meters). The winged captured at 160 meters correspond to the trap number 8 which
was located in the area of S. Pedro near the premises of the television network. The reason
for this large distance might be due to the great effectiveness of ultraviolet light
attractiveness and due the vast space between the probable area of origin and the trap
where there are almost no houses facing east, which obviously reduces the number of
attractive lights competing with our light trap. Although on the opposite direction, to west,
there are some houses that were not surveyed and so the flight distance might be slightly
smaller than the 160 meters. But the trap that gives us a more confident result is the trap
number 10, where 5 individuals were captured. This trap, located next to Monte Brasil, was
originally facing north in the direction of Angra do Heroísmo and no captures were obtained
until we turned it towards the Bay of Angra do Heroísmo (facing East) in direction to Rua da
Rocha (at a distance exceeding 200 meters). Following this change, we started to catch
alates on this trap. Interestingly, despite the trap faced east, the closest possible origin was
from a house located about 100 meters away (North of the trap). This suggests that either
the alates came from houses 200m away or that the alates performed a very sinuous flight
from the closest house, through the trees until they reached the trap. Also, this trap is the
one that we have the utmost confidence because there are no other sources of infestation
nearby. Therefore, the value of 100 meters is an acceptable and trustful distance to
characterize dispersion flight of this termite.
As the rate at which the alates leave their colonies varies in time, we collected the indoor
light trap samples within the same day as the outdoor ones (Figure 2.28).
a)
b)
Figure 2.28: Indoor sticky trap (a); and container underneath to collect some of the alates that
were not glued to the trap (b).
42
The number of individuals caught per sample on both situations is presented in Figure 2.29
for the whole swarming period.
Number
of individuals
captured
on the Light
traps
Number
of individuals
captured
outdoors
35
of individuals
capturedindoor
indoor
NumberNumber
of individuals
captured
2500
JULY, 33
JULY, 2264
30
2000
25
20
1500
15
1000
10
500
5
AU
G
US
T
O
CT
OB
ER
b)
JU
LY
JU
LY
JU
LY
JU
NE
JU
NE
O
C
TO
BE
R
AU
G
U
ST
JU
LY
JU
LY
JU
LY
JU
NE
JU
NE
JU
NE
a)
JU
NE
0
0
Figure 2.29: Number of alates captured outdoors with the UV light traps (a); and number of
alates captured indoor (b).
As mentioned in the methodology section, the glued cardboard was removed from the traps
whenever possible, but the time of exposure was not regular. Thus, the number of winged
captured per day of exposure is the most appropriate way to present this result and is shown
in Figure 2.30.
Number
of individuals
captured on the
Light traps
per day per
Average
number
of individuals
captured
outdoors
day
4
250
3
200
JULY, 3
Average number
ofindividuals
individuals
captured
indoor
Number of
captured
indoor per
day per
day
JULY, 206
150
2
100
1
50
O
C
TO
BE
R
AU
G
U
ST
JU
LY
b)
JU
LY
JU
LY
JU
NE
JU
NE
JU
NE
0
O
C
TO
BE
R
AU
G
U
ST
a)
JU
LY
JU
LY
JU
LY
JU
NE
JU
NE
JU
NE
0
Figure 2.30: Number of alates per day captured outdoor on the UV light traps (a); and number
of alates captured indoor per day (b).
There is an obvious relation between the number of winged captured outdoors with the light
traps and those caught indoors in the surveyed habitation.
This set of results presented here are necessary to proceed to the next stage, the computer
modelling. Given these results, the computational model will be used to reproduce the
dispersion of the species in Angra do Heroísmo and compare it with the observed present
scenario.
43
587m
448m
1000m
900m
500m
Figure 2.31: Map of Angra do Heroísmo with actual infested areas and pest distance spread
from the centre to the furthermost places.
The observation of the infested map gives important details about the pest. For instance, it
gives us the necessary distance that the pest had to spread from an eventually starting point
that we refer as the centre of the infestation. This centre was chosen according to the
available pest data that showed us that the first buildings to have C. brevis symptoms were in
Rua da Palha and Rua da Sé. Therefore, we selected a place in the centre of those streets.
We have several indications that the species might have been introduced for at least 40
years. This means that if the species can propagate every year from a start point x to a
maximum possible distance y during the 40 years period, the pest had to advance at least 25
meters per year. This considering the distance from the centre to the furthest infested point
(1000m). However, we know that once the termites form a new colony, it will take at least 5
years until it becomes a source of infestation. Based on this ecological property, the pest can
only advance at each 5 years interval. This means that the average distance the
Cryptotermes brevis alates had to fly on each swarming period was of 125 meters (57 meters,
to achieve the shortest distance, following the same assumption) 9 . This result is in
agreement with the data we have obtained with the light traps and gives us confidence to
apply it in our computational model.
Besides the elevated number of Cryptotermes brevis alates captured, we also captured
Kalotermes flavicollis (Fabricius, 1793) alates. These alates were captured from the 15th of
August to the 12th of November. While not under the aim of this study, it is a curious result
obtained during this research, which confirms the efficiency of the traps. As an additional
9
This result is valid assuming a single source of infestation and ignoring human active contribution to its dispersion.
44
result, we present in the table 2.8 the number of individuals and places where they were
captured.
Table 2.7: Number of Kalotermes
flavicolis captured alates
Kalotermes flavicolis
PARQ.COMB
STA. LUZIA
RUA DO
DESTERRO
MEMÓRIA
S. CARLOS
PICO DA URZE
TOTAL
Figure 2.32: Kalotermes flavicolis
45
11
5
1
2
16
4
39
2.3.2 COMPUTATIONAL RESULTS
The computational work was carried out in different phases. The first phase was initiated by
a simple model that allowed us to understand the general mathematical properties of the
termite dispersion. The model was then applied to the city of Angra do Heroísmo. The results
are presented according to this order as well.
2.3.2.1 Cellular Automata
The cellular automata model has two parameters: the radius and the probability of infestation.
The radius is intrinsically related with the flight distance capability obtained with the light
traps and presented in the previous section. The probability of infestation is related with the
ecological capability of the species for forming new colonies. This is the probability of a
house becoming infested due to the presence of an infested house within a certain radius. It
is also indirected related with the habitant’s attitude and the characteristics of the houses.
(i)
General results
We performed several simulations from which we present a small example at some defined
steps of the simulation. The reason for presenting only a few images is due to the obvious
fact that the results expressed through graphs and numbers are much more meaningful and
easy to analyse than the images, which in this case would be of the order of thousands.
46
a)
b)
c)
d)
e)
Figure 2.33: Images from the first tested model at different time steps. Time steps: 0 (a); 1 (b); 6
(c); 11 (d); and 21 (e). Used parameters: radius 8 and probability 1 (upper), 0.2 (middle) and 0.01
(inferior). Yellow cells – recently infested cells, red cells – cells sources of infestation.
The images shown in Figure 2.33 are from the simplest model that was tested. We seek to
learn how the model behaves in relation to changes in its key parameters. In this model all
cells are potential cells to be infected and in the beginning no other type of cell exists (with
exception of the cell on the centre). The infestation can spread out without any barrier. The
examples shown are of a simulation where the healthy cells in an 8 cells radius from any
highly infested cell (red cell) have a probability of becoming infested of 1, 0.2 and 0.01,
respectively. As can be seen in time steps 1 and 6 (Figures 2.33 b and c respectively) the
radius of action is identical, only the number of recently infected cells and cells source of
infestation has increased. After five years, these cells evolve to the stage of highly infected
cells which means that they become a source of infestation to other cells nearby. Therefore,
the initial infestation spreads and increases at each five years. In the deterministic case there
are no changes at the intermediate time steps. For values of probability lower than 1, there
are changes occurring at every time step. One notices that at the end of the simulation the
two scenarios with higher probability are very similar, even though they are very different at
earlier stages. The evolution of the lower probability scenario (0.01) is quite different from the
other two. The numbers of infested and highly infested cells are much lower and there are
healthy cells nearby the origin of infestation. Also, the shape of the infestation is different
from the other two being less symmetric.
We present in Figure 2.34 the result of numerous runs of the model for different values of the
probability parameter. The results presented are average values of several simulations
47
where the same conditions were repeated 20 times in order to obtain a representative
average result. These repetitions are necessary due to the stochastic nature of the model.
1
0.2
0.01
Figure 2.34: Average values of several interactions using the same parameters that were use
on the Figure 2.33 (red, blue and black circles).
The values marked on the graph (red, blue and black circles) represent average values of
the final scenarios of the simulation shown in Figure 2.33.
To understand how the variation of the parameters influences the behaviour of our model we
use the behaviour space tool on the NetLogo platform. All data presented in Figure 2.35
were obtained with this tool and the results presented are the average values. The graphs
presented show the values obtained in the simulations joined by smooth lines. These lines
are used for clarity purposes only.
Figure 2.35: Average number of infested cells (red cells) as a function of probability and radius.
The graph presented above shows the relation of the different radius and probability values
with the final number of infested cells. The number of infested cells increases as the radius
increases and for p≥0.1 this increase is very closely proportional to the radius square. For
48
values of probability between 1 and 0.1 the final results are very similar. The same does not
happen to smaller probability values (e.g. p= 0.01). For these values there is also a trend of
increasing average number of the infested cells number with radius. However, this is not so
marked and the values are clearly lower. The coefficients of variation 10 of some of the
presented averages are shown in Figure 2.36.
Figure 2.36: Coefficient of variation of the red cells as a function of probability and radius.
These results show that the coefficient variation is very small for probability values superior
to 0.1 (p≥1) and that it decreases with increasing radius. For these values of probability, the
higher coefficient of variation obtained is 0.16.
In order to understand the model behaviour for probability values below 0.1, we analyse the
maximum and minimum values of the number of infested cells.
Maximum and Minimum values
Number of infested cells
10000
CV = 0,008072
1000
CV = 0,150111
CV = 0,03128
0.1 Max
100
0.1 Min
CV = 0,16026
0.01 Max
CV = 0,45947
0.01 Min
10
CV = 0,55947
1
0
2
4
6
Radius
8
10
12
Figure 2.37: Maximum and minimum values of infested cells for different radius (1, 5 and 10) at
different probability values (0.01 and 0.1).
10
CV =
The coefficient of variation is
σ
N
, where σ is the standard deviation and
49
N
the average value.
These results show that not only the coefficients of variation are small but also the extreme
values are close together. For the lowest probability considered the extreme values attain
significantly different values.
The results for the recently infested cells (yellow cells) follow a similar pattern.
Figure 2.38: Average number of recently infested cells (yellow cells) as a function of probability
and radius.
The average number of newly infected cells increases significantly with the radius and for
p≥0.1 this increase is very closely proportional to the radius square. For values of probability
as low as 0.1 the final result is very close to deterministic. Only for very low probabilities (e.g.
p=0.01) one obtains final results significantly distinct from the deterministic case.
feature is repeated for any value of radius.
Figure 2.39: Healthy fraction as a function of probability and radius.
50
This
The healthy fraction is related to the number of healthy cells (black cells) and the number of
infected cells (yellow and red cells) in the radius of action of infection from any infectious cell.
