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 REFERENCES Babcock RC (1991) Comparative Demography of 3 Species of Scleractinian Corals Using AgeDependent and Size-Dependent Classifications. --> 61:225-244 Bak RPM, Meesters EH (1998) Coral population structure: the hidden information of colony size-frequency distributions. --> 162:301-306. doi: 10.3354/meps162301 Box SJ, Mumby PJ (2007) Effect of macroalgal competition on growth and survival of juvenile Caribbean corals. --> 342:139-149 Bythell JC, Gladfelter EH, Bythell M (1993) Chronic and catastrophic natural mortality of three common Caribbean reef corals. Coral Reefs 12:143-152. doi: 10.1007/bf00334474 Cebrian E, Uriz MJ (2006) Grazing on fleshy seaweeds by sea urchins facilitates sponge Cliona viridis growth. --> 323:83-89. doi: 10.3354/meps323083 Chaves-Fonnegra A, Zea S (2011) Coral colonization by the encrusting excavating Caribbean sponge Cliona delitrix. Mar. Ecol.-Evol. Persp. 32:162-173. doi: DOI 10.1111/j.14390485.2010.00416.x Chornesky EA, Peters EC (1987) Sexual Reproduction and Colony Growth in the Scleractinian Coral Porites astreoides. --> 172:161-177 de Ruyter van Steveninck ED, Breeman AM (1987) Deep water vegetations of Lobophora variegata (Phaeophyceae) in the coral reef of Curacao: population dynamics in relation to mass mortality of the sea urchin Diadema antillarum. --> 36:81-90. doi: 10.3354/meps036081 Edwards HJ, Elliott IA, Pressey RL, Mumby PJ (2010) Incorporating ontogenetic dispersal, ecological processes and conservation zoning into reserve design. --> 143:457-470 González-Rivero M, Ereskovsky AV, Schönberg CHL, Ferrari R, Fromont J, Mumby PJ (2013) Life-history traits of a common Caribbean coral-excavating sponge, Cliona tenuis (Porifera: Hadromerida). -->:1-20. doi: 10.1080/00222933.2013.802042 González-Rivero M, Ferrari R, Schönberg CHL, Mumby PJ (2012) Impacts of macroalgal competition and parrotfish predation on the growth of a common bioeroding sponge. --> 444:133-142. doi: 10.3354/meps09424 Gosselin LA, Qian PY (1997) Juvenile mortality in benthic marine invertebrates. --> 146:265282. doi: 10.3354/meps146265 Hedley J (2006) VidAna, 1.2.1 edn. Marine Spatial Ecology Lab, University of Exeter. http://www.marinespatialecologylab.org/resources/vidana/, Exeter, UK Highsmith RC, Lueptow RL, Schonberg SC (1983) Growth and Bioerosion of three massive corals on the Belize Barrier-Reef. Marine Ecology-Progress Series 13:261-271. doi: 10.3354/meps013261 Hoyt WD (1907) Periodicity in the production of the sexual cells of Dictyota dichotoma Contributions from the Botanical Laboratory of the Johns Hopkins University, No. 6. Botanical Gazette 43:0383-0392. doi: 10.1086/329243 Hughes TP (1984) Population-Dynamics Based on Individual Size Rather Than Age - a GeneralModel with a Reef Coral Example. --> 123:778-795 Hughes TP, Connell JH (1987) Population-Dynamics Based on Size or Age - a Reef-Coral Analysis. --> 129:818-829 Hughes TP et al. (2007) Phase shifts, herbivory, and the resilience of coral reefs to climate change. Curr Biol 17:360-365. doi: 10.1016/j.cub.2006.12.049 29 Huston M (1985) Variation in coral growth rates with depth at Discovery Bay, Jamaica. Coral Reefs 4:19-25. doi: 10.1007/bf00302200 Jackson JBC, Buss LW, Cook RE (eds) (1985) Population biology and evolution of clonal organisms. Yale University Press., New Haven. (US) Jarvinen BR, Neumann CJ, Davis MaS (1984) A