Disertation-CP-Ruiz-Diaz-May 2014

UNDERSTANDING CORAL IMMUNE RESPONSE TO DISEASES:
EXPERIMENTAL AND MATHEMATICAL MODELING APPROACH
By
Claudia Patricia Ruiz-Diaz
Advisors:
Alberto Sabat Ph.D. and Mariano Marcano Ph.D.
A dissertation submitted to the
DEPARTMENT OF ENVIRONMENTAL SCIENCES
FACULTY OF NATURAL SICENCES
UNIVERSITY OF PUERTO RICO
RIO PIEDRAS CAMPUS
In partial fulfillment of the requirements for the degree of
DOCTOR IN PHILOSOPHY
May, 2014
Río Piedras, Puerto Rico
i
UNDERSTANDING CORAL IMMUNE RESPONSE TO DISEASES:
EXPERIMENTAL AND MATHEMATICAL MODELING APPROACH
ii
For you…
iii
ACKNOWLEDGEMENTS
I wish to thank my committee members Alberto Sabat, Mariano Marcano, Carlos
Toledo-Hernández, Loretta Roberson and Rafael Rios for their help, advice,
patience and supporting me in all the phases of this research. To Juan David
“Colo”, Francisco Soto, Tania Hernández, Paco López, Rubert Rodríguez, for
their field assistance. To my unconditional friends who have supported me in this
special way; Carlos, Alex, Natalia, Marianne, Nora H., Nora A., Panky, Jessica,
Mónica, Branco, Dany, Kassan, Hagmel, Sofia, Brenda, Pascal, Jeiger, Luz
Dary, Marconi, Andrés, Paul, Judimar. I also thank my parents (Leticia and
Facundo), my sisters Sofia, Margarita and Diana and my nieces Camila and
Alejandra and my whole family, whom despite the distance, they have supported
me at all times. This project was supported by institutional funds of the UPR-RP,
UPR Sea Grant (NOAA award NA10OAR41700062, project R-92-1-10) and
UPR-Sea Grant.
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TABLE OF CONTENTS
TABLE OF CONTENTS………………………………………..…………..................iii
LISTS OF TABLES………..……………………………………………..………...….vii
LIST OF FIGURES……………………………………………………………….……viii
ABSTRACT …………………………………………………………………………….xi
INTRODUCTION………...…………………………….…………...…..…………..…xiii
CHAPTER 1: MODELING THE IMMUNE RESPONSE TO PATHOGEN IN SEA
FAN COLONIES ………………………...……………………………….…..….2
ABSTRACT…………………….………………………………………...............3
INTRODUCTION…………………………………………………………….......4
MATHEMATICAL MODEL ……….………………………………………..……6
RESULTS …………………….……………………………………………..…19
DISCUSSION ………………………………………………………………..…22
TABLES…………………………………………………………………….……26
FIGURES……………………………………………………………………..…28
CHAPTER 2: INDUCED RECOVERY OF DISEASED SEA FANS GORGONIA
VENTALINA: SCRAPING OR EXTIRPATING? ………………….…….......33
ABSTRACT…………………………………………………………………...…34
INTRODUCTION…………………………………………………..………...…36
METHODOLOGY……………………………………………………….….…..39
RESULTS……………………………………………………………….…….…43
DISCUSSION……………………………………………………………….…..46
TABLES………………………………………………………………………….51
FIGURES…………………………………………………………………….….54
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CHAPTER 3: DO ENVIRONMENTAL FACTORS AFFECT THE LESION
RECOVERY OF SEA FANS? …………..………….…………………………………58
ABSTRACT………..………………………………………………….………...59
INTRODUCTION………………………………………………………….….…60
METHODS……………………………………………………………………....62
RESULTS……………………………………………………………………..…66
DISCUSSION…………………………………………………..…………....….67
TABLES……………………………………………………………………….…70
FIGURES…………………………………………………………………….….72
CHAPTER 4: MODELING LESION RECOVERY OF SEA FANS ………………77
ABSTRACT………………….…………………………………………….…….78
INTRODUCTION…………………….…………………….……………………79
MATHEMATICAL MODEL …………………………………….…….…..……81
RESULTS ………………………………………………….……………………87
DISCUSSION ………………………………..……………………….………...89
TABLES…………………………………………………………………..….…..92
FIGURES………………………………………………………….…..………...95
GENERAL CONCLUSIONS …………………………………....………………….. 99
LITERATURE CITED ....…………………………………………….……………..101
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LIST OF TABLES
Table 1.1. Empirical and theoretical parameters ….……………………….………29
Table 1.2. Initial values of model variables …………………….………………..…29
Table 2.1. Rate of tissue recovery …..………………..…………………………….52
Table 2.2. Cost: lesion elimination of Gorgonia ventalina colonies in a reef .......53
Table 3.1. t-test sadistic between shallow and deep sites for light intensity and
temperature for different time’s periods. ………...………………………………….71
Table 4.1. Initial values of model variables ………………………………….……..93
Table 4.2. Model parameters ……………..………………………..………………. 95
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LIST OF FIGURES
Figure 1.1. Schematic diagram that represents the immune response of a
Gorgonia ventalina colony after the detection of a pathogen ..............……….…29
Figure 1.2. Temporal dynamics of polyps, pathogen, stem cells, phagocytic,
humoral cells and chemical signal for the three health states ….....................…30
Figure 1.3. Phase diagram………………………………………………..….…........32
Figure 2.1. Map of Puerto Rico showing the study sites. …………..…………….55
Figure 2.2. Example of healing process …………………………………………....56
Figure 2.3. Recovery rates of scrapped colonies …………….…………………...57
Figure 3.1 Diagram representing different Gorgonia ventalina tissue recovery
treatments per replicate station ……………………………….....…………..……...73
Figure 3.2 Example of wound-healing process.…………………...………..……...74
Figure 3.3 Sensors used to measure light intensity, temperature and water
motion………………………………………………………………...…………………75
Figure 3.4 Boxplot showing mean (bold line) ± one standard error (box) and two
standard errors (whiskers) of tissue recovery treatments of fragments (A) and
clones (B). ………………………………………………………..…………….……...76
Figure 4.1 Dynamics of healthy and purple tissue for total recovery …………....96
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Figure 4.2 Dynamics of healthy and purple tissue for the chronically diseased
state 1 ………………………………………………………..……………….……..…97
Figure 4.3 Dynamics of healthy and purple tissue for the chronically diseased
state 2 ………………………………………………....……………...……………..…98
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ABSTRACT
In the last decades the sea fan G. ventalina has suffered from several infectious
diseases. Sea fans can either recuperate or succumb to these afflictions
depending, in part, to the strength of their immune system. However, the effect of
environmental stress on the immune response of sea fans is not well understood.
Chapter 1 presents a model that analyzes the capacity of G. ventalina to
eradicate a micro-pathogen under three immune states: healthy, chronically and
terminally diseased. Under the optimal immune condition, the pathogen is rapidly
eradicated. Under the sub-optimal immune condition, polyps and pathogen
coexist. And when the colony is immunologically compromised, immune cells are
unable to stop pathogen growth, and the colony dies. In Chapter 2 the
rehabilitation capacity of G. ventalina after diseased-induced lesions were either
scraped or extirpated is examined in a field experiment. With the scraping
technique over 51% of the colonies recovered between 80-100% of the lost
tissue. With extirpation, lesions did not reappeared in any of the colonies. We
conclude that lesion scraping is useful for eliminating relatively small lesions, as
these are likely to recover in a short period of time, whereas for relatively large
lesions it is more appropriate to extirpate the lesion. Chapter 3 compares the
recovery capacity of diseased G. ventalina colonies at two different depths (5m
and 12m) with significant differences in light intensity, temperature, and water
motion while correcting for genetic differences. We found that the rate of tissue
regeneration was not influenced by depth-related conditions or by genetic
variability. We also found that lesions recovery occurred within similar time spans
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in shallow and deep stations. Finally, Chapter 4 presents a model that analyzes
the capacity of recovery of G. ventalina under contrasting health conditions after
a lesion has been induced. The model predicted three solutions: i) a lesion
completely and exclusively covered by healthy tissue; ii) a lesion completely
covered by healthy and purpled tissues; and iii) a lesion completely covered by
purple tissue. The model was accurate in reproducing three of the macroscopic
levels of recovery that have been observed in the field.
xii
INTRODUCTION
Coral reef ecosystems provide a diverse array of goods, services and ecological
functions vital to human society. Over 10 million individuals across the World’s
tropical coasts depend on coral reefs for their livelihood or protein intake (Moberg
and Folke 1999; Salvat 1992). Reef-related fishing comprises about 9-12% of the
World total fisheries (Moberg and Folke 1999), and revenues associated to
recreational activities are estimated as hundreds of millions of dollars (Dixon et
al. 1993). In the Caribbean, for instance, the estimated economic revenues
obtained from coral reef associated activities range from US$350-$850 million
annually (Young et al. 2012).
Reefs are also a major source of carbon
sequestration (Remoundou et al. 2009) and nitrogen fixation (Shashar et al.
1994). Further, together with rainforests, reefs are the major centers of the
Earth’s biological diversity (McIntyre 2010).
Coral reefs, however, are undergoing dramatic declines worldwide (HoeghGulberg et al. 2007). These declines are particularly significant in the Wider
Caribbean where nearly 80% of the coral cover has been lost during the past
decades (Voss and Richardson, 2006). Reasons for these declines are variable
and complex, but there is a general consensus that coral diseases have played a
major role, being one of – if not – the major cause of partial and total tissue
mortality in many coral species (Efrony et al. 2009). This is the case for one of
the more conspicuous coral members of the tropical and subtropical Atlantic
shallow-water fauna, the Caribbean octocoral, G.ventalina. In the last decades G.
xiii
ventalina have suffered from several infectious diseases, e.g., protozoan
infections, red band disease, skeleton eroding band, and aspergillosis. It is
known that sea fans can completely recuperate from any of these afflictions due
to their strong immune system. However, the effect of environmental stress on
the immune response of sea fans is not well understood. This is important
because environmental stress can compromise the immune response of a
healthy colony making it susceptible to infection or by affecting the capacity of a
diseased colony to recover by regenerating new tissue and eliminating a lesion.
In Chapter one we present and analyze a system of differential equations that
simulates the general cellular response of the sea fan coral Gorgonia ventalina
against a generic microbial pathogen and the effect of this pathogen on the
growth capacity of its host. The specific aims of this chapter were to study by
means of a mathematical model: 1) the cellular response of sea fans under
different health states (i.e., healthy and immune-compromised) after a pathogen
has challenged their immune system and 2) the pathogen’s ability to survive
under these health states. Under the optimal immune condition, the immune cells
rapidly eradicate the pathogen and the coral returns to the infection-free state.
Under the sub-optimal immune condition, coral and pathogen co-exist. In
contrast, when the colony is immunologically compromised, immune cells are
unable to stop the pathogen growth and the colony dies.
In Chapter two we compare the rehabilitation capacity of G. ventalina after
diseased-induced lesions were scraped or extirpated. Scraping consisted of
xiv
removing from a diseased area –any organisms overgrowing the axial skeleton
plus the purpled tissue bordering the diseased area using metal bristle brushes.
Extirpation consisted of cutting the diseased areas, including the surrounding
purpled tissue, using scissors. Both strategies proved to be very successful in
eliminating sea fan lesions. In the case of the scraping technique over 51% of the
colonies recovered between 80-100% of the lost tissue. When lesions were
extirpated, they did not reappear in any of the colonies. The number of colonies
that recovered from scraping was similar between sites and among colony sizes
but differed depending on the relative amount of lesion to colony area ratio
(LA/CA). We conclude that lesion scraping is useful for eliminating relatively
small lesions (i.e., LA/CA< 10%), since these are likely to recover in a short
period of time, whereas for relatively large lesions (LA/CA≥ 10%), it is more
appropriate to extirpate the lesion.
In Chapter three we compared the recovery capacity of diseased G. ventalina
colonies at two different depths (5m and 12m) with significant differences in light
intensity, temperature, and hydrodynamics while correcting for genetic
differences. We found that the rate of tissue regeneration (healing) was not
influenced by either depth-related conditions or by genetic variability. We also
found that lesions recovery began within similar time spans in shallow and deep
stations. Our results suggest that the rate of tissue regeneration may be more
related to intrinsic factors (e.g., energy budget) rather than factors external to the
colony.
xv
In Chapter four we present a model that analyzes the capacity of recovery of G.
ventalina under contrasting health conditions after a lesion has been artificially
induced. The model predicted three solutions based on the strength of the
immune response of a colony: 1) a lesion completely and exclusively covered by
healthy tissue, after it was first covered by purpled tissue; 2) a lesion completely
covered by healthy and purpled tissues; and 3) a lesion completely covered by
purple tissue. In conclusion, the model was accurate in reproducing three of the
macroscopic levels of recovery that have been observed in the field.
xvi
UNDERSTANDING THE IMMUNE RESPONSE OF CORALS TO DISEASES:
EXPERIMENTAL AND MATHEMATICAL MODELING APPROACHES
1
CHAPTER ONE
MODELING THE IMMUNE RESPONSE TO PATHOGEN IN SEA FAN
COLONIES
2
ABSTRACT
The sea fan coral Gorgonia ventalina, one of the most abundant gorgonians in
the tropical and subtropical Atlantic waters, has suffered several diseases that
have diminished its abundance throughout their range. In this study, we present
a model that analyzes the capacity of G. ventalina to eradicate a micro-pathogen
under three immune responses: strong, moderate, and very weak. The model
assumes that: 1) polyps are the main unit of the coral; 2) the population of polyps
is homogeneously distributed; and 3) the immune system is activated by a signal.