This means that a cell infested with a certain probability of infestation and a radius of
dispersal may infest a given number of cells (which corresponds to the total number of
healthy cells), after a few steps inside the radius of action some cells will be infected and
others not. Thus, the healthy fraction it is the proportion of infected cells and not infected
cells within the radius of infection probability of an infectious cell (red). Therefore, on higher
probability values the healthy fraction decreases when the radius increases. Exactly the
opposite happens with lower probability values (see 0.02 and 0.002). As the probability of
infestation is lower and the radius increases the proportion of healthy cells also increases.
Min-Dist Prob. Vs Radius
45
Number of cells
40
1
35
0,8
30
0,5
25
0,4
20
0,2
15
0,1
10
0,01
5
0
0
2
4
6
8
10
12
Radius
Figure 2.40: Average values of the minimum distance as a function of probability and radius.
The min_dist is the minimum distance from the initial infected cell, in the centre 0.0, to the
closest non-infested cell. This is a complementary tool to the healthy fraction and, as before,
for p≥0.1 the minimum distance is almost independent of the probability. For very low
probability it is possible to find healthy cells very close to the initial source of infestation.
The maximum_distance is the maximum distance from the origin of the infestation to the
farthest high infested cell (red cell). This value can be interpreted as the spread radius of the
pest at a given time.
51
Max-Dist Prob. Vs Radius
35
Number of cells
p=0.2 cv 0,0025
30
p=0.1 cv 0,0041
25
p=0.01 cv 0,4068
20
1
p=0.2 cv 0,0789
0,8
15
p=0.1 cv 0,1330
p=0.2 cv 0,0032
10
p=0.01 cv 0,4676
p=0.1 cv 0,0235
0,5
0,4
0,2
p=0.01 cv 0,1926
5
0,1
0,01
0
0
2
4
6
8
10
12
Radius
Figure 2.41: Average values of the maximum distance as a function of probability and radius.
The maximum distance has an obvious variation with the increase in radius. However, there
are no major differences between the values of probability, with the exception of the lowest
value, of 0.01.
The Max-Mais_Dist gives the largest diameter of the infestation. It is the largest distance
between two highly infested cells (red cells).
If the infestation spreads symmetrically then this is twice the value of Max-Mais_Dist.
Otherwise, it is smaller. The combination of these two tools allows us to determine the
degree of asymmetry that can arise in this stochastic model.
30,00
27,47
25,00
20,00
Max
15,00
Min
10,00
4,29
2,77
5,00
0,00
0
0,05
0,1
0,15
0,2
0,25
probability
Figure 2.42: Minimum and maximum asymmetry values for radius 10.
Figure 2.42 presents the maximum and minimum asymmetry obtained from the parameters
min_dist and Max-Mais_Dist for a radius 10. This asymmetry varies from 100% (when the
diameter is equal to the radius, completely asymmetric) to 0% (when the diameter is twice
the radius, perfect symmetry). The graphic results show us that the maximum asymmetry is
27% for p=0.01, 4% and 3% for p=0.1 and 0.2, respectively. The lowest asymmetry obtained
in the simulations is 0% for all probabilities considered.
52
We conclude that the stochastic nature of the model can only originate a small geometrical
asymmetry in the dispersion and that this asymmetry increases as the radius and probability
decreases.
The results of this general and simple model allow us to have a greater understanding of the
model and allow us to proceed to the next step. This next phase consists in the
implementation of the model in the urban environment of Angra do Heroísmo.
(ii) Angra Model Results
The results that we present of the model of Angra do Heroísmo derive from an initial
approach of trying to reproduce the insect pest since its initial state. Only through the
simulation of some cases it is possible to find the appropriate conditions for a reliable
reproduction of reality. Then, following the assumption that the Cryptotermes brevis
infestation exists since the last 40 years, we present some possible initial scenarios.
a. How the pest may have begun
The first simulation has the following characteristics:
Probability of infestation 0.25 and Radius 10 (corresponding to 100 meters). This choice of
radius was chosen in accordance with the light traps experiments. The choice of probability
was chosen taking into account that the final results of the model are insensitive to its exact
value unless it takes extremely small values. This possibility was excluded based on what is
known about the infestation process.
Initially only one infestation source exists (red cell).
The location of the source of the infestation was selected according to the interviews on the
city centre following the previews Borges et al. (2004) results as presented in section 2.3.1.1.
The oldest reference to the termite’s presence was made in Rua da Palha (green arrow) in
1972 (see Table 2.3).
53
a)
b)
c)
d)
Figure 2.43: Simulation of Cryptotermes brevis in Angra do Heroísmo at different time steps.
Time step 0 (a); at time step 10 (b); 20 (c); and 30 (d).
The final result of the simulation, after 40 time steps, is represented Figure 2.44.
Figure 2.44: Simulation of Cryptotermes brevis in Angra do Heroísmo after 40 time steps.
By comparing the model results with the present situation one concludes there are significant
disparities. The pest did not achieve the same size that currently exists. For example, in the
area of S. Pedro, where the pest is currently quite dispersed, the simulated infestation did not
reach the area. This means that some of the original considerations may not be the most
appropriate. For instance:
The flight distance might have been underestimated and therefore the alates could disperse
through longer distance flights. If so, one should apply a larger radius in the model.
Increasing the radius from 10 to approximately 14, corresponding to 140m, would allow the
infestation to reach this area. This larger value is not incompatible with the light traps
experiments, or;
54
The location of the source of the infestation was not correct. This means that the initial
spread house was not in the Rua da Palha but somewhere else. If so, one cannot identify the
initial spot once no other information concerning this issue exists. However the dislocation of
the source of the infestation in the model could easily be made;
Or, more than one initial source of infestation exists. If two houses were infested by the C.
brevis on the same occasion the pest might have spread at the same time but on two distinct
origin spots. This may perhaps have happened if the host material or materials (furniture,
books, clothes or construction lumber) arrived on the island to more than one house at once.
Or even on the hypotheses that the host material was a wood boat located on the Baia de
Angra do Heroísmo probably might have spread on more than one house on that area.
In order to understand the influence of each of these hypotheses, one should address them
one at a time. Here we explore in detail the assumption about the initial number of infested
cells.
We present below (Figure 2.45) the results of a second simulation, where we used the same
parameters as the previous one (Probability of infestation 0.25 and Radius 10), but we
initially have two infested cells on different locations (green arrows). The location for the
second initial source of infestation was chosen following the hypothesis that this second
infestation source had the same origin as the one at the first simulation. We are considering,
for instance, that this might had originated from an infested boat on the Angra do Heroísmo
Bay. Therefore, we opted for a location close to the previous one and also relatively close to
the City bay and on a severely infested area at present.
a)
b)
c)
d)
Figure 2.45: Second simulation of Cryptotermes brevis on Angra do Heroísmo at different time
steps. Time step 0 (a); at time step 10 (b); 20 (c); and 30 (d).
55
This last simulation is more in agreement with what currently exists. The infested area
predicted by the model at the end of the simulation is more similar to the real one (see Figure
2.46).
Figure 2.46: Second simulation of the Cryptotermes brevis species in Angra do Heroísmo after
40 time steps.
To better analyze the results we present a map where we overlap the infested areas of
Angra do Heroísmo and the outcome of the simulation (Figure 2.47).
S. Bento
Guarita
Corpo Santo
Figure 2.47: Simulation of Angra do Heroísmo after 40 time steps overlapped with the infested
map.
The model simulation previews a quite similar result to the existing pest spread map. The
simulation forecasts the spread of the pest areas that are not existent on the map of Borges
et al. (2004). This is not a characteristic exclusive to this simulation but is common to both
simulations shown. The areas are situated on Corpo Santo (Green dots circle) and Guarita
(Blue dots circle) city locations (see Figure 2.47).
56
As shown in Figure 2.31, the assumed origin of the infestation is far from the geometrical
centre of the known infested area. This asymmetric growth of the infestation is very unlikely a
result of the stochastic properties of the propagation of the infestation, as shown in section (i).
Another possible explanation is that our assumption that all houses are equal is strongly
violated in these areas. In fact, a large number of houses in these areas are more recent and
have less wood than the traditional houses in the city centre. However, the most interesting
explanation is that the model is correct and the infestation has indeed reached these
locations. Indeed, combining the model with the data obtained from the Pest Control
interviews and the data obtained with the light trap number 1 where seven alates were
captured strongly supports this view. The Corpo Santo area is also an area where it was not
possible to conduct a proper survey to the houses and therefore there are no indications that
the pest did arrive there. In addition, the number of alates captured with the trap number 1 is
indicative of the C. brevis presence nearby.
On the Guarita location the presence of the species is only related to the pest control
enterprise that referred a house that was treated for C. brevis infestation. In the future, the
proposal that the infestation has reached these areas must be looked at in detail.
There is one area affected by the species that our model is unable to explain. This is in the S.
Bento area (Pink dots circle). This happens because on this simulation the model only
assumes the natural spread of the species. From the light traps result one could assure with
confidence that the S. Bento area was not infested by the natural spread from the city centre
because the alates captured at the longest distance (196 m) were very few (see Table 2.4).
Therefore, it is very unlikely that a pair of alates had flown from an infested area in the city
centre for more than 1000 meters until the S. Bento area (see Figure 2.31).
This motivates us to suggest that in the future the model includes the possibility of infestation
by direct human action. This could be the normal relocation of goods among people, on this
particular case the traffic of infested wood, furniture, books or other ways to the species
individuals be carried from house to house.
Also, the model could be improved in many other aspects (e.g. more cell states) aiming to
develop a more realistic and complex model.
2.4
DISCUSSION
Methodological limitations
In this chapter we were concerned to the study of the local dispersal of the drywood termite
Cryptotermes brevis with two complementary approaches, fieldwork and computational work.
The field work consisted in interviews and light traps experiments.
57
The interviews allowed us to obtain an idea of how the pest has developed since the last
survey (Borges et al., 2004) as well as to determine the most likely initial infested house. The
interviews covered a significant number of houses originating fruitful results. The ideal
situation would be to perform a survey covering all the houses in Angra do Heroísmo, but
such work would be extremely difficult to pursue without the support of a large-scale financed
project. In fact, this difficulty is partly due to the large number of houses and also because in
many places it was not possible to conduct an appropriate survey for several reasons: some
buildings were locked and (in appearance) unoccupied; some owners did not show interest
and did not allow an effective inspection and, especially, the limited time for the research. In
many cases the person inquired participated but it was not possible to have a complete
survey of the house.
Another methodological issue is related with the distribution of the traps that was conceived
according to the Angra do Heroísmo infested map of 2004. This map had some gaps that
induced us to place some traps closer to infested houses than previously thought. However,
this could have been avoided if an earlier house survey had been made. Instead, this was
done simultaneously with the traps experiment.
In order to work on the most integrated possible conditions, all the responsible intervenient
institutions were contacted. Those were the local municipalities affected by the species and
the main pest control enterprises that operate in the archipelago. The reason for this contact,
in addition to incorporating important elements of the studied subject, was to get more
information on the current situation in the archipelago, particularly in Angra do Heroísmo.
