Asymmetric competition prevents the outbreak of an opportunistic species after coral reef
degradation
Manuel González-Rivero1,
2,* ζ
, Yves-Marie Bozec1, Iliana Chollett1,
2 ξ,
Renata Ferrari1,φ,
Christine H. L. Schönberg3, Peter J. Mumby1, 2
1. School of Biological Sciences and Australian Research Council Centre of Excellence for
Coral Reef Studies, University of Queensland, St. Lucia, Qld 4072 Australia.
2. College of Life and Environmental Sciences, University of Exeter, EX44PS. United Kingdom.
3. Oceans Institute, University of Western Australia, 39 Fairway, Crawley, WA 6009, Australia
*Corresponding author: Telephone: +61 7 336 53452. E-mail: m.gonzalezrivero@uq.edu.au
ζ Current address: Global Change Institute, University of Queensland, St Lucia, Qld, 4072,
Australia.
ξ Current address: Smithsonian Marine Station, Smithsonian Institute, Fort Pierce, Florida. USA
φ Current address: University of Sydney, Coastal and Marine Ecosystems Group, School of
Biological Sciences & Australian Centre for Field Robotics, NWS, Australia.
Author Contributions: MGR and PJM conceived and designed field surveys and the ecosystem
model. MGR, RF and PJM performed field surveys. MGR, YMB, IC and PJM designed and
performed data analysis. MGR, PJM, IC, and YMB wrote the manuscript; other authors provided
editorial advice.
1
Online Resource 1. Spatio-temporal variations of benthic community composition,
detailing the composition of macroalgae
Coverage of benthic species was monitored over time from 1998 to 2009 using randomly placed
photo-quadrats or transects for three locations at Glover’s atoll, Belize (as described on the
manuscript and Online Resource 3). Here we present a comparative characterization of the
benthic community across sites and between two periods of time. While benthic composition was
monitored until 2009, here we present a spatial and temporal comparison between 1998 and 2007
because only one site (E1) was monitored in 2009.
When aggregating the benthic composition in functional groups, the results show a consistent
decrease in coral cover between 1998 and 2007 across sites (Figure S1), from 18.5 % ± 4.8 % to
8.5 ± 0.3 % (mean ± se among sites). In contrast, cropped turf algae, defined in the model as
available space for recruitment and growth of benthic species, increased from 35.7 ± 4.8 % to
43.1 ± 7.9 % (mean ± se among sites, Figure S1). Macroalgae remained the most dominant group
of benthic functional groups across sites and between periods of time (Figure S1), averaging 36
% ± 3.9 % (mean +/se across sites and time). Similarly, sponges only represented an average of
1.7 % ± 0.32 % (mean +/se across sites and time), where Cliona tenuis dominated the
composition (averaging 1.1 % ± 0.3 % cover, mean ± se across sites and time).
Looking in detail at the spatio-temporal variability of relative macroalgal composition (Figure
S2), Lobophora variegata and Dictyota spp, the model macroalgae species in this study,
consistently dominated the species composition across time and space, representing 78.1 +/- 0.1
% (mean +/- se across sites and time) of the total macroalgae coverage. Between time periods,
Dictyota spp showed a consistent increase in cover, relative to total macroalgae abundance, from
2
46.2 +/- 0.1 % to 60.3 +/- 0.1 (mean +/- se across space and time, Figure S2). In contrary, L.
variagata showed no changes between 1998 and 2007. While the figure provided (Figure S2)
summarises other macroalgal species by algal groups (e.g., Rhodophyta, Clorophyta,
Phaenophyta), here we provide the full taxonomic list of macroalgae identified to lowest possible
taxonomic resolution (Table S1).
3
Fig S1. Spatial variability of benthic composition at Glover’s Atoll, Belize, between A) 1998 and B) 2007. Pie
charts represent the percentage cover of functional groups of benthos monitored at each study site. Base map
source: Millennium Coral Reef Mapping Project (MCMP).
4
Fig. S2. Macroalgal composition for each study site at Glover’s atoll and between two periods of time: A) 1998
and B) 2007. The values presented here are the relative proportion of each group for the total macroalgal cover
for each site and period of time. For graphic representation, identified species of macroalgae have been
categorised into major groups (e.g., Chlorophyta, Phaenophyta and Rodophyta) with the exception of
Lobophora variegata, Dictyota spp and Halimeda spp, being the most dominant species. Note that Filamentous
cyanobacteria (Cyanophyta) are also included here as a category despite the fact that cyanobacteria are not
formally considered to be macroalgae. Base map source: Millennium Coral Reef Mapping Project (MCMP).
5
Table S1. Macroalgal species list recorded at Glover’s Atoll, Belize, from video surveys between
1998 and 2009.
