Tesis Leonor Valenzuela - Repositorio UC

PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE
Facultad de Ciencias Biológicas
Programa de Doctorado en Ciencias Biológicas
Mención en Ecología
TESIS DOCTORAL
PATRONES DE DIVERSIDAD ALFA, BETA Y GAMMA EN SISTEMAS
INSULARES.
Por
LEONOR ADRIANA VALENZUELA OSPINA
Enero, 2013
Santiago, Chile
PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE
Facultad de Ciencias Biológicas
Programa de Doctorado en Ciencias Biológicas
Mención en Ecología
PATRONES DE DIVERSIDAD ALFA, BETA Y GAMMA EN SISTEMAS
INSULARES.
Tesis entregada a la Pontificia Universidad Católica de Chile en cumplimiento parcial de los
requisitos para optar al Grado de Doctor en Ciencias con mención en Ecología
Por
LEONOR ADRIANA VALENZUELA OSPINA
Director de tesis Dr. Pablo A. Marquet
Enero, 2014
Santiago, Chile
“…a la luz de la teoría de la evolución, son las semejanzas y no las diversidades en estas
lejanas islas las que son más difíciles de explicar… no podemos llegar a ninguna conclusión
confiable en cuanto a cómo el estado actual del mundo orgánico se produjo, hasta que
hayamos comprobado con cierta exactitud las leyes generales de la distribución de los seres
vivos sobre la superficie de la Tierra”
Alfred Russel Wallace
“Las islas y archipiélagos son, en muchos aspectos, microcosmos del resto del mundo”
Jonathan Losos y Robert Ricklefs
i
AGRADECIMIENTOS
Doy las gracias a mi tutor Pablo Marquet por su estímulo, confianza y su ayuda en el
desarrollo de las ideas y los métodos que subyacen a esta tesis. En especial estoy
profundamente agradecida con él por compartir conmigo su forma única de ver el mundo, a
través de la cual una compleja maraña de ideas y datos se convierten en una explicación clara
y novedosa. De igual manera agradezco a los miembros del comité por sus aportes y
observaciones tanto en el proyecto que antecedió a este trabajo como en el documento final
del mismo.
Mi sincero agradecimiento a mis compañeros y profesores del doctorado por proporcionarme
un entorno estimulante en el que aprender y en especial a Mauricio Lima por su apoyo en
todos los aspectos que implica estar en un doctorado y a Andrés Parada y Tamara Catalán por
los muchos debates estimulantes y también por el compañerismo y la risa que me han
sostenido durante mis estudios de postgrado. Gracias a todos los compañeros del laboratorio
que han hecho más ameno e interesante todo este proceso y siempre han estado dispuestos a
colaborarme, en especial Pamela Martínez, Guillermo Espinoza, Juan Manuel Barreneche y
Sebastián Abades ya que sin su ayuda parte de esta tesis no habría sido posible. A mis amigos,
Gabriela Flores, Paula Giraldo, Robert Márquez, Gabriel Castaño, Renzo Vargas, Alejandra
Troncoso, Andrea Najera y Jimena Guerrero mil gracias por su compañía y amistad.
Quiero agradecer a muchas personas que sin conocerlas han hecho posible la realización de
esta tesis, ya que su arduo trabajo ha hecho accesible al público un gran conjunto de datos sin
los cuales esta tesis no se habría podido realizar. Doy las gracias al Programa de becas VRI de
la Universidad Católica, la beca Conicyt para estudiantes latinoamericanos y la beca de
término del Instituto de Ecología y Biodiversidad IEB por el apoyo financiero que me permitió
desarrollar y completar mis estudios.
Mi familia, especialmente mis padres Mercy Ospina y Jaime Valenzuela, me han brindado un
apoyo incondicional durante mis estudios de posgrado, como lo han hecho en toda mi vida y
por eso estoy muy agradecida con ellos. Por último, no podía tener completa esta tesis sin el
apoyo incondicional y fomento de Daniel Osorio, que ha estado siempre ahí para mí y en
ningún momento dudó de que pudiera hacerlo.
ii
TABLA DE CONTENIDO
RESUMEN GENERAL.............................................................................................................1
INTRODUCCIÓN .....................................................................................................................3
CAPÍTULO 1 .............................................................................................................................6
ON THE DETERMINANTS OF ALPHA AND BETA DIVERSITY IN INSULAR
BIOTAS ..................................................................................................................................... 6
Abstract ....................................................................................................................................... 6
INTRODUCTION ...................................................................................................................... 7
METHODS ............................................................................................................................... 10
Data ....................................................................................................................................... 10
Statistical Analysis ................................................................................................................ 12
RESULTS ................................................................................................................................. 14
DISCUSSION ........................................................................................................................... 16
REFERENCES ......................................................................................................................... 20
Table Legends ........................................................................................................................... 27
Figure Legends ......................................................................................................................... 27
Supplementary material ............................................................................................................ 28
CAPÍTULO 2 ...........................................................................................................................47
SPECIES DIVERSITY UNDER A NEUTRAL COLONIZATION RULE.......................47
Abstract ..................................................................................................................................... 47
INTRODUCTION .................................................................................................................... 48
METHODS ............................................................................................................................... 49
Model .................................................................................................................................... 49
Previous work ................................................................................................................... 49
Extensions ......................................................................................................................... 51
Simulations and Model performance ................................................................................ 54
Neutral diversity in real archipelagos ............................................................................... 55
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RESULTS ................................................................................................................................. 56
Model Performance............................................................................................................... 56
Neutral diversity in real archipelagoes ................................................................................. 57
DISCUSSION ........................................................................................................................... 58
REFERENCES ......................................................................................................................... 61
Figure Legends ......................................................................................................................... 64
CAPÍTULO 3 ...........................................................................................................................73
THE ROLE OF SPATIAL CONFIGURATION, HETEROGENEITY AND SPECIES
POOL ON SPECIES RICHNESS AND PHYLOGENETIC DIVERSITY OF INSULAR
MAMMALS ............................................................................................................................ 73
Abstract ..................................................................................................................................... 73
INTRODUCTION .................................................................................................................... 74
Determinants of species richness and phylogenetic diversity .............................................. 76
Partitioning taxonomic and phylogenetic diversity in alpha and beta components .............. 78
METHODS ............................................................................................................................... 79
Data ....................................................................................................................................... 79
Statistical Analysis ................................................................................................................ 82
Bivariate analysis .............................................................................................................. 82
Structural equation model ................................................................................................. 82
RESULTS ................................................................................................................................. 84
Determinants of species richness and phylogenetic diversity .............................................. 84
Partitioning taxonomic and phylogenetic diversity in alpha and beta components .............. 85
DISCUSSION ........................................................................................................................... 86
REFERENCES ......................................................................................................................... 90
Figure Legends ......................................................................................................................... 96
Table Legends ........................................................................................................................... 97
Supplementary material ............................................................................................................ 97
CONCLUSIONES GENERALES ........................................................................................107
LITERATURA CITADA ......................................................................................................111
iv
RESUMEN GENERAL
La ecología de comunidades y la biogeografía buscan entender los procesos que determinan
los patrones en la naturaleza, pero generalmente a distintas escalas espaciales y enfatizando
diferentes procesos. La ecología de comunidades por lo general se ha centrado en los efectos
de los procesos de selección a pequeña escala, mientras que la biogeografía se ha enfocado en
los efectos de la dispersión y especiación a gran escala, aunque recientemente han convergido
a una escala regional, donde se tienen en cuenta cuatro procesos generales: selección, deriva
ecológica, dispersión y especiación. En este sentido, descomponer la diversidad regional
(diversidad γ) en sus componentes α, que representa la diversidad local y β, que da cuenta de
la variación en la composición de especies, ayuda a entender los vínculos entre las diferentes
escalas espaciales y como esta influye en los patrones de diversidad.
Los archipiélagos son sistemas relativamente bien estudiados para los cuales existe
una considerable base empírica y teórica, están compuestos por unidades discretas (islas),
cuantificables, numerosas y variables en tamaño, forma y distancia, lo cual los hace un sistema
idóneo para entender cómo interactúan diferentes factores tales como: el tamaño, la
heterogeneidad, la configuración espacial, el aislamiento y el pool continental, que dan cuenta
de los cuatro procesos ya mencionados. En esta tesis se estudiaron las causas de los patrones
de diversidad alfa, beta y gamma en sistemas insulares a dos escalas, intra archipiélagos, es
decir entre islas de un mismo archipiélago (capitulo 1) e inter archipiélagos, es decir entre
archipiélagos (capitulo 2 y 3). Para esto utilizamos la diversidad de mamíferos terrestres no
voladores de 21 archipiélagos (155 islas) ubicados alrededor del mundo.
Nuestro estudio muestra que esta nueva aproximación puede ayudar a entender mejor
los procesos detrás de las relaciones entre diferentes factores y los componentes de la
diversidad. A menor escala, es decir entre islas de un mismo archipiélago (capitulo 1), los
factores relacionados con los procesos de selección, como el área, la diversidad de hábitats y
el tamaño corporal, tienen un mayor efecto que los relacionados con dispersión (distancia al
continente y distancia entre islas), mientras que a mayor escala (entre archipiélagos, capitulo
3), la dispersión cobra mayor relevancia y los patrones de diversidad pueden ser explicados
1
por los efectos conjuntos de los factores relacionados con procesos de dispersión entre las
islas, que dependen de la configuración espacial y procesos de selección, relacionados con la
heterogeneidad del sistema. A nivel inter-archipiélagos, bajo el modelo de colonización
neutral (capítulo 2), los patrones de diversidad se vieron afectados por la tasa de migración, el
tamaño y topología de los archipiélagos, lo cual nos indica que los procesos de deriva
ecológica pueden generar diferentes patrones a través de los efectos de estos factores. Sin
embargo, los resultados indican que los procesos no-neutrales disminuyen la riqueza de
especies presentes en una metacomunidad y aumentan la diferenciación entre las comunidades
locales (diversidad β, capitulo 3).
2
INTRODUCCIÓN
Desde los inicios de la ecología, han existido dos perspectivas que se han considerado
diametralmente opuestas, sobre cómo se estructuran las comunidades ecológicas: la teoría de
nicho y la teoría neutral. Esta aparente contradicción es lo que se conoce como la paradoja de
MacArhur (Schoener, 1983; Loreau & Mouquet, 1999), ya que su trabajo se centro tanto en el
concepto de nicho para explicar la diversidad a escala local (Macarthur et al., 1967) como en
la teoría de biogeografía de islas (MacArthur & Wilson, 1967). Sin embargo, al igual que
como lo considero el propio MacArthur en algunos de sus trabajos (MacArthur & Levins,
1964; Horn & Arthur, 1972) la teoría de metacomunidades considera que la paradoja de
MacArhur más que representar una dicotomía ilustra diferentes extremos de un continuo
(Chase & Bengtsson, 2010), los cuales representan dos partes complementarias de una visión
más amplia que examina como el determinismo (e.g interacciones entre las especies y el
ambiente) y los procesos estocásticos (e.g dispersión) interactúan para dar cuenta de la
estructura metacomunitaria (Chase, 2007). Dentro de los procesos deterministas se encuentran
los procesos de selección asociados normalmente al nicho de las especies, mientras que entre
los procesos estocásticos comúnmente se encuentran la deriva, la dispersión y la especiación,
aunque estos dos últimos pueden tener un componente determinístico (Chase & Myers, 2011).
Debido a que las dinámicas de la diversidad de especies a escala local y regional, no
son independientes, descomponer la diversidad en sus componentes ayuda a entender los
vínculos entre las diferentes escalas espaciales y como esta influye en los patrones de
diversidad (Leibold et al., 2004). A escala local, la diversidad o riqueza de especies
corresponde a la diversidad-α, la variación entre la composición de las especies entre una
localidad y otra representa la diversidad-β, mientras que la diversidad regional o diversidad-γ
se puede derivar de una partición multiplicativa (γ= α/β, Whittaker, 1972) o aditiva (γ= α + β,
Lande, 1996).
En términos generales existen cuatro procesos que pueden afectar de manera
diferencial los componentes de la diversidad: 1) Procesos de selección, que son aquellos que
favorecen diferentes especies en diferentes ambientes, 2) deriva ecológica o estocasticidad
3
demográfica, 3) limitación a la dispersión y 4) especiación (Vellend, 2010). En este sentido, es
relevante entender el efecto y la interacción de factores que dan cuenta de estos cuatro
procesos a diferentes escalas espaciales. La teoría de biogeografía de islas (MacArthur &
Wilson, 1963, 1967) enfatiza la importancia del área, el aislamiento y el pool de especies
como factores determinantes de la riqueza de especies a través de procesos de colonización
(dispersión) y extinción estocástica (deriva). La teoría de nicho, enfatiza la importancia del
área, la heterogeneidad ambiental, la energía disponible y rasgos de las especies que reflejan
su auto-ecología como el tamaño corporal o nivel trófico, como factores relevantes que dan
cuenta de procesos de selección. La teoría de metacomunidades abarca explícitamente la
deriva, la selección y la dispersión (Holyoak et al., 2005), mientras que los estudios que tienen
en cuenta las relaciones local- regional (Ricklefs & Schluter, 1993) destacan los efectos del
pool de especies y la latitud, ya que de manera indirecta permiten entender los efectos de la
especiación y la dispersión (Ricklefs, 1987). Sin embargo, la mayoría de los estudios se
centran en los patrones.
Adicionalmente, es necesario considerar que existen dos niveles de abstracción, bajo
los cuales se puede analizar los patrones de diversidad. Dentro de una metacomunidad, se
puede analizar la variación en la riqueza de especies entre comunidades (diversidad α,
componente sobre el que se enfocan la mayoría de los trabajos) y la variación en la
composición de la comunidad entre los sitios (Legendre et al., 2005), mientras que el análisis
de la variación en la diversidad beta entre los grupos de sitios (Legendre et al., 2005;
Tuomisto & Ruokolainen, 2006) y de la diversidad regional, solo se puede llevar a cabo
comparando metacomunidades (nivel al cual existen pocos estudios observacionales, Logue et
al., 2011). En este sentido, los archipiélagos, que son un conjunto de islas generalmente de un
mismo origen geológico, son un buen sistema de estudio, debido a su carácter discreto y
variable en términos de tamaño, forma y aislamiento, sumado al hecho de ser sistemas
relativamente bien estudiados para los cuales existe una base empírica y teórica considerable
(Whittaker & Fernández-Palacios, 2007; Lomolino & Brown, 2009), además que permite el
estudio de los patrones de diversidad a nivel intra e inter archipiélagos. Como grupo de estudio
se escogió a los mamíferos, ya que son un grupo bien estudiado, cuya taxonomía y sistemática
está relativamente bien definida y se conocen sus relaciones de escalamiento alométrico
(Damuth, 1981).
4
En esta tesis se estudiaron las causas de los patrones de diversidad alfa, beta y gamma
en sistemas insulares. Para esto utilizamos la diversidad de mamíferos terrestres no voladores
de 21 archipiélagos (155 islas) ubicados alrededor del mundo. En primer lugar, evaluamos los
efectos de la capacidad de carga, el aislamiento y el tamaño corporal en los patrones de
diversidad dentro de los archipiélagos, identificando las diferencias en los tamaños de efecto
de cada variable a través de un meta-análisis, con el fin de poder evaluar la generalidad y la
validez de los patrones observados (Capitulo 1). En segundo lugar, analizamos los patrones de
diversidad entre los archipiélagos, ya que esto permite entender cómo se estructuran los
ensambles de especies a una mayor escala, en este sentido, son pocos los antecedentes dentro
de la teoría insular (pero ver Patterson & Atmar 1986, Schoener 1976). Para esto evaluamos
cómo los componentes básicos de un modelo de colonización neutral: procesos de dispersión
asociados a la conectividad y procesos de deriva asociados al tamaño de la metacomunidad,
determinan la diversidad de los archipiélagos (diversidad- γ) y sus componentes α y β, además
determinamos bajo que dominio nuestro modelo puede adaptarse eficazmente a los datos de
un mundo no neutral (Capitulo 2). Adicionalmente, analizamos como la heterogeneidad, la
configuración espacial, el tamaño, la latitud, el pool de especies y aislamiento de los
archipiélagos afectan la partición de la diversidad a través de modelos de ecuaciones
estructuradas que permiten entender los efectos directos e indirectos de los factores y así
determinar cuáles son los procesos involucrados en la estructuración metacomunitaria
(Capitulo 3).
Los resultados de esta tesis permiten identificar los factores y procesos involucrados
en la formación de los patrones de diversidad de mamíferos insulares a nivel intra e inter
archipiélagos. Como lo señalaron MacArthur & Wilson (1963), entender la dinámica de la
distribución de las especies en los archipiélagos puede ayudar a comprender la variación en el
tamaño y la variedad distribución ecológica de los taxones a nivel continental (por ejemplo,
Brown, 1995; Gaston, 2009) y nuestro conocimiento en general sobre la biogeografía y
ecología de comunidades, ayudando de igual manera a entender los sistemas antrópicamente
modificados (por ejemplo, Terborgh, 1974; Laurance, 2010).
5
CAPÍTULO 1
ON THE DETERMINANTS OF ALPHA AND BETA DIVERSITY IN INSULAR
BIOTAS
Abstract
Understanding the processes that determine the number and identity of species in local
communities remains a vexing problem and a major goal in both community ecology and
biogeography. Islands biotas have historically been used to test simple hypotheses on the role
of different factors in affecting changes in species numbers. However, as yet we do not have
an overall agreement on what are the important factors driving the observed changes. In this
study we perform a meta-analysis based on mammalian species inhabiting 19 archipelagoes
across the world. Unlike previous studies we focus on two diversity components (alpha and
beta diversity) and distinguished between the spatial and nestedness component in beta
diversity. For both the alpha and beta components of diversity we analyzed the relative
importance of area, habitat diversity and productivity, which are related to the capacity of
islands to sustain species, and two measures of isolation (geographical distances between
islands and distance to the nearest mainland). Since body size affects species incidence across
archipelagoes we repeated the analysis for species in different body size classes (quartiles).
Each relationship was characterized by two effect sizes, strength (correlation coefficient) and
the slope. Our analysis shows that alpha diversity increases with island area and habitat
diversity. Island productivity, however, had no significant effect. The spatial component of
beta diversity decreases with increased body mass and with decreases in the distance between
islands, while the nestedness component increases with increased body mass, islands area and
habitat diversity.