When an endosymbiont exceeds a density threshold, it becomes pathogenic,
increasing polyp mortality. As a consequence, the colony emits a signal to its
stem cells to differentiate into phagocytic and humoral cells, both of which
combat the pathogen. Given a strong immune response, the pathogen is rapidly
eradicated by the immune cells and the coral polyp population returns to a steady
state. With a moderate immune response, polyps and pathogen coexist, but the
maximum capacity of polyp density is never reached.
An immunologically
compromised colony offering a weak immune response is unable to stop
pathogen growth, and the colony dies. This analysis suggests an alternative
explanation for the spatial and temporal variability in disease incidence and
mortality, which is based on the strength of the immune system of hosts rather
than the virulence of the pathogen.
3
INTRODUCTION
Sea fans (Gorgonia spp.) are among the most conspicuous members of the
tropical and subtropical Atlantic shallow-water fauna (Toledo-Hernández et al.
2007). An increasing number of afflictions have been reported in sea fans:
protozoan infection (Morse et al. 1981; Goldberg et al. 1984), red band disease
(Williams and Bunkley-Willians 2000; Weill and Hooten 2008), and aspergillosis
infections (Nagelkerken et al. 1997). These diseases can cause partial tissue
mortality and, under severe infection, entire colony mortality (Nagelkerken et al.
1997; Toledo-Hernández et al. 2009). However, field observations have also
documented full colony recovery (Toledo-Hernández et al. 2009), presumably
due to strong immune responses. The immune response of corals involves a
chain of reactions that start with recognition of self from non-self (Mydlarz and
Harvell 2007). Once a foreign entity has been detected, a signal is produced for
the amoebocytes to stream into the invaded area to initiate phagocytosis
(Meszaros and Bigger 1999). Amoebocytes are the putative immunocytes of
anthozoans and are scattered throughout the mesoglea in gorgonians
(Hildemann et al. 1977; Mullen et al. 2004). When the invader is large enough to
be engulfed by a single phagocyte, i.e., protozoan or fungi, they may be
encapsulated by the amoebocytes surrounding it (Goldberg et al. 1984). In
addition to this cell-mediated response, other mechanisms employed by corals
against pathogens are the production of lipid-based anti-fungal metabolites (Kim
et al. 2000a; 2000b) and antioxidant enzymes such as peroxidase (Mydlarz and
Harvell 2007) and chitinase (Douglas et al. 2007).
4
As corals lack adaptive
immunity (Kurtz 2004), they exhibit non-specific responses to immune insults.
Mathematical models describing the dynamic interactions between pathogens
and coral hosts and the consequences of disease on the vital rates of the coral
hosts are scarce (Ellner et al. 2007). This is probably due to the poor
understanding of the immune response of coral-hosts against intruders and the
few studies documenting the effect of diseases on coral growth and survivorship
(Toledo-Hernández et al. 2009; Bruno et al. 2011). Nonetheless, once the
immune response is better understood and parameterized, models can provide
quantitative analysis of the host-pathogen interaction, including the capacity of
predicting the outcomes of the interaction under different immune conditions or
environmental factors. An example of this approach is the model developed by
(Ellner et al. 2007) in which the virulence potential of the pathogen (Aspergillus
sydowii) is analyzed in terms of the amount of continuous tissue consumed in a
short time interval on its host, G. ventalina.
In this study, we present and analyze a system of differential equations that
simulates the general cellular response of the sea fan coral G. ventalina against
a generic microbial pathogen and the effect of this pathogen on the growth
capacity of the coral. We use the model to explore the growth capacity of hosts
under three immune responses, i.e., strong, moderate, and very weak. Under the
strong response, the host cellular immune response is able to eradicate the
pathogen allowing the host to reach its maximal growth capacity. Under the
moderate response, the host is unable to establish a strong cellular immune
response against its pathogen. Under the weak response, the host is unable to
5
control pathogen growth rate and the pathogen increases in abundance until the
host dies.
Mathematical Model
In this section we introduce the model assumptions, present the model
equations, compute stable steady-state solutions, and describe the parameter
choices.
Model assumptions
We assume that polyps are the main functional units of a sea fan colony. Being a
modular organism, polyps encompass all the physiological processes of the
colony, including heterotrophic and autotrophic energy production, reproduction,
growth, and immune response. We assume a single compartment model with a
population of polyps homogenously distributed on a 1cm2 tissue fragment. The
organism that causes the disease is a single strain generic micro-pathogen. This
is the micro-pathogen that causes the polyp mortality. The presence of the micropathogen activates the host immune system through a signal, the strength of
which is proportional to pathogen abundance.
The immune system of the host is composed of three cell types: stem cells,
which differentiate into phagocytic and humoral cells after the signal is turned on;
phagocytic cells, which engulf pathogens; and humoral cells, which secrete antipathogen chemical compounds.
6
Model equations
Figure 1.1 shows a diagram for the interaction of the micro-pathogen with the
immune system of the sea fan.
The rate of change in polyp abundance ( ) is given by:
(
where
)
(1.1)
is the birth rate constant of polyps. The growth rate is limited by the
maximum capacity of polyps
within a 1 cm2 of tissue. The natural death rate
constant of polyps (with constant
due to the pathogen (with constant
), and the mortality rate constant of polyps
) are also represented.
The rate of change in pathogen abundance ( ) is represented by:
(1.2)
where
is the birth rate constant of pathogen,
constant of pathogen, and
and
is the natural mortality rate
are the mortality rate constant caused by
phagocytes and humoral cells, respectively.
The rate at which the chemical signal ( ) is produced by the presence of the
pathogen is represented by:
(1.3)
7
where
is the rate constant at which the concentration of the chemical signal
increases,
is the pathogen density, and
is the rate constant at which the
signal decays.
The rate of change in the number of stem cells abundance ( ) is represented by:
(
where
)
(1.4)
represents the birth rate constant of stem cells,
natural rate constant of mortality of stem cells, and
and
represents the
represent the rates
constant at which the stem cells differentiate into phagocytic and humoral cells,
respectively.
The rate of change in the abundance of phagocytic cells ( ) is given by:
(1.5)
where
represents the phagocytic index and
is the natural rate constant of
mortality of phagocytic cells.
The rate of change in the abundance of humoral cells ( ) is given by:
(1.6)
where
represents the humoral index and
is the natural rate constant of
mortality of humoral cells. For all equations, time ( ) is measured in days.
Steady-state points and stability
We obtained a steady-state solution of the system of equations (1.1)-(1.6) by
setting the time derivatives equal to zero and solving the following equations:
8
(
)
(1.7)
(1.8)
(1.9)
(
)
(1.10)
(1.11)
(1.12)
Infection free-solution
For a healthy and thus infection-free colony, there should be no signal (
equations (1.9)-(1.12), therefore, from equation (1.9),
; from equation (1.12),
From equation (1.7), when
) in
; from equation (1.11),
0; and from equation (1.10),
.
0, one gets;
(
)
(1.13)
Hence, the disease-free solution (healthy state) is
(
)
((
)
)
(1.14)
In a continuous model, the steady-state solution (1.14) will be stable provided
that the eigenvalues of the characteristic equation (associated with the linearized
problem) have negative real part, i.e.,
( ) for all
(Edelstein 1988). The
Jacobian matrix (1.15) of the right-hand side of equations (1.7)-(1.12) is given by
9
(1.15)
and then, we evaluate the Jacobian matrix at P* (1.14) to obtain the eigenvalues
(1.16)
This matrix (1.16) has four negative eigenvalues:
,
,
, and
. The
remaining eigenvalues are negative provided that:
(
)
(1.17)
Therefore, the steady-state solution (1.14) is stable, whenever the inequalities in
(1.17) holds. This means that for any initial value close to (1.14) and satisfying
(1.17) the solution of system (1.1)-(1.16) is going to be (1.14).
10
Infections-state solutions
Chronic disease: If the colony is infected by a pathogen,
or equivalently
. By considering s as an unknown variable of the algebraic system (1.7)(1.12), one can reduce the system to a quadratic equation of s as explained
below.
From equations (1.9) and (1.10), we get an expression for
and
as a function
of s, respectively,
( )
(1.18)
and
( )
.
(1.19)
By substituting the expression of
( ) from equation (1.19) into equation (1.11)
(
)
and rearranging, we get
( )
(
(
(1.20)
) )
The substitution of ( ) from equation (1.20) into equation (1.12), after
rearrangement, yields
( )
(
(
(1.21)
) )
And by replacing the expressions of
( ) and
(1.21) into equation (1.8), we get, whenever
( )
(
In particular, note that if
(
) )
, then
(
.
11
( )from equations (1.20) and
,
(
) )
(1.22)
Finally, by substituting the expressions for ( ) and ( ) from equations (1.18)
and (1.22) into equation (1.7), respectively, we obtain a second degree equation
of ,
, where the coefficients , , and
are expressions of the
model parameters:
(
)
(1.23)
(
)
(
(
)
)
(1.24)
(1.25)
For any set of feasible parameters, the coefficient
is nonnegative,
)(
is positive and whenever C
is positive, and the solution of the quadratic function is
nonpositive. Thus, to obtain a positive value of s, the coefficient C must be
negative and this imposes the following condition on the parameters:
(
)
(1.26)
√
and the solutions is given by
.
Terminal disease: If the polyp population is zero (
), the signal is equal to
zero and one gets the following solution for the system of equations (1.7)-(1.12):
(
)
(
)
(1.27)
A substitution of this point into the Jacobian matrix (1.15) gives a lower triangular
matrix, in which all eigenvalues are negative except one (
). The remaining eigenvalue is negative whenever the following
condition is satisfied:
(1.28)
12
Therefore, the point
is a stable steady state (Edelstein-Keshet 1988).
Model parameters
The model’s parameters were either estimated using fieldwork data from ToledoHernández et al. (2009) or estimated in the laboratory as part of this study (see
Subsection Empirical Parameters). The parameters that could not be estimated
empirically because published information is not available or could not be
estimated in the laboratory or in the field were estimated and adjusted to
satisfying either of the conditions (1.17), (1.26), or (1.28) (see Subsection
Theoretical Parameters).
Empirical Parameters
The birth rate of polyps, natural mortality rate of polyps, and mortality rate of
polyps due to pathogen were estimated using fieldwork data from ToledoHernández et al. (2009). In that study, growth of sea fan, tissue loss due to
disease and fragmentation, and whole colony mortality were estimated following
64 healthy and diseased Gorgonia ventalina colonies from several reefs across
the eastern coast of Puerto Rico from July 2006 to October 2007. Estimates of
the parameters are presented in Table 1.1.

Birth rate of polyps (
) is the number of polyps born in 1cm2 of healthy
sea fan per day. This was estimated as:
(1.29)
13
where
is the average growth of healthy sea fan tissue (cm2/day) and
is
the average number of polyps within a known area of healthy sea fan tissue.
was estimated using the fieldwork data from Toledo-Hernández et al. (2009)
with the following equation:
∑
–
(
)
(1.30)
where
is the area of healthy sea fan tissue after a 452 days observation
period,
is the tissue area of healthy fans at the initial observation period, t =
452 is number of days between initial and final dates,
is the number of healthy
sea fans followed through time (which in this case was 64 colonies), and
is
the area by which we normalize, given that the model is of one compartment, and
in our case was one cm2.
was estimated as:
∑
(
∑
(
where
)
)
(1.31)
is the total tissue area obtained from 9 histological tissue slides from 9
different healthy sea fans,
preparation,
is the area of each polyp within each histological
is the number of polyps per slide (in this case we measured 81
total polyps from 9 colonies) and
is the number of slides.
14

Natural mortality rate of polyps (
) is defined as the death rate of polyps
in a 1cm2 of healthy sea fan tissue caused by fragmentation. Fragmentation is
the main cause of tissue loss and thus of polyps in sea fan colonies regardless of
their health condition (Toledo-Hernández et al. 2009). This was estimated as:
(1.32)
where
is the average natural fragmentation rate of healthy sea fan tissue.
is the average area of polyps within a known area of healthy sea fan tissue
(see equation (1.31) for details).
was estimated using the fieldwork data from Toledo-Hernández et al. (2009)
in the following equation:
∑
(
where
–
(
)
)100
(1.33)
is the loss of healthy tissue due to fragmentation after 452 days of
field observations,
is the tissue area of healthy colonies at the initial
observation period, t is number of days between initial and final dates,
is the
number of healthy colonies used to calculate fragmentation of tissue.