Group
Chlorophyta
Species
Amphiroa spp
Microdictyon spp
Penicillus capitatus
Rhipocephalus spp
Halimeda spp
Phaeophyta
Padina spp
Sargassum hystrix
Turbinaria spp
Dictyota spp
Lobophora variegata
Rhodophyta
Galaxaura spp
Jania spp
Jania adhaerens
Laurencia spp
Wrangelia spp
6
Online Resource 2. Spatio-temporal variations of the population attributes of
Cliona tenuis at Glover’s atoll between 1998 and 2009
Population attributes of Cliona tenuis, such as Skewness, Kurtosis, Geometric mean size and size
distribution are compared among time periods and detailed in Table S2, and summarized in
Figure S3. Size-frequency distribution at each period was compared against a lognormal
distribution using Kolmogorov-Smirnov (K-S) normality test on log-transformed data. Sample
size and sampled area are shown in Table S2. Populations attributes describing the structure of
the sponge populations did not varied significantly among sites and over 11 years, describing a
size distribution strongly biased towards individuals between 0 and 100cm2 (Fig. S3).
7
Table S2. Demographic attributes of Cliona tenuis at Glover’s Atoll from 1998 to 2009, showing
the skewness, kurtosis, geometric mean size, Shapiro-Wilk normality test of the log transformed
sample (W Shapiro Wilk statistic, p: significance level), and the sampling effort (sampled area,
number sampling units and of sampled individuals) for specific sponge populations at each site
and time. Populations were sampled in time and space using 1-m2 quadrats, which two
exceptions highlighted in the table with the asterisks.
Year
1998
2003
2007
2009
Site
Skewness
Kurtosis
Geometric
mean Size
(cm2)
Log-Normality
test
Sampling effort
W
p
Area (m2)
Sampling
units
Ind.
E1
5.14
38.81
12.65
0.984
0.279
30
6*
100
E2
0.96
2.64
9.97
0.960
0.694
5
1*
15
W1
2.86
12.96
12.85
0.988
0.684
15
3*
79
E1
1.12
3.22
27.06
0.958
0.087
13
13
47
E2
1.15
2.93
7.12
0.888
0.092
18
18
13
W1
10.01
102.13
3.57
0.953
0.001
19
19
106
E1
5.69
34.20
14.82
0.968
0.341
23
23
38
E2
5.24
33.95
28.18
0.959
0.043
40
40
60
W1
2.08
5.93
11.78
0.934
0.095
30
30
26
E1
5.22
33.78
9.89
0.993
0.291
100**
10
241
E2
9.28
94.21
10.42
0.931
<0.001
100**
10
136
* Belt transects (0.5 x 10 m)
** Belt transects (1 x 10 m)
8
Fig. S3. Demographic attributes of Cliona tenuis populations between 1998 and 2009. The
dotted line in panned A to C show the global averages among sites and years, dots represent
averages among sites, and vertical bars denote the 95% confidence intervals. A) Geometric mean
size of individuals. B) Skewness. C) Kurtosis. In panels D and E, the bars indicate the observed
size frequency distribution and the red dashed lines show the fitted log-normal size frequency
distribution given the mean and standard deviation. D) Size-frequency distribution of C. tenuis in
2009 at site E1. E) The same distribution when size is log-transformed.
9
Online Resource 3. Parameter estimation of the hypothesized drivers of Cliona
tenuis population structure
Four processes are here hypothesized to drive the population structure of C. tenuis: Competition,
Stock-Recruitment, individual mortality and partial tissue mortality. The parameterization of
these drivers was estimated from Glover’s Atoll, Belize on the windward side of the atoll (E1
and E2, Fig. S4), and it is discussed in turn for each driver bellow.
Fig. S4. Location of study sites at Glover’s Atoll (A) in the Mesoamerican Barrier Reef, Belize (B), and
the relative location of the atoll in the wider Caribbean region (C). Dashed line show the approximate
boundaries of the Glover’s Atoll Marine Reserve. Vital rates of the Cliona tenuis populations were obtained
from site E1, while sites E1, E2 and W1 were monitored over time and used for testing the model
simulations. Map Source data: global coastline by the Global Self-consistent, Hierarchical, High-resolution
Shoreline database (GSHHS) and Mesoamerican coastline and reef locations by the Millennium Coral Reef
Mapping project (MCRM).
10
Competition: The growth rate of Cliona spp. is strongly dependent on the intensity of
competition, given by the identity of the competitor and the proportion of tissue in direct contact
(Cebrian and Uriz 2006; Chaves-Fonnegra and Zea 2011; López-Victoria et al. 2006). Pairwise
competition coefficients, such as the rate of advance or retreat during confrontation, were
obtained from a previous field study at Glover’s atoll (E1, Fig. S4 during 2009 (González-Rivero
et al. 2012), and the results are summarized in the manuscript (Table S4).