6
INTRODUCTION
Understanding the processes that determine the number and identity of species in local
communities remains a vexing problem and a major goal in both community ecology and
biogeography (Hortal et al., 2012). Ever since MacArthur and Wilson (1967) and Diamond
(1975) island biotas have had a prominent role as study systems, due to its discrete nature and
quantifiable variation in size and isolation, which allows an the role easy quantification of
dispersal and resource availability upon species richness. This is reflected in that a substantial
amount of theoretical and empirical work is currently available for insular communities
(Whittaker & Fernández-Palacios, 2007; Lomolino & Brown, 2009) and the proliferation of
alternative hypotheses to explain diversity patterns in islands (e.g., Connor & Mccoy, 1979;
Kalmar & Currie, 2006; Whittaker et al., 2008). Many authors have postulated that the
number of species in a given community depends on the processes that affect the availability
of limited resources for consumers (Brown, 1981; Wright, 1983; Ernest & Brown, 2001;
Hubbell, 2001; Monte-luna et al., 2004), and have used factors such as the area, habitat
heterogeneity and available energy, which are related to the variety and availability of
resources in islands, as predictors of their richness (Wright, 1983; Currie & Fritz, 1993;
Rosenzweig, 1995; Whittaker & Fernández-Palacios, 2007). The mechanisms that support a
role for these variables in affecting richness are: (i) area affects susceptibility to extinction; as
the area of the island increases so does the amount of resources and population size, thus
reducing the probability of local population extinction (MacArthur & Wilson, 1967), hence
higher richness should be expected in larger islands (ii) the habitat heterogeneity allows
greater possibilities for niche partitioning and therefore a larger number of species that can
coexist (Williams, 1964; MacArthur & Wilson, 1967; Triantis et al., 2003), and (iii) the
availability of resources, which can be measured in terms of energy or productivity, would
increase the number of individuals and species that a given island could sustain (Wright,
1983). Similarly island isolation is an important determinant of species richness (MacArthur &
Wilson, 1967), as it affects colonization and extinction (MacArthur & Wilson, 1967; Brown &
Kodric-Brown, 1977) and the positive effect it has on speciation rates (Heaney, 2000). Thus
factors related to isolation such as the distance to the mainland and the distance between
islands can be important in determining species richness. However, the number of species in a
7
local community or insular biota can provide limited information on the processes shaping
community assembly, and a closer look at the factors that account for variation in species
composition or beta diversity (Whittaker, 1972; Condit et al., 2002; Myers et al., 2013) can be
important.
Beta diversity (β), the same as species richness, is influenced by ecological processes
that determine the distribution of species, including niche differentiation, competition and
dispersal and spatial characteristics of the physical environment where in which these
processes occur (Nekola et al., 1999; Koleff et al., 2003). β-diversity can be generated by loss
and replacement of species or a combination of the two (Baselga, 2010) and therefore, it can
be divided in two components; the nestedness-resultant (Bnes) and the spatial species turnover
(Bsim) (Harrison et al., 1992; Baselga, 2007). The nestedness component of β-diversity is high
when the identity of species found in depauperate sites tend to be a subset of the species found
in sites with greater richness (Wright & Reeves, 1992; Ulrich & Gotelli, 2007), which is a
result of a non-random process of species loss (Patterson & Atmar, 1986; Cutler, 1994; Gaston
& Blackburn, 2000), or addition due to differential colonization (Kadmon, 1995; Lomolino,
1996) or a nested distribution of habitats (Simberloff & Martin, 1991). On the other hand,
spatial turnover reflects the fact that some species are replaced by other species as a result of
changes in the environment or because of spatial and historical constraints (Qian et al., 2005)
or due to stochasticity. The spatial species turnover component emphasize changes in species
composition independent of changes in richness, while the nested component quantifies the
addition or loss of species that affect richness among sites.
Overall, environmental dissimilarity and geographical distance are the two most
important factors in explaining beta diversity (Harrison et al., 1992; Nekola et al., 1999). The
change in the composition of species across environmental gradients is a function of the
difference between habitats and is mainly explained by species sorting, whereby, different
environments favors different species so that the better competitor on a given resource
outcompetes other species and ‘wins’ on that resource (Huston, 1999; Chase & Leibold, 2002;
Leibold & Holyoak, 2004; Davies et al., 2009). The effect of geographic distance, on the other
hand, is explained in large part by differences in the biogeographic history and dispersal
ability of species (Harrison et al., 1992; Condit et al., 2002; Chase, 2003). Most of these
studies, however, have been done in continuous systems, where the role of isolation would be
8
difficult to see, whereas for island systems it has been reported that beta diversity is regulated
by the distance and area in birds (Guerrero et al., 2005; Fattorini, 2010) or only by the distance
between islands for invertebrates and reptiles (Hausdorf & Hennig, 2005; Dapporto et al.,
2007; Fattorini, 2010).
Traits such as body size and species dispersal ability could have a detectable effect on
insular diversity patterns, the same as in continuum systems (Meiri & Thomas, 2007; Soininen
et al., 2007). For example, the data reported for mammalian dispersal distances and dispersal
ability are inversely related to body size and (e.g., 10- 150 km for large mammals vs. 410 km
for small, see Whittaker & Fernández-Palacios, 2007). Further, since there is a negative
relationship between abundance and body size (Damuth, 1981; Peters, 1986) and that the same
amount of resources can support few large or many small due to the positive scaling between
body size and the rate of resource consumption and the energetic equivalence it entails
(Damuth, 1981; Calder, 1984; Peters, 1986; Marquet et al., 1995; Ernest & Brown, 2001;
White et al., 2007), it is expected that the distribution of body sizes differ between high
species richness and low richness areas, due to metabolic as well as community processes that
regulate the assembly of communities (Brown & Nicoletto, 1991; Marquet & Cofré, 1999).
According to the hypotheses proposed by Brown and Nicoletto (1991), across continental
mammals assemblages, competitive exclusion among medium size species, differential
extinction of large species and specialization of the smaller ones drive changes in species
composition, hence beta diversity across spatial scales. Similarly, Marquet and Taper (1993)
suggest that in insular systems, the smallest and the largest species would tend to change the
most as landmass area changes due to differential extinction, such that the smallest islands
would tend to have a nested subset of the species present in the larger ones. In this sense,
extreme size species would show high beta diversity and may only be present in islands with
high carrying capacity, while according to Brown and Nicoletto (1991) the modal size species
would also show a high spatial turnover. Further, because of competitive exclusion modal size
species would also show high turnover the same as small ones due to specialization on
energetically rich resources (Brown & Nicoletto, 1991).
Finally, in addition to factors mentioned above (i.e., resource availability and variety,
isolation and body size), the history of insularization, or how a particular system came into
existence (i.e. the island geologic history), may be very important in affecting diversity
9
patterns as the relative importance of extinction and colonization vary depending on the
island´s origin; continental, oceanic or barrier (e.g., Whittaker & Fernández-Palacios, 2007;
Lomolino & Brown, 2009; Weigelt & Kreft, 2012).
In this contribution, we evaluated the effects of carrying capacity, isolation and body
size upon diversity patterns, identifying the differences in effect sizes for each variable
through a meta-analysis. In particular we test the following hypotheses:
1. As it has been commonly observed we expect that species richness increases with factors
associated to island carrying capacity and decreases with those related to isolation. Further,
because the diversity of oceanic islands arises largely by colonization and endemic radiation,
while in landbridge islands assemblages may be shaped largely by extinctions, and can be in a
non-equilibrium state, we expect differential effects of carrying capacity and isolation factors
across island type.
2. Carrying capacity (total NPP and number of Habitat types) have a larger effect size than
area (see Wylie & Currie, 1993).
3. Changes in island carrying capacity affect beta diversity, specifically through the
component of nestedness-resultant. In this sense, the effect should be stronger in land-bridges
islands.
4. Geographical distances between islands affect beta diversity, specifically through the
component of spatial turnover.
5. There is a nonlinear effect of body size on beta diversity with a maximum at intermediate
sizes for spatial turnover component and an opposite pattern for nestedness-resultant.
METHODS
Data
To assess the effects of carrying capacity, isolation and body size distribution in the diversity
of insular mammals, we compiled presence-absence data of species on islands by carrying out
a literature review including only recent, terrestrial, non-volant mammal fauna found in 243
islands, spread over 17 archipelagos around the world (Table 1). The total area of the sampled
islands within each archipelago corresponds in all cases more than 80% of total area. With
10
these data, we calculated alpha diversity as the number of species per island and total beta
diversity (βsor) between each pair of islands within archipelagoes using Sorensen´s index
(Baselga, 2010). The contribution of spatial turnover (βsim) was measured with the Simpson
index (Koleff et al., 2003) and beta diversity due to nestedness-resultant (βnes), was measured
as the difference between βsor and βsim (Baselga, 2010). These measures do not overestimate
the fraction of total dissimilarity can be attributable to richness differences and evaluate
nesting patterns considering both on paired overlap and matrix filling (Baselga, 2012).
To determine the carrying capacity of the islands, we use three measures: total area of
the island, total net primary productivity (NPP) and the choros measure proposed by Triantis
et al. (2003), choros (K) arises as the result of the multiplication of the area of the region with
the number of the different habitat types present on the region (K = H*A), where H is the
number of habitats and A is the total area of the region. Subsequently, we analyzed the effect
of average net primary productivity and the number of habitats. The isolation of each island
was determined using two measurements, the closest distance to the mainland and the average
minimum distance to other islands of the archipelago. To measure the effect of body size, we
divided the distribution of all insular mammals (transformed to log2) in four groups using the
body size quartiles (< 32.44, 32.45-162.02, 162.03-2288.2, >2288.2 g). To determine the
spatial location, area and isolation of islands we used the GSHHS-A Global Self-consistent,
Hierarchical,
High-resolution
Shore
line
Data
Base
version
2.1.
(http://www.ngdc.noaa.gov/mgg/shorelines/gshhs.html). The NPP was calculated from the
MODIS GPP / NPP (Zhao & Running, 2010), and the number of habitats from the GlobCover
2009 (Global Land Cover Map), using the software ArcGIS 10. Body mass was obtained from
the PanTHERIA database (Jones et al., 2009) otherwise we used the midpoint of the range of
body size given in Walkers Mammals of the World (Novak & Novak, 1999). Additional data
were compiled from other sources (Kays & Wilson, 2009; Okie & Brown, 2009; Alviola et al.,
2011; Heaney et al., 2011; Rickart & Heaney, 2011). For species for which we could not find
any published measurement of body mass (n= 57), we relied on the fact that phylogenetically
close species tend to be similar in size (Smith et al., 2003) and used the geometric mean body
mass of the closest phylogenetic relative for which information on body mass was available
(Table S1). To assess the effect of island origin on species diversity we recognize two main
types of geological origins: land-bridge and oceanic islands. Land-bridge or continental
11
islands are either part of the continental shelf or were once connected to continental
landmasses but became isolated from it. Oceanic islands are mainly of volcanic origin and
have arisen as newly formed land from the sea floor. We classify the archipelagos considering
the origin of most of the islands following Heaney (1986); we defined whether an archipelago
was ‘land-bridge’ or ‘oceanic’, based on the ocean depth separating it from a continental land
mass and using as a threshold a depth of 120 m; below that depth we considered an island as
landbridge and oceanic otherwise.
Statistical Analysis
We conducted linear regressions between species richness and the explanatory variables (area,
NPP, NPP/area, number of habitats and choros) (log transformed) for each of the 17
archipelagos. For the analysis of beta diversity, we used distance or dissimilarity matrices, the
dissimilarity matrix of environmental variables (area, PNN and habitat) was computed as the
Mahalanobis distance between each pair of islands (Orlóci, 1978) for isolation variables we
used Euclidean distance matrices. The values of the respective distances and beta diversity
components were used to perform linear regressions. To calculate the effect sizes for the metaanalysis we considered the correlation coefficient (r), slope (standardized between -1 and 1, b)
and the error of the slope.
We measured two effect sizes that reflect different aspects of the relationships, the
strength and steepness. The strength quantifies the amount of variation in diversity with
respect to the explanatory variables, and defined as Fisher's Z transformation of the correlation
coefficient (rz), weighted by the sampling variance (Rosenberg et al., 2000). The steepness
indicates how quickly diversity changes with respect to the variable of interest, and is reflected
in the slope (b) with SEb as variance estimate (Hillebrand et al., 2001). We used a weighted
meta-analysis on rz and b (Rosenberg et al., 2000; Hillebrand et al., 2001) to calculate the
grand mean effect sizes, and their 95% confidence intervals (CIs) using the bootstrapping
procedure in MetaWin 2.0 (Rosenberg et al., 2000). We calculated the Q statistic and its
significance (using 9999 randomizations) to assess if the studies have very heterogeneous
effect sizes, which would imply that the average effect does not adequately represent the set of
studies, We complemented our Q estimates with reports of the I2 index, which can be
interpreted as the percentage of total variability in a set of effect sizes because of true
12
heterogeneity, that is, between-study (or between-comparison) variability. For instance, I2 =
50 means that half of the total variability among effect sizes is caused not by sampling error
but by true heterogeneity between studies or comparisons. To assess the effect of islands type,
we used the random-effects model for categorical data, an algorithm referred to as the mixed
effects model (Gurevitch & Hedges, 1999). This model is analogous to ANOVA and is based
on the more realistic assumption that a given class of studies shares a common effect and that
random variation among studies exists (Gurevitch & Hedges, 1993; Rosenberg et al., 2000).
Under this approach, heterogeneity of results across comparisons or studies (i.e. the
amount of variation in r-scores) was estimated by the Q statistic, a measure that partitions total
heterogeneity into variance explained by the model (QM) and residual error not explained by
the model (Qe; i.e. Qt = Qb + Qe; Rosenberg et al., 2000). This partitioning is analogous to F
in ANOVA tests (Rosenberg et al., 2000). Both Qb and Qe were tested against an X2distribution (alpha= 0.05). A statistically significant Qb implies that here are differences
among cumulative effect sizes for the groups; statistically significant values of Qe imply that
there is heterogeneity among effect sizes not explained by the model (Rosenberg et al., 2000).
Upon detecting statistically significant heterogeneity we considered the bootstrapped 95%
confidence interval linked to each effect size to determine which categories were different.
To determine the effect of body size on alpha diversity, we calculated the average
values and the standard deviation in the richness of each body size quartile standardized by the
total number of species. We calculated effect sizes using the Hedges’ d, in which effect size
corresponds to the standardized mean difference d (Gurevitch & Hedges, 1993). To obtain the
standard mean difference (d), we divided the difference between group means by the pooled
standard deviation (SD) for all pair-wise comparisons of body size classes. To determine the
effect on beta diversity, we perform the same procedure, but calculating the mean and standard
deviation for each of the measures of beta diversity. We used Comprehensive MetaWin 2.0 for
all calculations (mean effect size, confidence interval and Q statistic). For each weighted mean
r and Hedges´d, we calculated the fail-safe number of studies, the number of additional
‘negative’ studies (studies in which the intervention effect was zero) that would be needed to
increase the P value for the meta-analysis to above 0.05 (Rosenthal, 1991). The larger the failsafe number of studies, the greater our confidence in that the observed results are a reliable
estimate of the true effect is high (Rosenberg et al., 2000). In general, effect sizes of 0.20,
13
0.50, and 0.80 are thought to represent weak, moderate, and strong effects, respectively
(Rosenberg et al., 2000).
We use the model developed in the chapter 2 as a null model against which compare
empirical patterns in alpha and beta diversity. Comparisons were made through a test of
Wilcoxon paired test for each of the archipelagos. To determine the effects of the factors of
interest we repeated the meta-analysis to model results.
RESULTS
We found an overall significance of carrying capacity and alpha diversity relationship (Fig 2),
although more than one third of the original studies did not show significant relationships.
Significant differences, were detected between the five measures of carrying capacity: area,
total NPP, choros, NPP/area and number of habitats in the strength (Qb = 6.93, df = 4, 80, P =
0.003) and slope (Qb =53.99, df = 4, 80, P = 0.001) because of the effect of NPP/area. The
effect size for area, total NPP, choros and number of habitats was strongly positive and
statistically significant, while the effect of mean NPP was negative and no significant (Fig 2).
The size effect of measures of carrying capacity (area and number of habitats) on alpha
diversity did not differ across island types (Table 2). Significantly positive effects were
recorded for both land-bridge and oceanic islands for all measures.
Isolation also had a significant effect upon alpha diversity (Fig 2), but this was weak
and negative. Both isolation measures, distance to the mainland (rz = -0.27 and b = -0.05) and
distance among islands (rz = -0.25, b = -0.05) had similar effects upon alpha diversity (Qb =
0.03, df = 1, 32, P = 0.87 and Qb = 2.32, df = 1, 32, P = 0.87 respectively). Also, the effect
size of isolation respect to the mainland on alpha diversity did not differ across island type,
although the effect was positive but not significant for oceanic islands (Table 2).
Regarding the effect of body size upon alpha diversity no significant differences were
found between the first quartile and the other quartiles and between the third and fourth
quartile. In contrast, significant reductions were found in third and fourth quartile compared
with the second quartile with moderate and strong effect sizes (d2-3 = -0.42 and d2-4 = 0.97; Fig
3).
14
The effect size of carrying capacity on beta diversity (Bsor) did not differ across
capacity measures for strength (Zr) or slope (b) (Qb = 3.72, d.f. = 2, 48, P = 0.08; Qb = 0.78,
d.f. = 2, 48, P = 0.14; respectively Fig. 4). Carrying capacity has a significant positive effect
for both strength and slope, but higher for Zr (0.15) than for the slope (0.02). Significantly
positive effects were recorded for the differences in area and for differences in the number of
habitats, but not for mean NPP (Fig. 5). This result is due to the effect of differences in area
and habitat number in the nestedness-resultant component (Bnes; Fig 5). The effect size of
delta-area or delta-habitat on nestedness-resultant diversity did not differ across island type,
although the effect of delta-habitat is greater in land-bridge islands (Table 2).
Isolation affect positively and significantly beta diversity (Zr= 0.19; b= 0.03)
principally through spatial turnover component (Bsim; Zr= 0.14; b= 0.02; Fig 4). The effect
size did not differ between differences in distance to mainland and inter-island distances (Qb =
0.59, d.f. = 2, 32, P = 0.28; Qb = 0.08, d.f. = 2, 32, P = 0.08; for Zr an b respectively), but the
effect of distance inter-islands is higher than distance to mainland (Fig 4).
Body size has opposite effects on turnover (Bsim) and nestedness-resultant (Bnes)
components of beta diversity. For Bsim, significant differences were found between the first
quartile and the other quartiles (greater diversity in the first quartile), whereas, for the fourth
quartile BNES increases significantly with respect to the other (Fig 5).
Regarding the analysis of bias, for both alpha and beta, values of I2 ranged from 0% to
4% in the analysis of carrying capacity and isolation, indicating that no exist large variation in
the size of the effect. However, body size analysis showed I2 values between 0% and 52%
indicating that the variation in the effect size in across factor-level categories exists and needs
to be explained (Table S2, S3). The fail-safe number of studies was higher for alpha than for
beta.