Some important information was requested to Angra do Heroísmo city hall concerning the
main construction characteristics of the buildings in the city. In spite of the fact that this
information is available, it is not in a digital format and is very difficult to consult. This
information would allow one to establish a relationship between the houses structural
characteristics and their likelihood of becoming infected by the pest.
The light traps allowed us to obtain information concerning the C. brevis flight capacity, and
therefore lead to an understanding of the capacity of dispersal of C. brevis in the local
environment of Angra do Heroísmo. As far as we are aware, this is the first estimate of the
flight distance of this termite and this constitutes an important contribution to our knowledge
of its biology and ecology. Other methodologies11 could have been applied to understand the
flight capacity of the species. However, these methodologies either raised some ethical
problems or would not be done in the termite’s natural environment.
The traps captured a significant number of individuals of Cryptotermes brevis and, by chance,
also captured individuals of another species, the Kallotermes flavicolis. These traps can also
11
Another possible approach would move wood infested with C. brevis to a zone (without the presence of the species) which
could release the winged to recapture and subsequent verification of the distance of flight.
58
be used as a simple and cheap tool to determine the presence of this or other termite in a
given location.
Dispersal and spread of the pest
We have developed a computational cellular automata model in order to improve our
understanding of the spatial-temporal evolution of the infestation. The model has four
important parameters: the radius of infestation, the number of initially infested houses and
their locations, the date of the initial infestation and the probability of an infested house
infesting a healthy house. The interviews and the light experiments aimed at constraining
these parameters. Our results show that evolution is only weakly dependent on the
probability and that large asymmetric dispersions are very unlikely. The model can reproduce
the general features of the present situation of C. brevis in Angra do Heroísmo if the capacity
of dispersion is similar to that obtained with the traps experiment. In this sense, the model
and the experiment are in agreement. The model also predicts that some previously
unknown areas are infested. This prediction must obviously be verified in the future.
However, the model is in an initial state of development and the obtained results should be
analysed taking this into consideration. For instance, the second simulation of the evolution
of the infestation in Angra do Heroísmo has two initial sources of infestation. Their
positioning was just one possibility among several. Also, other probability values should be
considered. In addition, the present model does not take into account the human contribution
to the spread of this infestation. The transportation of infested material can have an important
role in its dispersion and in the future the model could easily be adapted to integrate this.
These numerous hypotheses should be further studied and analysed.
Future work should include other details such as: increased number of cell states
(representing cells of different types of infestation according to the materials used, methods
of preservation, methods of treatment, etc.), a more complex and realistic variation of
probability with radius, apply the model to other infested cities in the Azores, etc. Those
details will increase the realism of the model and therefore provide more interesting results
and contribute to our understanding of the species dispersion.
The model here developed is one important tool to the C. brevis pest control once it allows
us to understand the species spread along time and space. This is particularly important in
places where the species is present, in an initial stage. The model could be useful to aware
the habitants and authorities to the radius of spread of the species. This model is a first step
towards a powerful tool that has the potential to be used to study the spread of other exotic
species, including other species of termites already present in the Azores and even some
problematic plant invaders.
59
Our results show the local potential spread ability of Cryptotermes brevis in the Azores. We
can also conclude that our model can perform simulations of the spatial-temporal spread of
the species Cryptotermes brevis in Angra do Heroísmo and other cities in the Azores. The
traps have demonstrated functionality in determining the potential capacity of dispersal of the
species under study, as well as other species of termites in the islands.
60
Chapter III
Predicting the potential distribution of Cryptotermes
brevis at local and regional scales
3.1
INTRODUCTION
The potential extend of occurrence of Cryptotermes brevis in the Azorean Archipelago is
crucial information for the implementation of a prevention strategy. Some important questions
about the specie establishment in the archipelago remain to be answered. These are related
to the specie brief period of colonization of the Azores, which is of a few decades (at least
four), according to several entomologists (Myles, 2004; Borges et al. 2006). The first issue is:
Has the specie colonization already achieved a climax in the infested islands due to local
geographic or climate constrains? Or, on the contrary, is the C. brevis plague just in the
beginning of a much larger scale of colonization? Another important concern is due to the
inexistence of prevention measurements. Therefore, it is imperative to understand which
places, that are so far not affected, are more vulnerable to this specie. Thus, our goal is to
determine where the conditions are appropriate for the establishment of the specie.
To forecast where the specie might occur we use an ecologic niche model that employs the
Maximum Entropy principle. In order to have a more precise and accurate result, world and
regional samples of C. brevis presence spots where used to determine the specie possible
occurrence places in the Azores Archipelago. This model evaluation is related with the
exterior conditions, which means that the specie might occur under exterior unfavourable
conditions when suitable conditions inside buildings exist 12 . Obviously, the natural
proliferation must be extremely difficult in those places. The critical step in formulating the
ecological model is defining a suitable set of features. Indeed, the constraints imposed by the
features represent our ecological assumptions, as we are asserting that they represent all
the environmental factors that constrain the geographical distribution of the species (Phillips,
et al., 2006).
12
There is a record of C. brevis presence on a Berlin Museum and private house in Germany. See Becker & Kny (1977).
61
3.1.1 ECOLOGICAL NICHE MODELS
Ecological niche models are used to predict species distribution based on environmental
data, like climate, topography, vegetation, soil, site moisture, disturbance and specie’s
presence data. This information is used to define conservation plans that usually require
accurate estimates of the spatial distributions of species that need to be protected. Such
information allows conservationists to predict how the specie’s distribution will respond to
landscape alteration and environmental (climate) change (Hernandez, et al., 2006; Sérgio, et
al., 2006).
It is not the goal of this geographic distribution models to determine the population density, or
understand the competition between species or other population feature. There are many
geographic distribution models and comparative studies aiming to determine which model is
more suitable to determine the species distribution (Philips, et al., 2004; Elith, et al., 2006;
Phillips, et al., 2006). Hernandez, et al. (2006) tested four modelling methods (Bioclim,
Domain, GARP, and Maxent) across 18 species (one insect, five amphibians, tree reptiles,
seven birds and two mammals) with different levels of ecological specialization using six
different sample size treatments and three different evaluation measures. To run the models
simulations, ten different environmental variables were used equally in all models:
Variables
Annual temperature range
Isothermality (mean diurnal range/temperature annual range)
Annual mean precipitation
Precipitation of the warmest quarter
Coefficient of variation of monthly precipitation
Annual total radiation
Annual radiation range
Coefficient of variation of monthly relative humidity
Elevation
Slope
Following Hernandez et al. (2006) study, we present a brief description of the tested models
(Bioclim, Domain, GARP, and MAXENT).
− Bioclim: this is a bioclimatic analysis and prediction algorithm, which identifies locations
that have environmental values that fall within the range of values measured from the
occurrence dataset.
− Domain: This method derives a point-to-point similarity metric to assign a classification
value to a potential site based on its proximity in environmental space to the most similar
occurrence.
− Genetic algorithm for rule-set prediction (GARP): This is an artificial intelligence-based
approach which employs four distinct modelling methods: atomic, logistic regression,
bioclimatic envelope, and negated bioclimatic envelope rules to derive several different rules.
62
GARP uses these rules to iteratively search for non-random correlations between the
presence and background absence observations and the environmental predictors.
− MAXENT, a Maximum Entropy Distribution Model: MAXENT is an ecological niche
model that uses a statistical mechanics approach called maximum entropy to make
predictions from incomplete information. MAXENT estimates the most uniform distribution
(maximum entropy) across the study area given the constraint that the expected value of
each environmental predictor variable under this estimated distribution matches its empirical
average (average values for the set occurrence data). When MAXENT is applied to
presence-only species distribution modelling, the pixels of the study area make up the space
on which the MAXENT probability distribution is defined, pixels with known species
occurrence records constitute the sample points, and the features are climatic variables,
elevation, soil category, vegetation type or other environmental variables, and functions
thereof (Phillips et al. 2004, 2006).
According to Hernandez et al. (2006) results, MAXENT has the best results performance of
the methods tested in his study, because it performed well and fairly stable in both prediction
accuracy and the total area predicted present across all sample size categories. It also
executes the highest accuracy and spatial concordance, especially for the smallest samples
categories. These results indicate that MAXENT can somewhat compensate for incomplete,
small species occurrence data sets and perform near maximal accuracy level. Hernandez
results are supported by those obtained by Phillips et al. (2006) and Elith et al. (2006) who
also found that MAXENT was one of the strongest performers in a large model comparison
study. Besides, MAXENT is a friendly user program compatible with the IDRISSI and DIVA
Geographic Information Systems (GIS) and both programs are free and easy to obtain in the
World Wide Web.
63
3.2
METHODOLOGY
Two different modelling approaches were made with MAXENT ecological niche model in
order to determine the potential distribution of C. brevis in the Azores. The reasons to have
two different modelling courses are related to the different number of available variables that
characterize the world and regional contexts. To the world modelling we have available only
a few of the important variables but a large number of sample sites all over the world.
To the regional modelling we have a larger number of important variables available to
simulation but a smaller number of presence sites.
The first model uses a large number of world records were C. brevis occurs (cf. Figure 3.1),
and world and regional available environmental features which are considered important to
the species establishment according to several authors (Becker & Kny, 1977; Becker, 1978;
Rusty & Cabrera, 1994; Woodrow et al., 2000; Scheffrahn et al., 2008). The use of world
occurrence sites is important to understand where suitable conditions exist to the species
survival and natural spread in the archipelago. This information is very significant due to
recent arrival of the species in the archipelago and due to the considerable number of
heterogeneous sites used on this simulation.
For the second approach, we use the regional confirmed occurrence sites (Table 3.2) to
model and project into each island the potential occurrence of C. brevis. Contrary to the
world model, on the regional scale we have accessed and use the humidity feature, an
important climatic variable.
In Figure 3.1 we present an illustrated scheme of the two modelling approaches, one using
the world samples (red box) and the other using the regional samples (blue box). The red
dotted box contains the world sample approach and the two different sets of variables13 used.
13
Source: http://www.worldclim.org/
64
Regional Sample
World Sample
Variables
Rain
Max.Temp.
Min. Temp.
Rain
Max.Temp.
Min. Temp.
Hr. Max.
Hr. Min.
Max.Temp.
Min. Temp.
S.Min.Temp.
Hr. Max.
Hr. Min.
Max.Temp.
Min. Temp.
S.Min.Temp.
Alt
Land Use
Alt
World
Regional
World
Regional
Regional
Local
Regional
Local
Hr. Max.
Hr. Min.
Max.Temp.
Min. Temp.
S.Min.Temp.
Regional
Local
Results
Discussion
Figure 3.1 The two different model approaches (see text for further explanations and for
variables names.
The blue box presents the regional Azores approach. We have three different sets of
features with five common variables: Maximum Relative Humidity (Hr. Max.), Minimum
Relative Humidity (Hr. Min.), Maximum Temperature (Max. Temp.), Minimum Temperature
(Min. Temp.) and Summer Minimum Temperature (S. Min. Temp.). All these features are
based on annual values with the exception of the Summer Minimum Temperature which is
obviously related to this specific season. This season variable was included as a category
because this is the principal and most important period to the Cryptotermes brevis allate
spread. It is on the summer season and principally during the June, July and August months
that the spread flight occurs in the Azores and therefore the sexual individuals leave the
interior timber colonies (indoor) and expose themselves to the outdoor climatic conditions.