In previous research, we observed that the linear extension of C. tenuis in competition with
cropped algae, or turf, significantly varied as a function of the developing state of this algal
community, indicating that the competitive strength of turf increase as it get denser and taller
(González-Rivero et al. 2012). Here we estimate growth of the sponge in confrontation with the
average cropped algae state at Glover’s Atoll (including tall and short turf algae). From tagged
sponges in 2009 on the windward side of the atoll (see González-Rivero et al. 2012 for details),
we selected those individuals which withstood over 90% of their perimeter in competition with
turf algae (95.6 ± 0.2 %; mean ± CI0.95, n = 27). Assuming a radial expansion of C. tenuis,
average linear extension was estimated by calculating the difference between the radius of the
sponge (∆r) at two time steps (0 and 286 days during year 2009) from each individual (Equation
1).
∆𝑟 = 1.35 ∙
1
1
𝐴𝑓 ⁄2 − 𝐴𝑖 ⁄2
1
𝜋 ⁄2
eqn 1
Where A is the size of the individual at 0 (Ai) and 286 days (Af), estimated from video footage
using the software VidAna (v 1.2.1; Hedley 2006). Linear extension (∆r) is linearly extrapolated
to a year, using the constant coefficient of 1.35. The average growth of the sponge in
confrontation with major benthic components is presented in the manuscript (Table S3).
11
Stock-recruitment dynamics: Given the poor swimming capabilities of clionaid larvae their
abundance is strongly spatially correlated to the abundance of adults (Mariani et al. 2006;
Mariani et al. 2005). Therefore, the modelled populations are assumed to be sustained by stockrecruitment dynamics determined by the number of individuals and the fecundity associated with
each. Fecundity is a function of colony size (Ramirez Llodra 2002), and although the exact
nature of the fecundity-size relationship has not yet been determined in clionaids, here we
assume a simple linear increase in fecundity with tissue area. The reproductive index is the
proportion of propagules per unit of tissue, and assuming that this index remains constant with
size, the number of propagules and larvae produced will proportionately increase with the
individual size of the sponge.
Whole-individual mortality: Newly settled individuals are prone to high mortality rates caused
by extrinsic physical or biological selective pressures, and as individuals increase in size they
become less vulnerable, eventually reaching a size at which they escape from these sources of
mortality (Gosselin and Qian 1997). Thus, whole-individual mortality rates tend to decrease as
benthic invertebrates grow (Babcock 1991; Hughes and Connell 1987; Jackson et al. 1985). Here
we modelled mortality as a negative power function of size (Peterson and Wroblewski 1984):
M=0.16(size-1.42) (eqn 2), where the parameters were estimated by the non-linear least square
regression fitting, and size is the initial area of the sponge, described below. Equation 2 was used
to calculate the mortality rate per year. We then divided this value by two to obtain the rate per
time step in the model (6 months).
253 sponges were randomly tagged in January 2009 at E1 (Fig. S4), and followed during 286
days (see González-Rivero et al. 2012 for details). The number of dead individuals was recorded
at the end of this period, and the initial size of each individual was estimated from high definition
12
footage videos, using the software VidAna (Hedley 2006). The probability of mortality as a
function of size was then calculated by subdividing the dataset into 5 cm2 size classes. The nolinear regression was fitted using R and the ‘nls’ package.
Partial tissue mortality: The age and size structure of sessile organisms are largely decoupled,
and this especially true in marine ecosystems (Bak and Meesters 1998; Hughes 1984; Hughes
and Connell 1987). Individuals of a given age can vary considerably in size by sustaining large
partial tissue mortality or shrinkage (Bak and Meesters 1998; Hughes and Connell 1987). Here
we modelled the partial tissue mortality of sponges by using the probability of shrinking per
individual at each time step and, the probable extent of tissue mortality as a proportion of size.
Shrinking of the tagged sponges was commonly observed in the field. Although partial mortality
is generally overlooked in demographic studies of benthic organisms, this attribute could be
important for the dynamics of these populations. To calculate the per capita probability of
occurrence and intensity of partial mortality we followed sponges that were not subjected to
macroalgae or coral competition throughout the year in 2009. These sponges had 95.6 ± 0.2 %
(mean ± CI0.95, n = 27) of the perimeter in contact with turf, therefore minimizing any possible
confounding effect of competition in the estimates of partial mortality. The probability of partial
mortality was then calculated as a proportion of shrinking sponges against those that did not
change in size.
13
Online resource 4. Partitioning the direct competitive interaction of C. tenuis
with other space occupiers at Glover’s atoll, Belize.
Over the course of a year, 247 individuals of C. tenuis were monitored at sites E1 and E2 (Figure
S2, Online Resource 2). The methodological approach is described in Gonzalez-Rivero et al
(2011), and data were used to parameterize the model as described in the Online Resource 2.