In most cases, the neutral model overestimates alpha diversity, finding significant
differences in 10 of 17 archipelagos (Table 3). Moreover, the model underestimates beta
diversity, finding significant differences in 14 of 17 archipelagos. However, in the neutral
model as well as empirical data, carrying capacity measures have the same effect on alpha
diversity, while the distance to the mainland showed significant differences (Figure 6). To beta
diversity, significant differences in effect size of the area and the distance between islands is
observed (Figure 6).
15
DISCUSSION
Species diversity is governed by multiple processes operating at different spatial and temporal
scales (Brown & Lomolino, 2000; Gaston & Blackburn, 2000; Whittaker et al., 2001). Ever
since (MacArthur & Wilson, 1963) area and isolation have been thought to be among the main
factors affecting species richness in island systems, With time, however, other variables, have
been added to the list of potential drivers of alpha diversity in insular system, such as
productivity and complexity of habitats (Williams, 1964; Wright, 1983), and as yet we do not
have a clear picture on their relative importance. In this contribution we used a meta-analytic
framework to disentangle the relative contribution of several potential drivers of alpha
diversity (area, NPP, NPP/area, choros and number of habitats). Our results show that effects
of carrying capacity measures upon changes in the mammal species richness vary statistically.
Choros showed slightly higher effect sizes while total productivity (NPP) showed smaller
effects. Similarly, the numbers of habitats present a significant effect on species richness but
lower than the effect of area, while NPP / area had no significant effect. In this sense, the nonflying mammal species richness is determined primarily by an area per se effect and by the
interrelationship between the area and habitats. Species-energy theory (Wright, 1983), is based
on the resource requirements of the species and the production of resources in the islands, in
this sense, the NPP /area represents general resources for herbivorous mammals and indirectly
resources for higher trophic levels. Our results show that there is no effect of NPP/are upon
alpha diversity. Other researchers working in continuous systems, however, have found an
effect of NPP / area in global mammals richness (Waide et al., 1999; Luck, 2007), similarly,
Kalmar and Currie (2006) found a significant effect of temperature (used as a proxy for
productivity) on the richness of birds. Thus the he lack of correlation within islands could
reflect an interaction between area and / or isolation effects and NPP / area, such that the most
productive islands tend to be smaller or more isolated than the most productive ones. To test
for this hypothesis we looked for associations between island area, isolation and NPP/area,
finding a positive and significant effect between isolation and the NPP / area 0.27 (95% CI:
0.04 – 0.53) and a not significant effect of area (0.17; 95% CI: -0.01-0.42). This suggests that
the relationship between NPP / area and richness of mammals is affected by dispersal
limitation. As predicted by the theory of island biogeography (MacArthur & Wilson, 1967),
16
there is a negative effect of isolation, no matter how it is measured as distance from the
mainland or average distance between islands, according to reports from Kalmar and Currie
for island birds.
Beta diversity was also affected by island carrying capacity as reflected in the
nestedness-resultant component of beta diversity and measured as area and number of habitats,
implying that changes in habitat and area have a significant effect on the differential gain and
loss of species. Further, the slope observed between habitat changes either number of habitats
and Bnes, indicates that species extinction are susceptible to both area and habitat loss.
Because there is a positive relationship between the area and the number of habitats, large
mammals are the most affected by these changes. Isolation, on the other hand, affected beta
diversity in different ways. Distance to the continent, while having a significant and positive
effect on beta diversity, it had similar impact on the nestedness-resultant and species
replacement or turnover component of beta diversity. Inter-island distance, however, affected
mostly the turnover component. This is an interesting result that can be explained by
considering that the replacement of species associated with geographic distance is explained
largely by biogeographic history and the dispersal capability of species (Harrison et al., 1992;
Condit et al., 2002; Chase, 2003). For example, general climatic gradients could affect a
compositional change between more distant locations, and therefore can influence Bsim.
Greater spatial turnover of species may be due to a steeper gradient, that strongly influences
the distribution of species, especially in land bridge island systems because the underlying
spatial heterogeneity of the landscape prior to isolation and greater area (Tscharntke et al.,
2012). Moreover, given that the distance between islands has a significant effect upon Bsim,
but the effects of distance to the continent are not significant, we conclude that the majority of
colonization is determined by exchanges between the islands, indicating that the colonization
especially in oceanic islands is of a stepping stone type (Fattorini, 2010). However, our
analysis cannot distinguish between differential colonization and spatial heterogeneity.
Our data partially support the hypothesis that median body size have higher
alpha
diversity, due its high frequencies of island occurrences (Okie & Brown, 2009), because even
the smallest mammals (<32.5) are not significantly different from other quartiles, the
mammalian body size between 32.5 and 162 g have higher alpha diversity than mammals of
larger body sizes. Mammals within this body size range have low beta diversity in terms of
17
Bnes as Bsim, which may be a result of good dispersion capability, coupled with small
energetic requirements and generality in resource (Brown & Nicoletto, 1991; Whittaker &
Fernández-Palacios, 2007; Okie & Brown, 2009). The positive and significant effect of
maximum body size range with Bnes, together with the low alpha diversity of this size range,
indicates a differential extinction of the species, which may be an indirect effect of area
because, as has been reported by Marquet and Taper (1998) and confirmed by other studies
(Okie & Brown, 2009; Millien & Gonzalez, 2011) and as shown by our data (rz = 0.73, b =
0.49) there is a positive relationship between the maximum size and the area of the islands, as
a result of habitat requirements, trophic status and likelihood of extinction of species (Brown
et al., 1993; Marquet & Taper, 1998). The effects of body size distribution on species turnover
are contrary to those of βnes, in this case, the smaller species have high spatial turnover, which
may be associated to the existence of strong restrictions associated to metabolic requirements
such as space, food and other environmental conditions (Brown & Maurer, 1986; Marquet &
Taper, 1998; Okie & Brown, 2009). This can lead to high competitive exclusion exists within
this range of body size, that include modal size of all insular mammals studied (32.35g),
agreeing with the findings of Brown and Nicoletto (1991) for mammals in North America,
although its modal value is a little higher (45g), which added to the high dispersal capabilities
in relation to large mammals (Whittaker & Fernández-Palacios, 2007) can account for the
observed pattern.
Island type is considered as a strong determinant of species diversity, although, this
factor is a problematic variable. It is collinear with other variables (e. g. area, isolation) thus
limiting biological inference. It is likely that this is one of the reasons why we did not find a
significant effect of island type. On land-bridge islands, we expected greater effect of carrying
capacity because many assemblages represent ‘relaxation’ faunas as result of selective or
random extinction, but extinction may also play an important role in oceanic islands.
Assemblages on oceanic islands are likely to be shaped predominantly by colonization and
endemic speciation, determined by isolation, although in land-bridge islands the distance to
the mainland can affect the probability of recolonization and speciation of the species.
Therefore regardless of geological origin, large and remote islands have endemic species
associated with a high diversity (e.g Luzon and Mindanao in Philippines and Borneo and Java
18
in Sunda shelf), although these features are more common in oceanic islands, which may
explain the tendency to a positive effect of distance in this type of islands.
The results provided here describes the patterns of alpha and beta diversity for nonflying mammals in various archipelagos, which allows to establish whether factors influencing
diversity patterns are consistent across scales and geographical context. Alpha diversity is
primarily determined by a carrying capacity effect mediated by area and habitat, as seen in the
model neutral. While for beta diversity species body size is the factor that has a larger effect,
but it has a reverse effect in both beta components. According to our results beta diversity is
likely affected by differential extinction accounting for the importance of the nestednessresultant component, while mass effects and historical factors affect spatial turnover and are
mostly associated to distance effects. For these reasons, we found differences in the effect size
of the area and the distance between islands between the observed values and expected under a
neutral model.
The data analyzed in this study, have an intrinsic bias, because with the exception of
bats, generally native mammals are not a feature of most isolated oceanic islands (Whittaker &
Fernández-Palacios, 2007). Similarly, there is a bias with respect to the geographical location
of the islands studied. There are few studies in the southern hemisphere. However, bias
analysis indicate that there is little unexplained variance within the analysis performed and for
most of the correlations fail-safe number is relatively high. With regard to the strength of
effect sizes, we found that alpha diversity depends mainly on the islands intrinsic factors
(carrying capacity measures), while beta diversity has a strong relationship with body size. So
it would be interesting to examine in future studies whether beta diversity may be influenced
by other species traits such as trophic level and dispersal ability.
19
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Table Legends
Table 1. General characteristics of the studied archipelagos. It shows the mean and standard
deviation for each variable.
Table 2. Comparisons between the types of islands (Statistical Qb) for the relationship of
variables studied with alpha and beta diversity. It also presents mean effect size, strength (rz)
with 95% confidence intervals, fail-safe number and I2 index
Table 3. Comparisons between observed and expected alpha and beta diversity under neutral
model.
Table 4. Differences in mean effect size (95% confidence intervals) strength rz for observed
and expected alpha and beta diversity under neutral model.
Figure Legends
Figure 1. Geographical location of the islands considered in the study
Figure 2. Mean effect size (95% confidence intervals) strength rz (a,c) and slope b (b,d) for
alpha diversity. a-b, Effect sizes for carrying capacity measures: Area, total productivity (totalNPP), mean productivity, choros and number of habitats.c-d, Effect sizes for isolation
measures: distance to the mainland and mean inter islands distance.
Figure 3. Effect size (Hedge´s d) for alpha diversity in relation to body mass, considering its
distribution quartiles.
Figure 4. Mean effect size (95% confidence intervals) strength rz (a,c) and slope b (b,d) for
beta diversity (Bsor, black squares) and its components; nestedness-resultant (Bnes, triangles)
and turnover (Bsim, circles). a-b, Effect sizes for carrying capacity measures: Area, total
productivity (total-NPP), mean productivity, choros and number of habitats.c-d, Effect sizes
for isolation measures: distance to the mainland and mean inter islands distance.
Figure 5. Effect size (Hedge´s d) components of beta diversity, turnover (circles) and
nestedness-resultant (triangles) in relation to body mass, considering its distribution quartiles.
27
Supplementary material
Table S1. Mean body size for all species.
Table S1. Mean effect size, strength (rz) with 95% confidence intervals, heterogeneity
analysis, fail-safe number and I2 index for variables determinants of alpha and beta diversity
Table S2. Mean effect size, slope (b) with 95% confidence intervals, heterogeneity analysis,
fail-safe number and I2 index for variables determinants of alpha and beta diversity
28
Table 1.
29
Table 2.
Diversity
Variable
Area
Alpha
Number of habitats
Distance to
Mainland
Δ Area
Bnes
Δ Number of
habitats
Mean
Effect (Zr)
LCI
UCI
All
0.93
0.68
1.17
Landbridge
0.97
0.62
1.34
Oceanic
0.87
0.45
1.21
All
0.79
0.68
0.92
Landbridge
0.82
0.66
1.00
Oceanic
0.74
0.65
0.86
All
-0.27
-0.49
-0.05
Landbridge
-0.44
-0.69
-0.18
Oceanic
0.02
-0.29
0.25
All
0.30
0.16
0.47
Landbridge
0.30
0.07
0.55
Oceanic
0.30
0.23
0.36
All
0.36
0.21
0.53
Landbridge
0.40
0.16
0.59
Oceanic
0.30
0.18
0.57
Island type
30
Fail-safe
number
I2 (%)
18.85 1, 15 0.28
233.80
0.05
14.55 1, 15 0.56
539.50
-0.24
12.74 1, 15 0.69
20.70
-0.41
14.09 1, 15 0.59
65.70
-0.28
15.06 1, 15 0.52
90.10
-0.20
Qb
df
P
Table 3.
Alpha diversity
Archipelago
Observed Expected
Beta diversity (Bsor)
W
P
W
P
Adriatic
6.5
12.9
105
0.000
Observed Expected
0.3
0.3
2761
0.008
Alexander
7.0
48.6
299
< 0.001
0.5
0.2
34400
< 0.001
Phillipines
6.0
167.1
861
< 0.001
0.8
0.2
335500 < 0.001
Eolie
3.0
7.1
28
0.015
0.1
0.2
191
0.007
Napolitan
5.0
1.7
10
0.120
0.3
0.0
21
0.030
Ponziane
2.0
2.1
9
0.810
0.3
0.1
45
0.080
Sardinian
3.0
4.3
40
0.530
0.5
0.2
1453
< 0.001
Tremiti
2.5
1.6
10
0.120
0.3
0.0
20
0.063
Tuscan
4.0
4.7
11
1.000
0.4
0.1
217
< 0.001
Japan
8.5
110.4
78
0.001
0.7
0.1
2211
< 0.001
Kuril
5.5
36.1
36
0.008
0.8
0.2
404
< 0.001
Lake Huron
2.0
1.2
188
0.009
0.5
0.7
17090
< 0.001
Maine
4.0
2.0
240
0.001
0.5
0.8
26530
< 0.001
Mar de Cortez
2.0
7.9
507
< 0.001
1.0
0.9
118400 < 0.001
Sunda Shelf
18.0
231.8
99
0.002
0.7
0.4
Texas
16.0
8.2
17
0.218
0.4
Virginia
3.0
3.3
34
0.558
0.5
31
3198
< 0.001
0.2
75
0.422
0.4
722
0.020
Table 4.
Diversity Variable
Area
Total NPP
Choros
Alpha Mean NPP
Habitats number
Mainland distance
Inter-islands distance
Area
Mean NPP
Bsor
Habitats number
Mainland distance
Inter-islands distance
Effect size
0.94
0.88
0.96
0.00
0.79
-0.26
-0.25
0.17
0.05
0.24
0.15
0.23
Observed
LCI
UCI
0.68
1.18
0.63
1.12
0.74
1.20
-0.21 0.19
0.68
0.91
-0.47 -0.05
-0.45 -0.07
0.07
0.31
-0.02 0.13
0.13
0.40
0.09
0.21
0.08
0.34
32
Expected
Effect size
LCI
0.88
0.64
0.89
0.67
0.84
0.61
0.30
0.11
0.57
0.39
0.36
0.06
-0.53
-0.69
0.00
-0.05
0.18
0.10
0.14
0.03
0.13
0.04
0.57
0.42
UCI
Q
1.13 0.126
1.11 0.002
1.10 0.497
0.55 3.867
0.72 4.199
0.69 10.865
-0.41 4.498
0.07 2.791
0.30 1.671
0.30 0.994
0.28 0.043
0.73 11.104
P
0.723
0.967
0.481
0.050
0.050
0.001
0.034
0.048
0.196
0.319
0.835
0.001
Figure 1.
33
Figure 2.
34
Figure 3.
35
Figure 4.
36
Figure 5.
37
Table S1.
Species
Log mass Reference
Aeromys tephromelas
2.95
Smith et al 2003
Alces alces
5.55
Smith et al 2003
Ammospermophilus insularis
2.09
Geometric mean
Ammospermophilus leucurus
2.02
Smith et al 2003
Aonyx cinerea
3.58
Okie & Brown 2009
Apodemus argenteus
1.39
Geometric mean
Apodemus epimelas
1.39
Geometric mean
Apodemus flavicollis
1.39
Smith et al 2003
Apodemus peninsulae
1.39
Gage 1998
Apodemus speciosus
1.39
Geometric mean
Apodemus sylvaticus
1.33
Smith et al 2003
Apomys hylocetes
1.46
Geometric mean
Apomys insignis
1.63
Heaney et al 2010
Apomys littoralis
1.49
Smith et al 2003
Apomys microdon
1.55
Smith et al 2003
Arctictis binturong
3.83
Smith et al 2003
Arctogalidia trivirgata
3.35
Smith et al 2003
Atherurus macrourus
3.30
Smith et al 2003
Axis kuhlii
4.74
Smith et al 2003
Axis porcinus
4.52
Smith et al 2003
Barbastella barbastellus
0.90
Bassariscus astutus
3.05
Smith et al 2003
Smith et al 2003
Batomys hamiguitan
2.24
Balete et al 2008
Batomys salomonseni
2.27
Bullimus bagobus group
2.64
Smith et al 2003
Smith et al 2003
Callosciurus caniceps
2.41
Smith et al 2003
Callosciurus finlaysonii
2.44
Soligo & Martin 2006
Callosciurus melanogaster
2.44
Soligo & Martin 2006
Canis latrans
4.04
Brook & Bowman 2004
Canis lupus
4.23
Smith et al 2003
Capra hircus
Capricornis crispus
4.53
4.48
Smith et al 2003
Brook & Bowman 2004
Cervus alfredi
4.68
Whitehead, K. 1993.