Besides these common variables, two of the three sets use non climatic variables. In the first
one we use the altimetry to compare the regional result with the world one, and in the second
one we use Land Use, a categorical feature. This categorical variable represents the various
characteristics of land use by different classes and not on a continual form. For example,
describes the human use of the land as being urban or rural.
All the modelling results are projected on two Azorean islands with different species
occurrence status. These are Terceira Island, where the species is present, and Pico Island,
where the species is not yet known. All the results will be compared and discussed
afterwards and in addition, we will provide one validation simulation using some samples
65
(equal number of samples from each affected island) to project into one presence spot Island
to observe the model accuracy. Also in the world sample simulation some C. brevis presence
sites will be used has validation of the performed model.
The files containing the variables where transformed into Ascii files to be used in the
MAXENT model. Also, the geographic decimal position of the presence spots were placed in
a CSV (comma delimited) file. A sample of world14 presence sites was selected randomly
along the longitude while embracing all the globe latitude presence spots. This sample is
presented in Table 3.1.
Table 3.1: World spots sample places and number.
World positioning
Places
Samples
Caribbean Islands, North
and Central America
Jamaica, USA (Florida, Bermuda,
Porto Rico), Mexico, Costa Rica,
Belize and Honduras
18
South America
Brazil, Argentina, Chile, Peru,
Venezuela
9
Africa
South Africa, Western African Coast
and Israel
4
North Atlantic Ocean
Azores and Madeira Archipelagos
2
Indic Ocean
Reunion Island
1
Oceania
Australia
1
Pacific
Hawaii
1
TOTAL SAMPLE NUMBERS
36
The sample used for the regional model contained all the locations in the archipelago15 where
the presence of C. brevis is confirmed. In table 3.2 we present all the below islands and
locations in the sample.
Table 3.2: Known locations in the Azores infested with C. brevis
Island
Santa Maria
Place
Number of spots
Lagoinhas, Feteiras, Santa Barbara and
Calheta
18
S. Miguel
Ponta Delgada
19
Terceira
Angra do Heroísmo and Porto Judeu
11
Faial
Horta
9
TOTAL SAMPLE
14
57
According to Scheffrahn et al. (2008)
15
Only the locations where the specie is a source of infestation were included. Recently, the specie was identified in one house
in S. Bartolomeu in Terceira Island but the colonies in that house do not seem to succeed in colonizing the neighbouring
houses.
66
Besides the world and regional sites environmental data, MAXENT also requires the use of
environmental variables from each of the Azorean islands to build its predictions.
Figure 3.2 presents a simple sketch that illustrates how the MAXENT is used.
MAXENT PROCEDURE
INPUT
OUTPUT
World data
MinT
Rain
Regional Data
MaxT
MinT
Rain
World extent of occurrence
Projection
Alt
World Spots Samples: Lat. Long.
MaxT
Regional or local extent of
occurrence
Alt
Figure 3.2: Schematic presentation of Maxent’s procedure
MAXENT uses the environmental data (c.f. Figure 3.1) from the species presence sites and
projects into the local environmental geographic context, predicting which are the more and
the less probable spots for the occurrence of Cryptotermes brevis. The input of
environmental features is selected through individual tags for each chosen variable in the
program window (Figure 3.3).
Figure 3.3: MAXENT software window
The results are then analysed using the predicted maps and the corresponding table with the
estimate contribution of each of the environmental variables to the model prediction.
67
3.3
RESULTS
3.3.2 WORLD SAMPLE PROJECTION
Predictive model results agree with current knowledge of the environmental tolerance of C.
brevis (see Figs. 3.4 and 3.5).
Figure 3.4 World Map model prediction using the first set of features, which includes altimetry
(set 1), with used sample spots (white squares), world predicted occurrence probability and
world presence spots not used to model (red squares).
Figure 3.5: World map model prediction using only three environmental variables (Annual Rain,
Minimum Annual temperature and Maximum Annual temperature) including the used sample
spots (white squares) and world presence spots not used to model (red squares); The
probability of occurrence increases from the coldest colours (dark blue), to the warmer colours
(orange-red).
The two predictions are quite similar on a first general appreciation. In both cases, the model
predicts the same regions with low probability and with high probability. Clearly, there is a
systematic offset in probabilities between the predicted maps. However, despite this
probability difference, the predicted areas are fairly equivalent.
68
Table 3.3: Contribution value of each environmental variable to the MAXENT models.
Variable
Percent contribution (1st Set)
Percent contribution (2nd Set)
Annual Minimum Temp.
57.5
69.8
Altimetry
23.9
----
Annual Maximum Temp.
16.2
26
Annual Rain
1.8
4.3
The relative contribution of each of the environmental variables for both projections shown in
Table 3.3, indicates that the Annual Minimum Temperature is the single most important
variable in both cases. The altimetry has also an important contribution to the model with the
first set of features and it is responsible for the obvious differences between the two
predictions. One clear and important result is the low contribution of the Annual Rain for both
predictions.
In spite of the similarities in the two outputs (Figs. 3.4 and 3.5), there are some differences
between them, mostly along the equator line. Although it is not the aims of the present work
to determine the world probability of occurrence of Cryptotermes brevis, we will just analyse
some places that help us to understand the influence of the altimetry feature in the predicted
map. One interesting result is the prediction of a high probability of occurrence in the East
and South East Asia. Some Indonesian islands have a 0.85 probability value. This world
region has a suitable climate for C. brevis presence, yet the species is absent (Scheffrahn,
2008). The most likely explanation for this is the presence of endemic termite species that
are more competitive than C. brevis and therefore inhibit its establishment. The entomologist
Rudolf Scheffrahn (2008) states:
“The three Asian species may have unknown advantages over C. brevis,
such as competitive behaviors related to colony foundation and incipient colony
defense.”
The Far East maps obtained from both modelling sets are compared in Figure 3.6.
69
a)
b)
Figure 3.6: Comparison between the results of the MAXENT prediction model for the two sets
of variables in the South East Asia Region. Using altimetry (A); and not using it (B).
The two predicted maps for the South East Asia are quite similar but there is a trend for
higher probabilities in the case where the altimetry feature is not included. The yellow circles
indicate the most important exceptions to this trend. They indicate where there is a higher
probability area on set 1 and the same area on set 2. The red circles indicate the highest
probability regions for the set 2 map and the same regions for the set 1 map. The South
Asian map result shows us that there is a large resemblance between them.
Other interesting place is Europe, more precisely at the coast of the Iberian Peninsula, West
coast of France and some part of the north of Belgium and the Netherlands (yellow circles)
(Figure 3.7). In those places when using the altimetry feature the model predicts a high
probability of occurrence which is clearly different when not using it. The most interesting to
analyze is the high probability change on the two map results due the change of just one
variable, the altimetry. Those results could be easily observed and compared Figure 3.7.
a)
b)
Figure 3.7: Comparison between the results of the model for the two sets of variables in the
south west of Europe. Using altimetry a); and not using it b).
Here, there is also a reasonable similarity between the two maps with a small deviation on
the predicted probabilities (yellow circles). On the other hand, on the red circles the result
remains the same on both simulations. These are the only three places which have a high
probability of occurrence on both model predictions (red circles). These are in Spain, in the
Galicia coast near the Finisterra cape (between Pontevedra and La Coruña cities) and in
Portugal, in Lisbon region, between Cabo da Roca cape and Peniche city (this place has the
70
highest probability value) and in the extreme south west on Sagres Cape in Algarve region.
Note that the pink dots refer the places where the presence of the species was recorded
(Lina Nunes, personal communication; March 2009). Although these are interesting results,
more information is required to reach rigorous conclusions about the probability of the
species’s establishment in Europe.
Besides those world and regional model maps behave to altimetry feature, it is more
important to this thesis aim considering the Azores Archipelago situation. Therefore a model
behave in this specific region is interesting to observe and analyse.
We now focus our attention to the results of the model for the Azores that is presented in
Figure 3.8.
Using the altimetry feature
Azores Archipelago
Not using the altimetry feature
Figure 3.8: Comparison between the results obtained with the two sets of variables in the
Azores. Using altimetry (A); and not using it (B)
The two predictions may appear quite different at a first glance, but they are in fact quite
similar. A closer inspection shows that the predictions are similar, but with a systematic
probability offset between the two maps. The model predicts the lowest probability to the high
altitude areas using both the set 1 variables with altimetry and the set 2 variables without
altimetry.
We conclude that the only difference between the two predictions is related to the probability
value and not with which region has a low or high probability. In the first prediction all islands
have regions with suitable conditions, but only in some lower altitude zones. Among those
lower altitude places are Angra do Heroísmo, Faial and Ponta Delgada cities, already known
as being infested. Excluding Graciosa and Santa Maria Islands, that are islands with a lower
maximum altitude, all the other islands have more than 50% of their area with a probability
below 0.5 and at least 30% below 0.09. When one excludes the altimetry, the predictions
71
become quite dramatic once all the archipelago area has a probability above 0.31 and more
than 50% of it has probability above 0.77. For a better understanding of the results, we
present the model predictions for Terceira and Pico islands for both sets of variables in detail
(Figs. 3.9 and 3.10).
Terceira Island (with Altimetry feature)
Terceira Island (with no Altimetry feature)
Figure 3.9: Comparison between the results of the model for the two sets of variables in
Terceira island. Using altimetry (A); and not using it (B)
Both set model maps are quite similar in the sense that the lower and higher probability
locations are common to both prediction. It is also clear the existence of a systematic
probability offset between them. The high altitude places are on both maps the low
probability value predicted areas and is especially interesting the precise and accuracy on
set 2 map preview to attribute a low probability value to almost the same identical area on set
1 even not having the altimetry feature.
Another interesting result is that there is a large area around the island shore that has a 0.38
of maximum probability (light green) on set 1 and has a 0.85 (orange) probability value on set
2. This area is identical to both predictions with a 0.5 probability offset. This characteristic is
repeated in the Pico Island predictions (Figure 3.10)
72
Pico Island (with altimetry feature)
Pico Island (with no altimetry feature)
Figure 3.10: Comparison between the results of the model for the two sets of variables in Pico
island. Using altimetry (A); and not using it (B)
The results of the model for Pico Island (Figure 3.10) are identical to the ones obtained for
Terceira Island (Figure 3.9).
The low probability value areas are similar on both maps and are related to the high altitude
areas. Also, the high probability areas are the same on both maps and the offset between
the high probability values between both maps is identical to what we find for Terceira Island.
The area with a 0.31 probability (light green) on the set 1 map is the same area predicted on
the set 2 map but with a 0.85 probability value.