During these observations, the perimeter of each sponge in contact with other benthic species
was recorded at two points in time, January and December 2009. Here we summarize the relative
proportion of tissue of C. tenuis individuals in contact with other functional groups of
competitors, averaged for these two sampling periods (Figure S3). From these results,
macroalgae comprise the main competitor averaging a percentage contact with the sponge of
37% ± 8.4% (mean ± ci95%). Together, available space for cropped turf algae and macroalgae
represented an average of 68% ± 13.6% (mean ± ci95%) the perimeter of each sponge. A detailed
analysis of the interaction with the identified species or groups of algae show that Lobophora
variegata, Dictyota pulchella and dense algal mats have on average 26% ± 4.7% of their
perimeter in contact with C. tenuis (Figure S4). Although some variability was observed between
the two observation periods, these three groups of macroalgae represent the main competitors of
C. tenuis throughout the study (Figure S4).
14
Fig S3. Average proportion of the perimeter of C. tenuis individuals in contact with other
space occupiers at Glover’s atoll, Belize. Competitor categories are: Macroalgal species
(Macroalgae), Cropped turf algae (turf), Coral species (Coral), Crustose coralline algae
(CCA), Other invertebrates (Other), Sponges species (Sponges). Bars represent the average
percentage of the tissue in contact with each competitor group across 247 individuals
observed in January and December 2009. Error bars denote the 95% confidence intervals
from each mean value.
15
Fig S4. Average proportion of the perimeter of C. tenuis individual in contact with
macroalgae and cyanobacteria at Glover’s atoll, Belize and between two periods of
evaluation. Competitor categories are: Dictyota pulchela (Dpul), Lobophora variegata
(Lvar), Dense algal mat (Amat), Halimeda spp. (Hsp), Jania adherens (Jadh), Sargassum
hystrix (Shys), Cyanobacteria (Cyan), Filamentous Rhodophyta (F.rhodo). Bars represent
the average proportion of the tissue in contact with each competitor group across 247
individuals observed in January and December 2009. Error bars denote the 95%
confidence intervals from each mean value.
16
Online Resource 5. Detailed description of the ecosystem model
Overview
The model is an individual-based cellular automaton simulating the population dynamics of
benthic organisms dispatched across a regular square lattice of 20×20 cells. The lattice grid has a
toroidal structure so that every reef cell has continuous boundaries formed by 4 neighbouring
cells. Each cell contains a mixture of living substrata (Table S4) comprising multiple coral
colonies, sponge individuals and patches of algae. A number of cells are assigned to the class
“ungrazable substratum” (e.g., sand, soft-corals, etc) so that no benthic live cover can colonize
those cells.
The model captures rates of recruitment, growth, reproduction and mortality of benthic
individuals as well as their competitive interactions, calculated twice a year (every 6 months). At
each time step, the toroidal lattice structure helps define probabilistic rules (within a 4-cell von
Neumann neighbourhood) of competitive interactions of corals and sponges with macroalgae,
which reduce the growth rate of each coral and sponge taxon. Parrotfish grazing randomly
allocated over the grid mediates competition of macroalgae with other benthic components.
Grazing affects all algal classes and always results in cropped algae. The spatial arrangement of
elements within an individual cell is not explicit, but coral-coral and coral-sponge competition
can occur at intra-cellular scales.
Technically, the model updates a set of connected 20×20 matrices (one matrix for each benthic
cover) at discrete time steps according to the deterministic and probabilistic rules (sub models)
presented in Table S5. The model is implemented in MATLAB as a sequence of vectorized
instructions (see Fig. S6), so that all the cells of the lattice grid are processed simultaneously for
17
a given matrix. Each instruction reflects the action of a particular process occurring within a cell,
in isolation or as a result of its immediate environment (4-cell von Neumann neighbourhood)
defined at the previous time step. Within a time iteration, the four coral matrices are temporarily
fusionned within a three-dimensional array (20×20×5) for processing simultaneously all coral
and sponge species. At the initial step, a number of cells are randomly designated as “ungrazable
cells” to match the specified cover of ungrazable substratum. The remaining cells are filled with
coral colonies until the total cover of each coral species reaches the desired level (as a percentage
of the total reef area). Colony sizes are created based on a uniform distribution and each colony
is randomly allocated to a cell. Each cell cannot contain more than one colony per species
(50×50 cm cells). Algal patches are created in a similar way by filling the remaining space
according to their initial cover (Fig. S7). Cover matrices are then processed and the resulting
benthic covers are stored after every time-iteration. The whole process (including initialisation)
is repeated to obtain 100 independent reef trajectories over time.
18
Fig. S6. Overview of model implementation. For definitions of terms see Table 2 and Figure
4.
19
Fig. S7. Example diagram of the structure of benthic organisms and key processes represented in a lattice.
Note that x and y provide the coordinates for each cell. This diagram also shows that corals and sponges are
presented as individuals, while macroalgae, cropped algae and “ungrazable” substrate fills the remaining
space.
Table S4. Contents of individual cells within the grid lattice
BENTHIC COVER
Brooding coral 1 (BC1)
Brooding coral 2 (BC2)
Spawning coral 1 (SC1)
Spawning coral 2 (SC2)
Sponge (SPG)
Cropped Algae (A)
Macroalgae 1 (D)
Macroalgae 2 (L)
Ungrazeable substratum (U)
DESCRIPTION
Hermatypic coral with internal fertilization and larval
development (e.g., Agaricia agaricites, Porites
astreoides).