Mortality rate of polyps caused by the pathogen (
) is defined as the
death of polyps in a 1cm2 of sea fan tissue caused by the pathogen. We
estimated this parameter as:
(1.34)
15
where
is the average grow of diseased tissue in a sea fan colony.
is the
average area of polyps cover within a known area of total sea fan tissue.
was estimated using the equation described by Toledo-Hernández et al. 2009
with the following modification
∑
(
where
(
)
)
(1.35)
is the area of diseased tissue (i.e., lesions) after 452 days of field
observations,
is the area of diseased tissue in the initial observation period, t
is the number of days between initial and final dates, and
is the number of
colonies used to calculate lesion grow rate (in this case n is 17).

Maximum Capacity of polyps (
) is defined as the maximum number of
polyps within a cm2 of healthy sea fan tissue. To estimate
, we counted the
total number of polyps from a histological slide and divided that number by the
tissue area of that same slide. We repeated that procedure with 9 different slides
and selected the highest value as the

Phagocytic cells index (
.
) is defined as the percentage of phagocytic
cells with respect to the total number of cells within a cm2 of sea fan tissue. To
estimate this index, we collected 15 tissue fragments from healthy colonies plus
15 healthy and 15 diseased tissue fragments from 15 diseased colonies. The soft
tissue from each fragment was scraped and individually placed in 1.5ml tubes
with filtered seawater (FSW). Each tube was left for 15-30 minutes at room
16
temperature (RT) for debris to precipitate to the bottom. Then, 1ml of the
supernatant was transferred to a new 1.5ml tube containing 25μL fluorescent
beads (polysciences, 0.77µm diameter, 1:100 dil.) suspended in FSW. The tubes
were incubated with gentle agitation for 2hrs. Immediately after, the cells
suspension was centrifuged at 10000g for 1min, washed two times with FSW and
then fixed in a 1ml solution of 4% paraformaldehyde (PFA)/FSW for 15 minutes.
Two more FSW washes were performed to remove excess PFA after the 15min.
Then, 10μl of DAPI (diamidino-2-phenylindole, for nuclear imaging in
fluorescence microscopy) (5mg/ml) was added to each tube containing 1ml of
FSW. Cells with DAPI/FSW were incubated for 10 minutes at RT. Cells were
then centrifuged at 10000rpm for 1min and the supernatant with excess DAPI
was decanted.
Cells were washed several times with 1ml of FSW and
centrifuged as described previously to remove the excess of DAPI. The total
number of cells (defined as the stem cells) and cells containing fluorescent beads
were counted using a hemocytometer. Then,
was estimated as:
(1.36)
where
is the total number of phagocytic cells and
is the total number of
stem cells.
Theoretical parameters
The theoretical parameters are divided into two sets: fixed and variable. Fixed
parameters have the same values regardless of the health state, whereas
17
variable parameter values were assigned according to the health state of the
host colony.
Fixed Parameters
In this model the natural rate constant of mortality of stem cells
differentiation rate constant of stem cells from phagocytic
, and the
and humoral cells
, are the only fixed parameters as they showed rather discreet influences on
the final outcomes of the model after we vary their values during different
simulations (Table 1.1).
Variable Parameters
The variable parameters assume different values according to the health state of
the colony are adjusted to satisfy the corresponding condition (1.17), (1.26), or
(1.28). The variable parameters are as follows: the birth rate constant of
pathogens (
), mortality rate constant of pathogen due to phagocytes (
humoral cells (
), the rate at which the signal is produced( ), the rate at which
the signal disappears ( ), the reproductive rate of stem cells (
of humoral cells efficiency (
phagocytic (
) and
) and humoral (
) and the index
). Similarly, factors affecting the mortality rates of
) cells are unknown. Thus, to simplify we took
the parameter values of the humoral cells population equal to the ones of the
phagocytic cells (Table 1.1).
18
RESULTS
Table 1.1 shows the parameter values for each health state of the sea fan. The
parameters obtained experimentally were described in the Subsection Empirical
Parameters, the parameters which values were kept fixed were described in the
Subsection Theoretical Parameters, and the variable parameters were described
in the Subsection Variable Parameters. Table 1.2 contains the values of the
model variables at time t = 0.
Healthy State
A strong immune response results in a colony with a healthy state. This diseasefree solution is obtained by using the initial conditions in Table 1.2 and the
corresponding parameter values in Table 1.1. At the beginning of the simulation,
the sea fan host recognizes the pathogen (Figure 1.2, Plot B). Then signal is
triggered, and the stem cells start to differentiate into phagocytes and humoral
cells (Figure 1.2, Plots C, D, and E). After one day, the phagocytic and humoral
cells can reduce the pathogen abundance by 80% (Fig 1.2, Plot B), while the
number of polyps increases by 41% (Figure 1.2, Plot A). By the fifth day of the
simulation, the phagocytic and humoral cells reach their maximum abundance
and the pathogen is eradicated (Figure 1.2, Plots B and E). Simultaneously, the
signal declines and polyp abundance increases exponentially (Figure 1.2, Plots A
and B). By day 40, the maximum capacity of polyps is reached and the signal
attains pre-infection levels, resulting in a cessation of cells differentiation (Figure
1.2 Plots A and E).
19
Chronically diseased state
A moderate immune response produces a chronically diseased colony. This state
was obtained by using the corresponding parameters in Table 1.1 and applying
the quadratic formula with the plus sign. We got the following point:
(
The Jacobian matrix
)
(
)
(1.15) evaluated at
(1.37)
has the following eigenvalues:
–15.93, –0.01731, –0.01731, –0.1401, –0.2999, and –0.3000. Because the real
part of all the eigenvalues is negative, the point
is stable (Edelstein-Keshet
1988), see Figure 1.3.
Similar to the previous state, the host recognized a pathogen, triggering a signal
for the stem cells to differentiate into phagocytes and humoral cells (Figure 1.2,
Plots C, D, and E). By the second day of the simulation, the stem cells
abundance had declined exponentially as they differentiated into phagocyte and
humoral cells, reaching their highest abundance values, i.e., almost twice as high
as in the healthy state (Figure 1.2, Plots D and E). At this point, the pathogen is
near its lowest abundance, almost on the verge of eradication, while the
abundance of polyps is increasing exponentially (Figure 1.2, Plots A and B). By
day forty, the signaling is near its highest value and the stem cells are slowly but
constantly declining (Figure 1.2, Plots C and D). Consequently, the phagocytic
and humoral cells, and the polyps decline to their lowest abundances, while the
pathogen is near its highest abundance (Figure 1.2). After the fortieth day, the
population of polyps and pathogen exhibit damped oscillations until they stabilize
20
and reach a state of coexistence, which is below its maximal capacity (Figure 1.2
A and B).
Similarly, the signal fluctuates before stabilizing at a value two orders of
magnitude higher than that of the healthy state (Figure 1.2, Plot C). Likewise,
stem cells, and phagocytic and humoral cells continue declining until reaching
stable values (Figure 1.2, Plots D and E).
This suggests that polyps and
pathogen can coexist over an extended period of time (i.e., a colony can live for
many years diseased), see Figure 1.3.
Terminal diseased State
A weak immune response results in death of the colony. For this state the
empirical parameters satisfy the stability condition (1.28) for the point (1.27). In
this state however, the immune response is weak, and thus insufficient for the
host to eradicate or coexist with the pathogen. During the first 8 days of the
simulation, the polyp population declines as the number of pathogen increases
(Figure 1.2, Plots A and B). During this period, the phagocytes and humoral cells
increase as the stem cells differentiate when cued by the signal (Figure 1.2, Plots
C, D, and E). Shortly after, however, the abundance of the immune cells drops as
the signal and polyps continue to decline and are eventually overtaken by the
pathogen. After the tenth day of the simulation, polyps and pathogen steadily
declined and by day 60 of the simulation the colony dies (Figure 1.2, Plots A and
B).
21
DISCUSSION
The model describes the immune response of sea fans against a generic
pathogen when the host is healthy or immune compromised. It also simulates the
growth rates of sea fans under these health states. The main conclusion of the
model's analysis is that the strength of the immune response governs the
capacity of sea fans to (1) eradicate a pathogen, and thus allow the host to reach
its maximal growth capacity; (2) coexist with a pathogen indefinitely while
growing below its maximal capacity; or (3) succumb to the pathogen.
The level of success of the immune response to eradicate the pathogen is
controlled by: (1) the capacity of the host to activate a signal after a pathogen
has been detected; (2) the abundance of stem cells; and (3) the capacity of
phagocytic and humoral cells to eradicate the pathogen. In this respect, the
capacity to detect and activate a signal is higher in the healthy state than in the
chronically and terminal diseased states. Likewise, the number of stem cells,
precursors of phagocytic and humoral cells, are in greater abundance in the
healthy state than in the both chronically and terminal diseased states. Lastly,
the efficiency of phagocytic and humoral cells to eradicate the pathogen is also
greater in the healthy state, followed by the chronically and terminal diseased
states, respectively. Therefore, our model predicts that healthy fans are fast at
recognizing a pathogen and very efficient at displaying an immune response and
hence are able to eradicate the pathogen and reach its maximal growth capacity.
In contrast, chronically diseased hosts, are in a permanent struggle with the
pathogen population in which the immune system is capable of controlling the
22
pathogen population (an equilibrium is reached between the birth and death rate
of the pathogen by the host immune system), but not capable of eradicating it. In
this scenario the host will survive but the polyp birth rate will be reduced,
compromising the growth rate of the colony. If the immune system is further
compromised, by diminishing the efficiency of immune cells in killing pathogens,
a threshold is reached in which the pathogen death rate becomes smaller than its
birth rate. This causes the pathogen population to increase rapidly, resulting in
colony death.
Ellner et al. (2007) developed a model in which the main objective was to
simulate the cellular response of the sea fan tissue after the fungus A. sydowii
infected the host. In this model, the authors computed short-time solutions in
which the pathogen virulence controls how quickly the pathogen kills the host.
Consequently, the model is intended to display only the infection state. In other
words, the model was designed such that the fungus is continuously consuming
sea fan tissue and therefore the host will never recuperate from the infection.
Because the model is formulated in one space dimension, they were able to
simulate the effect of having several infection points simultaneously in a single
host. However, if the spatial dimension is ignored and the model is reformulated
as a single-compartment model as in our model, the equations of the
reformulated model have multiple solutions for the healthy or infection-free state,
and no solution is stable. In contrast, our model formulation exhibits a stable
infection-free solution. Stability is obtained because we assumed a logistic
growth for the polyp reproduction rate.
23
We are far from understanding how the immune system of cnidarians works and
what factors, intrinsic and extrinsic to corals, influence the strength of their
immune system. We also lack sufficient knowledge as to identify the different
cells involved and their roles given an immune insult. However, as in many
animals, environmental factors could negatively affect the immune systems of
corals. Thus, at one point, a perfectly healthy sea fan could be immunecompromised due to an environmental stressor and consequently, a commensal
or foreign microbe could invade and flourish producing tissue damage to it sea
fan host. The degree of damage, however, could be controlled by the host
immune strength or as in Ellner and coworkers model by the virulence of the
pathogen.
In our model, the three final health states (disease-free host,
chronically-diseased host, and terminally-diseased host) were reached assuming
constant pathogen virulence (i.e., the effect of pathogens on polyp death rate is
not altered) while varying the colony’s immune response. This suggests an
alternative paradigm of how to interpret the phenomenon of coral diseases.
Currently, the concepts of “one pathogen-one disease" and the variability in the
virulence of pathogens are readily accepted to explain the temporal variability in
prevalence and mortality of corals (e.g., Reshef et al. 2006; Harvell et al. 2007;
Sokolov 2009). This model suggests that one can obtain temporal variability in
prevalence (or incidence) and mortality in a population of corals in response to
temporal or spatial variability in some stress that compromises the immune
system of coral colonies (Lesser 2006). This leads us to suggest an alternative
explanation for a sea fan capacity to recover, based on its cellular immune
24
response as opposed to variation in the virulence of pathogens or due to
increased resistance at the population level as a result of selection of the most
resistant colonies after a mass mortality event (Flynn and Weill 2009; Palmer et
al. 2010; Bruno et al. 2011).