tropical cyclone data tape for the north Atlantic basin, 1886-1983: contents, limitations and uses NOAA Technical Memorandum NWS NHC 22. National Hurricane Center, p 24 Jompa J, McCook LJ (2002a) Effects of competition and herbivory on interactions between a hard coral and a brown alga. --> 271:25-39 Jompa J, McCook LJ (2002b) The effects of nutrients and herbivory on competition between a hard coral (Porites cylindrica) and a brown alga (Lobophora variegata). --> 47:527-534 Keim BD, Muller RA (2007) Spatiotemporal patterns and return periods of tropical storm and hurricane strikes from Texas to Maine. --> 20:3498-3509. doi: 10.1175/jcli4187.1 Lang JC, Chornesky EA (1990) Competition between scleractinian reef corals - a review of mechanisms and effects Lirman D (2001) Competition between macroalgae and corals: effects of herbivore exclusion and increased algal biomass on coral survivorship and growth. Coral Reefs 19:392-399 López-Victoria M, Zea S, Weil E (2006) Competition for space between encrusting excavating Caribbean sponges and other coral reef organisms. --> 312:113-121. doi: 10.3354/meps312113 Maguire LA, Porter JW (1977) A spatial model of growth and competition strategies in coral communities. --> 3:249-271. doi: 10.1016/0304-3800(77)90007-2 Mariani S, Uriz M-J, Turon X, Alcoverro T (2006) Dispersal strategies in sponge larvae: integrating the life history of larvae and the hydrologic component. Oecologia 149:174184 Mariani S, Uriz MJ, Turon X (2005) The dynamics of sponge larvae assemblages from northwestern Mediterranean nearshore bottoms. --> 27:249-262. doi: DOI 10.1093/plankt/fbh173 Meesters EH, Wesseling I, Bak RPM (1997) Coral colony tissue damage in six species of reefbuilding corals: Partial mortality in relation with depth and surface area. --> 37:131-144 Mumby PJ (1999) Bleaching and hurricane disturbances to populations of coral recruits in Belize. --> 190:27-35 Mumby PJ (2006) The impact of exploiting grazers (scaridae) on the dynamics of Caribbean coral reefs. Ecological Applications 16:747-769 Mumby PJ et al. (2006) Fishing, trophic cascades, and the process of grazing on coral reefs. Science 311:98-101. doi: 10.1126/science.1121129 Mumby PJ, Foster N, Fahy E (2005) Patch dynamics of coral reef macroalgae under chronic and acute disturbance. Coral Reefs 24:681-692 Nugues MM, Bak RPM (2006) Differential competitive abilities between Caribbean coral species and a brown alga: a year of experiments and a long-term perspective. --> 315:7586 Peterson I, Wroblewski JS (1984) Mortality Rate of Fishes in the Pelagic Ecosystem. --> 41:1117-1120. doi: doi:10.1139/f84-131 Ramirez Llodra E (2002) Fecundity and life-history strategies in marine invertebrates. --> Volume 43:87-170. doi: 10.1016/s0065-2881(02)43004-0 30 Tanner JE (1995) Competition between scleractinian corals and macroalgae - An experimental investigation of coral growth, survival and reproduction. --> 190:151-168 Van Moorsel GWNM (1988) Early maximum growth of stony corals scleractinia after settlement on artificial substrata on a Caribbean reef. --> 50:127-136 Williams ID, Polunin NVC, Hendrick VJ (2001) Limits to grazing by herbivorous fishes and the impact of low coral cover on macroalgal abundance on a coral reef in Belize. --> 222:187-196 Wulff JL (2006) Resistance vs recovery: morphological strategies of coral reef sponges. --> 20:699-708. doi: doi:10.1111/j.1365-2435.2006.01143.x 31