Cervus mariannus
4.70
Smith et al 2003
Cervus nippon
4.68
Brook & Bowman 2004
Chaetodipus arenarius
1.36
Smith et al 2003
Chaetodipus baileyi
1.42
Smith et al 2003
Chaetodipus fallax
1.27
Smith et al 2003
Chaetodipus intermedius
1.22
Smith et al 2003
Chaetodipus penicillatus
1.18
Smith et al 2003
Chaetodipus spinatus
1.21
Chimarrogale platycephala
1.51
Smith et al 2003
Smith et al 2003
38
Species
Log mass Reference
Chiropodomys calamianensis
1.61
Soligo & Martin 2006
Chiropodomys gliroides
1.26
Smith et al 2003
Chiropodomys karlkoopmani
1.46
Soligo & Martin 2006
Clethrionomys rufocanus
1.57
Smith et al 2003
Clethrionomys rutilus
1.44
Smith et al 2003
Crateromys australis
2.87
Geometric mean
Crocidura beatus
1.02
Smith et al 2003
Crocidura beccarii
1.02
Okie & Brown 2009
Crocidura dsinezumi
1.00
Gage 1998
Crocidura fuliginosa
1.08
Smith et al 2003
Crocidura grandis
1.02
Geometric mean
Crocidura horsfieldii
1.02
Geometric mean
Crocidura leucodon
1.02
Smith et al 2003
Crocidura malayana
1.02
Okie & Brown 2009
Crocidura negrina
1.02
Geometric mean
Crocidura orii
1.02
Geometric mean
Crocidura pachyura
1.02
Geometric mean
Crocidura palawanensis
1.02
Geometric mean
Crocidura sicula
1.02
Sara et al 2010
Crocidura suaveolens
1.02
Smith et al 2003
Crocidura parvacauda
1.02
Geometric mean
Crunomys melanius
1.78
Heaney et al 2010
Cynocephalus volans
3.10
Smith et al 2003
Dama dama
4.69
Smith et al 2003
Dendrogale murina
1.70
Smith et al 2003
Dicrostonyx torquatus
1.93
Smith et al 2003
Diplothrix legata
2.78
Hughey 2000
Dipodomys merriami
1.62
Smith et al 2003
Dymecodon pilirostris
1.08
Kubota et al 1975
Echinosorex gymnurus
2.98
Okie & Brown 2009
Eliomys quercinus
2.06
Smith et al 2003
Eptesicus serotinus
1.36
Smith et al 2003
Erinaceus europaeus
2.89
Smith et al 2003
Erinaceus roumanicus
2.88
Geometric mean
Euroscaptor mizura
1.46
Nowak, 1999
Exilisciurus concinnus
1.49
Smith et al 2003
Exilisciurus exilis
1.28
Okie & Brown 2009
Prionailurus bengalensis
3.52
Okie & Brown 2009
Galeopterus vartiegatus
3.00
Okie & Brown 2009
Glirulus japonicus
1.43
Soligo & Martin 2006
Glis glis
2.10
Gage 1998
Gulo gulo
4.16
Smith et al 2003
Haeromys margarettae
1.10
Okie & Brown 2009
Helarctos malayanus
4.58
Brook & Bowman 2004
Hemigalus derbyanus
3.18
Smith et al 2003
Herpestes brachyurus
3.15
Smith et al 2003
39
Species
Log mass Reference
Herpestes javanicus
2.88
Hylobates klossii
3.76
Okie & Brown 2009
Smith et al 2003
Hylomys suillus
1.81
Okie & Brown 2009
Hylopetes lepidus
1.70
Okie & Brown 2009
Hylopetes nigripes
2.73
Soligo & Martin 2006
Hylopetes sipora
1.95
Soligo & Martin 2006
Hylopetes spadiceus
1.70
Okie & Brown 2009
Hypsugo savii
0.70
Lehotska & Lhotsky 2006
Hystrix brachyura
3.90
Smith et al 2003
Hystrix cristata
4.10
Smith et al 2003
Hystrix javanica
4.36
Okie & Brown 2009
Hystrix pumila
3.44
Smith et al 2003
Iomys horsfieldi
2.08
Smith et al 2003
Iomys sipora
1.95
Soligo & Martin 2006
Lariscus insignis
2.30
Smith et al 2003
Lariscus obscurus
2.29
Geometric mean
Lemmus sibiricus
1.72
Smith et al 2003
Lenothrix canus
2.08
Okie & Brown 2009
Leopoldamys edwardsi
2.48
Okie & Brown 2009
Leopoldamys sabanus
2.54
Okie & Brown 2009
Leopoldamys siporanus
2.51
Geometric mean
Lepus alleni
3.57
Smith et al 2003
Lepus brachyurus
3.40
Geometric mean
Lepus californicus
3.40
Smith et al 2003
Lepus capensis
3.40
Smith et al 2003
Lepus europaeus
3.40
Smith et al 2003
Lepus insularis
3.40
Geometric mean
Lepus timidus
3.48
Smith et al 2003
Limnomys sibuanus
1.81
Heaney et al 2010
Lutra lutra
3.64
Smith et al 2003
Lutra sumatrana
3.74
Brook & Bowman 2004
Macaca fascicularis
3.51
Okie & Brown 2009
Macaca fuscata
4.00
Brook & Bowman 2004
Manis javanica
3.71
Smith et al 2003
Marmota camtschatica
3.78
Macdonald 2001
Martes flavigula
3.07
Smith et al 2003
Martes martes
3.11
Smith et al 2003
Martes melampus
3.00
Smith et al 2003
Martes zibellina
3.05
Smith et al 2003
Maxomys pagensis
1.97
Geometric mean
Maxomys panglima
2.33
Geometric mean
Maxomys rajah
2.18
Okie & Brown 2009
Maxomys surifer
2.14
Smith et al 2003
Maxomys whiteheadi
1.73
Okie & Brown 2009
Meles meles
4.00
Brook & Bowman 2004
Menetes berdmorei
2.29
Nowak, 1999
40
Species
Log mass Reference
Microtus montebelli
1.60
Geometric mean
Microtus oeconomus
1.60
Smith et al 2003
Microtus sachalinensis
1.60
Geometric mean
Miniopterus schreibersi
1.06
Smith et al 2003
Mogera tokudae
2.11
IUCN 1995
Mogera wogura
2.05
IUCN 1995
Mogera wogura robusta
2.05
IUCN 1995
Muntiacus muntjak
4.15
Okie & Brown 2009
Mus caroli
1.10
Geometric mean
Mus castaneus
1.10
Geometric mean
Mus musculus
1.18
Smith et al 2003
Mustela erminea
1.85
Smith et al 2003
Mustela nivalis
1.67
Smith et al 2003
Mydaus javanensis
3.40
Smith et al 2003
Mydaus marchei
3.40
Nowak, 1999
Myodes andersoni
1.39
Geometric mean
Myodes rufocanus
1.39
Pearson -1962
Myodes rutilis
1.39
Batzli, G. 1999.
Myodes sikotanensis
1.39
Geometric mean
Myodes smithii
1.39
Geometric mean
Myopus schisticolor
1.40
Smith et al 2003
Myotis myotis
1.39
Smith et al 2003
Nannosciurus melanotis
1.16
Hayssen 2008
Nasalis larvatus
3.95
Smith et al 2003
Neotoma albigula
2.31
Smith et al 2003
Neotoma anthonyi
2.29
Smith et al 2003
Neotoma bryanti
2.26
Smith et al 2003
Neotoma bunkeri
2.57
Smith et al 2003
Neotoma lepida
2.21
Smith et al 2003
Neotoma martinensis
2.39
Nyctereutes procyonoides
3.61
Smith et al 2003
Smith et al 2003
Niviventer bukit
1.88
Gage 1998
Niviventer cremoriventer
1.82
Smith et al 2003
Niviventer lepturus
1.93
Okie & Brown 2009
Notiosorex crawfordi
0.64
Smith et al 2003
Nyctalus lasiopterus
1.70
Smith et al 2003
Nyctalus leisleri
1.12
Smith et al 2003
Nycticebus coucang
2.62
Smith et al 2003
Ochotona hyperborea
2.23
Geometric mean
Odocoileus hemionus
4.72
Brook & Bowman 2004
Oryctolagus cuniculus
3.20
Smith et al 2003
Ovis canadensis
4.87
Smith et al 2003
Ovis orientalis
4.51
Brook & Bowman 2004
Paguma larvata
3.63
Smith et al 2003
Palawanomys furvus
2.01
Heaney et al 2010
Panthera pardus
4.66
Okie & Brown 2009
41
Species
Log mass Reference
Panthera tigris
5.16
Brook & Bowman 2004
Paradoxurus hermaphroditus
3.51
Okie & Brown 2009
Pentalagus furnessi
3.40
Nowak, 1999
Peromyscus boylii
1.33
Smith et al 2003
Peromyscus caniceps
1.51
Geometric mean
Peromyscus crinitus
1.51
Smith et al 2003
Peromyscus dickeyi
1.51
Geometric mean
Peromyscus eremicus
1.51
Smith et al 2003
Peromyscus eva
1.51
Smith et al 2003
Peromyscus guardia
1.51
Geometric mean
Peromyscus intermedius
1.51
Geometric mean
Peromyscus interparietalus
1.51
Geometric mean
Peromyscus maniculatus
1.51
Smith et al 2003
Peromyscus pembertoni
1.51
Geometric mean
Peromyscus pseudocrinitus
1.51
Geometric mean
Peromyscus segugis
1.51
Geometric mean
Peromyscus slevini
1.51
Geometric mean
Peromyscus stephani
1.51
Geometric mean
Petaurista elegans
2.98
Okie & Brown 2009
Petaurista leucogenys
3.07
Hayssen 2008
Petaurista petaurista
3.13
Okie & Brown 2009
Petaurista philippensis
3.22
Smith et al 2003
Petinomys crinitus
3.05
Soligo & Martin 2006
Petinomys genibarbis
2.04
Smith et al 2003
Petinomys hageni
1.74
Okie & Brown 2009
Petinomys vordermanni
1.61
Pipistrellus kuhlii
0.77
Okie & Brown 2009
Smith et al 2003
Pipistrellus nathusii
0.86
Smith et al 2003
Pipistrellus pipistrellus
0.76
Smith et al 2003
Pithecheir melanurus
2.03
Okie & Brown 2009
Plecotus auritus
0.89
Smith et al 2003
Plecotus austriacus
0.86
Smith et al 2003
Podogymnura truei
1.80
Heaney et al 2010
Presbytis melalophos
3.78
Brook & Bowman 2004
Presbytis potenziani
3.81
Smith et al 2003
Presbytis rubicunda
3.80
Okie & Brown 2009
Prionailurus viverrinus
3.89
Smith et al 2003
Prionodon linsang
2.85
Okie & Brown 2009
Pteromys momonga
2.11
Geometric mean
Pteromys volans
2.11
Smith et al 2003
Pteromyscus pulverulentus
2.43
Smith et al 2003
Ptilocercus lowii
1.63
Smith et al 2003
Rangifer tarandus
4.79
Brook & Bowman 2004
Rattus
2.17
Geometric mean
Rattus adustus
2.17
Geometric mean
Rattus anandalei
2.17
Geometric mean
42
Species
Log mass Reference
Rattus enganus
2.17
Geometric mean
Rattus everetti group
2.17
Gage 1998
Rattus exulans
2.17
Smith et al 2003
Rattus lugens
2.17
Geometric mean
Rattus norvegicus
2.17
Smith et al 2003
Rattus rattus
2.17
Smith et al 2003
Rattus remotus
2.17
Geometric mean
Rattus tiomanicus
2.11
Okie & Brown 2009
Ratufa affinis
3.05
Smith et al 2003
Ratufa bicolor
3.31
Smith et al 2003
Rhinolophus euryale
0.91
Smith et al 2003
Rhinolophus ferrumequinum
1.32
Smith et al 2003
Rhinolophus hipposideros
0.67
Smith et al 2003
Rhinosciurus laticaudatus
2.34
Smith et al 2003
Rhizomys sumatrensis
2.40
Okie & Brown 2009
Sciurus lis
2.37
Hayssen 2008
Sciurus vulgaris
2.52
Smith et al 2003
Simias concolor
3.90
Burton, F. 1995.
Sorex shinto
0.78
Gage 1998
Sorex caecutiens
0.73
Smith et al 2003
Sorex camtschatica
0.78
Geometric mean
Sorex daphaenodon
0.78
Geometric mean
Sorex gracillimus
0.78
Geometric mean
Sorex gracillumus
0.78
Geometric mean
Sorex hosonoi
0.78
Geometric mean
Sorex isodon
0.78
Smith et al 2003
Sorex lecuogaster
0.78
Geometric mean
Sorex minutissimus
0.78
Smith et al 2003
Sorex suaveolens
0.78
Geometric mean
Sorex unguiculatus
0.78
Geometric mean
Spermophilus parryii
2.88
Smith et al 2003
Spermophilus tereticaudus
2.19
Smith et al 2003
Spermophilus variegatus
2.84
Smith et al 2003
Suncus etruscus
0.26
Smith et al 2003
Suncus murinus
1.60
Smith et al 2003
Suncus palawanensis
0.74
Geometric mean
Sundamys muelleri
2.34
Smith et al 2003
Sundasciurus hoogstraali
2.41
Geometric mean
Sundasciurus lowii
1.93
Smith et al 2003
Sundasciurus moellendorffi
2.28
Hayssen 2008
Sundasciurus philippinensis
2.39
Hayssen 2008
Sundasciurus rabori
2.21
Hayssen 2008
Sundasciurus steerii
2.37
Hayssen 2008
Sundasciurus tenuis
1.88
Okie & Brown 2009
Sus barbatus
4.99
Okie & Brown 2009
Sus scrofa
4.93
Smith et al 2003
43
Species
Log mass Reference
Sus verrucosus
4.91
Okie & Brown 2009
Sylvilagus bachmani
2.81
Smith et al 2003
Sylvilagus mansuetus
3.04
Geometric mean
Tadarida teniotis
1.43
Smith et al 2003
Talpa europaea
1.89
Smith et al 2003
Tamias sibiricus
1.93
Smith et al 2003
Tarsius bancanus
1.89
Smith et al 2003
Tarsius syrichta
2.02
Smith et al 2003
Tarsomys apoensis
1.84
Heaney et al 2010
Thomomys bottae
2.06
Smith et al 2003
Tokudaia muenninki
2.25
Sutou et al 2001.
Tokudaia osimensis
2.11
Sutou et al 2001.
Trachypithecus cristatus
3.92
Smith et al 2003
Trachypithecus obscurus
3.81
Okie & Brown 2009
Tragulus javanicus
3.35
Smith et al 2003
Tragulus napu
3.60
Smith et al 2003
Tupaia belangeri
2.30
Smith et al 2003
Tupaia glis
2.20
Smith et al 2003
Tupaia gracilis
1.87
Smith et al 2003
Tupaia javanica
2.02
Okie & Brown 2009
Tupaia minor
1.77
Smith et al 2003
Tupaia palawanensis
2.16
Geometric mean
Tupaia splendidula
2.20
Okie & Brown 2009
Tupaia tana
2.30
Okie & Brown 2009
Urocyon cinereoargenteus
3.58
Smith et al 2003
Urogale everetti
2.54
Smith et al 2003
Urotrichus talpoides
1.65
Smith et al 2003
Ursus arctos
5.14
Smith et al 2003
Ursus thibetanus
4.89
Smith et al 2003
Viverra megaspila
3.95
Brook & Bowman 2004
Viverra tangalunga
3.87
Smith et al 2003
Viverra zibetha
3.94
Brook & Bowman 2004
Viverricula indica
3.43
Smith et al 2003
Vulpes vulpes
3.77
Smith et al 2003
44
Table S2.
Mean
Diversity
Bsor
Bsim
Bnes
Variable
Fail-safe
Effect (Zr)
LCI
UCI
Qe
P
number
I2
Area
0.93
0.68
1.17
18.85
0.28
233.80
0.05
Total NPP
0.87
0.61
1.12
18.25
0.31
204.00
0.01
Choros
0.96
0.70
1.17
18.48
0.30
261.70
0.03
Mean NPP
0.00
-0.21
0.21
13.81
0.61
0.00
-0.30
Number of Habitats
0.79
0.68
0.92
14.55
0.56
539.50
-0.24
Distance to mainland
-0.27
-0.49
-0.05
12.74
0.69
6.60
-0.41
Inter-islands distance
-0.25
-0.44
-0.06
17.39
0.36
14.50
-0.04
ΔArea
0.17
0.07
0.30
9.61
0.89
15.60
-0.87
ΔMean NPP
0.05
-0.03
0.13
5.18
0.99
0.00
-2.47
ΔNumber of Habitats
0.24
0.12
0.39
11.64
0.77
36.50
-0.55
ΔDistance to mainland
0.15
0.09
0.21
3.94
1.00
7.70
-3.57
Inter-islands distance
0.23
0.10
0.34
12.26
0.73
35.50
-0.47
ΔArea
-0.09
-0.21
0.04
12.41
0.72
0.00
-0.45
ΔMean NPP
0.04
-0.03
0.09
3.74
1.00
0.00
-3.81
ΔNumber of Habitats
-0.07
-0.16
0.02
7.65
0.96
0.00
-1.35
ΔDistance to mainland
0.04
-0.04
0.11
6.70
0.98
0.00
-1.69
Inter-islands distance
0.25
0.13
0.36
11.48
0.78
39.30
-0.57
ΔArea
0.30
0.16
0.47
14.09
0.59
62.00
-0.28
ΔMean NPP
-0.01
-0.06
0.07
4.11
1.00
0.00
-3.38
ΔNumber of Habitats
0.36
0.21
0.53
15.06
0.52
90.10
-0.20
ΔDistance to mainland
0.10
0.00
0.23
8.05
0.95
0.00
-1.24
Inter-islands distance
-0.10
-0.22
0.02
14.21
0.58
0.00
-0.27
45
Table S2
Mean
Diversity
Variable
Effect (b)
LCI
UCI
Qe
P
number
I2
Area
0.18
0.11
0.26
7.21
0.97
49.20
-1.50
Total NPP
0.17
0.10
0.25
7.01
0.97
40.90
-1.57
Choros
0.18
0.11
0.26
7.06
0.97
52.00
-1.55
-0.002
-0.04
0.04
2.39
1.00
0
-6.52
Number of habitats
0.15
0.09
0.21
4.15
1.00
28.10
-3.34
Distance to mainland
-0.05
-0.10
-0.01
2.32
1.00
0
-6.76
Inter-islands distance
-0.05
-0.09
0.00
3.24
1.00
0
-4.56
ΔArea
0.03
0.01
0.05
1.83
1.00
0
-8.82
ΔMean NPP
0.01
-0.01
0.02
0.90
1.00
0
-18.95
ΔNumber of Habitats
0.04
0.02
0.07
2.11
1.00
0
-7.53
ΔDistance to mainland
0.02
0.01
0.04
1.15
1.00
0
-14.71
Inter-islands distance
0.04
0.01
0.06
2.91
1.00
0
-5.18
ΔArea
-0.01
-0.04
0.01
2.43
1.00
0
-6.41
ΔMean NPP
0.01
-0.01
0.01
0.75
1.00
0
-23.08
ΔNumber of Habitats
-0.01
-0.03
0.00
1.76
1.00
0
-9.23
ΔDistance to mainland
0.01
0.00
0.02
1.25
1.00
0
-13.45
Inter-islands distance
0.03
0.01
0.07
4.31
1.00
0
-3.18
ΔArea
0.03
0.01
0.08
4.15
1.00
0
-3.34
-0.001
-0.01
0.01
0.76
1.00
0
-22.83
ΔNumber of Habitats
0.03
0.01
0.09
5.02
1.00
1.10
-2.59
ΔDistance to mainland
0.01
0.001
0.04
1.13
1.00
0
-14.94
Inter-islands distance
-0.01
-0.03
0.01
2.83
1.00
0
-5.37
Mean NPP
Bsor
Bsim
ΔMean NPP
Bnes
Fail-safe
46
CAPÍTULO 2
SPECIES DIVERSITY UNDER A NEUTRAL COLONIZATION RULE
Abstract
Metacommunity theory provides a conceptual foundation for understanding the processes
that determine which and how many species live in spatially structured communities. In this
framework, neutral theory has emerged as a useful approach to link spatial biodiversity
patterns to dispersal, speciation and ecological drift. Here, we advance the spatially explicit
neutral model by representing the metacommunity as a network of smaller communities
colonized from a continental species pool. We use this model to evaluate how the basic
properties of a metacommunity – connectivity and size– determine overall metacommunity
γ-diversity, and how that is partitioned into α- and β-components and under what conditions
observed patterns of mammalian diversity in archipelagoes fit the neutral model. We found
that spatial configuration of island within archipelagoes (network topology) can increase γdiversity through the β-component. In general terms, the neutral model explains the
observed diversity patterns in qualitative rather than quantitative terms, our results indicate
that non-neutral processes reduce species richness present in metacommunities and increase
the differentiation between local communities (β- diversity). Further, we found that αdominated metacommunities usually are of small size.