25
CHAPTER ONE
TABLES
26
Table 1.1 Empirical and theoretical parameters
Table 1.2 Initial values of model variables
27
CHAPTER ONE
FIGURES
28
Figure 1.1 Schematic diagram that represents the immune response of a
Gorgonia ventalina colony after the detection of a pathogen. The p-box
describes the change in polyp density, which is regulated by: the birth rate
constant of polyps ( ); the mortality rate constant of polyps ( ) and the
mortality rate constant of polyps caused by pathogen ( ). The q-box describes
the change in pathogen density controlled by: the birth rate constant of pathogen
( ) and three ways of mortalities; natural mortality rate constant ( ); the
mortality rate constant caused by phagocytes ( ) and mortality rate constant
caused by humoral cells ( ). The s-box represents the change in chemical
signal controlled by: the rate constant at which the concentration of the chemical
signal increases ( ) as a function of the pathogen abundance and the rate
constant at which the signal decreased ( ). The u-box represents the change in
stem cells abundance through time controlled by: the birth rate constant of stem
cells ( ); their natural mortality rate constant ( ) and the rate constant at which
the stem cells differentiate to phagocyte ( ) and humoral cells ( ). The a-box
represents the abundance of phagocytic cells through time given a phagocytic
index constant ( ); the rate constant at which the stem cells differentiate to
phagocyte ( ) and the natural mortality rate constant ( ). The h-box represents
the abundance of humoral cells, regulated by: the index constant of humoral cells
efficiency ( ); the rate constant at which the stem cells differentiate to humoral
cells ( ) and the natural mortality rate constant ( ).
29
Figure 1.2 Temporal dynamics polyps, pathogen, stem cells, phagocytic,
humoral cells and chemical signal for the three health states. Healthy state
HS (gray curve), chronic diseased state CDT (medium dashed black curve) and
terminal diseased state TDS (dotted black curve). [A] In the HS the polyp
population grows to its maximum capacity quickly. In the CDS the polyps never
reach their maximum abundance and oscillate until attaining a stable equilibrium.
In the TDS the polyps steadily decline, reaching extinction (i.e., colony death) by
day 60. [B] In HS the pathogen population disappears rapidly, while for the CDS
it coexists with the polyps, attaining a stable equilibrium. In the TDS the pathogen
population grows rapidly, killing all the polyps; followed by its own demise after
eliminating the host population. [C] In the HS the chemical signal is activated by
the pathogen presence, but when pathogen is eradicated the signal decays. In
the CDS the signal fluctuates through time in response to pathogen abundance,
achieving a stable equilibrium after the pathogen stabilizes. [D] In the HS the
stem cells population exhibits an exponential decay in the first 10 days (due to
their differentiation into phagocytes and humoral cells), but in the following days it
recuperates and their abundances remains almost constant. In the CDS the stem
cell population also has an exponential fall during the first days due to the
differentiation into phagocytes and humoral cells. In the TDS the stem cells
population has a slower decay in comparison with the other states in first days
until the population disappears with the death of the host. [E] The phagocytic
and humoral cell populations have the same behavior (see section model
assumptions). In the HS the phagocytic and humoral cells (dash gray line)
reduced the pathogen abundance to reach this minimum values but never reach
to zero. In the CDS the phagocytic and humoral cells (dashed black line) growth
exponentially during the first day and subsequently fall exponentially until
reaching stables values. Finally, in the TDS the phagocytic and humoral cells
(dash-dot black line) grow during the first 20 days, reaching higher abundances
than in the other states, but then decline steadily to death.
30
Figure 1.2
31
Figure 1.3 Phase diagram: The curve represents the dynamic behavior of
polyps (horizontal axis) and pathogen (vertical axis) populations for 20000 days.
It is noteworthy that the populations coexist.
32
CHAPTER TWO
INDUCED RECOVERY OF DISEASED SEA FANS GORGONIA VENTALINA:
SCRAPING OR EXTIRPATING?
33
ABSTRACT
Coral diseases are currently playing a major role in the worldwide decline in coral
reef integrity. In the Caribbean, one of the coral species most afflicted disease is
the sea fan Gorgonia ventalina. There is much literature focusing on the causes
and consequences of these afflictions. However, there is very little information
regarding the capacity of sea fans to recover after being infected. The aim of this
study was to compare the rehabilitation capacity of G. ventalina after diseasedinduced lesions were eliminated either by scraping or extirpating the affected
area.
Scraping consisted of removing any organisms overgrowing the axial
skeleton from the diseased area as well as the purple tissue bordering these
overgrowths using metal bristle brushes. Extirpation consisted of cutting the
diseased area, including the surrounding purpled tissue, using scissors. The
number of scraped colonies that fully or partially rehabilitated after being
manipulated and the rates at which the sea fans grew back healthy tissue were
compared among: 1) colonies at two sites with contrasting environmental
conditions; 2) colonies of different sizes; and 3) colonies with different ratios of
lesion to colony areas (LA/CA). Both strategies proved to be very successful in
eliminating lesions from sea fans. In the case of scraping, over 51% of the
colonies recovered between 80-100% of the lost tissue within sixteen months.
The number of colonies that recovered from scraping was similar between sites
and among colony sizes, but differed significantly depending on the lesion to
colony area ratio (LA/CA). Extirpation eliminated all visual signs of disease and
lesions did not reappear in any of the colonies. However, regeneration of tissue
34
in the extirpated area progressed very slowly. We conclude that lesion scraping
is useful for eliminating relatively small lesions (i.e., LA/CA< 10%), as these are
likely to recover in a short period of time, whereas for relatively large lesions
(LA/CA≥ 10%) it is more appropriate to extirpate them.
35
INTRODUCTION
Coral reef ecosystems provide a diverse array of goods, services, and ecological
functions vital to human society. Over 10 million individuals across the World’s
tropical coastal communities depend on coral reefs for their livelihood or protein
intake (Moberg and Folke 1999; Salvat 1992). Reef-related fishing comprises
between 9 and 12% of the World total fisheries (Moberg and Folke 1999); and
revenues associated to recreational activities are estimated on hundreds of
millions of dollars (Dixon et al. 1993). In the Caribbean, for instance, the
estimated economic revenues obtained from coral reef associated activities
range from US$350-$850 millions annually (Young et al. 2012). Reefs are also a
major source of carbon sequestration (Remoundou et al. 2009), nitrogen fixation
(Shashar et al. 1994), and together with rainforests, are the major centers of the
Earth’s biological diversity (McIntyre 2010).
However, coral reefs are undergoing dramatic declines worldwide (HoeghGulberg et al. 2007). These declines are particularly significant in the Wider
Caribbean where nearly 80% of the coral cover has been lost during the past
decades (Voss and Richardson 2006). Reasons for these declines are varied
and complex, but there is a general consensus that coral diseases have played a
major role in recent coral decline (Efrony et al. 2009).
Coral disease studies have, for the most part, prioritized: 1) the etiology of these
afflictions and 2) the ecological impacts of these diseases at the colony,
population, and ecosystem level (Bruno et al. 2011; Nagelkerken et al. 1997;
Smith et al. 1996). Far less attention has been devoted to developing strategies
36
for treating afflicted colonies; even though field evidence suggests that corals, in
general, have relatively low natural recovery (Toledo-Hernández et al. 2009).
Two approaches have been proposed to treat diseased colonies: 1) physical
removal of the tissue with an active infection and 2) biological controls against
pathogen. Hudson (2000) used an underwater suction device to remove the
polymicrobial mat typical of black band disease (BBD), sealing the treated area
with modeling clay afterward. Teplitski and Ritchie (2009) used pathogen-specific
phages to contain infections produced by the bacteria Vibrio coralliiyticus and
Thalassomonas loyana on the Red Sea corals Pocillopora damicornis and Favia
favus, respectively (Efrony et al. 2007). However, none of these approaches
have been extensively tested in the field; therefore the applicability of these
methodologies as management tools is uncertain.
During the past few decades, Caribbean sea fans (Gorgonia spp.) have suffered
from several infectious diseases, e.g., protozoan infections (Morse et al. 1981,
Goldberg 1984), red band disease (Weil and Hooten 2008; Williams and
Bunkley-Williams 2000), skeleton eroding band (Croquer et al. 2006; Winkler et
al. 2004), and aspergillosis (Nagelkerken et al. 1997). These diseases induce a
macroscopic immune response consisting of an increase of purple sclerites,
together with the disappearance of polyps in the afflicted area of the sea fan. As
the infection proceeds, partial mortality of tissue occurs creating a lesion and
leaving the axial skeleton open for fouling organisms such as algae and
bryozoans. These lesions are likely to become permanent, but contained, or may
increase in size causing whole colony mortality, depending on the virulence of
37
the pathogen or the strength of the immune response of sea fans (Ellner et al.
2009; Ruiz-Diaz et al. 2013). It is unlikely to observe full colony recovery of a sea
fan colony if the lesions are overgrown by fouling organisms, even when the
pathogen has disappeared from its host (Toledo-Hernández et al. 2009).
The objective of this study was to analyze the effectiveness of two lesion
eradication strategies, scraping and lesion extirpating, as tools to rehabilitate
Gorgonia ventalina colonies in the field. Scraping consisted of removing, using
metal bristle brushes, fouling organisms overgrowing the axial skeleton and the
purpled tissue bordering these overgrowths. The success of this strategy was
measured by estimating the rates at which sea fans grow back healthy tissue on
the scraped area. Three factors that can potentially affect the rehabilitating
process for the scraped colonies were considered: 1) environmental conditions,
2) colony size, and 3) the ratio between the size of the lesion and the size of the
colony. With respect to environmental conditions, we hypothesized that relatively
few colonies would completely rehabilitate and would exhibit slower rate of
regrowth of healthy tissue at the sites with poor water quality (i.e., high turbidity,
sedimentation, and nutrient concentration) when compared to colonies at the
sites with good water quality. Colonies inhabiting sites with poor water quality
have been shown to exhibit higher abundances of lesions than colonies in sites
with better water quality (Peters 1997). Turbid waters may induce physiological
stress on colonies, ultimately depleting the resources necessary for recovery.
With respect to the effect of colony size, we hypothesize that lesion recovery
should be independent of colony size, as stated by the localized regeneration
38
hypothesis since tissue regeneration is exclusively dependent on the amount of
healthy tissue bordering the lesion (Bak and Steward-Van 1980; Meester et al.
1994; Oren et al. 2001). Finally, with respect to the effect of the lesion
area/colony area ratio (LA/CA) on the rehab process, we hypothesized that
colonies with a higher lesion to colony area ratio (LA/CA) should exhibit slower
recovery than colonies with small lesion to colony area ratio – colony integration
hypothesis (Oren et al. 2001). The colony integration hypothesis argues that the
higher the proportion of healthy tissue with respect to the lesion, the more energy
available for healing through translocation of resources, not just from the tissue
bordering the lesion but from areas further away from the lesion.
The extirpation treatment consisted of cutting from sea fans, the diseased areas
using scissors. The success of this treatments was evaluated based on the
amount of new tissue growing were the lesion existed and the reappearance of
purpled band at the extirpated edge during the growth process.
Methodology
Study site
The study was conducted from July 2011 to July 2013 in two natural reserves
located along the Northeastern and Eastern coast of Puerto Rico: The Luis Peña
Channel Natural Reserve at Culebra (LPR) and, Isla Verde Urban Natural
Reserve at Carolina (IVR, see Figure 2.1). LPR is characterized by low urban
development and no agricultural activities. Consequently, there is high water
39
transparency, averaging a light intensity of 11673.3lm/m2, relatively low
suspended particle matter, sedimentation rate, and algal cover (ToledoHernández et al. 2007; Carlos Toledo-Hernández personal observation). The
coral assemblage is dominated by small colonies of Diploria labyrinthiformis,
Orbicella (Montastrea) annularis, and Porites astreoides. IVR, on the other hand,
is impacted by urban runoff and discharges from a nearby estuary that drains into
the ocean. There is low water transparency (averaging a light intensity of 5781.9
lm/m2), relatively high-suspended particle matter and sedimentation rate year
round, a high algal cover, and low coral cover (<5%) dominated by small-sized
colonies of resilient species such as Porites astreoides and Siderastrea radians
(Torres and Morelock 2002).
Lesion scraping experiment
Two criteria were used to select the colonies: 1) the health state of the colony
(i.e., diseased or healthy) and 2) the size of the colony (i.e., small, medium, or
large). Diseased colonies exhibited lesions overgrown primarily by algae and the
purple tissue that surround them. Causations of lesions were unknown to us, as
we did not perform any microbiological or histological analyses to identify and
diagnose the etiology of the lesions. However, most of the sea fan disease
literature use macroscopic features, such as the one used in this study to
diagnose colonies as diseased or healthy (Smith et al. 1996; Nagelkerken et al.
1997; Smith and Weil 2004). Healthy colonies in contrast, exhibited neither
purpling nor bared skeleton. A total of 32 diseased and 14 healthy colonies were
tagged at LPR, whereas 28 diseased and 15 healthy colonies were tagged at
40
IVR. Colonies with a total surface tissue area ranging from 300-500cm2 were
classified as small, those with a total surface tissue area from 501-1000cm 2 were
classified as medium, and colonies bigger 1000cm2 were classified as large
(Toledo-Hernández et al. 2009). To estimate the size of the tagged colonies and
their lesions, pictures were taken, at an angle approximately perpendicular with
respect to the surface of the colony, with a digital submersible camera by placing
a calibrated board as background to eliminate noise during the image analysis
process.
Lesions from diseased colonies were scraped using metal bristle brushes.