This world projection into the Azores is very important once it allows one to determine the
more probable places for this species’s occurrence. The scenarios presented, using two
different variable sets, both point towards a likely species occurrence on all islands. However,
there is a clear systematic probability offset between these scenarios and one is bound to
ask which is the most accurate of them. This leads us to discuss the use of the altimetry
variable. On the one hand, altimetry is not a direct restriction to the presence of C. brevis, on
the other hand, it has an indirect influence as it is correlated with climatic variables such as
pressure and humidity that are not included in the model. Also, as shown in Table 4, this
termite is known to exist at different altitudes.
Table
3.4:
Altitude
data
in
some
sites
with
confirmed
presence
(source:http://www.weatherbase.com/)
Place
Altitude (m)
C. brevis
San Jose, Costa Rica
Antofagasta, Chile
Tenerife – Spain
Ponta Delgada
Arica, Chile
Iquique, Chile
Valparaiso, Chile
Horta
920
120
72
71
54
47
40
40
Introduced
Endemic
Introduced
Introduced
Endemic
Introduced
Endemic?
Introduced
73
of
C.
brevis
The model attributes low probabilities to high altitude places because the great majority of
sites in the sample are at very low altitudes. Another matter is that once we know that the
species only survives inside buildings (if not on the endemic region), the Rain feature is
undesirable. However, together with the altimetry feature it somehow replaces the Relative
Humidity variable. This is appropriate to characterise the Azorean climate because there is a
correlation between altimetry and Rain with Relative Humidity.
The high probability values obtained using the set 2 variables are mainly based on the
temperature variables. A truthful prediction is likely to lie between the two presented results,
but more climatic information, such as Humidity, is necessary to confirm this claim. However,
these variables are not available at the present.
For comparison with the results obtained with the local sample (cf. Sect. 3.3.2), we opted for
the more complete set of variables, the set 1, which also provides the more conservative
results.
3.3.3 LOCAL SAMPLES PROJECTION
Figure 3.11 shows the model projection for the Archipelago using the variables in set 3. At
this level of detail, the predictions for the other sets of variables are similar and are not
shown.
Figure 3.11: Local model prediction for the Azores.
The map presented in Figure 3.11 is not clear enough to provide detailed information about
the species probability of occurrence on each island. However, it is sufficient to observe that
there are some areas with higher probability than others. Most of the areas with higher
74
probability occur near the coast. Also, the island with the highest average probability is Santa
Maria on the Eastern group, and the lowest average probability occurs in the Western group
islands of Flores and Corvo.
To have a more detailed and accurate information we present the relative contribution of
each variable for the three modelling approaches (see Table 3.5).
Table 3.5: Variables used in each set and their percentage contribution to the model. The grey
box is the categorical variable. The blue boxes correspond to the most significant
environmental variable.
set 1
set 2
set 3
Percent
Variable
contribution
Min. RH
46.6
Min. Temp.
21.2
Altimetry
13.4
Max. RH
12.7
Sum.Min.Temp.
4.5
Max. Temp.
1.6
Percent
Variable
contribution
Land use
45.6
Min. RH
34.1
Min. Temp.
12.3
Max. RH
6.3
Max. Temp.
1
Sum.Min.Temp.
0.7
Percent
Contrbution
Min. RH
64.1
Min. Temp.
21.1
Max. RH
11.3
Sum.Min.Temp
2.3
Max. Temp.
1.2
Variable
In order to understand the implications of the different choices of sets of variables, we
present the results for Terceira Island obtained with the different possibilities.
set 1: In this set the most important variable is the Minimum Relative Humidity, followed by
the minimum temperature. The altimetry variable has also some importance to the model
prediction. The 13.4 percent contribution to the model of altimetry is enough to influence the
prediction. This becomes obvious once one compares Figure 3.12 with Figure 3.14. With
altimetry there is a more abrupt probability change as one move away from the low
probability interior towards the coastal region. Also, the low probability region, represented in
dark blue, is more extended. One can also notice that, contrary to set 3, the high probability
regions, represented in yellow, do not occur in detached areas with any contact with the sea.
75
Figure 3.12: Terceira Island set 1 image preview.
This means that the altimetry feature influences the result by predicting a higher probability
value to the low altitude places, once the sample spots are mostly on the coastal shore low
altitude areas.
set 2: In this set the Land use categorical variable has a very clear influence. It is the most
important variable with 45.6 percent contribution to the model. This means that almost half of
the entire available information used by the model is based on this categorical variable. The
possible values for this variable are: urban, roads, agriculture, florest, etc.. Figure 3.13
demonstrates exactly the variable strong influence, by attributing a high probability value
when the land use variable is of the road or house type.
Figure 3.13: Terceira Island set 2 image preview.
This model prediction shows us a clear deviation from what is intended with this model. Our
aim is to understand where the species may occur due to suitable outside environmental
76
conditions independently of whether there is a house in a particular place at this particular
time. Therefore, this variable set is not the most appropriate to serve our purposes.
set3: This variable set represents only environmental features and produces one interesting
result. This variable set is the simplest of the sets and its forecast is quite similar to the one
obtained with the set 1. Here, the most important variable is the Minimum Relative Humidity
and its contribution to the MAXENT model is the highest in this set and in all the other sets.
The model predicts that the high probability values are mainly along the coast, principally on
the North, South and East shores. Also, the low probability values occur in the interior of the
island (cf. Figure 3.14).
Figure 3.14: Terceira Island set 3 image preview.
It is worth noticing that the three most important environmental variables for all sets are in
decreasing order of importance: Minimum Relative Humidity, Minimum Temperature and
Maximum Relative Humidity.
Hereafter, we no longer consider the set 2 group of variables as it introduces unwanted bias
in our model.
We now compare in detail the results obtained for Terceira and Pico with these two sets of
variables.
77
Set 1
Set 3
Figure 3.15: Probability of occurrence of C. brevis for Terceira Island using both sets of
variables (using altimetry – set 1, and not using altimetry – set 3).
There is a great resemblance between the maps from the two different environmental sets.
The low probability area is quite the same and the high probability values are majority on the
South and East shore. Obviously there is a slightly difference between the two maps, mostly
due to the altimetry variable that leads to a higher probability on some of the low altitude
areas for set 1. A more detailed analyse shows that the most affected areas are the same
with a slightly difference in the probability values, which is higher in the first set, 0.85
probability value, and lower in the second (0.77 probability value). Also the affected area with
higher probabilities (greater or equal than 0.77) is larger in the first map. However, the area
affected by an intermediate probability value (0.55) is quite larger in the second map than in
the first one.
We now analyse the result of the model to Pico Island, where as yet there is no record of C.
brevis.
Set 1
Set 3
Figure 3.16: Pico Island Maxent picture modelling for both variables set.
Similarly to the results for Terceira, the two model predictions for Pico Island are much alike
(Figure 3.16). This shows that altimetry variable may somehow substitute some of the
78
environmental features used on the set 3. This is possible due to the climatic characteristics
of the Archipelago, where the altimetry has a correlation with some of the environmental
variables. In particular, low altitude spots have lower Relative Humidity values when
compared with high altitude spots, and the values of Maximum Temperature are also higher
than in the interior and higher altitude places (Azevedo et al., 1999; Azevedo, 2007).
The higher values of probability obtained with set 1 are related with the used sample spots
that were only from low altitude places. Therefore, the results obtained with the set 3 are
more significant and accurate once they represent the local environmental conditions. This
analysis leads us to argue that the altimetry variable is neither necessary nor adequate to
model the probability of occurrence of C. brevis in the Azores when using the local sample.
The inclusion of altimetry in the world model is partially justified by the lack of a variable
measuring humidity, which does not happen in this case.
Hereafter, the set 1 world projection result and the local set 3 results are presented
simultaneously for each individual island. The justification to these jointly analyses is related
to the different sample scale. The first result is obtained with a larger, heterogeneous and
world wide sample but a smaller number of variables. The second result is obtained with a
smaller number of local samples but a more complete set of environmental variables.
79
3.3.3.1 Islands Results
In the model prediction for Corvo island there is an obvious resemblance between the two
model projections (Figure 3.17). Both approaches predict higher and lower values to the
same areas, despite the different probability value. The probability varies much more
smoothly in the world approach than in the local approach. A closer look shows that there
are spots with very high probability of occurrence on both predictions. In particular, with the
local approach the probability reaches more than 0.85 in some pixels. It is worth pointing out
that the only village on the island, Vila Nova do Corvo, is located in the region with the
highest probability of occurrence.
Corvo Island
Set1 World Samples
Set 3 Local Samples
Figure 3.17: Model prediction for Corvo Island.
80
Flores Island
Set1 World Samples
Set 3 Local Samples
Figure 3.18: Model prediction for Flores Island.
Concerning the island of Flores, at a glance, the two predictions look very different (Figure
3.18). However, a closer and more detailed observation shows significant similarities. Both
approaches attribute a low probability to the interior area and higher probability to several
places near the shore. The probability values are much lower than on other islands,
especially in the local approach. This is probably due to the island geographic position.
Flores Island is the north-western Island on the archipelago and some climatic differences
exists between this island and the islands where the samples are from. With the world
approach the maximum probability value is between 0.54 and 0.69 and only occurs on the
low altitude places, such has Santa Cruz das Flores, Fajã Grande, Ponta Delgada and
Fajãzinha. There are also some other places with the same probability value, like Quebrada
Nova and Fajã da Ponta Ruiva, but those places are just small portions of land by the
seashore that are not inhabited and possibly will never be. The same places have a 0.31
probability, in the local approach, which is significantly lower. This second simulation
anticipates that the species might have some difficulties to establish itself, once almost the
entire island has near 0 probability of occurrence. However, one should attend that the small
number of local samples and the island geographic position might induce the model to
attribute a lower probability. Nonetheless, if not the whole island, at least the places
mentioned before (Santa Cruz das Flores, Fajã Grande, Ponta Delgada and Fajãzinha)
should have some cautious measures to prevent infestation by Cryptotermes brevis.
81
Faial Island
Set1 World Samples
Set 3 Local Samples
Figure 3.19: Model prediction for Faial Island.
Faial is one of the islands known to have termites, and both model predictions are alarmistic
to the possibility of a major spread from Horta city to several other parts of the island. The
presented images have several similarities. The lower probability area and the higher
probability areas are very similar (despite the probability offset between the two images). The
main difference among these images is related to altimetry influence on the first image,
which predicts higher probability to low altitude areas that on the second image which
doesn’t consider the altimetry variable. On a closer look both images predict with quite
similarity to the same areas a maximum 0.77 probability value. These areas are the Horta
Bay, Praia do Almoxarife, Pedro Miguel, Ponta da Ribeirinha on the East shore of the Island.
On the South shore these areas are almost all the shore from Praia do Porto Pim to Castelo
Branco. On the West and Northwest the most vulnerable areas are from Ponta do Varadouro
to Ponta dos Capelinhos and from here until the Praia do Norte. On the North shore of the
island the probability value is not so high (0.54 - 0.62) and the affected area is located in
Cedros.
82
Pico Island
Set1 World Samples
Set 3 Local Samples
Figure 3.20: Model prediction for Pico Island.
Pico island projection results have similarities mostly for the low probability area, which is
clearly at the higher altitude and more humid and cooler interior zones (Figure 3.20). Also on
the predicted high probability area the models look similar, predominantly on the West and
East Island extremes. The World model forecasts a higher probability on the lower altitude
areas than the Local model map. There are some places, mainly on the south shore, where
the important town of Lajes is located, and also on the North shore, where S. Roque do Pico,
the second most important village, is located, for which the two predictions do not agree.