47
INTRODUCTION
Islands have played a central role in ecology and biogeography both theoretically and
experimentally (Whittaker & Fernández-Palacios, 2007). No island-inspired ecological
theory has had more impact than MacArthur and Wilson´s equilibrium theory of island
biogeography (MacArthur & Wilson, 1963; Losos & Ricklefs, 2009), which predicts
species richness through colonization and extinction processes under a neutral model at the
species-level.
The unified neutral theory of biodiversity and biogeography is based on equilibrium
theory of island biogeography (Hubbell, 2001). It is also an unabashedly neutral theory, but
at individual-level. This means that individuals are essentially identical in their per capita
probabilities of giving birth, death, migration, and speciation (Hubbell, 2001). Because the
neutral theory proposes that the local community receives immigrants from a species pool,
this theory has a high potential to be applied in island systems (Hubbell, 2009).
The neutral theory is one of the four general frameworks of metacommunity theory
(Leibold et al., 2004). The four canonical metacommunity models: neutral, patch dynamics,
species sorting and mass effects, make different assumptions regarding how species
respond to environmental and spatial gradients. These models differ in the relative
importance
of
three
ecological
processes:
environmental
influences
(termed
‘‘environmental filtering’’), dispersal among patches, and species interactions (Biswas &
Wagner, 2012). In all, the neutral model is the simplest one, assuming that communities
are structured only by dispersion and stochastic processes. In this regard, neutral theory is
thus a good starting point for an explanation of species richness patterns (Hubbell, 2001),
with which one can test whether the effects of niche differentiation penetrate the summary
statistics being studied, such as species diversity patterns (Rosindell et al., 2011).
Neutral metacommunity models can be classified as either spatially implicit or
spatially explicit (McGill et al., 2006). Although spatially explicit models have been
explored with stochastic simulations and analytic methods (Bell, 2000; Hubbell, 2001;
Chave & Leigh, 2002; Chave et al., 2002; McGill et al., 2005; Rosindell & Cornell, 2007),
few studies have taken into account the internal structure of metacommunities that
determine spatially explicit patterns in richness (but see Economo & Keitt, 2008).
48
Moreover, colonization driven neutral models have focused on the dynamic between an
island and the mainland (e.g, Conlisk et al., 2010), without considering the effect of the
other islands within archipelagos; although the within archipelago effect was recognized by
MacArthur and Wilson (1963, 1967) when dealing with stepping stone colonization of
islands. Similarly, it has become prominent in spatially realistic models of metapopulations
(Hanski & Ovaskainen, 2000).
In this contribution we extend the model proposed by Conlisk et al (2010) to predict
the patterns of diversity within and among islands in archipelagos (metacommunities) with
different spatial structures and different continental species pools. We investigate how the
basic components of the model (i.e. connectivity, and metacommunity size) determine
overall metacommunity γ-diversity and its components α-diversity and β-diversity (Lande,
1996) and under which domain our model can effectively fit the data from a non-neutral
world.
METHODS
Model
Previous work
Following Conlisk et al. (2010), we start by focusing in an island with room for J ≥2
individuals, which is located near a large mainland. Individuals on the island may have
emigrated from the mainland, or may be the offspring of island parents. Let us further
assume the existence of S species and that on the mainland, species coexist in unchanging
proportions P1,…,Ps . On the island, the species coexist in variable proportion
where
represents the current abundance of species k, thus ∑
∑
,
denotes the total
island abundance. The vector N1,…,Ns will change as colonization proceeds. Finally, let us
assume that colonization does not depend on the age, origin, or other detailed characteristic
of individuals, i.e., neutrality assumption (Hubbell, 2001)
Following Conlisk et al (2010) we assume that the island is colonized one
individual at a time, and that there are no deaths. A stochastic colonization rule will
determine the species i of the next colonist, given the current state N1,N2,…,Ns . Once the
colonist is determined, the vector N1,N2,…,Ns will be updated by adding one to abundance
49
Nk. Starting from an initial condition of zero abundance, this colonization rule will be
repeatedly applied until the island reaches saturation at ∑
.
To understand how this rule is implemented let us denote by h the probability that
the next colonist is an immigrant offspring of a mainland parent, and thus let 1-h be the
probability that the next colonist is an offspring of an existing colonist. The probability that
the next colonist is an immigrant of species k from the mainland is then the product of h
and Pk. Similarly the probability that the next colonist is an island offspring of species k is
the product of 1-h and
∑
∑
. That is, provided that the island is not saturated (so long as
).
We want to estimate (at every time step) the probability that the next colonist will
be of species k, given current abundances, that is:
(
|
)
(
)∑
(1)
The first term corresponds to the effect of the mainland and the second term corresponds to
the effect of the island (birth process). The immigration probability (h) is a variable
function determined by
(
(
) (
)
)∑
(2)
where m is a fixed parameter obeying 0 < m < 1 (akin to the immigration parameter in
Hubbell´s model). Notice that at the beginning of the colonization process the island
receiving colonists is empty, implying that ∑
. Under this circumstance h=1 in
eqn.2 as it should. As colonization proceeds h steadily declines until h=m, when ∑
, and only one individual is required to saturate the island at the final step of the
colonization process. As noticed by Conslick
et al. (2010), m corresponds to the
immigration probability in Hubbell´s model when only one empty spot is to be filled. In
eqn (2) it is apparent that the mainland sends migrants at a constant rate while the island
sends propagules in proportion to proportional to the number of islanders. Hence, the ratio
⁄(
) is proportional to ⁄∑
∑
. That is,
∑
∑
50
(3)
where C corresponds to the rate of migrants from the mainland. As mentioned, it follows
directly from the above expression that when t = 0 (initial state) h = 1. However, for later
times t the function h need to take into account the effect of the islanders. For that reason,
one could assume that the effect of the mainland when t goes to infinity tends to decrease
until the value h = m (Hubbell’s immigration parameter), and since ∑
( where J is
the maximum island capacity, proportional to the area) then we obtain that:
(
(
)
)
which implies the final expression
(
(
)
)
∑
(
(
) (
)
(4)
)∑
Using the last equation to eliminate h from the next colonist probability we obtain that
(the next colonist is of species |current
)
(
(
)
(
) (
)
)∑
J repetitions of this rule yield a colonization outcome. Colonization can be easily simulated
using the final equation with parameters number of individuals (J), immigration probability
(m) and proportion of the species on the mainland (Pk’s).
Extensions
In our model we now consider a mainland and n islands connected by an adjacency matrix
A which is fixed. In graph theory, the adjacency matrix is a zero-one symmetric matrix
where
if there exists an edge between the islands i and j and 0 otherwise. In this
extension we consider the following variables and parameters: an archipelago with S
species
corresponds to the abundance of the species k on island i. Each species can be
represented by a vector of abundances, ⃗⃗⃗⃗
⃗⃗⃗⃗ each of length N and where each value
represents the abundance of species k in island i. As before, we will assume that on the
mainland, species coexist in unchanging proportions P1,…,Ps.. To implement the
colonization rule in this context we need to define as h the probability that the next colonist
is an immigrant offspring of a mainland parent, hi,i as the probability that the next colonist
51
is an offspring of an existing colonist in island i and hi,j as the probability that the next
colonist is an offspring of an individual in island j, which is in the neighborhood of i.
In this context, we will obtain two abundances distributions: one will be a local
distribution (one for each island) and the other will be a joint metacommunity distribution
for the archipelago or ensemble of islands. As before we want to estimate the probability
for the next immigrant arriving to the system, which will depend on the mainland and the
island distribution of abundances, that is,
(the next colonist is of species |current ⃗⃗⃗⃗
⃗⃗⃗⃗ )
Using the Bayes formula for total probabilities we have:
(the next colonist is of species |current ⃗⃗⃗⃗
∑ (
⃗⃗⃗⃗
|
⃗⃗⃗⃗ )
⃗⃗⃗⃗
) (
In the last expression, the probability choosing island i can be considered from an
uniform distribution, in which case it will be 1/n, or from any other distribution for that
matter, as inversely proportional to the distance to the mainland. For that reason, we will be
interested on the probability of the next colonist given the current state on the island i
(fixed). Assuming as Conlisk et al (2010), that each island is colonized one individual at a
time, and that there are no deaths and that h is constant we have that:
(the next colonist is of species |current ⃗⃗⃗⃗
∑
∑
⃗⃗⃗⃗ on island )
∑
( )
The first term corresponds to the probability that the next colonist is an immigrant of
species k from the mainland, the second term corresponds to the probability that the next
colonist is the offspring of a parent of species k already in island i and the third term
corresponds to the effect of the neighborhood, that is the probability that the next
immigrant is the offspring a parent of species k in island j, which is connected to i (i.e.
ai,j=1) . Eqn (5) is subjected to the boundary condition:
52
)( )
∑
( )
Again, we need to compute an expression for the variables
. In this case, we
extend the results of Conlisk et al. (2010) in the following way. In our case, the ratio
∑
will be inversely proportional to the total number of islanders, that is,
∑
∑
∑
∑
But, from the boundary condition we can simplify the above expression and obtain
that
∑
∑
∑
and solving for the constant C we get:
∑
∑
( )
∑
Assuming that the colonization of the archipelago starts for all islands at the same
time, then at time t = 0 (initial state) the function h needs to be 1 because the immigration
occurs only from the mainland, which is satisfied by eqn. (7). Further, if we assume that
each island is able to sustain a maximum number J of individuals, then when ∑
, and only one individual is required to saturate a given island at the final step of the
colonization process, eqn (7) will become equal to m the immigration probability in
Hubbell´s model, that is
(
)
∑
(
( )
)
implying that
[(
)
∑
(
)]
Finally, the immigration probability h is a variable determined by
53
[(
[(
)
∑
(
)]
(
∑
)
(
)]
In the same way, we can obtain the value for the other
)
∑
(
∑
]
expressions
)∑
(
[(
∑
)[∑
)]
(
∑
)[∑
∑
]
and
)∑
(
∑
[(
)
∑
(
)]
∑
(
∑
)[∑
∑
]
Using the last expressions to eliminate the h variables from eqn. (5) yields the colonization
rule
(the next colonist is of species |current ⃗⃗⃗⃗
[(
[(
∑
)
)
∑
(
)]
(
)]
(
⃗⃗⃗⃗ on island )
)
(
)[∑
)∑
(
∑
∑
]
( )
In this case, colonization can be easily simulated using the final equation with parameters:
number of individuals (J), immigration probability (m), proportion of the species on the
mainland (Pk’s), number of islands (n), probability choosing islands (Pi`s) and adjacency
matrix (A).
Simulations and Model performance
To simulate Hubbell’s neutral colonization model with dispersal limitation, first we
evaluate the performance of the model using a toy system. We consider the effect of the
migration rate on diversity patterns in two extreme network structures, a linear chain of
islands (chain topology) and a network where all the islands are connected to each other
(island topology). Diversity levels were calculated for networks of 14 local islands,
considering all the islands equal in terms of capacity (equal area and number of individuals,
J= 19228) and probability of selection (Pis= 0.074).
Metacommunity size is determined by the number of individuals and is expected
that it will directly control the equilibrium diversity under neutrality. To determine this
54
relationship, we increase the number of individuals per island, holding constant
immigration probability (m= 10-6), the number of islands (14) and network topology (chain
or island). The number of islands, is another factor that can alter patterns of diversity,
fragmentation per se (i.e. altered spatial arrangement of remaining habitat) may increase
gamma diversity through its effect on the beta component (Tscharntke et al., 2012). To
measure the effect of fragmentation per se, we maintained constant both the total number of
individuals of the archipelago as the rest of the parameters and increase the number of
islands.
To determine the effect of network topology on diversity patterns, we hold
migration probability and number of links constant while changing the architecture of the
network. We consider a linear chain topology, a randomly connected topology, a star
topology and a completely connected topology. We considered networks with the same
characteristics as those used to measure the effect of migration; the migration rate was set
to values between 0.1 and 10-6. We measure topological differences through the diameter;
which is the minimum distance between the furthest nodes (Albert & Barabasi 2002). We
measure the effect of the topology through a linear regression between the logarithm of the
diameter and the logarithm of α- and β-diversity.
Neutral diversity in real archipelagos
The model described above serves as a null model against which to compare empirical
patterns in abundance and diversity. In particular, we are interested in comparing empirical
patterns in α, β and γ diversity observed in 21 archipelagos with different spatial structure
and different species pool. For each archipelago we calculated four parameters: Carrying
capacity (J), the probability of choosing species k (
), the probabilities of choosing island i
( ) and network structure or the adjacency matrix connecting the islands (A). Carrying
capacity represents the total number of individuals that can colonize an island and we
considered it to be proportional to area ( J µ A1 ) as usually assumed in island biogeography
(see MacArthur & Wilson, 1963, 1967). To identify the mammal species belonging to the
species pool associated to each archipelago, using ArcGIS 10 we counted and identified all
species whose polygons of geographic distributions (Taken from Grenyer et al., 2006),
overlapped a buffer of 1000 km centered at the archipelago under analysis. We calculate
55
the probability of selecting a species of mainland ( ), dividing the density of each species
k(
) by the total density of species (∑
). Because we have no density data for each
species, we estimated from the body size (
, (Damuth, 1981)). We estimate the
probability of choosing an island ( ) as function of the minimum distance to the mainland
( ) normalized by the largest minimum distance (
),
.The network
formed by the islands within the archipelago that exchange individuals was estimated in the
form of an adjacency matrix (A) estimated by computing the minimum spanning tree
(MST, the shortest length tree that connects all islands) based on the minimum
geographical distances (Urban & Keitt, 2001) between them. For each archipelago we ran
the model 1000 times, thus obtaining an average value for γ-diversity and α and β
components (we use additive partition methods). We compared simulations results directly
with field data through a paired t-test to see if they are quantitatively equal and with a
Spearman correlation test to determine if they behave similarly. We also examined whether
deviations of the empirical data from the neutral model (empirical data minus simulated
data) are affected by the total area of the archipelago and network topology (diameter).
RESULTS
Model Performance
We find that γ-diversity increased monotonically with increasing migration rate (m). In
general the mayor contribution to γ-diversity was made by the a -component. The
contribution of the β component was more important at intermediate migration rates and for
graphs with low connectivity (chain topology) (Fig 1). Regardless of the type of network
topology, the average α diversity increases with increasing migration rate and beta diversity
increases to a maximum when the migration rate is equal to 10-4, to diminish afterwards.
In our spatially explicit model, the relationship between metacommunity size and g
-diversity is linear the same as the relationship with α and β components (R2= 0.99,
P<0.001 in all cases, Fig. 2). The effect of size on gamma diversity does not vary between
network topologies. However, β-diversity increases and α-diversity decreases in linear
network topology as compared to the situation in the island topology. The effect of
fragmentation per se (number of islands) on biodiversity depends on the network topology
56
(Fig 3). When all of the islands are connected to each other (i.e. in the island graph),
gamma diversity does not change as the number of islands increases (slope = -0.02, P =
0.22), since the effects on alpha and beta components are similar in magnitude but opposite
in sign (α-slope = -0.21, β-slope = 0.2, P <0.001). When the islands are connected as a
chain graph α-diversity steadily decreases (slope = -0.47, P <0.001) while β -diversity does
the opposite (slope = 0.72, P <0.001). Interestingly there is a cross-over effect such that
when the archipelago is composed of few islands (ca. 15 in Figure 3) the α-components is
more important in determining γ-diversity, but for systems with a larger number of islands
the β -component becomes more important causing a significant increase in gamma
diversity (slope = 0.25, P <0.001).
With respect to the effect of network topology, we find that that networks with
longer diameters have lower alpha diversity (R2= 0.76, P=0.05) and larger beta diversity
(R2= 0.89, P=0.01) especially when the migration rate is high (m=0.1), as with the real data
(Fig 7d). When the migration rate is very low (m= 10-6), the effect on α-diversity is not
significant (P = 0.28) and is marginal on β-diversity (P = 0.05) (Fig 4).
Neutral diversity in real archipelagoes
Above a threshold in total area of the archipelago and diameter our model overestimates
both α- and γ-diversity and underestimate β-diversity (Figure 5). In quantitative terms, there
are significant differences between observed and predicted values for both α-diversity (t=
2.25, P= 0.04) and β-diversity (t= -2.45, P= 0.02) and marginally so for γ-diversity (t= 1.82,
P= 0.08). However, there is a high and significant correlation between observed and
predicted values for all diversity components, ranging from 0.83 (P< 0.001) for β-diversity
to 0.6 for α-diversity (P= 0.003), with an intermediate value for γ-diversity (rs= 0.75, P<
0.001).
In the neutral model as well as in the empirical data α-, β- and γ-diversity exhibit a
power law relationship with total area of the archipelago (Fig 7a and 7b). However, under
the neutral model, α- and β-diversity increase at the same rate with the size of the
metacommunity (t = 0.08, P =0.93), whereas for the observed data, β-diversity has a higher
slope than alpha diversity (t = 2.08, P =0.04), which lead to a cross-over. Similarly, under
57
the neutral model, there is always a dominance of the α-diversity component while for the
observed data, dominance changes according to the total area of the archipelago; for in
small archipelagoes there is dominance by the α- diversity component but for large ones the
β-diversity component dominates.
For α- and γ-diversity, the deviations of empirical data from simulated results are
kept close to zero for metacommunities with an area less than 10,000 km 2 with fit (R2) of
91% and 84% respectively, after this point neutral model values are much greater than the
observed (Fig 5 and Fig 7a). For β-diversity, the inflection point increases to 100,000 km2,
but with a smaller fit (R2 = 0.70) and for larger metacommunities the observed values are
greater than predicted (Fig 5 and Fig7a)
When using the diameter to determine the effects of the network topology upon
diversity, we found that archipelagos with large diameters have a greater allocation of
diversity into the α- and β-component (Fig 7c and 7d). However, as with total area of the
archipelago, the slope of β-diversity tends to be steeper than the ones for α-diversity (t=
1.94, P=0.05) while the α- and β-diversity under neutral model exhibit the same slope (t=
0.58, P=0.56).
Regarding deviations empirical data from simulated results, for β-diversity above a
diameter of 100 km, there is a high deviation with respect to the neutral model with fit (R2)
of 70%. However, network diameter has a smaller explanatory power for the deviations
observed in α- and γ-diversity (38% and 27% respectively), especially for values above the
inflection point (Fig5 and 7c).