Scraping resulted in the elimination of the fouling organisms overgrowing the
axial skeleton and the purple tissue surrounding the overgrowth at both sides of
the fans. While scraping, caution was taken not to break the axial skeleton. To
determine if recovery was affected by the health state of the colony an area
equivalent to 10% of the whole surface area of a healthy colony was scrapped as
explained previously. To document the progression of wound-healing process,
close-ups pictures of each lesion (from diseased and control colonies) were
taken after scraping at monthly intervals for the following 16 months or until
lesions healed completely (see Figure 2.2). Lesions were deemed healed (fully
recovered), if the axial skeleton was completely covered by healthy sea fan
tissue or if the scraped area (axial skeleton) fragmented. In order to estimate the
percent of tissue that healed or recovered in those colonies that did not fully
recover within the experimental time-period we subtracted the area not covered
by tissue at the end of the experiment to the initial area (bared axial skeleton) just
41
after scraping the lesion. If the skeleton fragmented during the experimental
period, the estimated fragmented area at the end of the experiment was
subtracted from the initial bared axial skeleton area. Sigma Scan Pro Image
Analysis version 5.0 Software was used to analyze all colony pictures.
Measurements obtained from the Sigma Scan software were validated after
comparing them with in situ measurements.
Lesion Extirpation experiment
This experiment was conducted in a 500m2 plot, 1-3m deep in the LPR. For this
experiment, 27 not previously manipulated colonies were tagged, 17 were
diseased colonies while the remaining 10 were healthy (as defined previously).
The area of each lesion was estimated by analyzing the digital images as
explained earlier. Extirpation of lesions consisted of cutting with scissors the axial
skeleton overgrown by fouling organisms including the purple tissue ring
bordering the overgrowth. Cuttings equivalent to 10% in average of total surface
area were performed on healthy colonies (to measure the effect of colony health
state) as control for the effect of tissue extirpation. Colonies were followed at
monthly intervals for one year by means of pictures. Analyses of pictures were
performed as explained above. In this experiment, colonies that did not show any
signs of disease, i.e., purpling tissue or mortality, after lesions were extirpated
were considered fully recovered. If disease signs re-appeared, these were
measured and followed as previously explained (see Figure 2.2).
42
Statistical analyses
We conducted three χ2 analyses (α = 0.05) comparing the number of colonies
that fully recovered or yielded some level of tissue recovery between 1) study
sites; 2) size classes; and 3) lesion ratios having LA/CA<5, 5≤LA/CA<10, and
LA/CA≥10. In addition, we compared the rates of tissue recovery (change in
lesion area through time) between sites, among size classes, and among LA/CA
ratios using linear regression. To perform these analyses, the rates of recovery
per size classes and LA/CA ratios were averaged at each study site and log
transformed for data linearization. The slopes from the obtained linear
regressions were then compared with an analysis of equality of slopes as
described by Sokal and Rohlf (1981). Statistical analyses were performed using
the software R 2.11.1.
Results
Scraping Technique
Three distinct modes of lesions recovery were observed: 1) tissue regeneration,
i.e., growth of healthy tissue over the exposed skeleton from tissue bordering the
lesion, 2) partial fragmentation of axial skeleton, and 3) a combination of the
tissue regeneration and partial fragmentation of exposed axial skeleton (Table
2.1). Average percent of the initial lesion size with respect to the whole colony
area at LPR was 13.61 ± 15.99SD, while at IVR was 7.59 ± 3.84. For statistical
purposes, we created three categories of lesion recovery: colonies that healed
between 80-100% of their lesion; colonies that healed between 8-79%; and
43
colonies that did not recover (Table 2.1). When analyzed based on these
classifications, colonies at LPR and IVR showed similar patterns of recovery (χ2
= 0.0201; df = 1; p = 0.8873), with 22% and 29% colonies reaching full recovery
at LPR and IVR, respectively. Similarly, 50% of the colonies manipulated at LPR
and IVR recovered ≥80% of tissue. Ten percent of colonies at LPR and 7% at
IVR showed an increase in lesion area with respect to their initial size.
To further analyze the effect of colony size on lesion recovery, we pooled the
data based on colony size, i.e., small, medium, and large colonies.
The
statistical analysis showed no significant differences between colony size and
recovery success (χ2 = 0.0357; df = 2; p = 0.9823; Table 2.1). Tissue
regeneration was the most common mechanism of recovery (57%), as recovery
by fragmentation was rare (Table 2.1).
Finally, we pooled the colonies based on a lesion size/colony size ratio to test if
relative lesion size affects the recovery capacity of colonies. Three categories
were created: 1) those colonies with LA/CA<5% ratio; 2) those colonies with 5≤
LA/CA<10% ratio; and 3) those colonies with lesion to colony size ratio greater or
equal than ten percent (LA/CA ≥10%). Recovery success varied significantly with
respect to relative lesion size (χ2 = 6.483; df =2; p = 0.039). For instance, 75% of
the colonies with relatively smaller lesions (LA/CA<5%), recovered completely
whereas the number of colonies with relatively larger lesions (5%≤LA/CA<10%
and LA/CA ≥10%), showed 68% and 42% of lesion recovery, respectively. Most
of the healthy colonies exhibited full recovery, i.e., 12 of 14 colonies at LPR, and
13 of 15 at IVR. Of the remaining two healthy colonies that did not recover
44
completely at LPR, one showed between 80-99% of lesion recovery, while the
other exhibited between 60-79% of lesion recovery. The remaining two colonies
at IVR showed between 60-79% tissue recovery.
Rates of tissue recovery
Rate of recovery for diseased and healthy colonies followed an exponential
decrease through time (R2=0.77, p< 0.05 with Log Recovery tissue = e–.002t+1.483
for diseased colonies and R2=0.55, p< 0.05 with Log Recovery tissue = e–003t+1.26
for healthy colonies). Rate of recovery of healthy colonies was significantly faster
than diseased ones (Fs(1,33) = 6.243, p < 0.05, Figure 2.3A). Rate of tissue
recovery of diseased colonies did not vary between sites (Fs(1,28) = 1.65, p > 0.05)
nor with respect to colony size (Fs(2,21) = 0.027, p > 0.05), or relative lesion size
(Fs(2,21) = 0.080, p >0.05), Figure 2.3B-D. Rate of tissue recovery of healthy
colonies did not vary between sites (Fs(2,21) = 0.09383, p > 0.05), or with respect
to colony size (Fs(2,21) =0.042, p > 0.05), Figure 2.3 B-C.
Colonies with extirpated lesions
None of the 27 colonies (17diseased and 10 healthy) exhibited any physiological
stress, i.e., purpling tissue, throughout the monitoring period after lesions were
extirpated. However, rate of tissue regrowth, which in this case included
production of skeleton and soft tissue, was very slow. For instance, by the end of
the experiment, diseased colonies had only regrown 11% of the original
extirpated area (see Figure 2.2).
45
Discussion
Lesions are small-scale disturbances common to all corals. Yet, the causes, as
well as the consequences, of these lesions are variable, i.e., abiotic and biotic
(Nagelkerken et al. 1999). For instance, predation-induced lesions for the most
part, heal in a relatively short time and leave no permanent scars (personal
observation). Thus, they may have no other consequence than the loss of tissue
and the corresponding resource investment in tissue regeneration. However,
disease-induced lesions are unlikely to heal in a short time period (ToledoHernández et al. 2009). Most likely, a colony will struggle to eradicate the
disease and may either contain it or succumb to it, depending on the strength of
its immune response (Ruiz-Diaz et al. 2013). In such cases, human intervention
is desirable and may contribute towards recovery. To our knowledge, the present
study is the first to document the fate of disease-induced lesions after being
removed by scraping or extirpation.
Tissue regeneration after scraping
Three factors with the potential to affect tissue recovery were considered: 1)
colony location, i.e., LPR vs. IVR; 2) sizes of colony, and 3) the LA/CA ratio. Our
results showed that sites, and thus water quality, had negligible effects on the
number of colonies that fully or partially recovered, and on the time taken for
lesions to recover. These results were surprising as we were expecting to
observe fewer colonies recovering and a lower rate of lesion recovery at IVR due
to stresses caused by lower water quality parameters. Previous studies have
linked the capacity of corals to recover their lesions with the level of water
46
degradation (Pastork and Bilyard 1985; Rogers 1990; Fisher et al. 2007; ToledoHernández et al. 2007). In fact, Fisher et al. (2007) has proposed to use the
abundance of lesions on corals as an indicator of environmental stress. However,
our data suggests that sea fans have an impressive resiliency in their
regeneration capacity. This might explain why sea fans are one of the most
dominant corals across the inshore, degraded, reefs in Puerto Rico.
On the other hand, we failed to find an effect of colony size on recovery. This is
in accord with the studies of Wahle (1983) on gorgonians, and those of Fisher et
al. (2007) and Lirman (2001) on scleractinian corals; but in contradiction of Bak
et al. (1977). Colony size, per se, does not appear to be a good predictor of
recovery capacity.
Interestingly, the only factor considered in this study that had a significant impact
on lesion regeneration capacity of sea fans was the LA/CA ratio. For example,
between 75% and 68% of colonies with LA/CA<5% and 5%≤LA/CA<10%,
respectively, exhibited between 80-100% tissue regeneration. In contrast, only
42% of the colonies with LA/CA≥10% ratio exhibited between 80-100% tissue
regeneration. As hypothesized, the smaller the LA/CA ratio the higher the
probability of fully recovering, whereas the larger the LA/CA ratio the lower the
probability of fully recovery. In fact, the average tissue recovery increases as the
LA/CA ratio decreases (e.g., 80% for LA/CA <5%, 69.9% for colonies with a 5%≤
LA/CA<10%, and 58.7% for colonies with LA/CA ≥10%). Oren et al. (2001)
argued that the higher the amount of healthy tissue vs. lesion area, the more
47
resources available for healing because resources produced away from the
lesion can be translocated to the affected area.
As in previous studies, injury recovery was a time dependent process, being
faster at the onset of experiment, and decreasing as time passed (Meester et al.
1994; Lirman 2000). Hence, the longer the time taken to recovery, the more likely
the injury will become permanent either, as a consequence of resource depletion,
fouling organisms or both. In this study, unrecovered lesions were colonized by
algal turf and as at the onset of the experiment, were surrounded by purpledtissue ring suggesting that the colonies were immunologically active.
Tissue growth after extirpation
Lesions extirpation was successful in that the very small areas with exposed
skeleton remaining after cutting, sealed in a very short period of time, thus no
fouling organisms nor purpling tissue were observed on the impacted area. In
fact, these colonies regained their healthy state rather quickly. This held true in
all colonies regardless of colony or the lesion size. On the other hand, if
compared with tissue scraping, extirpation showed a much slower regeneration
of tissue, as it exhibited a maximum of just over 10% of regeneration by the end
of the experiment. Evidently, it takes more resources and time to regenerate the
axis and associated components than to only regenerate scraped tissue.
However, as in scraping, the resources necessary to regenerate the lost tissue
might have come from the available healthy tissue (Oren et al. 2001).
48
We are still far from preventing coral diseases as most of the pathogens causing
these diseases are unknown to us and the role of environmental factors on
diseases etiology are still poorly understood. However, this study shows that
scrapping or extirpation lesions are effective techniques for rehabilitating sea
fans with lesions. Lesion scraping might be appropriate when LA/CA ratio is <
10% as these are likely to readily recover in relatively short period of time.
Moreover, scraping seems to be a safe procedure as, at least in this study, the
incidence of lesion across colonies adjacent to the manipulated ones did not
increase, suggesting that scraping did not have a negative effect on adjacent sea
fans. It is also worth to mention that the state of the colony may have an effect on
the recovery rates of lesions, as diseased fans recovered at a slower rate than
healthy fans. As these fans were immunologically activated previous to the
experiment, they may have depleted part of their resources (i.e., amoebocytes or
energy), and consequently have less assets for tissue regeneration.
Extirpation of the lesion, on the other hand, may be better when lesions LA/CA ≥
10%, as these seldom recover completely if scraped. The success of these
techniques is yet to be tested on other coral species, but if successfully applied
they could be implemented as a cost-effective management plan to rehabilitate
coral communities. Furthermore, this study demonstrates that sea fans have the
capacity of recovering with the help of human intervention. Hence, we
demonstrate that involvement could help improve coral health state and thus is a
desirable strategy for the management and control of sea fan diseases.
49
Cost analysis
These recovery strategies can be proposed as a low cost management plan that can be
implemented with the objective of eradicating sea fan lesions at localities impacted by
disease. Below we elaborate a cost analysis for lesion eradication in two
reefs
with Gorgonia ventalina colony densities and lesion prevalence obtained from
Toledo-Hernández et al. (2007). We assume a 10,000m2 reef area with an
average depth of 6m. One reef (R1) has 0.84 colonies of G. ventalina colonies
per m2 and a lesion prevalence of 6%. The other reef (R2) has a density of 0.13
and a prevalence of 25%. We also assume an average colony size of 900cm2,
and an average lesion area of 9% of the colony total area.