Both models predict a high probability on an area between Bandeiras and Candelária,
affecting the larger locality on the Island, Madalena16. The other high probability area is
located along the East shore, from Ribeirinha to Calheta do Nesquim.
16
This Village has a harbour with the highest movement of people and goods between islands in the entire Archipelago. This
traffic occurs on a daily basis and it is between the infested city of Horta (Faial Island) and the not infested Pico Island.
83
S. Jorge Island
Set1 World Samples
Set 3 Local Samples
Figure 3.21: Model prediction for S. Jorge Island.
MAXENT forecasts to S. Jorge Island very similar scenarios in both approaches (Figure
3.21). The low and high probability regions are common to both cases. It is possible to
observe that the most vulnerable places are on the Island South shore from Velas village to
Manadas and from Fajã Grande to Fajã dos Vimes embracing Calheta town. On the north
shore the predicted high probability area is quite smaller than on the south shore. The
affected places lie on the low altitude areas with a temperate climate. These are Fajã do
Ouvidouro, Fajã dos Cubres and Fajã de Santo Cristo. There is also one other spot with a
high probability value which is on the extreme Southeast edge of the Island on the Topo
locality.
84
Graciosa Island
Set1 World Samples
Set 3 Local Samples
Figure 3.22: Graciosa Island pictures preview from two different model sets.
The two model approaches predict significant different scenarios for Graciosa Island (Fig
3.22). But, a closer observation shows similarities between the two maps. The lower
probability regions in the world model correspond to the lower probability regions in the local
model. The same happens for the higher probability regions. There is a clear systematic
probability offset between the two models, with the world model predicting higher
probabilities. This is likely due the lack of samples on the Island for the local model. This
issue repeats on the Islands distant from one infested island (used sample islands) and
where Cryptotermes brevis is absent (the only exception is Corvo Island). There are some
places that should be mentioned due the high probability of occurrence, even if only on the
world simulation. These places lie along the Island North shore from the Sr.ª da Vitoria
location to Santa Cruz da Graciosa which is the Island most important town. On the East
shore, the entire strait between Baia da Lagoa and Fenais embracing the Praia town also
have a high probability of occurrence. On the South shore the affected area is from Baía do
Filipe to Carapacho and on the west shore only one small spot is affected, the Baia da
Caldeirinha.
85
Terceira Island
Set1 World Samples
Set 3 Local Samples
Figure 3.23: Terceira Island pictures preview from two different model sets.
Following the patterns observed for other islands, Terceira Island predictions are also very
similar in both models (Figure 3.23). Despite some difference on the probability values,
mostly in the interior, the higher probability areas are the same for both maps. Even in the
interior, the only difference is related to a clear systematic offset, being the low probability
area the same for both models. Terceira most affected areas have a probability value of 0.77
on both simulations. The high probability value places are just beside the already affected
areas (that were obviously selected as samples). Those are around Angra do Heroísmo City,
and Porto Judeu locality. Other places with equal probability are spotted along the south
coast affecting the following localities: Cinco Ribeiras, S. Bartolomeu, S. Mateus, S. Carlos,
parts of Terra-Chã, S. Bento, Feteira and Ribeirinha. Also on the East coast there are some
areas with a high probability, such as: Porto Martins, Cabo da Praia, Praia da Vitória City and
Lajes Town. On the North shore the areas with higher probability are: Vila Nova, Quatro
Ribeiras, Biscoitos and parts of Altares. On the West shore the probability is much lower and
only in Ponta do Queimado there is a high probability value (0.69). However, this high
probability value appears on a small area classified as Site of Community Interest and is not
suitable to human habitation construction.
86
S. Miguel Island
Set1 World Samples
Set 3 Local Samples
Figure 3.24: S. Miguel pictures preview from two different model sets.
Similarly to Terceira, the two model approaches forecast very similar scenarios for S. Miguel
Island (Figure 3.24). The regions with high probability and the regions with low probability are
common to both predictions. There is also a systematic offset on the predicted vales among
both models, especially in the interior low probability area.
In spite of this, the maps
similarities ensure a high level of confidence on the results. So, the areas with higher
probability of occurrence are: On the South shore from Ponta de Relva until Caloura,
affecting Ponta Delgada (the major city on the Island and on the Archipelago), Arrifes,
Livramento, Lagoa, Santa Cruz and Água de Pau. It is important to perform a more cautious
observation on some pixels on this area, around Livramento and Lagoa localities, once at
here the probability value reach the 0.92 and 1, the maximum probability of occurrence. Also
on the South shore but with an intermediate probability value (0.54 - 0.62) are Água de Alto,
Vila Franca (one of the major cities on the Island) and Ribeira das Tainhas localities. On the
North shore there is a high probability value in the entire low altitude zone from Capelas to
Ribeirinha, embracing Capelas, São Vicente Ferreira, Fenais da Luz, Calhetas, Rabo de
Peixe, Ribeira Seca and Ribeira Grande (one of the major cities in the Island). On the North
shore with a slightly small probability value are the localities between Ponta Formosa and
Fenais da Ajuda, affecting the Porto Formoso, Gorreana, Maia and Lomba da Maia localities.
There are other two small points on the North shore which are the Ponta da Ajuda and Ponta
da Ribeira (this last one on the Northeast region). On the West shore there is an area with a
probability value between 0.54 and 0.92 along the Feteiras, Candelária and Ginetes localities.
Also, on the West shore, where the Mosteiros locality lies, is the area with the highest
probability of occurrence. Here, there are a large number of pixels with maximum probability
value (1), and the lowest probability value is 0.62 (on both maps). S. Miguel is the larger
island on the Archipelago and has several localities on the interior, and some of those are
not at high altitude spots. This is the case of Furnas, where MAXENT forecast a probability
between 0.38 and 0.62 which is a relatively high probability value of occurrence.
87
Santa Maria Island
Set1 World Samples
Set 3 Local Samples
Figure 3.25: S. Maria pictures preview from two different model sets.
Santa Maria is the Island for which we had the second best data on confirmed presences. It
is also the island where more differences exist between the world and local predictions.
However, there are some similarities between the two predictions. These similarities occur
mostly on the high altitude zones, where both models forecast a low probability value. Other
resemblance is that both models predict a high probability tendency to the West part of the
island. Besides those similarities, the maps do not have the same level of resemblance that
we see for the other islands. This might happen due the Island extreme south positioning on
the Archipelago and to the large number of spots in the local sample originating from Santa
Maria. One must point out the higher number of pixels with maximum probability (probability
1) obtained with local model. This is important, once Cryptotermes brevis is present in
several places on the island, there is an elevated and obvious risk for the infestation to
spread. According to the local forecast, the high probability places are: Lagoinhas, Feteiras,
Santa Barbara (sample areas), Azenhas, Norte, Ponta do Norte, Calheta (sample area),
Malbusca, Praia, Almagreira, Carreirinha, Valverde, Vila do Porto (the only town on the
Island), S. Pedro, Santana, Paúl and Anjos. All these have a probability value between 0.85
and 1. The entire Island, with exception of the high altitude central area, has a probability of
occurrence higher than 0.46. This is by far the Island with the most suitable conditions to
Cryptotermes brevis spread and establishment. Santa Maria is the southern island of the
Azores with the driest and warmest climate. Therefore, these results are in agreement with
the fact that the Minimum Relative Humidity and Minimum Temperature are the most
important variables for this termite distribution. On a world scale, due to the large
heterogeneity of the sample, the variations from island to island are not as significant as in
the local model.
88
3.3.4 VALIDATION TEST
In this section we present some simulations in order to verify and corroborate the results
previously obtained. The Local simulation results were obtained using all the samples
available to all the islands. These samples contained all known infested areas from all the
Azorean Islands (cf.Table 3.2). Different islands have different number of presence spots or
none at all. Once different islands contribute with a different number of spots to the total
sample, the MAXENT Model attributes different importance to those samples on each island.
For instance, Santa Maria Island has 18 presence sample spots and Flores none. Obviously,
the model will attribute a major relevance and probability of occurrence to Santa Maria than
to Flores. So, here we provide some other simulations using different number of samples to
understand how this influences the results of the Model.
We first use Terceira Island to perform a simulation with a sample containing only spots from
this island.
Figure 3.26: Terceira image (Set3 variable set) using the Island samples
The map shows us clearly that only the places with equal or very similar conditions to the
spots in the sample are given a significant probability of occurrence. These places are
around Angra do Heroísmo (sample spot site), on the southwest and southeast shore (Porto
Judeu, other sample spot site), on the north shore at Biscoitos and Quatro Ribeiras and on
Praia da Vitoria City. Also the interior centre of the island has a low probability. Those results
are in agreement with the presented result using all the archipelago samples.
Figure 3.27: Terceira image (Set3 variable set) using all the Archipelago samples.
89
These first two maps demonstrate that the model is quite consistent. The map presented in
Figure 3.27 give us a more robust result to the species occurrence, once all the 57 presence
spots were used. The results do not show such a high probability value as in Figure 3.26.
Also, the probable occurrence area (with probability above 0.5) is significantly more
extensive when using the complete sample.
In the next simulation we use the entire sample except the spots from Terceira Island.
Figure 3.28: Terceira picture simulation using the available occurrence samples from all the
islands, except from Terceira.
The map in Figure 3.28 has a significant similarity with the map obtained with the complete
sample and confirms the consistency of the model. Also demonstrate that the probability
value is important but not the most important to analyse, instead the predicted area is a
significant indicator of where the species might occur.
In this next step we analyse the model behaviour using the same number of samples from
every island. The maximum possible number of samples is nine samples per island, because
is the maximum number existing on Faial (the island with minor number of samples). The
largest possible sample available is nine spots per island. We reduce the number of spots on
every island to observe the model consistency. Figure 3.29 shows the model predictions
when using a sample with nine and three spots from each island.
a)
b)
Figure 3.29: Model prediction for Terceira using a sample of nine (a) and three (b) spots from
each of the infested islands.
90
Also on these maps is shown that the model is consistent and provide us significant results.
These simulations validate the model as they are globally consistent with the simulation
obtained with the complete sample. For instance, the interior predicted area is quite equal to
all presented maps from Terceira on this validation issue as well the probable occurrence
area is similar to all maps. Is true that the probability value vary from map to map, however
the predicted area is significant equal.
This validation procedure is applicable to the other islands as well. In order to support the
validation procedure we also apply it to Faial Island. The maps are disposed together for an
easier comparison. The lower and higher probability regions were delineated to stand out the
results.
Set3 Archipelago all
samples
Faial using only local island
Samples
b)
a)
3 samples
9 samples
Other archipelago samples
d)
e)
c)
World samples
f)
Figure 3.30: Model predictions for Faial using different samples. All available samples on the
archipelago (a); only the Faial local presence samples (b); nine samples from each one of all
infested islands (c); three samples from each one of all infested islands (d); all available
samples on the archipelago with exception of Faial samples (e); and, using the world samples
(f).