Hermatypic coral with internal fertilization and larval
development (e.g., Mycetophyllia).
Hermatypic corals with external fertilization through
broadcast spawning of gametes (e.g., Montastraea
cavernosa, Meandrina)
Hermatypic corals with external fertilization through
broadcast spawning of gametes (e.g., Orbicella complex)
Bioeroding and encrusting sponge belonging to the
species complex of Cliona viridis (Cliona tenuis)
Filamentous, coralline red algae and short turfs (< 5mm
height)
Dictyota pulchella
Lobophora variegata
Abiotic or biotic substrate not colonized by algae (e.g.,
sand patch, soft corals, other non-represented benthic
groups). Fills an entirely cell (e.g., 10% means that 40
cells are filled with sand for a 400 cells reef).
20
Design concepts
Emergence: Population dynamics emerge from the behaviour of the individuals, but the
individual’s life cycle and behaviour are represented by empirical rules, which describe, for
example, mortality and competitive interactions. Adaptation and fitness seeking are not modelled
explicitly nor included in the empirical rules.
Interactions: A number of interactions among benthic groups, herbivorous fish and environment
are represented in the model and explained in the sub-models section. Competition between and
among corals and sponges occurs within each cell, where the competitive coefficients determine
how much tissue is lost by the inferior competitor and gained by the superior competitor at every
time step (Table 5). Competitive asymmetry of macroalgae is represented in the model by
considering the average size of macroalgal patches surrounding each cell. This size-asymmetric
advantage of macroalgae pre-empt available space for coral and sponges to growth and recruit,
as well as reduce their growth rate (Table 5). Furthermore, the amount of tissue lost by
macroalgae overgrowth is represented as a function of the algal cover (size) across the
surrounding cells. Environmental interactions are modelled explicitly for algal seasonal mortality
and hurricane-induced mortality using empirical data. D. pulchella dies-off in winter and grows
faster in summer. Hurricanes occur probabilistically within each simulation, and the probability
for a hurricane to occur within a time span is given by the record of hurricane events for the
study area and within the modelled time frame. Herbivorous fish randomly graze over
macroalgae and cropped algae. When cropped algae are not grazed within a cell for a time step,
this category becomes macroalgae. Grazing intensity (proportion of algae removed by fish) is
proportional to the amount of living tissue and ungrazable substrate; therefore as coral cover
declines, grazing becomes less efficient (Table S5).
21
Observation: Model outputs include the cover (%) of each benthic species as well as size
structure of sponge populations for every simulation run. Visual inspection of model outputs
(percentage cover of all benthic groups) and observed values in the field served to test the
performance of the model at simulating ecosystem dynamics. The simulated size-structure of
sponge populations was validated using different good-of-fit metrics (see Online Resource 5 and
main text).
Initialization
At the initial step, a number of cells are randomly designated as “ungrazable” to match the
specified cover of ungrazable substrate. The remaining cells are then randomly filled. Live coral
colonies of different sizes (i.e., areas in cm2) are randomly generated over available substrate so
the proportion of the surface area of the reef substrate covered by corals matches the input value
of coral cover (%). Algal patches are created in a similar way by filling the remaining space in
every cell according to their initial cover.
For each coral and sponge species, individual sizes are randomly generated following a
lognormal distribution (Table S5) and randomly dispatched across the grazable cells. The
number of living coral colonies and sponge individuals per cell is limited to one. As a result,
initialisation of coral cover leads to the creation of a 20×20×5 matrix of mixed individual sizes
for each species, where 5 is the number of coral and sponge species.
For every replicate simulation (n = 100), ungrazable cover, initial coral cover (%) per species
and initial macroalgal cover are randomised parameters that follow a normal distribution N(μ, σ)
based on empirical observations. This generates different starting coral populations and reef
22
structures that reflect the variability observed among sampled sites. The initial size structure for
sponge, on the other hand, is generated explicitly following field observations in 1998.
Sub models:
Complete details on the full parameterization of the ecosystem model is provided in this section
(Table S5). A summary of the model structure is provided in this manuscript, while a detailed
description and validation of this modelling approach can be found in Mumby 2006 and Mumby
et al. 2007. The model integrates major benthic components of a typical Caribbean reef,
parameterized for Orbicella reefs, one of the most common and diverse reef habitats found in the
region. Table S5 describes each of the processes parameterized for the model, as well as the
reference values used for this study.
23
Table S5. Description and rationale for deterministic and probabilistic model rules or submodels that control the dynamics of benthic individuals across time
Parameter
Details
Coral recruitment
Corals recruit to cropped algae, because algal turfs are not heavily sediment-laden. Recruit at size
1 cm2. Recruitment rate of brooders and spawners (respectively): 2 and 0.2 per 0.25 m2 of cropped
algae per time interval. Recruitment rate was adjusted for rugosity (~2) and the cover of cropped
algae at Glovers Reef (Mumby 1999).