DISCUSSION
We have shown that the neutral metacommunity model developed by Conslik et al (2010)
can be applied to understand diversity patterns in insular systems and in particular the
existence of a cross over between the relative contribution of alpha and beta diversity. In
particular, one simple and generic extension of the classic neutral model for one local
community connected to a single metacommunity, to one in which several local
communities are included and their pattern of connectivity is included as well as the
network topology, provide a more realistic description of insular metacommunities
58
(Rosindell et al., 2011). Because our neutral model is a model of colonization, which takes
into account the continent, γ-diversity always increases monotonically with increasing
migration rate, contrary to what was reported by Economo & Keitt (2008) for
metacommunities. We found that beta diversity shows a maximum at an intermediate
migration rate probably because an increase in the rate of migration of individuals, from the
mainland and from surrounding islands, leads to an increase in beta diversity at the
beginning of the colonization when arriving individual most likely belong to different
species thus increasing beta diversity, however, when rate of migration increases further, it
tends to homogenize the diversity of the system as expected.
Under a neutral model, fragmentation (i.e. measured as the number of islands or
local communities) decreases alpha diversity but the opposite was observed for beta
diversity. The increase in beta diversity is likely affected by an increase in the likelihood of
finding different combinations of species co-occurring in different islands as the number of
islands increases especially when the species pool is large (Chase, 2003). Decreasing size
of the islands by effect of further fragmentation decreases the probability of persistence of
some species leading to a lower alpha diversity. (Tscharntke et al., 2012). However, the
effects on gamma diversity are observed only when there is low connectivity between the
islands, which suggests that under a neutral model, fragmentation per se can increase
regional diversity. This result together with the fact that the model underestimates observed
beta diversity, suggests that other factors control β-diversity such as in situ selection,
speciation and extinction associated with different species traits. None of these factors are
considered in the present model and may be important for mammals in insular biotas (e.g.,
Heaney, 1986; Marquet & Taper, 1998; Okie & Brown, 2009; Chapters 1 and 3).
The linear scaling of γ-diversity with total area of the archipelago is consistent with
the linearity of interprovincial species–area curves (Rosenzweig, 1995), although under the
neutral model, the slope is twice the observed in our data (Zneutral= 0.47, Zobs=0.23, t= 4.96,
P<0.001), mainly due to the overestimation of alpha diversity, which indicate that other
non-neutral processes reduce species richness in archipelagoes.
Topological differences in metacommunity reflect different spatial arrangements of
islands. As in the model of Economo and Keitt (2008), we found that for higher migration
rates negative effects of topology upon the contribution of α-diversity to gamma diversity
59
becomes apparent (Figure 3). Although the effect is not as strong as the migration rate, our
spatially explicit neutral colonization model underscores the importance of geometry in
patterns of insular diversity. Considering all the islands equal, in terms of size and distance
to the mainland, and keeping the number of links fixed, the chain topology allows for
greater differentiation between communities thus beta diversity increases, because the
topology has an effect on the isolation of the islands, which in turn affects the likelihood of
colonization of some species. In nature, some archipelagos are arranged in long chains,
such as barrier islands and other arrangements have star type with a central island. Our
measure of diameter depends of the number of links and the geometry of the connections;
however, if we consider the Adriatic and Sunda shelf archipelagos, which have the same
number of islands, we see that their geometry and extension have a great effect, as both are
quite different in terms of deviations from the model (Indicate in Figure 6). Because
topological changes are also linked to changes in the size and number of islands, in the
simulations under real conditions, the diameter has a positive effect on beta diversity as
alpha diversity.
With respect to the fit of the model to natural systems, our results show that under
certain conditions, the neutral model may account for the diversity patterns of
archipelagoes, taking into account the internal structure of the networks and stochastic
colonization processes. These conditions are for α-dominated archipelagoes, which are
mainly limited by the area of the metacommunity and number of islands. When the number
of islands is small and/or their average area is less than 50 Km2, α-diversity contributes
more to metacommunity richness, than β-diversity (Figure 7). Since the complexity of
habitat and environmental gradients increase with island size and in archipelagos with
greater total area (Williams, 1964; MacArthur & Wilson, 1967), it is more likely to find a
greater number of organisms differing in variables such as body size, trophic level, life
history and habitat affinities, which makes the assumption of neutrality more difficult to
maintain.
60
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Figure Legends
Figure 1. γ-diversity (black line), partitioned additively into α-diversity (gray) and βdiversity (dark gray) in a network of 14 nodes plotted as a function of migration rate.
Individual node sizes (J) and probability of being selected (D) were equal for all
(J=19228 individuals and D=0.074) for a network with island completely connected and
chain structure. Pool containing 151 species (dashed line).
Figure 2. γ-diversity (black squares), partitioned additively into α-diversity (triangles)
and β-diversity (circles) in a network of 14 nodes plotted as a function of metacommunity
size (total number of individuals). Number of islands, pool and probability of being
selected (D) were equal for all (14 islands, pool= 151 species and D=0.074) for a network
with island completely connected (a) and chain (b) structure.
Figure 3. γ-diversity (black squares), partitioned additively into α-diversity (triangles)
and β-diversity (circles) in a network of 14 nodes plotted as a function of fragmentation
(number of islands). Number of individuals (J), pool and probability of being selected
(D) were equal for all (J=30000, pool= 151 species and D=0.074) for a network with
island, completely connected (a) and chain (b) structure.
Figure 4. Effect of network topology on diversity patterns, α-diversity (squares) and βdiversity (triangles) as function of network diameter (the longest path between any two
nodes in the graph, where the path length between these nodes is itself the shortest
possible path) for the metacommunities with connected, star, chain, random or MST
(minimum spanning tree for real network) or random topologies, with migration
rate=1x10-1 (black) or m= 1x10-6 (gray) and otherwise similar parameter values (14
nodes, J=19228 individuals ,D=0.074).
Figure 5. Deviations (observed minus simulated neutral values) from neutral model for
diversity components with respect to the area the metacommunity, a, α-diversity, b, βdiversity and c, γ-diversity. The line represents the equivalence between the data and the
neutral simulations.
64
Figure 6. Deviations (observed minus simulated neutral values) from neutral model for
diversity components with respect to the network topology (Diameter), a) α-diversity, b)
β-diversity and c) γ-diversity. The line represents the equivalence between the data and
the neutral simulations.
Figure 7. Observed (a,c) and neutral (b, d) alpha and beta diversity components as a
function of metacommunity area (a,b) and network topology (c,d).
65
Figure 1.
66
Figure 2.
67
Figure 3.
68
Figure 4.
69
Figure 5.
70
Figure 6.
71
Figure 7.
72
CAPÍTULO 3
THE ROLE OF SPATIAL CONFIGURATION, HETEROGENEITY AND
SPECIES POOL ON SPECIES RICHNESS AND PHYLOGENETIC DIVERSITY
OF INSULAR MAMMALS
Abstract
Metacommunity theory predicts that both dispersal rates and heterogeneity have the
potential to alter patterns of local and regional species diversity through dispersion and
selection processes. However, the relative importance of heterogeneity and dispersal
remains unresolved in real landscapes, because other factors related to stochastic and
speciation processes may be acting. In this sense, working with phylogenetic diversity
may help to better understand the processes because assemblage-level phylogenies carry
the signature of ecological and evolutionary processes. Island systems have been
considered natural laboratories for investigating the structure and dynamics of species
assemblages at the community level, and in this study, we analyze the relationship
between phylogenetic diversity and species richness of mammals with six factors: size,
heterogeneity, spatial configuration, distance to the mainland, pool of species and
latitude, through a SEM- PLS in order to determine the processes that account for
observed patterns. We found that the processes of community assembly in islands are
mostly independent of phylogeny, although, the alpha component exhibits a negative
relationship with the spatial configuration. This low phylogenetic diversity may be
associated with speciation in situ and/or colonization rates associated with
phylogenetically conserved traits. Dispersal and selection processes are the main
determinants of species richness. Species richness of archipelagos increases with
increasing heterogeneity and spatial configuration, as predicted by some theoretical and
experimental studies in metacommunities. This increase is due mainly to the effect of
these factors, in interaction with the pool of species on β-component, suggesting an
interaction between stochastic dispersal processes and selection processes of
establishment or extinction mediated by local conditions.
73
INTRODUCTION
Ever since MacArthur and Wilson (1963, 1967) species richness has been seen as
resulting from the interaction between ecological factors affecting colonization,
persistence and extinction of species and historical factors affecting the pool of species
available to colonize local communities. More recently, metacommunity theory predicts
that both dispersal rate between patches and heterogeneity have the potential to alter
patterns of species diversity at local and regional level (Loreau & Mouquet, 1999;
Mouquet & Loreau, 2003; Mouquet et al., 2006). When the dispersion connects local
communities to form a metacommunity (a set of species that persist in a series of
interconnected habitat patches), local processes (such as availability of resources, species
interactions and niche partitioning) and regional (such as speciation rates, history of
dispersal and climate stability) may play a role in determining the structure, diversity and
composition of species (Ricklefs, 1987, 2004; Nally & Lake, 1999).
The estimation of phylogenetic diversity is a useful tool for examining the
contributions of history and evolution of the community structure features (Anacker &
Harrison, 2012). Locally, a low phylogenetic diversity associated with sites with few
resources, may suggest that the community is affected by habitat or
phylogenetic
filtering (Grime et al., 2008; Dinnage, 2009), while a high phylogenetic diversity may be
indicative of competitive exclusion (Darwin, 1859; Elton, 1946) whereby closely related
species tend to exclude each other. Moreover, when the phylogenetic distance across
communities is high (i.e. high phylogenetic beta diversity) along environmental
gradients, this could be indicative niche conservatism or in situ evolution (Graham &
Fine, 2008). Similarly, the study of the co-variation between phylogenetic diversity and
species richness may help elucidate the evolutionary and biogeographic processes
shaping local community assembly (Davies & Buckley, 2011; Morlon et al., 2011). A
fast speciation rate and low immigration rate may lead to low phylogenetic diversity in
relation to species richness, while a low diversification and frequent long distance
migrations may lead to high phylogenetic diversity (Davies & Buckley, 2011). Since
immigration rate within archipelagoes as well as between the archipelago and the source
area (i.e. mainland) is affected by isolation and the topology of the island networks
74
(MacArthur & Wilson, 1963; Chapter 1 and 2 this thesis, 1967), it is expected that both
heterogeneity and the spatial configuration of the islands affect phylogenetic diversity.
Although there are many studies on the determinants of species richness, there are
few studies about metacommunity structure from a macroecological perspective
especially in terrestrial vertebrates (Logue et al., 2011). Therefore, the relative
importance of heterogeneity and dispersal remains unresolved in real landscapes where
the spatial configuration as well as environmental and historical factors can alter the
relative contributions of each factor (Ricklefs, 1987; Cottenie, 2005; Cadotte, 2007;
Leibold et al., 2010; Chisholm et al., 2011). Similarly, there are few studies on the
determinants of changes in phylogenetic diversity at metacommunity level (Davies &
Buckley, 2011).
In general, studies on species diversity, have focused on the relationship between
species diversity and area, latitude or heterogeneity; the relationship between local and
regional species diversity, the relationship between species composition and abiotic
environment, distance-decay
and connectivity patterns (Rosenzweig, 1995; Morin,
1999). Most of these patterns have multiple explanations that can be understood by
considering the interaction among four general processes: selection, drift, dispersal and
speciation (Vellend, 2010). Species are added to communities through speciation
(creation of new species) and dispersion (movement of individuals in space), while the
relative abundance of these species is established by drift (stochastic changes in the
abundances of species) and selection or the dynamics of fitness advantages resulting from
biotic and abiotic changes (Vellend, 2010) in this context, for example the theory of
island biogeography (MacArthur & Wilson, 1967) represents a balance between drift and
dispersion, the spatial "mass effect" represent a combination of dispersal and selection,
niche
and "species sorting" models represent selection, whereas local-regional
relationship result from the interaction among speciation, selection and drift (Vellend,
2010).
Island systems have been considered natural laboratories for investigating the
factors affecting species diversity and the structure and dynamics of species assemblages
at the community level (MacArthur & Wilson, 1967; Simberloff, 1976; Grant & Abbott,
1980; Gilpin & Diamond, 1981; Cardillo et al., 2008; Wilson, 2009). In this paper, we
75
use them to shed light on the relationship between phylogenetic diversity and species
richness of insular mammals at the metacommunity level (or archipelago level). First, we
determine the direct and indirect effect of heterogeneity and spatial configuration, taking
into account factors that may affect these relationships, such as the size of the archipelago
(total area and number of islands) and the distance to the mainland or continental pool,
upon species richness and phylogenetic diversity. Second, we analyze how the above
factors affect regional species richness and phylogenetic diversity and their alpha (local
diversity) and beta (changing composition) components.
Determinants of species richness and phylogenetic diversity
The main evolutionary processes that influence taxonomic or phylogenetic diversity in
archipelagoes are speciation, dispersion and extinction, which are often associated with
environmental features like area, heterogeneity (topographic or habitat diversity), the
spatial configuration of islands, the isolation and pool of species (MacArthur & Wilson,
1967; Ricklefs, 1987; Rosenzweig, 1995; Loreau & Mouquet, 1999; Losos & Schluter,
2000; Chase, 2003; Kraft et al., 2011). However, these factors usually interact in complex
ways. Similarly, since the phylogenetic diversity (PD) tends to co-vary with species
richness, PD needs to be controlled by richness for understand the direct effects of the
above factors (Fig 1, richness-PD relationship).
An increase in the size of the archipelago (area and number of islands) would
have a direct positive effect per se on species richness (Fig 1) produced by stochastic
processes that increase the passive uptake of settlers with increasing area (Gilpin &
Diamond, 1981) or by minimizing the extinction rate (MacArthur & Wilson, 1963, 1967).
Similarly, large islands may accumulate more species through their higher rate of in situ
speciation (e.g. MacArthur & Wilson 1967; Whittaker & Fernández-Palacios, 2007),
which also directly affect, in a negatively way, phylogenetic diversity (Losos & Schluter,
2000; Fig 1).
However, area could also have an indirect effect upon species richness through
the heterogeneity and spatial arrangement of island areas (Fig 1). The heterogeneity
present in each archipelago would have a direct positive impact promoting greater species
76
richness (Fig 1). In the presence of habitat selection, archipelagos with greater variety of
habitats would accommodate a larger number of communities and therefore would have a
higher species richness (Rosenzweig, 1995), which would generate an indirect positive
effect on phylogenetic diversity. However, this could also have a direct negative effect on
phylogenetic diversity (Fig 1), as it would allow the coexistence of closely related species
(Darwin, 1859; Grant, 1966) and in situ speciation (Losos & Schluter, 2000).
In systems composed of several patches, as archipelagos, the arrangement or
spatial configuration of the patches (islands) and
the distance between them can
influence the movement and thus the end result of species interactions and thus
community assembly (Forbes & Chase, 2002; Leibold et al., 2004), and species richness.
Increased spatial structuring may lead to increased species richness, because a low
connectivity between islands would allow the coexistence of different communities
(Quinn & Harrison, 1988; Forbes & Chase, 2002; Economo & Keitt, 2008). Similarly, the
spatial configuration of islands in an archipelago may affect the likelihood of in situ
speciation and coexistence of closely related species, thus affecting phylogenetic
diversity patterns (Fig 1).
As established in the theory of island biogeography (MacArthur & Wilson, 1967),
a greater distance to the mainland decreases the rate of species migration, decreasing
species richness (Fig 1). In addition, a smaller distance to the source of colonization
could rescue species populations from a possible demographic crisis and extinction
(Brown & Kodric-Brown, 1977), so the distance of the archipelago to the mainland or
source of colonists is negatively correlated with species richness (Fig 1). Considering
that species colonization ability is a phylogenetically conserved trait, it is expected that
with increasing isolation, the species present in islands would be more related to each
other and therefore exhibit lower phylogenetic diversity.
Finally, since part of the idiosyncrasy in communities assembly is due to the
effect of biogeographic and evolutionary processes that have shaped the structure of the
species pool (Ricklefs, 1987), it is expected that a reduction in the "pool of species”,
which in this case would be the continental pool, would decrease the number of species in
the archipelago (MacArthur & Wilson, 1963) and thus phylogenetic diversity (Fig 1). In
turn, it is expected that latitude has a negative effect on the continental species pool (Fig
77
1), since several studies have shown as the latitude is an aggregate variable that explains
many of the changes in species richness across different regions (Hillebrand, 2004).
These changes may occur by regional / historical and climatic effects (Kalmar & Currie,
2006).
Summarizing, a direct relationship between area and diversity suggests that
ecological drift is acting, while an indirect effect through the spatial configuration and
heterogeneity, suggests that dominant processes are selection and dispersion between
islands. The relationship between diversity and distance to the mainland is also related to
dispersal processes, which may occur by simple stochasticity and / or conditioned by
dispersion capabilities associated with the life history characteristics of each species. The
effects of continental pool may influence the type and number of species that co-occur
locally. Because it is more likely that the patterns of the community can be understood as
the result of interaction processes (Vellend, 2010), we set out to test the hypotheses raised
with a structural equation model (Fig 1).
Partitioning taxonomic and phylogenetic diversity in alpha and beta components
The partition of species diversity into components alpha, beta and gamma is conceptually
useful for understanding the structure of diversity patterns. On a local scale, diversity and
richness of species corresponds to α-diversity , the variation between the species
composition from one locality to another represents the β-diversity, while regional
diversity or γ-diversity can be derived from a additive partition (γ = α + β, eg Lande,
1996). Beta diversity provides a link that connects the measures through the local (alpha
diversity) and regional scale (gamma diversity) (Legendre et al., 2005). Understanding
the factors that determine each of these components and their interrelationships can help
to understand the mechanisms that structure the diversity of mammals in island systems.
In this sense, one can propose two models. First, gamma diversity determines alpha and
beta components (Figure 2a). Second, regional diversity is the result of local diversity
and spatial variation in species composition (Figure 2b). In both models, the
heterogeneity and the spatial structure may directly or indirectly affect alpha diversity
78
and beta diversity, while the size, isolation, and the pool of species have only indirect
effects.
Considering that heterogeneity and spatial structure increases species richness at
the regional level via increasing the number of different communities, these factors
should have a greater effect on beta diversity, because increased connectivity in systems
with a high heterogeneity of habitat can lead to the homogenization of local communities
which results in a low beta diversity and therefore a low regional diversity (Quinn &
Harrison, 1988; Harrison, 1997; Forbes & Chase, 2002; Nally & Fleishman, 2004). While
these same factors can have an opposite effect on alpha diversity, because high
connectivity associated with spatial structure can maintain local diversity by promoting
the movement or dispersal of individuals between adjacent patches by spill-over or mass
effects (Shmida & Wilson, 1985; Mouquet & Loreau, 2003). For the alpha and beta
components of phylogenetic diversity, we predict a negative relationship with both
factors due to the effect of competitive exclusion on small islands and / or processes of
colonization and extinction determined by species traits phylogenetically conserved and a
positive indirect effect determined by species richness.