For R1 we have a total of 8400 G. ventalina colonies, of which 504 are diseased;
thus, we have 504*900cm2*0.09= 40,824cm2 of tissue to scrape or cut. Lesions
are removed by scraping at a rate of 50cm/minute and by cutting at a rate of 160
cm/minute, so we need a total of 13.61hours for the scraping process and 4.25h
for the cutting process.
For R2 we have a total of 1,300 G. ventalina colonies, of which a total of 325 are
diseased, so we have 325*900cm2*0.09=26325cm2 of tissue to either scrape or
cut. For this reef we will need 13.61 hours for the scraping process and 4.25 to
cut out all the lesions in the coral reef Table 2.2.
50
CHAPTER TWO
TABLES
51
Table 2.1 Rate of tissue recovery. Number of small, medium, and large colonies
per locality (LPR or IVR, see Methods) that exhibited different amounts of
recovery by different mechanisms: tissue regeneration (R), fragmentation (F), or
a combination of both (R-F).
Sites
100-80%
Total
Recovery 80Recovery
99
Size
R
F
R-
R
F
R-F
Rate of tissue recovery
79-8%
Recovery 60Recovery 4079
59
R
F
R-F
R
F
R-
Recovery 39-8
R
F
small
LPR
medium
large
small
IVR
medium
large
F
R-F
N R*
F
1
0
2
0
0
2
0
0
1
2
0
1
0
0
0
2
2
0
2
4
0
0
1
0
1
0
1
1
3
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
3
0
1
0
0
1
0
0
0
2
1
1
2
52
Table 2.2: Cost: lesion elimination of Gorgonia ventalina colonies in a reef.
Analysis assumes a reef area of 10,000m2, with densities of 0.84 or 0.13 colonies
by square meters and disease prevalence of 6% and 25%, R1 and R2,
respective. The analysis also assumes an average colony size of 900cm2, with
lesions not greater than 10% of the total area of the colony.
Cost ($)
R1
Details
Price per unit
Maritime Transportation
225 (per day)
Metal scissors
Metal brushes
Scuba divers (3)
500 (per day)
Waterproof tables
20
TOTAL
R2
Scrp.
900
Extirp
225
Scr-Ext
225
Scrp.
225
Extirp
225
Scr-Ext
500
10
60
60
60
60
60
60
6
48
48
48
48
48
48
6000
1500
4500
3000
1500
3000
80
80
80
80
80
80
7088
1913
4913
3413
1913
3688
53
CHAPTER TWO
FIGURES
54
Figure 2.1 Map of Puerto Rico showing the study sites. La Isla Verde Urban
Natural Reserve at Carolina (IVR, box A) and, The Luis Peña Channel Natural
Reserve at Culebra (LPR, box B).
55
Figure 2.2 Example of healing process of a colony with a lesion that was (A)
scraped and (B) extirpated.
A
August 12, 2011
August 12, 2011
October 18, 2011
March 27, 2012
June 13, 2012
B
June 23, 2012
June 23, 2012
June 12, 2013
56
February 7, 2014
Figure 2.3 Recovery rates of scrapped colonies. Linear regressions of tissue
recovery rates of scrapped colonies between (A) control and experimental
colonies, (B) Luis Peña (LPR) and Isla Verde (IVR) sites (C) among size classes;
small, medium, and large colonies, and (D) among lesion to colony area ratio
(LA/CA) categories.
57
CHAPTER THREE
DO ENVIRONMENTAL FACTORS AFFECT THE LESION RECOVERY OF SEA
FANS?
58
ABSTRACT
Despite the plethora of studies describing the relationship between the octocoral
Gorgonia ventalina and its fungal-induced disease, aspergillosis, we lack basic
understanding on how environmental factors affect lesion recovery. This restricts
our ability to comprehensively understand the real impact of the disease at the
colony, population, and community levels.
In this study we compared the
recovery capacity of diseased G. ventalina colonies at two different depths (5m
and 12m) with significant differences in light intensity, temperature, and
hydrodynamics, while correcting for genetic differences. We found that the initial
health state of colonies (i.e., being diseased or healthy) had a significant effect
on tissue regeneration (healing). However, no effect of either depth or genetic
variability was found. All healthy fragments and clones, regardless of treatment
exhibited full recovery, whereas diseased fragments and clones did not. Our
results suggest that the rate of tissue regeneration may be more related to
intrinsic factors, such as energy budget, rather than to factors external to the
colony.
59
INTRODUCTION
In the last few decades, coral diseases have increased in prevalence, incidence,
as well as in severity (Bruno et al. 2007; Burns and Takabayashi 2011; Pollock et
al. 2011). Current research supports the link between environmental factors and
disease prevalence and incidence. For example, elevated seawater temperature
has been associated to outbreaks of white syndromes of hermatypic corals in the
Pacific (Bruno et al. 2007). Poor water quality (nutrients, rainfall and associated
runoff) has also been associated with disease outbreaks as is the case of
atramentous
necrosis,
a
disease
that
impacts
the
coral
Montipora
aequituberculata in the Great Barrier Reef (Haapkylä et al. 2011). Similarly, black
band disease, which affects several coral species in the Caribbean, has been
linked to both high water temperature and high concentration of nitrite and
orthophosphate (Kuta and Richardson 2002).
As diseases impair vital functions of corals such as survival, growth, reproduction
as well as immunological response (Burns and Takabayashi 2011; Ruiz-Diaz et
al. 2013), diseases may compromise the functionality of coral reef ecosystems as
a whole. In order to develop initiatives to mitigate the effect of coral diseases at
the species, population, and community levels, is not only necessary to
understand the role of environmental factors on disease outbreaks, but also how
environment factors affect the capacity of corals to recover from disease. Corals
frequently experience tissue loss due to predation, wave-action, competitive
interactions or diseases, among other factors. The capacity of corals to
regenerate new tissue and recover from these lesions is influenced by the
60
location of the lesion on the colony, their size and shape, size of the colony
bearing the lesion, resources available for recovery, the state of the immune
system of the colony, and species-specific attributes (Bak and Steward-Van;
1980; Meester et al. 1994; Oren et al. 1997; Ruiz-Diaz et al. 2013). Another
important consideration is the amount of time the lesion remains open, because
the likelihood of recovering will dramatically decrease within that time, as the
bare skeleton tends to be quickly overgrown by fouling organisms such as algae
(Whale 1983). Similarly, diseased-induced lesions are likely to remain
unrecovered, if the immune response of the colonies is weak (Ruiz-Diaz et al.
2013) and/or the virulence of the pathogens is high (Ellner et al. 2009).
High lesion prevalence in sites with poor water quality (Toledo-Hernández et al.
2007) could be explained by the effect of high turbidity and/or sedimentation
increasing the probability of an infection (for example, by compromising the
immune response of corals against a pathogen, Ruiz-Diaz et al. 2013) or by the
effect of these variables on the capacity of corals to recover from diseasedinduced lesions. For example, light attenuation could reduce photosynthetic rate
and consequently the energy budget of zooxanthellate corals (Kirk 1994),
compromising not only the immune response, but also the capacity to generate
rapidly new tissue.
The objective of this study was to measure the effects of light intensity,
temperature, and water motion on tissue recovery rate of healthy and diseased
Gorgonia ventalina corals. To pursue this objective we compared the recovery
rate of healthy and diseased colonies at two different depths using a factorial
61
design with four replicate blocks per depth, each having two healthy and two
diseased sea fan fragments per block and two healthy and diseased clones (i.e.,
fragments from the same colony). Tissue fragments and clones from healthy and
diseased colonies were scraped and the tissue recovery measured through time.
Light intensity, water motion, and temperature were measured at each depth to
associate these parameters to tissue recovery. Given that light intensity,
temperature, and water motion are positively related to photosynthetic
performance of G. ventalina (Finelli et al. 2007; Mass et al. 2010; Sebens et al.
2003), we hypothesized that recovery would be faster at shallow depths due to
higher light intensity, water motion, and temperature.
Methods
Study sites
The study was conducted in Cayo Largo (CL), located 6.5km off the Northeastern
coast of Puerto Rico (N 18° 19.09’ 42’’ W 65° 35.01’ 75’’), between April and
August, 2013. CL is a patch reef with a coral assemblage dominated by large
colonies of Gorgonia ventalina, Pseudopterogorgia acerosa and small colonies of
the Montrastea annularis, Acropora palmata, and Porites astreoides (for further
description of the study area see Hernández-Delgado (2005)).
62
Experimental design and environmental data
A total of eight blocks were established at two different depths, 5m and 12m, four
blocks at each depth. At each block, four tissue fragments of approximately
165.5cm2 were collected from nearby G. ventalina colonies. Two of these
fragments were healthy and the other two were diseased. Diseased fragments
were characterized by a necrotic area surrounded by purple tissue, which
represented between 5 and 35% of the total area of the fragments. Each
fragment was attached to an extended nylon line tied to metal rod 2m apart so
that the fragments were suspended approximately 1m above the substrate.
Each block contained a replicate of the following treatments: one non-scrapped
healthy and diseased fragment (i.e., control - HF and DF, respectively) and one
scraped (see below) healthy and diseased fragment (HF-S and DF-S,
respectively). For the HF-S, the equivalent of ten percent of the total tissue area
was scraped off. For the DF-S treatment, the total injured area – the necrotic
area overgrown by fouling organisms plus the purpled tissue – was scraped.
Scraping resulted on the exposure of the axial skeleton.
To evaluate the effect of depth on the recovery capacity of G. ventalina, while
controlling for the genetic variability, we replicated each of the above treatments
with tissue fragments from the same colony (i.e., clones) by cutting two identical
halves, one of which was placed at a shallow block and the other at a deep
block. Thus, each block contained a replica of the following clone treatments: one
healthy and one diseased non-scraped clone (HC and DC, respectively) and one
63
healthy and one diseased scraped clone, (HC-S and DC-S, respectively). In the
case of DCs, they were split so that roughly each resulting half has similar
amount of injured area. In the case of HC-S, the equivalent of 10% of the total
areas was scraped. Lesions from the DC-S were scraped as previously
described. At the end, each block per depth had one HF, HF-S, HC, HC-S, DF,
DF-S, DC, and DC-S (see Figure 1).
To document the progression of the wound-healing process, close-ups pictures
of each fragment and clone were taken after scraping, eight times every two
weeks between April and August or until the lesions healed completely (see
Figure 2). Lesions were deemed healed (fully recovered) whenever the bared
skeleton was completely covered by healthy tissue. Percent of tissue recovered
for those fragments that did not fully recover within the experimental time-period
was estimated by subtracting the remaining area without soft sea fan tissue at
the end of the experiment to the initial area (bared axial skeleton) just after
scraping the lesion. Sigma Scan Pro Image Analysis version 5.0 Software was
used to analyze all fragments and clones pictures. Measurements obtained from
the Sigma Scan software were validated after comparing them with in situ
measurements.
At each depth (5m and 20m), the following environmental variables were
measured: light intensity, water temperature, and water motion. Light and
temperature were measured using a Hobo Pendant temperature/light data logger
64k-UA-002-64 (Onset Company), with three digits decimal places of accuracy,
attached to the metal rods using a zip tie, one device for each depth (see Figure
64
3). These devices were programmed to record every 15 minutes for 14 days
each from April 26 to May 3, May 16 to June 7, June 28 to July 12, and August 9
to August 23, 2013. Light intensity data was obtained during the first 10 days of
placement, as seaweeds overgrowth on the device, the collected data can be
affected if left for more than 10 days (pers.obs). Water motion was monitored
using the Hobo Pendant G acceleration/tilt data loggers & sensor UA-004-64
(Onset Company). These devices were placed following the recommendations of
Evans and Abdo 2010. Briefly, the devices were inserted in a sphere of
polystyrene of 12cm diameter covered with waterproof tape and attached to the
metal rods using a stainless braided of 30cm long. Water motion data was
monitored every 10 seconds for a period of 2.5 days at each depth.
Measurements were performed twice (December 4 to 6, 2013 and January 14 to
16, 2014).
Statistical analysis
Lesion recovery was expressed as the rate at which tissue regenerated (in cm2)
through time. This can be represented as the slope of a linear regression with
time (in days) in the x-axis and lesion area in the y-axis (log transformed). In this
analysis, the slope value (obtained in the previous regressions) was the
explanatory variable and the lesion area/fragments or clones area ratio was the
independent variable. An additional linear regression was used to analyze
whether there was a relation between lesion recovery rate and the initial lesion
area.
65
To determine whether depths (5m and 12m) and fragment treatments (DF, DFS, and HF-S) had an effect on the tissue regeneration through time, the slope of
each fragment was compared using a two-way ANOVA with depth and
treatments as fixed factors. The results from clonal fragments were analyzed
separately from the individual fragments analysis using a repeated measure
ANOVA, as clones are not independent from each other. Statistical analyses
were performed using R version 3.1 (R Core Team, 2014).