A comparison of the different predictions supports the model consistency and reliability. On
these maps we opted to do a contour of the predicted areas, yellow to low probability and red
to high probability different simulations despite the different number and origin of the samples.
As for Terceira, as the sample size is reduced so are the regions with extreme low and high
probabilities (compare Fig 3.30 c with d). If one analyses closely the map (e), one notes that
the predicted areas (low and high probability) are similar to a), but because there were no
local spots in the sample, the probability attributed by MAXENT is smaller. This points to the
91
importance of putting as much information as possible in the model. From this validation
result, it is possible to affirm that where the MAXENT local model predicts a low probability
one cannot conclude that the probability of the species occurrence is small. But where the
local model predicts a high probability, one can say, with a high degree of confidence, that
the probability to C. brevis occurrence is indeed high.
This effect is also noted on islands where no presence spots exist. One of those islands is
Flores. MAXENT simulations with the local sample results a low probability of occurrence to
Cryptotermes brevis in Flores. We present a final set of validating simulations in order to
understand the model behaviour in this case. On this occasion, we perform one simulation
using the local samples from each island one at a time.
Set3 Archipelago all
samples
World samples
b)
a)
S. Miguel samples
Santa Maria samples
Terceira samples
Faial samples
e)
d)
c)
f)
Figure 3.31: Model predictions for Flores using samples with different origins. World samples
(a); All available samples on the archipelago (b); Santa Maria spots (c); S. Miguel spots (d);
Terceira spots (e); and, only the Faial spots (f).
Also on this occasion MAXENT if one looks close to the presented maps there are great
similarities among all the maps concerning the predicted low and high probability areas. The
low probability area of occurrence is even remarkably similar in all the maps. Naturally, the
model predictions are affected when the number of spots in the sample is reduced or when
the origin of the spots is limited to one island. In some cases, as seen in maps c) and e) of
Figure 3.31, it can attribute high probability to regions where a low probability is predicted
when using the complete set of spots.
92
From all these simulations, we conclude that the MAXENT model predictions are quite robust
and not too dependent on the number of spots in the sample and their origin. Naturally, the
larger and more heterogeneous the sample, the larger is the confidence in the results.
3.4
DISCUSSION
In this work I provided several predicted models for the spread of the drywood termite C.
brevis in the Azores based both in a local and a regional modelling approach. Although the
presence of C. brevis in the Azores is relatively recent, it has already provoked important
economic damages in buildings and structures in the occupied islands (Faial, Terceira, São
Miguel and Santa Maria). At present, the species’s potential for proliferation to other regions
in the archipelago is not known. If one knows the potential occurrence of the species one
could apply, supported on much certain and accurate information, planning decisions to
minimize or to stop the pest proliferation into other parts of the archipelago. The present
chapter aims provide this information and therefore contribute to a future politic and
administrative solution to this current problem in the Azorean archipelago.
Methodological details and limitations
The methodology applied in this chapter seeks to understand the probability of Cryptotermes
brevis occurrence on the Azores through the use of a maximum entropy model, called
MAXENT. We use two different samples sets and project into the Azores geographic and
climate environmental data. These different sets contain the world and local spots where the
species is present. The use of a sample containing several world places looks to include
distinct and wide climate characteristics where the species is known to occur. Therefore,
besides the extreme northern position of the archipelago compared to other C. brevis world
presence sites, the Azores weather is not a limiting environmental condition to the species
survival (see Table 1.1 page 5). This approach seeks to understand if all the Azores Islands
are suitable to the species optimal survival. The local presence samples were used with the
same objective. However, this second modelling approach was made due to limiting
environmental variables available to the world modelling and because a more complete
number of variables were available to local context. The use of different sets of variables was
directly related with the used samples. On the world samples projection we use two different
paths: one using a set of variables where the altimetry variable was included; and in the
other path we use the same set of variables, but, this time not including the altimetry variable.
The main reason to follow this procedure is because we do not have one important (grid)
variable, to the species occurrence. This important variable is the Relative Humidity variable
and in order to minimize its absence, we used the altimetry and rain variables. The use of the
altimetry variable might introduce bias in the results because the majority of the world sample
93
spots are from low altitude areas. However, there is a correlation17 between altimetry,
temperature and relative humidity, particularly in the Azores, so that this has not a significant
influence in the results.
For the local sample we have available all the necessary climatic variables and also some
non climatic variables. On this occasion we use three different sets: one set containing only
climatic variables, another set containing the climatic variables and the altimetry variable,
and a final set containing the climatic variables and the land use variable. The main reason
why we considered the inclusion of the land use variable is because this termite lives mostly
indoors. However, this induces the model to attribute an extreme importance to this variable
and this introduces bias in the results. Also, in this case the altimetry variable was
considered unnecessary even though its inclusion does not change the results in any
significant way. We cannot conceive a reason why altimetry, per se, could influence the
occurrence of the species. The most significant and unbiased result is the one obtained
using only climatic variables.
Predictions
We briefly considered the model prediction for the world potential distribution of this termite.
For example, the model predicts a high probability of occurrence in South East Asia. This is
in agreement with the results of several previous authors 18 who consider the climate
conditions in this zone to be suitable for the species existence.
The model also predicts a significant probability of occurrence in several places in Europe. In
particular, the model points out Lisbon as being at risk of infestation.
The model prediction for the Azores within the world approach depends on whether the
altimetry variable is included or not. With altimetry, the model predicts a significant probability
of occurrence not only on the low coastal areas, but also on the interior adjacent zones. For
the high altitude regions the model predicts a low probability of occurrence, most likely
because most spots in the world sample are from low altitude areas
In comparison with the previous scenario, the probability of occurrence increases in all areas
when altimetry is not included. However, the lower and higher probability regions are
common to both scenarios, showing the model’s consistency. The variable rain is found to be
unimportant for the model predictions in both scenarios. We choose the set of variables with
altimetry for the world approach to be the most adequate as it is also the most conservative
one.
17
18
This correlation is linear only until the dew point (100% humidity, saturated air). See Azevedo et al. 1999 and Azevedo 2008
See Erhorn (1934); Light and Zimmerman (1936); and Bacchus (1987) in Scheffrahn et all (2008)
94
The set 3 simulations from local samples results were by far the most interesting. We
presented the results of the model using the local sample together with the world results for
an easier comparison. With the exception of Graciosa and Santa Maria Islands, the two
approaches produced very similar predictions to all islands. The world sample produced
smaller regions with low probability than the local sample. One should not interpret the
probabilities produced by the model quantitatively. The model results are qualitatively but not
quantitatively extremely similar.
The local model predictions are affected by the fact that this infestation is recent and that
most infested localities are at low altitudes with a mild climate. This implies that where the
model predicts a low probability it does not necessarily mean that the probability is low. Our
predictions are therefore conservative with respect to the potential of occurrence of C. brevis
in the Azores.
For Graciosa Island the world approach predicts a relatively high probability of occurrence,
while the local model predicts a very low probability of occurrence. This discrepancy is very
likely because the local sample does not contain spots from Graciosa nor from spots with a
climate sufficiently similar to Graciosa’s.
Santa Maria Island has also some significant differences between the local and world
projections. These differences are on the high probability values. On the local projection the
probability value is much higher than on the world projection. This discrepancy is very likely
because the local sample contains several spots (18) so that MAXENT predicts high
probability values to similar areas. Both models predict a very similar low probability area.
We performed extra simulations in the end of the results section to understand how the
MAXENT model behave with samples variation in terms of number and origin. These
simulations on the validation section are quite useful to confirm the previous obtained results.
We demonstrate how the model is quite consistence and accurate despite the number of
variables and that the most important to the obtained predicted distribution surface is not the
probability value attributed by the model but instead the extent of occurrence
By performing several validating simulations we have demonstrated the consistency and
robustness of the model concerning the dependency of the results on the number and origin
of the spots in the sample.
However, it is important to mention that even if the outdoor environment is inappropriate to C.
brevis and MAXENT predicts a very low probability of occurrence, when suitable indoor
conditions exist, the species can eventually occur, but the natural spread to surrounding
houses may be limited.
95
This work could be improved in future studies. These should include other important
variables during the swarm period in the Azores. The conduct of further simulations, on the
world projection, would be also interesting including other important climatic variables to the
species, such as humidity. Also interesting would be to carry out a simulation including the
local
and
world
as
samples
using
96
all
the
important
climate
variables.
3.5
CONCLUSION
In this chapter we have determined the potential of occurrence of Cryptotermes brevis in
the Azores. Our results show clearly that the species could spread to all the islands and
that appropriate condition exists principally where the main human settlements are. The
results also point to the importance of elaborating a proper C. brevis control program on
each island in order to prevent the spread of the infestation to other islands as well as to
minimize the economic and social impact in the islands where it already occurs.
97
Chapter IV
General Conclusions and Future Perspectives
4.5 GENERAL CONCLUSIONS
This work is a contribution towards a better understanding of the potential geographic
occurrence and the dispersal capacity of the species Cryptotermes brevis at both local and
regional scales. The two approaches used in this work allow an innovative analysis to the
this termite pest problem, looking not to solve the problem immediately, but aiming to
determine its present and future spread in order to facilitate a more effective management
and control. Therefore, the application of the two computational tools developed in this thesis
is essential towards an integrated plan of action where prevention is the main key to the
problem.
The first important result we have obtained is the better understanding of the flight capability
of the drywood termite Cryptotermes brevis on the Azorean Islands urban environment,
which will be crucial to understand how the spread of the pest will occur. To our knowledge,
this is also the first time that the flight capability of this species has been studied in detail, so
that this result has implications not only to the Azores but also to other world places where
the species occurs.
The questionnaires allowed us to gain a better knowledge of the pest evolution both in time
and space in the city of Angra do Heroísmo. Another important result obtained during the
questionnaires was the finding that different materials are currently in use replacing the
original and traditional wood construction method in buildings infested with termites. Also, the
number of empty buildings in the infested area in the city centre is quite large. During the
survey, it was not possible to determine if they are infested or not. If infested, those empty
buildings are a likely out of control infestation source to other nearby occupied buildings.
The CA (Cellular Automata) model, although still in a development stage, gives a better
understanding of the dispersal at the local scale. The model has a strong potential due to its
ability to evaluate different scenarios, creating rather illustrative animations and therefore
allowing us to investigate whether our ideas of how the infestation develops are correct. It
can also be used to conduct simulations in other places or even concerning other invasive
98
species. Obviously the reliability of the model is always related to the information available
for each situation under study.
The results obtained with the Maximum Entropy – MAXENT, geographic distribution model
are both significant and worrying. They are clear to indicate that if no measurements are
taken, the species might spread to the other Islands and, if so, large economical and
patrimonial impacts are assured. The model forecasts allow for a risk planning map to be
sketched and the application of prevention strategies in the local population.
Combining the two different methods developed in this thesis constitutes a significant new
step towards prevention and control of this termite, especially in places where the species
was recently spotted or is very likely to occur.
4.6 FUTURE PERSPECTIVES
This thesis presents interesting results not only for the fields of termite research and pest
management, but also for practical reasons, i.e. is contributing to the emergent necessity of
having an effective plan to control the species in the Azores. Even so, the work presented in
this thesis should be further developed, improved and used in different future applications.