Understanding which factors determine beta diversity can help us understand
what processes are involved in the structure of communities. In neutral theory (Hubbell,
2001) beta diversity is predicted to increases along a spatial (distance) gradient due to
dispersal limitation. Because under this theory it is assumed that individuals are
ecologically equivalent, the theory also predicts that beta diversity does not change along
environmental gradients. Moreover, niche theory predicts that the observed patterns must
be exactly the opposite, i.e. beta diversity changes along environmental gradients but not
along spatial gradients (Chase & Myers, 2011).
METHODS
Data
Diversity
For this study we compiled presence-absence data through a literature review of 21
archipelagos (255 islands) around the world, including extant native non-flying terrestrial
79
mammals (Table S1). Phylogenetic diversity was assess by using a dated global mammal
phylogeny containing 4510 species constructed with parsimony (Bininda-Emonds et al.,
2007). We use a version with corrected node ages to prevent software errors. For the
partition of diversity we used an additive model, regional richness corresponds to the
total number of species found in the archipelago (γ) and can be divided into the average
number of species within each island (α) and the average number species absent from an
island (β; Veech et al., 2002).
To calculate the regional phylogenetic diversity (γ-PD), we use two measures;
Faith's PD and mean pair wise distance (MPD). Faith's PD is defined as the total branch
length spanned by the tree including all species in a metacommunity (Faith, 1992). MPD
down weights the influence of one or a few distantly related taxa on phylogenetic
diversity by using the average distance among species pairs in an assemblage (Webb et
al., 2002; Helmus et al., 2007). We did not use abundance weighting because we have no
abundance data for the species in different archipelagoes. The α-PD was calculated as the
average of the sum of the lengths of branches of the species present in each island, and
finally the β-PD as the difference between γ-PD and α-PD.
Size
To determine the size of each archipelago, we use two measures, the number of islands
and the total area, calculated as the sum of the area of all the islands. We use Behrmann
equal-area projection and a Global Self-consistent, Hierarchical, High-resolution Shore
line Data Base version 2.1. (http://www.ngdc.noaa.gov/mgg/shorelines/gshhs.html) in
ArcGis 10 software (Table S1).
Spatial configuration
To measure isolation we used the GSHHS database, to obtain the minimum distance to
the mainland and the diameter of the archipelago, which allows determining the effect
they can have the other islands in the processes of colonization (Keppel et al., 2009;
Weigelt & Kreft, 2013). The diameter is a measure used in graph theory and is defined as
the longest path between two islands, where the path length between these islands is itself
the shortest possible path (Urban & Keitt, 2001). To build the networks for each
archipelago, we use the minimum spanning tree (MST), which is the shortest length tree
80
that includes all islands. Following Urban and Keitt (2001), we compute the diameter of
an MST based on geographical distance to determine the effect of the isolation and the
diameter of an MST based both on the geographical distances and in the area of the
islands to determine the effects of isolation and target effect.
To calculate the MST based on distances, we used a dispersion probability matrix
P, where the probability that two island were connected was::
where dij is the minimum Euclidean distance between the edges of the islands i and j, θ is
the decay coefficient calculated as
distance (
(
)⁄
. To determine the maximum dispersal
) we measure the distance between the islands and the farthest continental
distribution of the species, for which we used the geographical range maps (Cardillo et
al., 2008).
For the MST based on the distances and area, we calculate the flow weighted by area
(
):
(
where
)
is the flow between the island i and j, given by:
́
Where
is the area of island i,
is the archipelago area and ́ is the normalized
dispersal probability (Table S1).
Heterogeneity
We calculate the heterogeneity through two variables: 1. heterogeneity of sizes of the
islands of each archipelago and 2. habitat heterogeneity. Both were measured as
(citation?):
⁄
where N is the total number of islands or number of habitats and H is the Shannon index:
∑(
where
)
is the area of the island or habitat i
the area of all islands or habitats.
The number and area of habitats were calculated using the GlobCover 2009 (Global Land
Cover Map). For this analysis we only took into account terrestrial habitats (Table S1).
81
Isolation
We determine the isolation of the islands as the minimum distance to the mainland,
considering only the islands that have at least two mammalian species
Mainland Pool and Latitude
To determine the mainland pool, following Cardillo et al (2008) we identified all species
found within a buffer of radio 1,000 km around the archipelago. The list of species
belonging to the pool was obtained overlaying geographic range polygons for all species
(Cardillo et al., 2008) using ArcGIS 10. Additionally, we measured midpoint latitude to
determine their effect (Table S1).
Statistical Analysis
Bivariate analysis
To test the hypotheses related to the effect of heterogeneity and spatial configuration
upon specie richness and phylogenetic diversity (PD), we performed simple regression
analysis using species richness and Faith´s phylogenetic diversity (PD) as response
variables, and area, habitat heterogeneity and spatial configuration, measured as distancebased diameter, as explanatory variables.
Structural equation model
To quantify the direct and indirect effects of heterogeneity and spatial configuration we
carried out a structural equation model (SEM) using the partial least squares (PLS)
approach (Sanchez, 2013), taking into account other factors that may affect these
relationships, such as the size of the archipelago, the distance to the mainland and the size
of continental pool upon species richness and phylogenetic diversity using logtransformed data (Fig 1). The same analysis was repeated but now using gamma diversity
and its components, alpha (local diversity) and beta (changing composition) for both
phylogenetic diversity and species richness.
We have used this approach, because the covariance-based SEM (MC) requires
strong distributional assumptions, while the PLS have minimum requirements on
measurement scales, sample size and residual distributions (Monecke & Leisch, 2012). In
82
the SEM model using the PLS approach the explained variance of the endogenous latent
variables is maximized by estimating partial model relationships in an iterative sequence
of OLS regressions (Monecke & Leisch, 2012).
One advantage of SEM is that one can use the latent variables, which are not
directly measured, but whose effect can be inferred from a set of observed variables.
Latent variables are also known as constructs, hypothetical variables, or theoretical
concepts and factors (Sanchez, 2013). In our model, we describe archipelago size, spatial
configuration and heterogeneity as latent variables measured through their consequences
or effects reflected on their indicators (reflective variables). The total area and number of
islands in the archipelago are considered indicators of the size of the archipelago. For
spatial configuration we consider two measures, one based on distance and other flowbased. Finally, we measure heterogeneity through habitat heterogeneity and heterogeneity
of sizes of the islands. This approach allows us to include hypothetical variables,
summarizing a number of variables into many fewer factors and explain the association
between two or more observable variables (Sanchez, 2013).
We solved the model using the centroids weighting system, calculating the
standardized coefficients values using the PLS Path Modeling package in R (http://cran.rproject.org/web/packages/ PLS Path Modeling). We evaluated the significance of each
pathway through a bootstrap with 5000 randomizations. Additionally we calculated the
R2 are the coefficients of determination of the endogenous latent variables. R2 indicates
the amount of variance in the endogenous latent variable explained by its independent
latent variables. To measure the overall quality of a model we used the GoF index that is
a pseudo Goodness of fit measure that accounts for the model quality at both the
measurement and the structural models.
To determine the unidimensionality of latent variables we calculated the DillonGoldstein's rho. Unidimensionality implies that the reflective indicators must be in a
geometrical space of one dimension and therefore are good indicators of latent variable.
Unidimensionality is considered to hold when values of Dillon-Goldstein's rho are greater
than 0.7 (Sanchez, 2013). In addition, with loadings and the cross-loadings we evaluate if
all the indicators in each latent variable should be good indicators (greater than 0.7) and
the extent to which a given construct differentiates from the others. Finally, we repeated
83
the analysis for each reflective variable in order to determine the contribution of each
one.
RESULTS
Determinants of species richness and phylogenetic diversity
The simple regression analysis shows that species richness and phylogenetic diversity are
positively related to area (R2 = 0.78 and R2 = 0.68, respectively, P <0.001), heterogeneity
(R2 = 0.64, R2 = 0.60 P <0.05) and spatial configuration (R2 = 0.72, R2 = 0.57, P <0.05),
although in all cases the slope for species richness was higher than for the phylogenetic
diversity (Fig 3). However, relationships are not so simple, as evidenced by the
subsequent structured model equations.
The manifest variables were highly and significantly correlated with the latent
variables. The number of islands show a better correlation with the size of the
archipelago than with area of the archipelago (r = 0.89 vs r = 0.85, Table S2). For the
spatial configuration, the diameter based on distance and area was the best measure (r =
0.93 vs. r = 0.91, Table S2). Habitat heterogeneity was a slightly better measure than
heterogeneity of areas (r = 0.89 vs r = 0.87, Table S2). While for the continental pool and
phylogenetic diversity there was no difference between the measures (r = 0.94 and r =
0.98 respectively, Table S2). For all latent variables Dillon-Goldstein's rho was greater
than 0.7 and the loadings was greater than 0.8, indicating that latent variables are
unidimensional and all the indicators in each latent variable are good indicators .
The path analysis conducted for the relationship between species richness,
phylogenetic diversity indicated that the prediction power of the model is of 80% (GoF=
0.80), when you remove the direct effect of the size of the islands and the archipelago
size and mainland distance relationship. Spatial configuration, heterogeneity, and species
pool had a significant direct and positive effect on species richness, while the isolation
had a negative effect (-0.24). With regards to the effect of spatial configuration on
richness (0.48), the effect of flow-based diameter was 8.8%, greater than the effect of
distance diameter . For heterogeneity-richness relationship (0.39), habitat heterogeneity
explains 6.8% more than the difference in area of the islands. Archipelago species
84
richness and size of the continental pool were the only variables that had a significant
effect on phylogenetic diversity: archipelagos with a smaller continental pool and greater
species richness showed more phylogenetic diversity. Although the direct effects of
spatial structure and heterogeneity were not significant, they negatively affected
phylogenetic diversity (Fig 4). All direct ways account for 87% of the variance in species
richness and 98% of the variance in phylogenetic diversity.
The size of the archipelago had a strong effect on heterogeneity and spatial
structure, resulting in a high indirect effect size upon both species richness and
phylogenetic diversity, being slightly greater the islands effect than the area effect (8.8%
greater for richness and 9.5% for PD). With regard to the total effect of the studied
variables, as shown in Figure 5, archipelago size and spatial structure are the main
determinants of species richness (total effect > = 0.5), followed by heterogeneity, pool
size, latitude and isolation. Regarding phylogenetic diversity, we found that it is mostly
driven by archipelago species richness and therefore is also affected the same variables
that affect species richness (i.e., archipelago size, spatial structure and heterogeneity).
The direct and indirect effects of isolation and pool size upon PD have similar magnitude
but opposite in sign, resulting in a non-significant overall effect.
Partitioning taxonomic and phylogenetic diversity in alpha and beta components
The first model (Figure 3), which considers that gamma determines alpha and beta
components is able to predict how diversity is decomposed explaining 77% of the
variance for species richness and 74% for PD while the second model, which considers
that alpha and beta diversities determine gamma diversity, predicts only 74% of the
variance for species richness and 67% for phylogenetic diversity. For species richness,
beta diversity is affected directly and positively by regional species richness, through
spatial structure and heterogeneity, although the latter does not have a significant effect,
while alpha diversity, is positively affected by species richness and negatively by
heterogeneity and spatial configuration (Fig 6a). In terms of total effects, the factors that
contribute to variability in beta diversity are size, gamma diversity and spatial
configuration (total effect> = 0.5, Fig 6a and Table 1), followed by pool size and
85
heterogeneity. Finally, isolation and latitude had negative but significant effects. Alpha
diversity was positively affected by gamma diversity and pool size (total effect> = 0.5,
Table 1) and negatively by isolation and latitude, but the size, heterogeneity and spatial
configuration had no significant overall effect (Fig 6a).
For phylogenetic diversity the best model is one that considers that gamma
determines alpha and beta components and includes species richness, although most of
the paths are not significant. Alpha diversity is significant and negatively affected by the
heterogeneity and spatial configuration and positively by gamma phylogenetic diversity,
while only beta diversity is affected by gamma phylogenetic diversity (Fig 6b). In terms
of total effects, the size of the archipelago is the only variable that has an effect on
gamma diversity and this in turn is the determining factor for the alpha and beta
components. For species richness, the model can explain 85% of the variation in gamma
diversity, 83% for alpha and 97% for beta (Fig 6b and Table 1). While for phylogenetic
diversity, the model had lower explanatory power for beta (R2 = 0.47) but its explanatory
power increases for the α-component of phylogenetic diversity and gamma diversity (R2
= 0.91 for both).
DISCUSSION
Our study represents the first global analysis of factors and processes that are responsible
for the variation in patterns of mammal diversity across archipelagos. Our analysis took
into account four factors: archipelago size, heterogeneity, spatial configuration, isolation
and species pool, and evaluated their effects on species richness and phylogenetic
diversity. This approach allows examining the patterns in the diversity and coexistence of
species in a phylogenetic context (Losos, 1995; Losos et al., 2003; Cardillo et al., 2008).
The phylogenetic diversity of archipelagoes is mainly determined by species
richness, which indicates that the processes of community assembly within archipelagoes
is mostly independent of phylogeny (e.g. random colonization and extinction) as has been
shown to be the case for islands (Cardillo et al., 2008). Therefore, in terms of total
effects, the factors studied propagate their effects on phylogenetic diversity through
species richness. However, the phylogenetic signals may be weak or obscured; we find a
86
negative and significant
component of phylogenetic diversity, which suggests that the
assemblages exhibit phylogenetic clustering. This clustering can be associated with in
situ speciation, as indicated by the presence of endemic species in the islands with larger
total area and diameter (Philippines, Sunda Shelf, Japan, Sea of Cortez and the West
Indies). This suggests that the processes of diversification in non-flying mammals depend
on a size threshold and isolation, as with the species of Caribbean Anolis (Losos &
Schluter, 2000). Similarly, this result may indicate that the rate of colonization is
determined by phylogenetically conserved features. Darwin (1859) proposed that there
should be a negative relationship between area and phylogenetic diversity due to the
effects of competitive exclusion. Our results indicate a positive relationship between the
area and the phylogenetic diversity (Fig. 3). However, removing the effect of species
richness due to its positive relationship with area, there is a negative effect of -0.18,
which supports Darwin's hypothesis.
The spatial configuration, mainly the flow-based measure, is also one of the main
determinants of archipelago species richness. This result plus the fact that β-component is
also strongly affected by the spatial configuration, supporting the hypothesis that greater
spatial structuring (larger diameter) generates a lower connectivity between islands,
allowing the coexistence of different communities and greater regional species richness
(Quinn & Harrison, 1988; Forbes & Chase, 2002; Economo & Keitt, 2008). Similarly, a
larger diameter indicates that islands are more dispersed in space, making them more
likely to be encountered by potential colonists (MacArthur & Wilson, 1967). Because
area weighted flux diameter is better predictor of species richness than
the distance-
based diameter, the emergence of edges as ‘‘spokes’’ from larger patches reflects the area
effect on dispersal rates, consistent with a ‘‘core–satellite’’ (mainland–island) model.
Additionally, in situ speciation mentioned above, also contributes to the increase in
species richness.
Another determinant of species richness is the heterogeneity, as niche theory
predicts an increase in the heterogeneity leads to an increase in species richness, because
heterogeneous environments provide more opportunities for niche segregation and
resource specialization than relatively uniform environments (MacArthur, 1972;
Whittaker et al., 1973; Rosenzweig, 1995)., Greater heterogeneity, however, reduces the
87
amount of available area suitable for each species and, therefore, increases the probability
of stochastic extinction (Kadmon & Allouche, 2007), thus in heterogeneous systems with
low connectivity between islands, species can go locally extinct, especially in small
islands, resulting in a lower average α-diversity.
Since both spatial configuration and heterogeneity are strongly affected by the
size of the archipelago, specifically by the number of islands, there may be an interaction
between the positive effect of species pool, the spatial configuration and heterogeneity. A
large pool of species, reduces the likelihood that the same species colonize the same
island, whereby if there is a priority effect, that is, if the random order of arrival is
important, it is more likely that each species can settle in the archipelago if it has several
islands (Quinn & Harrison, 1988), especially if they have a high heterogeneity. Similarly,
this type of archipelagos, may maintain more stable configurations if the dynamics of
important species generates multiple stable equilibrium (Cole, 1983).
As predicted by the theory of island biogeography, isolation from the mainland
has a negative effect on species richness, because colonization rates decrease with
increasing distance from the pool of species (MacArthur & Wilson, 1963, 1967),
although from all the factors studied this is the one that explain the least of the observed
patterns. Similarly, island biogeography theory predicts a positive relationship between
area and species richness, given by lower rates of extinction (area per se hypothesis), but
our analysis do not support this hypothesis, since the positive effect of area is an indirect
effect which is due to its effect on the spatial configuration and heterogeneity, however,
given its large overall effect size is the best predictor of species richness. Finally, our data
indicate that there is an effect of latitude on diversity patterns; archipelagos located near
the Equator have higher species richness than those in temperate areas, as has been
reported in the continents (Hillebrand, 2004) and in islands due to the relationship
between latitude and climate (Kalmar & Currie, 2006). However, our study was not
designed to differentiate between climatic and historical factors.
Most of the factors studied in this work, can affect species richness through four
processes: selection, drift, dispersal and speciation. Given our results, we conclude that
island mammal assemblages are determined primarily by processes of selection and
dispersal between islands. The relationships found among the pool, heterogeneity and
88
spatial configuration with beta diversity, suggest that increased beta diversity is due to an
interaction between stochastic dispersal processes and deterministic processes of
establishment and extinction (principally in landbridge islands) mediated by local
conditions ( selection processes). At the phylogenetic level, we did not find a direct effect
of heterogeneity and the spatial configuration upon phylogenetic beta diversity.
This
points out to the importance of including species functional traits related to dispersal
ability, establishment and habitat requirements, among others. Although a phylogeny is
assumed to encapsulates many of the ecological niche of species (Wiens, 2004), it is
known that there may be a large ecological differentiation between phylogenetically close
species (Losos et al., 2003). Unfortunately, as yet this type of data are still quite scarce to
make feasible its inclusion, a further investigation of this issue should be left for future
studies.
Finally, we believe that this study on the determinants of diversity patterns in
naturally fragmented systems like archipelagoes can help to increase our knowledge of
how to manage and conserve anthropogenically modified systems. Although it has been
recognized that the configuration of habitats with respect to connectivity and network
arrangement are important in systems composed of multiple patches (Chisholm et al.,
2011), most work has focused on its effects at the level of a single species (Urban &
Keitt, 2001; Hanski & Ovaskainen, 2003). In addition, spatial configuration frequently
confounded with composition of habitat (e.g., amount of habitat; Ewers & Didham, 2006)
and habitat loss in transformed systems (Fahrig, 2003). In this study, we found that the
network structure of the islands and heterogeneity are the main determinants of the
richness and species composition at local and regional scales. Similarly, the spatial
configuration contributes, to some extent, to explain phylogenetic diversity locally. In
this regard, graph theory showed to be a useful tool that easily allowed measuring the
connectivity between patches, given by their spatial configuration, as happens in
metapopulations studies (Urban & Keitt, 2001). However, we believe it is important to
incorporate SEM models to test hypotheses about the processes that account for the
observed patterns in the diversity of insular ecosystems.