RESULTS
Environmental variables and recovery
Light intensity and temperature showed statistical differences between depths
(see Table 3.1). Average temperature at 5m was 28.555 ± 0.012°C (mean±SE),
while at 12m it was 28.334 ± 0.006°C. Average light intensity at 5m was
11203.55±459.410Lux, while at the 12m it was 3429.36±129.11Lux. Average
water motion for the December 5-6, 2013 period was 10.503±0.190m/s2 at 5m
and 9.810±0.166m/s2 at 12m; this difference was significant (t =358.701,
df=33254.95 p <0.001). Likewise, for the January 15-16, 2014 period average
water motion at 5m was 10.221±0.199m/s2 and 9.801±0.197m/s2 at 12m; this
difference was also significant (t= 132.941, df=16209.3, p<0.001).
Tissue Recovery
All the healthy and scraped fragments and clones (HF-S and HC-S, respectively)
survived the experiment without any necrosis. The two way ANOVA indicates
that tissue regeneration was only affected by treatments (F(2,15)= 7.111, p =
66
0.007); depth (F(1,15)= 0.193 , p = 0.667); and their interaction (F(5,15)= 0.487 , p =
0.623) did not showed statistical differences, see Figure 4A. Tukey HSD test
revealed statistical differences between the treatments DF and HF-S (diff= 0.011,
p = 0.007). The results from the repeated measures ANOVA analysis performed
with the clones showed that tissue recovery was only affect by treatments
(F(2,15)=5.477, p= 0.0317). Depth (F(1,15)=3.587, p=0.095) and their iterations
showed no significant differences (F(5,15)=3.915, p=0.065). The average tissue
recovery of the clones was –0.024 ± 0.008cm2 for HC-S; –0.004 ± 0.008cm2 for
DC-S and –0.019 ± 0.017cm2 for DC (see Figure 4B). The results of the Tukey
HSD analysis showed significant differences between DC-S and HC-S
(diff=0.020, p= 0.001) and DC-S and DC (diff=0.015, p=0.016).
DISCUSSION
The relationship between environmental factors and coral diseases is not well
understood (Kuta and Richarson 2002; Haapkylä et al. 2011). The few studies
attempting to understand this relationship have focused primarily on how
environmental variables may induce a given disease rather than how they can
affect the recovery process (Croquer et al. 2002). This study is the first attempt to
document the relation between the recovery dynamics of a diseased coral colony
and environmental factors such as temperature, light intensity, and water motion
while controlling for genetic variability.
67
Fisher et al. (2007) found that colonies of Montastrea spp at 3m depths
regenerated significantly faster than colonies at 6, 9, and 18m. This is in
agreement with our working hypothesis, as we expected to find higher tissue
recovery rates in fragments placed at 5m than those fragments placed at 12m.
However, we found that colonies of G. ventalina at both depths recovered at
similar rates, even though, light intensity, temperature, and water motion differed
significantly between depths. Fragments from the same colony (i.e., clones)
placed at different depths (i.e., HC-S, DC-S, HC, and DC) showed very similar
results. A possible explanation for our results is that the observed reduction in
temperature, light, and water motion between 5 and 12m were not sufficient to
impair physiological processes of sea fans. It is known that zooxanthellate corals
have the capability to acclimate to different light environments to enhance
photosynthetic performance (Iglesias-Prieto and Trench 1994; Robison and
Warner 2006; Frade et al. 2008). The reduction in light intensity of approximately
32% and of 20% in water motion observed at the deeper station might not have
been sufficient to impair photosynthetic rate or diffusion in sea fans. Likewise, the
difference in temperature of 0.2°C, although statistically significant, is unlikely to
have had a significant biological effect.
The main finding of this study is that the initial health state of colonies (i.e., being
diseased or healthy) has a significant effect on tissue recovery. All healthy
fragments and clones, regardless of treatment exhibited full recovery, whereas
diseased fragments and clones did not. It took on average, less time for scraped
healthy fragments and clones to heal their lesions than for scraped healthy
68
fragments and clones (i.e., 78 days vs. 97 days, respectively). These results
suggest that diseased fragments and clones have less resource to invest into
regeneration of lesion than healthy fragments and clones because in diseased
colonies resources are already being allocated to the immune response
(Nagelkerken et al. 1997). Theoretically, life history traits such as immune
defense and tissue repair are supported by a common resource pool. Thus, it is
likely that the allocation of resources for healing were diminished in the diseased
tissues (Oren et al. 2001).
In conclusion, this study demonstrates that depth, light intensity, temperature as
well as water motion does not affect considerably the recovery capacity of the
sea fan G. ventalina. This may explain why this species thrive relatively well in
many coral reefs across Puerto Rico, regardless of environmental degradation.
69
CHAPTER THREE
TABLES
70
Table 3.1: t-test statistic between shallow and deep sites for light intensity
and temperature for different time’s periods. Experimental time April 26 to
August 23, 2014.
Light Intensity
Temperature
April 26 – May3
May 16 – June 7
June 28 – July 12
August 9 –August 23
t =15.134
t =15.552
t =17.589
t =17.553
df=363.398
df=992.628
df=902.605
df=897.812
p<0.001
p<0.001
p<0.01
p<0.001
t=10.422
t =17.497
t =12.866
t =26.723
df=838.223
df=3541.618
df=2274.336
df=3051.956
p<0.001
p<0.001
p<0.01
p<0.001
71
CHAPTER THREE
FIGURES
72
Figure 3.1 Diagram representing different Gorgonia ventalina tissue
recovery treatments per replicate station. HF: healthy fragment, HC: healthy
clone, HF-S: scrapped healthy fragment, DF-S: scrapped diseased fragment, DF:
diseased fragment, HC-S: scrapped healthy clone, DC-S: scrapped diseased
clone, and DC: diseased clone. Light green represents healthy tissue, black oval
represents exposed skeleton, and violet oval represents lesion. See Methods for
more details.
73
Figure 3. 2. Example of wound-healing process. Close-up pictures of a
scrapped healthy fragment showing healing process during experiment.
May 16, 2013
April 26, 2013
June 28, 2013
July 12, 2013
August 30, 2013
August 9, 2013
74
Figure 3.3 Sensors used to measure light intensity, temperature, and water
motion. (A) Light and temperature were measured using a Hobo Pendant
temperature/light data logger 64k-UA-002-64 (Onset Company). (B) Water
motion was measure using Hobo Pendant G acceleration/tilt data loggers &
sensor UA-004-64 (Onset Company).
B
A
75
Figure 3. 4: Boxplot showing mean (bold line) ± one standard error (box)
and two standard errors (whiskers) of tissue recovery treatments of
fragments (A) and clones (B). (A), DF: diseased fragment, DF-S: scrapped
diseased fragment, HF-S: scrapped healthy fragment. (B) DC: diseased clone,
DC-S: scrapped diseased clone, HC-S: scrapped healthy clone.
76
CHAPTER FOUR
MODELING LESION RECOVERY OF SEA FANS
77
ABSTRACT
In the last decades, the Caribbean sea fan coral Gorgonia ventalina has suffered
from several infectious diseases, e.g., protozoan infections, red band disease,
skeleton eroding band, and aspergillosis. These diseases have decimated many
populations across the Caribbean. However, recuperation from these illnesses is
possible. Sea fan recovery capacity is affected by the stress levels and the
colony health condition. In this study, we present a mathematical model that
analyzes the recovery capacity of G. ventalina under contrasting health
conditions after a lesion has been induced. In a healthy colony, after a lesion, a
purple tissue initially overgrows the bare skeleton; afterward the healing process
culminates when the purple tissue is replaced by healthy tissue, which
completely covers the afflicted area. The model predicted three solutions based
on the strength of the immune response of a colony: 1) a lesion completely and
exclusively covered by healthy tissue, after it was first covered by purpled tissue;
2) a lesion completely covered by healthy and purpled tissues; and 3) a lesion
completely covered by purple tissue. In conclusion, the model was accurate in
reproducing three of the macroscopic levels of recovery that have been observed
in the field.
78
INTRODUCTION
Coral diseases have decimated many coral species worldwide (Hoegh-Gulberg
et al. 2007). Since first documented, research has been conducted to understand
the causes and consequences of coral diseases (Efrony et al. 2009).
Nonetheless, the field of coral diseases is still in its infancy as the etiology of
most coral diseases is not yet fully understood. To advance our knowledge of
coral diseases new tools need to be developed to help us to understand, prevent,
and control these maladies.
Recently, researchers have developed mathematical models that simulate hostpathogen interactions in corals. Two good examples of these are the models
proposed by Ellner at al. (2009) and Ruiz-Diaz et al. (2013). Ellner and
coworkers simulate the cellular response of the Caribbean sea fan (Gorgonia
ventalina) to a fungal infection. In this model, short-time solutions are computed
in which the virulence of the fungus controls the rate at which the pathogen kills
its host. Ruiz-Diaz and collaborators, on the other hand, simulate the immune
responses of sea fans under three health state conditions: 1) infection-free, 2)
chronically-diseased, and 3) terminally-diseased. The importance of these
models is that they allow us to predict the fate of the host after an unforeseeable
event (by varying key model parameters) has occurred. Moreover, as both
models are abstractions of a real system, i.e., interaction between a pathogen
and sea fans, they help us to determine the roles and interactions of key
components on the biological system.
79
In this study, we present and analyze a system of two differential equations that
simulates the recovery of G. ventalina coral after a disturbance has occurred, i.e.,
scraping of tissue. Model’s main data were estimated from fieldwork studies in
which tissue from healthy and diseased fan colonies showing lesion overgrown
by fouling organisms and surrounded by purpled tissue, were scraped. Thus, the
model is used to explore the tissue recovery capacity of the corals, by following
the tissue-pigmentation changes, under two health conditions (healthy and
diseased) after a wound has been induced.
The wound healing process in corals is complex and poorly understood. The
cellular mechanisms of the healing process consist of four sequential, but
overlapping phases (Palmer et al. 2011): 1) clot formation via the degranulation
of melanin-containing granular cells that seals the injury, preventing the loss of
essential fluids and the entering of potential pathogens into the internal coral
environment; 2) inflammation response consisting in the infiltration of
amoebocytes (putative immune cells of anthozoans) into the wounded area, from
surrounding tissue area, which phagocyte microorganisms and cellular debris; 3)
proliferation of granular cells, i.e., fibroblast and the formation of granular
epithelium (fibroblast controls the extra-cellular matrix production and collagen
release, which help to form an epithelial-like layer across the lesion); and 4)
maturation, which is the reorganization of the new epithelium, with collagen
production and the apoptosis of excess of cells.
In gorgonian corals such as the sea fans, the most obvious response upon a
wound, whether abiotic or biotic, is the pigmentation of sclerites. Sclerites are
80
calcium carbonate elements secreted by scleroblasts (Leverette et al. 2008).
These elements have different sizes and shapes and are primarily seated on the
epithelial layer, giving structural support to the soft tissue while functioning as a
shield by protecting gorgonians from harmful organisms such as predators
(Etienne et al. 2007). During the early stage of the healing process, as new
tissue overgrow the wound, the number of pigmented (purpled) sclerites
dramatically increases, giving the tissue its purpling characteristic. As time
progresses, clear sclerites - from new healthy tissue - replace the recently
secreted purpled sclerites and thus the purple tissue begins to disappear and the
lesion is completely covered. Shortly after that, purpled tissue is completely
replaced by healthy tissue. However, if sea fans are immunological
compromised, purpled tissue might never disappear from the wound, even
though the wound has been covered.
Mathematical model
In this section we present the model equations, steady-state solutions, and
explain the parameter choices.
Model assumption
This model assumes that G. ventalina corals can be in two health states; healthy
or diseased. The causation of the disease is the same in all diseased colonies.
The lesion occurs in an interior region of the colony. We also assume that under
the diseased condition, the tissue surrounding the lesion is healthy. Regardless
of the health condition of the colony, healthy tissue will replaced the purple tissue
81
during the healing process. Thus, the health condition is only obtained when
skeleton is totally overgrown by healthy tissue and the purple tissue has
disappeared. Purple tissue is an intermediate state before gaining health. Finally,
we assumed a single compartment model, i.e., purple and healthy tissues grow
homogeneously across a specific area of bare skeleton (the lesion).
Model equations
The differential equation (4.1) represents the dynamic process of lesion
overgrowth by purple tissue. Let us denote the fraction of purple tissue by
and
the fraction of healthy tissue by . Thus, the rate of change of purple tissue is
given by:
(
where
)
(4.1)
(1/days) is the rate at which the purple tissue grows on the skeleton,
the maximum fraction of tissue, thus
, and
is
is the rate at which purple
tissue is reduced in presence of healthy tissue.
The differential equation (4.2) represents the rate of change of healthy tissue ( ),
which is given by:
(
where
)
(4.2)
(1/days) is the rate at which healthy tissue grows and
which the healthy tissue is reduced in presence of purple tissue.
82
is the rate at
Steady-state points and stability
Three steady-state solutions were obtained from the equation system (4.1)-(4.2)
by equating the derivatives to zero
(
(
and solving them for
)
(4.3)
)
(4.4)
and .