Coral growth
Coral size is quantified as the cross-sectional, basal area of a hemispherical colony (cm2). Brooder
corals have a lateral extension rate of 0.8 cm . yr-1 and spawner corals grow slightly faster at 0.9
Coral reproduction
cm . yr-1 (based on median rates for Porites astreoides, P. porites, Siderastrea siderea, Orbicella
annularis, Colpophyllia natans and Agaricia agaricites) (Chornesky and Peters 1987; Highsmith
et al. 1983; Huston 1985; Maguire and Porter 1977; Van Moorsel 1988)).
Excluded, assume constant rate of coral recruitment from outside reef (i.e. no stock-recruitment
dynamics).
Colonisation of cropped
algae
Cropped algae arise (i) when macroalgae is grazed and (ii) after all coral mortality events (Jompa
and McCook 2002a) except those due to macroalgal overgrowth (see coral-algal competition
below).
Colonisation of
macroalgae
Macroalgae have a 70% chance of becoming established if cropped algae are not grazed for 6
months (mostly Dictyota) and this increases to 100% probability after 12 mo of no grazing (mostly
Lobophora). Rates acquired from detailed centimetre-resolution observations of algal dynamics
with and without grazing (Box and Mumby unpub. data, Mumby et al. 2005).
Macroalgal growth over
dead
coral
(cropped
algae)
In addition to arising from cropped algae that are not grazed (above), established macroalgae also
spread vegetatively over cropped algae (mostly Lobophora as Dictyota spread shows little pattern
with grazing (Mumby et al. 2005). The probability that macroalgae will encroach onto the algal
turf within a cell, PA→M, is given by (1) where M4cells is the percent cover of macroalgae within
the von Neumann (4-cell) neighbourhood (de Ruyter van Steveninck and Breeman 1987). This is a
key method of algal expansion and represents the opportunistic overgrowth of coral that was
extirpated by disturbance.
PA→M = M4cells (1)
Competition
between
corals or between sponges
If corals or sponges fill the cell (2500 cm2), the larger individual overtops the smaller one (chosen
at random if more than one smaller coral or sponge share the cell). If corals or sponges have equal
size, the winner is chosen at random (Lang and Chornesky 1990).
Competition
between
corals and cropped algae
Corals always overgrow cropped algae (Jompa and McCook 2002a).
Competition
between
corals and macroalgae 1:
effect of macroalgae on
corals
a) Growth rate of juvenile corals (area <60 cm2) set to zero if M4cells ≥ 80%, and reduced by 70%
if 60% ≤ M4cells < 80%. Parameters based on both Dictyota and Lobophora (Box and Mumby
2007).
b) Growth rate of juvenile and adult corals (area ≥ 60cm2) reduced by 50% if M4cells ≥ 60%
(Jompa and McCook 2002a; Jompa and McCook 2002b; Tanner 1995).
24
c) Limited direct overgrowth of coral by macroalgae can occur (Hughes et al. 2007; Lirman 2001;
Nugues and Bak 2006) found that the upper 95% CL of the mean area of overgrowth ranged from
0-18 cm2 pa across a ~7cm length of coral edge, with an overall mean of 8 cm2 pa. This translates
to 4 cm2 in each 6-mo time step of the model. Overgrowth (cm2), OC→M, was scaled to entire
colonies using (2) where M4cells is the proportion of macroalgae in the von Neumann 4-cell
neighbourhood and Pi is the perimeter of the coral.
OC→M = M4cells × Pi/7× 4 (2)
Note that Nugues and Bak (2006) did not find significant effects of Lobophora on all coral species
studied. Whilst this was the correct interpretation of their data, the published results strongly
suggest that an effect does exist and that a larger sample size may well have resulted in significant
differences. Other studies have found negative effects of macroalgae on both massive (Lirman
2001) and branching corals (Jompa and McCook 2002a).
Competition
between
corals and macroalgae 2:
effect of corals on
macroalgae
The probability with which macroalgae spread vegetatively over cropped algae, PA→M (1) is
reduced by 25% when at least 50% of the local neighbourhood includes coral (de Ruyter van
Steveninck et al. 1988, Jompa & McCook 2002a)
PA→M = 0.75 × M4cells if C5cells ≥ 0.5
PA→M = M4cells if C5cells < 0.5
Where C5cells is the proportion of corals in the 5-cell neighbourhood comprising the focal cell
and the 4-cell von Neumann neighbourhood.