89
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Figure Legends
Figure 1. Conceptual model depicting the hypothesized relationships between diversity
components (grey ellipses) and determinant factors: heterogeneity, spatial configuration,
size, mainland distance, species pool and latitude.
Figure 2. Alternative relationship between the alpha and beta components with gamma
diversity. a) Gamma diversity determined alpha and beta components. b)
Gamma
diversity is the result of local diversity and spatial variation in species composition
Figure 3. Bivariate relationship between species richness and phylogenetic diversity with
a) area, b) heterogeneity, and
c) spatial configuration. D) Relationship between
phylogenetic diversity and species diversity.
Figure 4. Results of the structural equation model for archipelago richness and
phylogenetic diversity. The width of arrows is proportional to the magnitude of the path
coefficients. Dashed lines represent negative relationships. The significant paths are
indicated with an asterisk and not significant with ns.
Figure 5. Total Effects: Direct + Indirect paths on species richness (Rich) and
phylogenetic diversity (PD). Where, Lat is Latitude, Pool: Mainland pool, Isol: Distance
to the mainland, Size: Archipelago size, Top: Spatial configuration and Het:
Heterogeneity .
Figure 6. Results of the structural equation model for the partition of diversity, for
richness (a) and phylogenetic diversity (b). The width of arrows is proportional to the
magnitude of the path coefficients. Dashed lines represent negative relationships. The
significant paths are indicated with an asterisk and not significant with ns.
96
Table Legends
Table 1. Total Effects: Direct + Indirect paths on alpha and beta components of species
richness and phylogenetic diversity.
Supplementary material
Table S1. General characteristics of the studied archipelagos. Latitude, Pool measured in
terms of richness (Pool-rich) and phylogenetic diversity (Pool-PD), Isolation (distance to
the mainland in Km), Area (Km2), Number of islands (# islands), Diameter distancebased (Diameter1), Diameter flow weighted by
area (Diameter2), Heterogeneity of
islands area (Heter1), Heterogeneity of habitat (Heter2), Richness and Phylogenetic
diversity (mean pairwise distance, MPD; and Faith´s PD, PD). Latitude except all
variables are in logarithm 10.
Table S2. Correlations between latent variables and reflective variables. Latitude, Pool
measured in terms of richness (Pool-rich) and phylogenetic diversity (Pool-PD), Isolation
(distance to the mainland in Km), Area (Km2), Number of islands (# islands), Diameter
distance-based (Diameter1), Diameter flow weighted by
area (Diameter2),
Heterogeneity of islands area (Heter1), Heterogeneity of habitat (Heter2), Richness and
Phylogenetic diversity (mean pairwise distance, MPD; and Faith´s PD, PD). Latitude
except all variables are in logarithm 10.
97
Figure 1.
98
Figure 2
99
Figure 3
100
Figure 4
101
Figure 5
102
Figure 6
a)
Latitude
- 0.75*
Mainland
Pool
-0.38*
Heterogeneity
-0.33*
Alpha
Diversity
0.2*
Beta
Diversity
0.76*
Archipelago
Size
Species
Richness
0.8*
Spatial
Configuration
0.17
Mainland
distance
b)
- 0.88*
Latitude
Mainland
Pool
-0.48*
0.41*
Heterogeneity
Richness
-0.32*
0.76*
1.28*
Archipelago
Size
Alpha
PD
0.8*
Spatial
Configuration
- 0.26
Gamma
PD
Beta
PD
Mainland
distance
-0.4
-0.2
103
Table 1
Relationships
Effects - Phylogenetic Diversity
Effects - Species Richness
from
to
total
P
direct
indirect
total
P
direct
indirect
Latitude
Pool
-0.88
**
-0.88
0.00
-0.75
**
-0.75
0.00
Latitude
Gamma
-0.19
ns 0.00
-0.20
-0.27
**
0.00
-0.27
Latitude
Alpha
-0.27
ns 0.00
-0.27
-0.39
**
0.00
-0.39
Latitude
Beta
-0.19
ns 0.00
-0.19
-0.19
**
0.00
-0.19
Pool
Gamma
0.22
ns 0.22
0.00
0.36
**
0.36
0.00
Pool
Alpha
0.31
ns 0.00
0.31
0.51
**
0.00
0.51
Pool
Beta
0.22
ns 0.00
0.22
0.25
**
0.00
0.25
Mainland dist
Gamma
-0.16
ns -0.16
0.00
-0.28
**
-0.28
0.00
Mainland dist
Alpha
-0.23
ns 0.00
-0.23
-0.39
**
0.00
-0.39
Mainland dist
Beta
-0.16
ns 0.00
-0.16
-0.19
**
0.00
-0.19
Size
Topology
0.81
**
0.81
0.00
0.80
**
0.80
0.00
Size
Heterogeneity 0.75
**
0.75
0.00
0.76
**
0.76
0.00
Size
Gamma
0.69
**
0.10
0.59
0.64
**
0.00
0.64
Size
Alpha
0.36
ns 0.11
0.26
0.34
ns 0.00
0.34
Size
Beta
0.33
ns 0.58
-0.25
0.73
**
0.00
0.73
Spatial config
Gamma
0.37
ns 0.37
0.00
0.45
**
0.45
0.00
Spatial config
Alpha
0.14
ns -0.38
0.52
0.25
ns -0.39
0.64
Spatial config
Beta
-0.35
ns -0.71
0.36
0.51
**
0.20
0.31
Heterogeneity
Gamma
0.38
ns 0.38
0.00
0.36
**
0.36
0.00
Heterogeneity
Alpha
0.00
ns -0.53
0.53
0.18
ns -0.33
0.51
Heterogeneity
Beta
-0.09
ns -0.46
0.37
0.43
**
0.18
0.25
Gamma
Alpha
1.39
**
1.39
0.00
1.41
**
1.41
0.00
Gamma
Beta
0.98
**
0.98
0.00
0.69
**
0.69
0.00
104
Table S1
Archipelago Latitude Pool-rich Pool-PD Isolation Area # Islands Diameter1 Diameter2 Heter1 Heter2 Richness MPD PD
Adriatic
44.09
1.97
3.54
-0.50 3.43
1.15
2.22
0.95
0.26
0.38
1.11
0.05 2.77
Alexander
52.91
1.92
3.39
-1.02 4.53
1.38
1.86
0.90
0.54
0.62
1.36
0.13 2.97
Bazaruto
23.57
1.96
3.73
0.86
2.13 0.48
1.09
0.30
0.41
0.52
1.08
0.03 2.86
Egadi
39.19
2.01
3.53
2.13
1.63 0.48
1.37
0.30
0.10
0.52
1.00
0.00 2.78
Eolie
39.72
2.02
3.54
1.82
2.09 0.85
1.89
0.70
0.21
0.42
0.78 -0.11 2.67
Phillipinas
12.72
2.78
3.78
2.72
5.46 1.61
2.79
1.45
0.84
0.60
2.04
0.31 3.35
Japan
36.42
2.28
3.53
1.65
5.56 1.08
2.66
0.95
0.75
0.71
1.74
0.24 3.25
Kuril
46.36
1.90
3.37
1.23
3.96 0.90
2.86
0.85
0.36
0.50
1.26
0.10 2.88
Lake Huron
45.83
1.68
3.40
0.21
2.53 1.32
0.90
0.30
0.95
0.71
0.95 -0.02 2.80
Maine
44.40
1.69
3.33
-1.12 2.73
1.36
2.19
0.90
0.79
0.81
1.52
0.18 3.19
Mar
30.00
2.24
3.65
-0.87 3.64
1.51
3.05
1.23
0.70
0.86
1.93
0.29 3.03
Napolitan
41.54
2.02
3.53
0.32
1.82 0.60
1.44
0.30
0.47
0.38
0.90 -0.04 2.71
Pelagie
37.11
2.02
3.53
2.19
1.39 0.48
1.60
0.30
0.42
0.35
0.60 -0.22 2.58
Ponziane
41.70
2.02
3.51
1.31
1.15 0.70
1.75
0.60
0.43
0.33
0.60 -0.22 2.48
Sardinian
41.68
2.02
3.52
2.25
2.23 1.04
2.47
0.78
0.47
0.58
1.08
0.03 2.88
Sunda Shelf
1.84
2.76
3.77
1.22
6.12 1.15
3.12
1.11
0.81
0.66
2.29
0.36 3.60
Texas
29.78
1.88
3.66
-1.22 2.88
0.78
2.21
0.70
0.08
0.49
1.40
0.15 3.14
Tremiti
42.75
2.02
3.52
1.20
0.66 0.60
1.42
0.48
0.27
0.06
0.70 -0.16 2.50
Tuscan
43.19
2.02
3.51
0.94
2.48 0.85
2.01
0.78
0.64
0.44
1.20
0.08 2.95
Virginia
38.60
1.34
3.38
-0.77 1.92
1.00
0.89
0.90
0.31
0.59
1.00
0.00 2.86
West indians 21.22
2.62
3.69
2.27
5.28 0.48
2.35
0.30
0.21
0.66
0.90 -0.04 2.52
105
Table S2
Latent Variable Reflective Variable Latitude Pool Isolation Size Topology Heterogeneity Richness PD
1.00 -0.86 -0.32 -0.32 -0.38
-0.25
-0.57 -0.50
Latitude
Latitude
-0.75 0.95
0.56
0.42
0.51
0.20
0.52
0.39
Pool-rich
Pool
-0.88 0.94
0.36
0.15
0.28
0.02
0.40
0.31
Pool-PD
-0.32 0.49
1.00 -0.18 -0.05
-0.18
-0.16 -0.22
Isolation
Dist. To Mainland
-0.54 0.56
0.07
0.85
0.70
0.58
0.78
0.74
Area
Size
-0.05 0.01 -0.36 0.89
0.70
0.74
0.69
0.68
# Islands
-0.42 0.55
0.13
0.67
0.91
0.38
0.72
0.64
Diameter1
Topology
-0.28 0.25 -0.19 0.81
0.93
0.48
0.79
0.75
Diameter2
-0.19 0.13 -0.05 0.65
0.39
0.87
0.58
0.56
Heter1
Heterogeneity
-0.26 0.09 -0.26 0.69
0.43
0.89
0.65
0.66
Heter2
-0.57 0.49 -0.16 0.84
0.82
0.70
1.00
0.98
Richness
Richness
-0.48 0.39 -0.24 0.84
0.78
0.70
0.98
0.98
MPD
PD
-0.51 0.34 -0.18 0.75
0.70
0.66
0.94
0.98
PD
106
CONCLUSIONES GENERALES
En esta tesis se planteó el problema de entender los procesos determinantes de los patrones
de diversidad alfa, beta y gamma de mamíferos terrestres no voladores en sistemas
insulares. A nivel intra-archipiélago (capítulo 1), la diversidad α (diversidad local) y la
diversidad beta debida al efecto del anidamiento (βnes), son el resultado de procesos de
selección. Los resultados muestran, que el tamaño corporal de las especies y la capacidad
de carga de las islas, medida ya sea como área o número de hábitats son los factores
determinantes de estos dos componentes, indicando que las especies son susceptibles a
extinción diferencial (los mamíferos de mayor tamaño son los más afectados) tanto por el
área de la isla como por la pérdida de hábitats. Por otra parte, la distancia entre islas y el
tamaño corporal tuvieron un efecto significativo en el componente de recambio espacial de
la diversidad beta (βsim), lo cual sugiere que esta depende de procesos de dispersión,
asociados tanto a deriva ecológica como a selección.
A nivel inter-archipiélagos, bajo el modelo de colonización neutral (capítulo 2), los
patrones de diversidad se vieron afectados por la tasa de migración, el tamaño y topología
de los archipiélagos. Sin embargo, el modelo neutral solo logra reproducir los patrones en
términos cualitativos más no cuantitativos, sobre-estimando la diversidad alfa y gamma y
subestimando la diversidad beta. La diversidad regional escala positivamente con el tamaño
de la metacomunidad, tal como sucede con las relaciones especies-área a nivel
interprovincial (Rosenzweig 1995), aunque de manera más pronunciada, indicando que los
procesos no-neutrales disminuyen la riqueza de especies presentes en una metacomunidad.
La topología de los archipiélagos la cual refleja la conectividad de los sistemas y el grado
de fragmentación per se (número de islas), afectan principalmente a la diversidad beta,
incrementándola a medida que aumenta el aislamiento (e.g topología tipo cadena) y el
número de islas. Al comparar las desviaciones de los datos con respecto al modelo nulo,
observamos que el modelo se ajusta relativamente bien cuando la diversidad alfa es mayor
que la diversidad beta y ambas son relativamente bajas. Esto puede deberse a que la
influencia de los procesos estocásticos aumenta a medida que disminuye la diversidad alfa
y aumenta el pool de especies (Chase & Myers, 2011).
107
Al considerar varios factores relevantes para la estructuración de los archipiélagos
como: el tamaño, la heterogeneidad, la configuración espacial, el aislamiento y el pool de
especies y evaluar sus efectos sobre la riqueza de especies y la diversidad filogenética
(capitulo 3), encontramos que los procesos de formación de ensamblajes en los
archipiélagos son principalmente independientes de la filogenia (e.g. colonización y
extinción aleatoria) tal como ocurre a nivel de islas (Cardillo et al., 2008) y que los
procesos de dispersión y selección son los principales determinantes de la riqueza de
especies.
Sin embargo, las señales filogenéticas pueden ser débiles o estar obscurecidas, ya
que la configuración espacial de los archipiélagos tiene un efecto negativo, sobre el
componente α de la diversidad filogenética, lo cual nos sugiere que a este nivel los
ensambles presentan un agrupamiento filogenético. Este agrupamiento puede estar asociado
a especiación in situ, tal como lo indica la presencia de especies endémicas en los
archipiélagos de mayor tamaño y diámetro (Filipinas, Sunda Shelf, Japón, Mar de Cortez e
Indias Occidentales). Esto sugiere, que los procesos de diversificación en mamíferos no
voladores dependen de un umbral de tamaño y aislamiento, tal como sucede con las
especies de Anolis en el Caribe (Losos & Schluter, 2000). De igual manera, este resultado
puede deberse a que la tasa de colonización está determinada por rasgos filogenéticamente
conservados.
La riqueza de especies de los archipiélagos aumenta a medida que aumentan la
heterogeneidad y la configuración espacial, tal como lo predicen algunos estudios teóricos
en metacomunidades (Loreau & Mouquet, 1999; Mouquet & Loreau, 2003) y estudios de
microcosmos (Forbes & Chase, 2002; Cottenie et al., 2003). Este incremento, se debe
principalmente al efecto de estos factores, en interacción con el pool de especies sobre el
componente β de la riqueza de especies, lo cual sugiere una interacción entre procesos de
dispersión estocásticos y procesos de establecimiento (principalmente en islas oceánicas) o
extinción (principalmente en islas landbridge) mediados por las condiciones locales
(procesos de selección determinísticos).
La ecología de comunidades y la biogeografía buscan entender los procesos que
determinan los patrones en la naturaleza, pero generalmente a escalas espaciales diferentes
y enfatizando diferentes procesos, aunque recientemente han convergido a una escala
108
regional (Ricklefs & Jenkins, 2011). Nuestro estudio muestra que esta nueva aproximación
puede ayudar a entender mejor los procesos detrás de las relaciones entre diferentes
factores y los componentes de la diversidad. A menor escala, es decir entre islas de un
mismo archipiélago, los factores relacionados con los procesos de selección tienen un
mayor efecto que los relacionados con dispersión, mientras que a mayor escala (entre
archipiélagos), la dispersión cobra mayor relevancia y los patrones de diversidad pueden
ser explicados por los efectos conjuntos de los factores relacionados con procesos de
dispersión (configuración espacial) y selección (heterogeneidad).
Teniendo en cuenta, que los procesos de selección son importantes a las dos escalas
de estudio, consideramos que es importante incluir rasgos funcionales de las especies
relacionados con su capacidad de dispersión, establecimiento y requerimientos de hábitat
entre otros, ya que la aproximación utilizada en esta tesis, puede no ser la más apropiada,
ya que a pesar de que se asume que la filogenia encapsula muchas de las dimensiones
ecológicas del nicho de las especies (Wiens, 2004), se sabe que puede existir una gran
diferenciación ecológica entre especies filogenéticamente cercanas (i.e, Losos et al., 2003;
Forest et al., 2007). Desafortunadamente, a la fecha de realización de este trabajo los datos
de este tipo aún son bastante escasos como para hacer un buen análisis, por lo que una
investigación de este tema se debe dejar para futuros estudios.
Aunque se ha reconocido que la configuración de los hábitats con respecto a la
conectividad y el arreglo de red son importantes en estos sistemas compuestos por
múltiples parches, la mayoría de los trabajos se han centrado en sus efectos a nivel de una
sola especie (i.e, Hanski & Gilpin, 1991; Urban & Keitt, 2001; Wiersma & Urban, 2005),
además de que frecuentemente se confunden con la composición de hábitat (i.e cantidad de
hábitat) (Ewers & Didham, 2006) y con la perdida de hábitat en sistemas transformados
(Fahrig, 2003b). En este sentido, entender el efecto de la configuración espacial en los
patrones de diversidad de los archipiélagos fue posible por la utilización de herramientas de
la teoría de grafos. La medida del diámetro de la red de islas, permitió medir de manera
sencilla la conectividad, dada por la configuración espacial de las mismas, tal como sucede
a nivel de metapoblaciones (Urban & Keitt, 2001).
Finalmente, consideramos que este estudio sobre los determinantes de los patrones
de diversidad en sistemas naturalmente fragmentados como los archipiélagos, puede ayudar
109
a incrementar nuestro conocimiento en manejo y conservación de sistemas modificados
antrópicamente. Principalmente a través del uso de las herramientas que se utilizaron para
evaluar empíricamente los postulados teóricos que normalmente se evalúan a nivel de
micro o meso cosmos (Logue et al., 2011). El modelo de colonización neutral
espacialmente explicito desarrollado en el capitulo dos, permite poner a prueba la
neutralidad de los sistemas con un bajo número de parámetros. Los modelos de
confirmación de hipótesis como los modelos de ecuaciones estructurales (SEM) basados en
mínimos cuadrados parciales, que se utilizaron en el capitulo tres, permiten entender cuáles
son los procesos que dan cuenta de los patrones observados, sobre todo porque no impone
ninguna hipótesis de distribución de los datos que son difíciles de cumplir en la vida real,
especialmente para los datos no experimentales.
110
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