Total recovery state
For the total recovery of the lesion, i.e., skeleton is completely overgrown by
healthy tissue,
and
, and from equation (4.4), one gets that
.
Hence, the steady-state solution is
̂
( ̂ ̂)
(
)
(4.5)
Chronically diseased state 1
For the intermediate scenario of recovery (lesion is overgrown by purple and
healthy tissue),
and
, and from equations (4.3) and (4.4), after some
( (
algebraic manipulations, one gets that
( (
)) (
)) (
) and
). Then, the steady-state solution is
̃
( ̃ ̃)
(
(
)
(
)
)
83
(4.6)
Chronically diseased state 2
For the last scenario of recovery (skeleton is covered by purple tissue
exclusively)
and
, and from equation (4.3), one gets that
.
Hence, the steady-state solution is
̈
( ̈
̈ )
(
)
(4.7)
In a continuous model, a steady-state solution will be stable provided that the
eigenvalues
of the linearized problem have negative real part, i.e., Re ( ) < 0,
for all i (Edelstein-Keshet 1998). From equations (4.3) and (4.4), the Jacobian
matrix is given by equation (4.8).
[
(
)
]
)
(
(4.8)
We evaluated the point ̂ ̃ , and ̈ , from equations (4.5), (4.6), and (4.7),
respectively, in the Jacobian matrix (4.12).
At ̂ the Jacobian matrix is:
( ̂)
[
(
)
In matrix (4.9) one eigenvalue (
negative if
]
(4.9)
) is negative and the other eigenvalue is
. Therefore, the steady-state solution (4.5) is stable whenever
.
At the steady state ̃ the Jacobian matrix is:
84
[
(̃)
(
(
)
)
(
(
)
]
)
(4.10)
By setting
(
)
(
)
and
(
)(
)(
),
it can be verified that the eigenvalues of the matrix (4.10) are
√
.
If
and
then
,
Under these conditions,
positive sign,
√
, and
and the eigenvalue corresponding to the
, has negative real part, i.e.,
eigenvalue corresponding to the negative sign,
( )
.
.
At the steady state (4.7), the Jacobian matrix is
85
( )
. Moreover, the
, has negative real part too, i.e.,
( ̈)
[
(
]
For this matrix, one eigenvalue (
negative whenever
(4.11)
)
) is negative and the other eigenvalue is
. Therefore, the steady-state solution (4.7) is stable
whenever this condition is satisfied.
Model parameters
For the analysis of this model two types of parameters were used, empirical and
theoretical parameters.
Empirical parameters
The data to estimate the growth rate of the purple tissue ( ) and the growth rate
of the healthy tissue ( ) were obtained from the fieldwork conducted by RuizDiaz et al. (2014). To obtain the data, we tagged ten diseased and seven healthy
colonies. Lesions from diseased colonies were scraped and photographed at
monthly intervals for one year. We estimated
(in cm2/days) and
(in cm2/days)
by doing image analysis of the digital photos using Sigma Scan, then the values
were normalized by dividing them by the average area (cm2).
A similar
procedure was performed with healthy colonies, however, in this case the
inflicted lesions have an area equivalent to 10% of the total colony area.
Theoretical parameters
These parameters are divided into fixed and variable parameters. The fixed
parameters keep the same values irrespective of the recovery state of the
86
colony, while variable parameters were assigned according to the health state of
the recovering colony; the values of
and
were adjusted to satisfy the stability
conditions of each steady state.
Results
Table 4.1 shows initial values for model variables (i.e., at time t= 0) for each
state: healthy and chronically diseased one and two. Table 4.2 shows the model
parameters values.
Total recovery
The first simulation was obtained by choosing the value of
such that the
stability condition for the steady state (4.5) is satisfied (Table 4.2). In this
solution, the skeleton is overgrown completely and exclusively by healthy tissue
(Figure 4.1). From day 1 to day 10, purple tissue covered 9% of the bare
skeleton at a rate of 1% per day. Afterwards, the rate at which purple tissue
covers the lesion increased to 4% per day, such that by day 25 of the simulation,
purpled tissue covered 70% of the bare skeleton. Subsequently, however, this
rate decreases to levels similar to the start of the simulation (1.3% per day), thus
by day 45, 96% of the lesion area was covered by purple tissue.
While purpled tissue was covering the lesion, healthy tissue was replacing it.
Thus, by day 32 of the simulation, healthy tissue had replaced only 1% of the
purpled tissue area (at a rate of 0.03% per day). The rate at which healthy tissue
replaced purpled tissue steadily increases with time, so as by day 45 healthy
tissue had replaced 2% of the total area at a rate of 0.15% per day. From this
87
day until day 140 of the simulation, healthy tissue reached it maximal tissue
replacement rate (0.77% per day). Afterward, the rate at which the healthy tissue
replaced the purple one decreases until reaching complete recovery by day 300.
Chronically diseased state 1
This simulation was obtained by choosing the values of
and
less than one
such that the stability condition for the steady state (4.6) is satisfied (Table 4.2). It
results in the skeleton completely overgrown by healthy and purpled tissue
(Figure 4.2). During the first 62 days of the simulation, purpled tissue covered
only 1% of the skeleton at a rate area of 0.02% per day. Afterward, however, the
rate at which purpled tissue covered the bare skeleton increased to 1.8% per
day, so that by day 95 of the simulation, 60% of the lesion was covered. The
tissue continues to grow, though at a rate of 0.6% per day, until covering 89% of
the lesion by day 143. Thereafter, the rate at which purpled tissue covers the
bare skeleton was stabilized until the lesion is fully overgrown by purpled tissue
by day 700.
As previously described, healthy tissue slowly replaced purple tissue. Thus, by
day 73 of the simulation, healthy tissue has replaced 1% of purpled tissue area at
a rate of 0.01% per day. At day 95, healthy tissue had replaced 6% of the
purpled tissue; while by day 143 healthy tissue had doubled the area covered at
a rate of 0.34% per day. Healthy tissue continues to replace the purple tissue
however, it never completely replaced the total area covered by purpled tissue.
88
Thus, by the end of the simulation, purpled tissue covered 20% of the original
lesion area, while the remaining 80% is covered by healthy tissue (Figure 4.2).
Chronically diseased state 2
The last simulation was obtained by choosing the value of
such that the
stability condition for the steady state (4.7) was satisfied (Table 4.2). In this
solution the skeleton is exclusively overgrown by purpled tissue by the end of the
simulation (Figure 4.3). During the first 15 days of the simulation, purpled tissue
had covered 4% of the bare skeleton area, at a rate of 0.03% per day. However,
at day 60 of the simulation, purpled tissue covered 57% of the lesion area, at a
rate of 4% per day. From this day to day 100, purpled tissue covered 74% the
lesion at a rate of 0.38% per day and by day 360 the lesion was completely
covered by purpled tissue.
In this solution, healthy tissue only replaced 42% of the purpled tissue during the
first 69 days. Afterward, healthy tissue ceased to grow and was replaced by
purpled tissue at a rate of 1.07% per day, so as by day 360 of the simulation,
healthy tissue was completely replaced by purpled tissue (Figure 4.3).
Discussion
Even though, the model presented here is an abstraction of a highly complex
process, as
is the tissue healing process of sea fans, it is accurate in
reproducing three of the macroscopic levels of recovery that have been observed
in the field. The levels of recovery are represented in three different solutions: 1)
a lesion completely and exclusively covered by healthy tissue, after it was
89
previously covered by purpled tissue; 2) a lesion completely covered by healthy
and diseased tissues; and 3) a lesion completely covered by purple tissue.
Healing of a lesion starts when purpled tissue begin to overgrow the exposed
skeleton. This purpled tissue grows from the healthy tissue adjacent to the lesion.
As time progresses, healthy tissue replaces the recently overgrown purpled
tissue, until the lesion is completely covered, first by purpled tissue and then by
healthy tissue (first simulation). As purpled tissue has been associated to
immunologically active sea fans (Alker et al. 2004; Mydlarz and Harvell 2007;
Toledo-Hernández et al. 2012; Ruiz-Diaz et al. 2013), the fact that purple tissue
is completely replaced by healthy tissue brings about the activation of the
immune system of the colony.
However, under prolonged stressful conditions, the colony will maintain its
immune activation for an extended period of time. In such scenario, two
outcomes are observed: 1) the purpled tissue covers the exposed skeleton
completely, yet healthy tissue fails to replace the purpled tissue completely. In
such case, healthy and purpled tissue will cover the once open wound (second
simulation, Figure 4.2). And 2) purpled tissue covers completely the exposed
skeleton, with a subsequent partial replacement by health tissue, yet the healthy
tissue is replaced back by purpled tissue, leaving the lesion covered only by
purpled tissue (third simulation; Figure 4.3).
From a mathematical standpoint, the model most critical parameters were
. For example, in the total recovery case if
and
assume values slightly greater than
those in Table 4.2, the coral will improve its recovery capacity. In other words,
90
the time taken for the colony to fully recover the lesion will decrease. In this
regard, an increment in the value of
could be interpreted as a reduction in
stress. For a chronically diseased colony in state 1 large value of
will result in
the colony reverting to the total recovery case (i.e., 100% healthy tissue).
Biologically this would result when a stressful environmental condition that had
compromised the healing process disappears, and the colony is then able to fully
recover. Finally, for a chronically diseased colony in state 2, large values of
will
result in the unrealistic situation were healthy tissue covers the bare skeleton
without first being covered by purple tissue. Similarly, the greater the value of ,
the greater the stress and the longer it will take for the colony to recover. In this
case, as
continues to increase, the effect of
in the model becomes negligible
and the colony will cease to recover at all with the lesion covered 100% with
purple tissue. Biologically, this can be interpreted as the colony remaining in a
permanent immune activation mode.
To conclude, the model successfully simulated the real behavior of the recovery
dynamics of a sea fan in the sense that it was able to predict that the growth of
healthy tissue always occurs after the purple tissue overgrows the bare skeleton.
Moreover, by varying
and , the model allows us to simulate changes in stress
condition, with the consequent changes in health states. Thus, it allows us to
simulate the effect of the ever-changing stress conditions on the recovery of
corals.
91
CHAPTER 4
TABLES
92
Table 4.1 Initial values of model variables: Purple and healthy tissue.
Description
Healthy state
Chronic state 1
Chronic state 2
Purple tissue
0.01091
0.00001
0.01091
Healthy tissue
0.00191
0.00001
0.00009
93
Table 4.2: Model parameters
Empirical parameters
Health state of the colony
β
Theoretical parameters
Fixed parameter
Κ*
ρ
Variable parameters
λ
θ
Healthy
0.2103
0.1000
1
1.8601
0.1299
Chronically state 1
0.1458
0.0810
1
0.9759
0.8969
Chronically state 2
0.1025
0.2354
1
0.7800
1.0513
*
Normalized from the average lesion area, 37cm2.
94
CHAPTER FOUR
FIGURES
95
Figure 4.1 Dynamics of healthy and purple tissue for total recovery.
%
96
Figure 4.2 Dynamics of healthy and purple tissue for the chronically diseased
state 1; lesion is overgrown by purple and healthy tissue.
%
97
Figure 4.3 Dynamics of healthy and purple tissue for the chronically diseased
state 2; lesion is overgrown by purple and healthy tissue.
%
98
GENERAL CONCLUSIONS
The results of the studies conducted in this dissertation demonstrate that G.
ventalina is an organism resilient to changes in environmental factors. In
particular, those sea fans have a high regeneration capacity. This offers an
explanation as to why sea fans are capable of thriving relatively well in many
coral
reefs
across
Puerto
Rico,
independently
of
the
environmental
conditions. The two mathematical models could be used as tools to predict the
behavior of other coral species and also as a basis for understanding the
behavior of coral species with smaller habitat ranges.
The mathematical model presented in Chapter 1 predicts three final health states
(disease-free host, chronically-diseased host, and terminally-diseased host)
reached by assuming constant pathogen virulence (i.e., the effect of pathogens
on polyp death rate is not altered) while varying the colony’s immune response.
This analysis suggests an alternative explanation for the spatial and temporal
variability in disease incidence and mortality, which is based on the strength of
the immune system of hosts rather than the virulence of the pathogen. The
lesion removal experiments presented in Chapter 2 demonstrate that sea fans
have the capacity of recovering with the help of human intervention. The
experiments also indicate that scrapping might be appropriate when the lesion to
colony area ratio is < 10% as these are likely to readily recover in relatively short
periods of time, and that lesion removal by extirpation is most appropriate when
99
the lesion is large (the ratio between lesion and colony area ≥ 10%). The
experiment presented in Chapter 3 demonstrates that the differences in light
intensity, temperature and water motion between 5m and 12m of depth does not
affect significantly the recovery capacity of the sea fan G. ventalina. This may
explain why this species thrive relatively well in many coral reefs across Puerto
Rico, regardless of the environmental degradation. The mathematical model in
Chapter 4 predicted three solutions based on the strength of the immune
response of a colony. These solutions reproduced three of the macroscopic
levels of recovery that have been observed in the field.
100
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