The Cellular Automata model should be further developed to include different cell stages and
more complex situations. It could also be applied in other localities or adapted to model other
species.
In the future, the traps could be used as a cheap tool to detect the presence of termites in
other locations.
The MAXENT could be used to predict the probability of occurrence of C. brevis in other
locations as well as to incorporate other climate variables. Also, it could be applied to other
species of termites and forecast their probable geographical occurrence in the archipelago.
Although the present work is a part of a needed control plan, other major issues should be
concerned.
The implementation of a Regional and Local integrated control plan management should
include several measures in different areas such as educational, prevention, legal and
treatment methods.
With reference to Angra do Heroísmo, Horta and Ponta Delgada, it is necessary to
implement a complete survey on all the buildings in order to have a proper database in which
the building characteristics should be included, such as: construction materials, infestation
degree and occupation status. This is important for the safety of the habitants against
seismic events and an effective control and elimination of the termite in the cities. Parallel to
this survey there could be a cheap and easy distribution of simple light traps to economically
99
disadvantaged habitants of affected buildings. From this survey, all the proprieties should
have a proper certificate concerning the presence or absence of the termite.
The results obtained with the CA and MAXENT models can be used as an educational tool in
public presentations in places where the pest is present, or not yet present, to aware the
local habitants to the problem. This would elucidate the audience to the rapid spread of the
species, the difficulty to notice the infestation symptoms and, of course, the possible damage
and economic impact.
Legal actions should also be taken. The house owners that have their proprieties infested but
do not have economic capability to apply an effective treatment, should integrate the
Regional Assistance System. Those that have economic means should be obligated to
implement a treatment method to solve the situation. The ones that do not take a pro active
action on this matter should pay an annual fee to the local authorities in order to compensate
the impact of the new colonies that are emerging each year from their proprieties that are
obviously affecting other buildings. That fee could finance the traps to those with little
economic capability.
More preventive measurements should be taken on the ports and airports of the islands to
verify the wood materials coming from the exterior and being transported between the
islands. This requires the implementation of legal mechanisms and training of the customs
employees.
The present posture of laissez faire, laissez passer of the responsible authorities towards this
problem will cause a significant a future impact in the regional economy and heritage. It is
hoped that the work presented in this thesis can contribute to a change in mentalities and
provide
some
of
the
necessary
tools
100
to
minimize
the
termite’s
problem.
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APPENDIXES
110
APPENDIX A
INQUÉRITO
Morada:
Rua______________________________N.º__________ Freguesia:_______________
Tem Térmitas?
Sim
Não
Não tem a certeza
Não Sabe
Já teve
O que fez?: Nada.
Tratamento
Que tipo____________ ; Mudou de materiais
Quais?______
Viu algum destes indícios?
Pelotas fecais
Asas
Alados
Que tipo de estruturas tem em madeira em sua casa (de que material) e em quais encontou
vestigios de termitas?
Ano de
Tipo de
Estado
Existente
Vestigios? Infestada? Madeira
colocação
estrutura
Roda-Pé
Janelas
Portas
Mobiliario
Sobrados
Tecto
Sotão
Outro
Distancia à armadilha mais próxima___________
Armadilha n.º___
Grau de Infestação:
Observações
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
____
111
APPENDIX B
globals [
number-previous ;; number of houses infested in previous iteration
total-houses ;; number of houses (a fraction of the total number of patches)
probability-1 ;; probability of becoming infested with only one infested neighbor, setup by
slider
probability-2 ;; probability of becoming infested with two infested neighbors
probability-3 ;; probability of becoming infested with three infested neighbors
probability-4 ;;
probability-5 ;;
probability-6 ;;
probability-7 ;;
probability-8 ;;
probability-9 ;;
probability-10 ;;
probability-11 ;;
probability-12 ;;
probability-13 ;;
probability-14 ;;
probability-15 ;;
probability-16 ;;
probability-17 ;;
probability-18 ;;
probability-19 ;;
probability-20 ;;
probability-max ;; probability for more than 3 infested neighbors , setup by slider
infested-houses ;; number of infested houses in red scale
infested-houses2 ;; number of recently infested houses (yellow)
tempo
simuteseworld.csv
]
patches-own [
infested-neighbors ;; number of infested neighbors
years-source-infestation ;; tracks times the house is source of infestation
years-infested ;; tracks number of years the house has become infested
Ocean
]
;;; setup procedures
to setup-start
ca
set tempo 0
ask patches
[ set pcolor white ]
ask patch 8 -41 [set pcolor red]
end
to setup-Angrasimu
ca
import-world "simuteseworld.csv"
set total-houses count patches with [pcolor = white]
ask patch -4 -48 [set pcolor red]
end
to setup-randomhouses
ca
ask patches [
let probability random 100
ifelse (probability < percentagem-de-casas-criadas)
[ set pcolor white ]
[ set pcolor white ]
112
]
set total-houses count patches with [pcolor = white]
end
to setup [random?]
ifelse random?
[ random-infestation ]
[ mouse-infestation ]
set number-previous count patches with [ pcolor = red ]
end
to mouse-infestation
;; infest houses as already developed infestation
while [mouse-down?]
[ ask patch mouse-xcor mouse-ycor [ if pcolor = white [ set pcolor red set years-infested 1 ]]
set infested-houses count patches with [pcolor = red]
display ]
end
to YellowInfest
while [mouse-down?]
[ ask patch mouse-xcor mouse-ycor
[ if pcolor = white
[ set pcolor yellow] ;;blue
]
display ]
end
to random-infestation
;; seed with random number of rumor sources governed by init-clique slider
ask patches
[ let probability random 100
if (pcolor = white and probability < percentage-of-infested-houses)
[ set pcolor red set years-infested 1]
]
end
to put-ocean
while [mouse-down?]
[ ask patch mouse-xcor mouse-ycor
[ if pcolor = black
[ set pcolor 104 ] ;;blue
]
display ]
end
to remove-ocean
while [mouse-down?]
[ ask patch mouse-xcor mouse-ycor
[ if pcolor = 104
[ set pcolor black ] ;;blue
]
display ]
end
;; make a 100-step movie of the current view
to movie
print movie-status
movie-start "testeprob_0.5_4.mov"
movie-set-frame-rate 100
repeat 100 [
movie-grab-view
go
]
movie-close
end
113
to export
export-view "NEW2Angratest_R10_prob0.25_40st.png"
end
to go
setup-probability
ask patch -4 -48 [set pcolor red]
ask patches with [pcolor = white]
[ set infested-neighbors count patches in-radius 10 with [pcolor = red] ]
ask patches with [infested-neighbors != 0 and pcolor != black] [
let prob 0
if pcolor = red [ set years-source-infestation years-source-infestation + 1]
if (pcolor = yellow and years-infested <= 3) [set years-infested years-infested + 1]
if (pcolor = yellow and years-infested = 4) [
set years-source-infestation 0
set pcolor red
]
if (pcolor = white and infested-neighbors = 1) [set prob probability-1]
if (pcolor = white and infested-neighbors = 2) [set prob probability-2]
if (pcolor = white and infested-neighbors = 3) [set prob probability-3]
if (pcolor = white and infested-neighbors = 4) [set prob probability-4]
if (pcolor = white and infested-neighbors = 5) [set prob probability-5]
if (pcolor = white and infested-neighbors = 6) [set prob probability-6]
if (pcolor = white and infested-neighbors = 7) [set prob probability-7]
if (pcolor = white and infested-neighbors = 8) [set prob probability-8]
if (pcolor = white and infested-neighbors = 9) [set prob probability-9]
if (pcolor = white and infested-neighbors = 10) [set prob probability-10]
if (pcolor = white and infested-neighbors = 11) [set prob probability-11]
if (pcolor = white and infested-neighbors = 12) [set prob probability-12]
if (pcolor = white and infested-neighbors = 13) [set prob probability-13]
if (pcolor = white and infested-neighbors = 14) [set prob probability-14]
if (pcolor = white and infested-neighbors = 15) [set prob probability-15]
if (pcolor = white and infested-neighbors = 16) [set prob probability-16]
if (pcolor = white and infested-neighbors = 17) [set prob probability-17]
if (pcolor = white and infested-neighbors = 18) [set prob probability-18]
if (pcolor = white and infested-neighbors = 19) [set prob probability-19]
if (pcolor = white and infested-neighbors = 20) [set prob probability-20]
;if (pcolor = white and infested-neighbors > 20) [set prob maximum-probability]
if (pcolor = white and infested-neighbors > 20) [set prob probability-20]
if prob != 0 [
let probability random-float 1
if (probability < prob ) [ set pcolor yellow set years-infested 0]
]
]
tick
set infested-houses count patches with [pcolor = red]
show count patches with [pcolor = red]
set infested-houses2 count patches with [pcolor = yellow]
show count patches with [pcolor = yellow]
set tempo tempo + 1
if (tempo > 40) [stop]
do-plots
end
to do-plots
set-current-plot "Percentage of houses infested"
set-current-plot-pen "Recently infested"
let number-recently count patches with [pcolor = yellow]
plot (number-recently / total-houses) * 100
set-current-plot-pen "Source of infestation"
let number-infested count patches with [pcolor = red]
plot (number-infested / total-houses ) * 100
let total number-recently + number-infested
114
set-current-plot "Successive differences"
plot total - number-previous
set number-previous total
end
to setup-probability
ifelse one-neighbor-probability < maximum-probability
[ set probability-1 one-neighbor-probability]
[ user-message (word "Incorrect probabilities") stop ]
set probability-2 (2 * one-neighbor-probability - (one-neighbor-probability) ^ 2)
set probability-3 (probability-1 + probability-2 ^ 2 - probability-2 * probability-1)
set probability-4 (probability-1 + probability-3 ^ 3 - probability-3 * probability-1)
set probability-5 (probability-1 + probability-4 - probability-4 * probability-1)
set probability-6 (probability-1 + probability-5 - probability-5 * probability-1)
set probability-7 (probability-1 + probability-6 - probability-6 * probability-1)
set probability-8 (probability-1 + probability-7 - probability-7 * probability-1)
set probability-9 (probability-1 + probability-8 - probability-8 * probability-1)
set probability-10 (probability-1 + probability-9 - probability-9 * probability-1)
set probability-11 (probability-1 + probability-10 - probability-10 * probability-1)
set probability-12 (probability-1 + probability-11 - probability-11 * probability-1)
set probability-13 (probability-1 + probability-12 - probability-12 * probability-1)
set probability-14 (probability-1 + probability-13 - probability-13 * probability-1)
set probability-15 (probability-1 + probability-14 - probability-14 * probability-1)
set probability-16 (probability-1 + probability-15 - probability-15 * probability-1)
set probability-17 (probability-1 + probability-16 - probability-16 * probability-1)
set probability-18 (probability-1 + probability-17 - probability-17 * probability-1)
set probability-19 (probability-1 + probability-18 - probability-18 * probability-1)
set probability-20 (probability-1 + probability-19 - probability-19 * probability-1)
end
115