&
Grazing is spatially constrained (Mumby 2006; Mumby et al. 2006; Williams et al. 2001). The
dynamic basis of this grazing threshold is poorly understood seeing as most measures of grazing
take place at scales of seconds and most studies of algal dynamics take place on monthly scales
(hence the use of a 6 month time step). Nonetheless empirical studies (Mumby 2006b), and
experimental results scaled to the complex fore-reef (Williams et al. 2001), have identified a
grazing limit of 30%-40% of the reef during 6 months. This value allows for a numeric positive
response by parrotfish after severe coral mortality events during which colonisation space for
algae increases dramatically. For example, an increase in parrotfish biomass over 5 years
maintained the cover of cropped algae at Glovers Reef at 35% after Hurricane Mitch caused
extensive coral mortality and liberated new settlement space for macroalgae (Mumby et al. 2005)
(i.e. grazing impact remained at around 30% 6 mo. -1 even though coral cover dropped from around
60% to 20%, suggesting that the approach is robust during phase changes). The reasons for this
are not fully understood. All parrotfish species graze algal turfs and in doing so constrain the
colonisation and vegetative growth of macroalgae. Direct removal of macroalgae occurs through
the grazing of larger sparisomid species (up to 50% of bites in S. viride, Mumby unpub. data) and
natural fluctuations in algal dynamics including annual spawning events during which their cover
is decimated (Hoyt 1907). Of course, macroalgae increase once the availability of settlement space
exceeds the grazing threshold (e.g. as coral cover declines from disturbance). During a given time
interval, cells are visited in a random order and all algae consumed until the total grazing impact is
reached. This approach implies spatially intensive grazing, which appears to be more biologically
accurate than a spatially extensive approach because parrotfish feed repeatedly at particular sites
on time scales of days to weeks (Mumby unpublished data). All turf and macroalgae are consumed
(and converted to A6) until the constraint is reached.
mortality
Size-dependent, following empirical observations from Curaçao before major bleaching or
hurricane disturbances (Meesters et al. 1997). State variables reported in literature converted to
dynamic variables using least squares optimization until equilibrial state in model matched
observed data. Implementation uses equations (4a) and (4b) where Ppm is the probability of a
partial mortality event, Apm is the area of tissue lost in a single event, and χ is the size of the coral
in cm2:
Grazing by fishes
impact of fishing
Partial-colony
of corals
Ppm = 1-[60+(−12 ln(χ))] (4a)
Ln[(Apm × 100)+1] = −0.5 + (1.1 ln(χ)) (4b)
25
Whole-colony mortality
of juvenile and adult
corals
Incidence of mortality in juvenile corals (60-250 cm2), 2% per time interval (~4% per annum).
Halved to 1% (2% pa) for mature colonies (>250 cm2) (Bythell et al. 1993). These levels of
mortality occur in addition to macroalgal overgrowth. Algal overgrowth and predation affects
juvenile corals (see above and below).
Predation
recruits
Instantaneous whole-colony mortality occurs from parrotfish predation at a rate of 15% each 6
month iteration of the model (Box & Mumby 2007)
Predation is confined to small corals of area ≤5cm2, based on Meesters et al (1997) where between
60% and 95% of bite-type lesions were of this size.
on
coral
Hurricane incidence was measured using the Atlantic Hurricane dataset (1851-2008), which tracks
the location and intensity of the eye of tropical cyclones every six hours (Jarvinen et al. 1984). We
confined the analyses to storms that reached hurricane intensity (wind speeds higher than 166 km
h-1). Hurricane-force winds may extend several kilometres from the hurricane track. We calculated
the frequency of hurricanes in any given location using the approach described by Edwards et al.
(2010). Essentially, the area of influence of each hurricane is captured in buffers (up to 160 km
wide) that take into account the intensity of the storm, its asymmetry (because of the Coriolis
force) and the reduction in wind speed with distance from the hurricane track (Keim and Muller
2007). Using this approach, we mapped the total frequency of hurricanes for each Saffir-Simpson
intensity class for the entire record at 1 km2 spatial resolution.
Hurricanes can affect corals and macroalgae, but we assumed no effects on the sponge, giving its
encrusting growth from, sheltered from the breakage effects of water movement during hurricanes
(Wulff 2006).
Environmental
disturbance
Sponge Growth
Sponge growth (G) is subject of the amount and intensity of competition (equation 6). Sponge size
is quantified as the cross-sectional, basal area of a hemispherical individual (cm2). The final area
after each time step is calculated using the linear extension (le) of the sponge in front each
competitor (i: cropped algae, Dictyota, Lobophora or coral), and weighted by the proportion of
tissue in contact with each competitor (p), whereby:
G=∑
π(r+lei )2
pi
(eqn 6)
Where r is the radius of the sponge and p is calculated as the average local cover of the
competitor (in the von Neumann 5-cell neighbourhood).
The linear extension rates (le) for each competitor were:
1. Cropped algae: 0.35 cm . 6 mo-1; (Long turf, González-Rivero et al., 2012)
2. Dictyota: 0.14 cm . 6 mo-1 (González-Rivero et al. 2012)
3. Lobophora: -0.56 cm . 6 mo-1 (González-Rivero et al. 2012)
Coral: 1.02 cm . 6 mo-1 (González-Rivero et al. 2012)
Sponge recruit on cropped algae at a rate of 0.315 individuals per 0.25 m2 of cropped algae per
time interval (~2.5 ind/m2.y-1). Recruit size is 1 cm2 (González-Rivero et al. 2013).
Sponge Recruitment
Sponge fecundity
Fecundity is assumed to be a linear function of size, as bigger sponges contain a proportionally
higher number of reproductive propagules, assuming that the number of propagules per unit area
of tissue remains independent of size. Therefore, sponge reproduction is a function of the existing
population structure in the previous time step. Refer to stock-recruitment in Online Information 2
for more details.
Whole-individual
mortality of juvenile and
adult sponges
Probability of mortality follows a decline as a function of size. Here we used a least square
approach to fit a negative power function to observed mortality occurrence from field observations
(see Online Information 2 for details).
Partial
sponges
The age and size structure of sessile organisms are largely decoupled, and this is especially true in
marine ecosystems (Bak and Meesters 1998; Hughes 1984; Hughes and Connell 1987).
Individuals of a given age can vary considerably in size by sustaining large partial tissue mortality
or shrinkage (Bak and Meesters 1998; Hughes and Connell 1987). Here we modelled the partial
tissue mortality of sponges by using the probability of shrinking per individual at each time step
(ps = 0.15) and, the proportion of tissue lost in relation to the individual size (pms 0.36).
mortality
of
26
Online Resource 6: Detailed sensitivity analysis to understand the processes likely
driving the population structure of Cliona tenuis using a hypothesis testing
approach
The present study investigated the importance of candidate processes in regulating the population
of an opportunistic species, which are expected to increase in abundance following coral reef
degradation. Here we investigated for candidate mechanisms of population control: 1) stock
recruitment, 2) individual mortality, 3) partial tissue mortality and 4) macroalgal competition,
each of them described in the manuscript and in this supplementary information (Online resource
3). An orthogonal hypothesis testing approach was used to evaluate the relevance of each
parameter or interaction of them to contribute to the model fit. Iteration of candidate mechanisms
and their interactions were sequentially introduced into the model and simulated abundance over
an 11-year period was compared against field observations (please refer to the manuscript for
details). The following quantitative metrics of goodness of fit were used to evaluate the role of
each candidate mechanism: 1) Likelihood estimates (LL), 2) Residual Sum of Squares (RSS),
̅ 2 ). The latter refers the adjusted
Bayesian Information Criterion (BIC) and the Deviance (𝐷
Deviance, which penalises the deviance estimates (D2) by the number of parameters introduced
into the model (Table S6). Details on this approach and the metrics used evaluated and compare
the fit of each model is provided on the manuscript.
27
Table S6. Quantitative metrics of the fit of the simulated size structure of Cliona tenuis when
hypothesized regulating mechanisms are modelled for 11 years. The candidate mechanisms of
population regulation for this study were: Stock Recruitment (SR), individual Mortality (M),
Partial tissue Mortality (PM), and macroalgal Competition (C). The first three are considered
mechanisms intrinsic to the species life history, while Competition can be considered an extrinsic
factor of population control. The following metrics of goodness of fit and model comparisons
were used to evaluate the relative importance of each candidate mechanism of population
control: 1) Likelihood estimates (LL), 2) Residual Sum of Squares (RSS), Bayesian Information
̅ 2 ). The latter refers the adjusted Deviance, which penalises
Criterion (BIC) and the Deviance (𝐷
2
the deviance estimates (D ) by the number of parameters introduced into the model (n).
̅𝟐
Mechanisms Parameters
LL
RSS
BIC
n
𝑫𝟐
𝑫
None
NULL
-2761.84
1.70 15.85
0 0.000
0.143
SR
-2645.50
1.69 14.92
1 0.044
0.044
M
-2688.26
1.70 14.10
2 0.028
-0.166
SR + M
-2637.87
1.68 14.07
2 0.047
-0.143
Intrinsic
PM
-1077.14
1.19 12.27
1 0.640
0.568
SR + PM
-942.20
1.03 12.01
2 0.691
0.630
M + PM
-1055.11
1.19 11.39
2 0.648
0.473
SR +M + PM
-959.36
1.03 11.20
3 0.685
0.527
Extrinsic
C
-162.47
0.16 -9.34
1 0.987
0.987
SR + C
-131.64
0.05 -8.07
2 0.999
0.999
M+C
-164.27
0.17 -7.67
2 0.987
0.980
Interaction
PM + C
-132.86
0.01 -7.24
2 0.999
0.998
between
Intrinsic and SR + M + C
-131.38
0.05 -7.22
3 0.999
0.999
Extrinsic
SR + PM + C
-124.73
0.01 -7.12
4 1.000
1.000
M + PM + C
-131.74
0.01 -6.38
4 0.999
0.998
SR + M + PM + C
-129.45
0.01 -6.35
4 1.000
1.000
28
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