Coral reef community dynamics and disturbance: a simulation model

Ecological Modelling 175 (2004) 271–290

Coral reef community dynamics and disturbance: a simulation model O. Langmead a , C. Sheppard b,∗ a

Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK b Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, UK Received 22 April 2003; received in revised form 24 September 2003; accepted 27 October 2003

Abstract A spatially explicit model of coral community dynamics has been developed, based around a cellular automaton, with additional processes impacting upon it such as recruitment and disturbance. It represents a homogeneous plot on a Caribbean fore-reef slope with 10 coral species. Complexity that arises from species behaviour is shown to be realistic, generated by simple, repeated actions of the base units (coral polyps). The spatial resolution used here is high, and allows detailed demographic dynamics to be examined. Input parameters were based on values extracted from the literature for all processes (except disturbance, which is examined here). Natural background disturbance processes were explored in order to understand their importance in structuring coral communities and populations. Initially two disturbance parameters were investigated: spatial extent (proportion of plot affected) and size of disturbed patches. Both were found to be equally important in driving coral community structure, and subsequent diversity. The latter also influenced coral population size structure by altering mortality regimes. A power law model was introduced to distribute the total area disturbed into patches; its parameters were tuned using emergent size structure of the coral Agaricia spp. Differential mortality for species was also included, based on colony size and tissue regeneration rates. Model performance was assessed by running simulations with different levels of background disturbance, and resulting population size structures of each species were compared to field observations. Seven species compared extremely well, while accuracy of a further two could not be quantified due to a lack of suitable field data. Only one species, Siderastrea siderea, had unrealistic population size structures, which is discussed with respect to the life history of this species. Applications of this model include predicting communities under changing disturbance regimes, and colonisation and recovery processes following acute disturbances. © 2003 Elsevier B.V. All rights reserved. Keywords: Coral community; Disturbance; Cellular automaton

1. Introduction Recent decades have seen a dramatic decline in reef health in almost every region where reefs are found (Wilkinson, 2002). There is an urgent need for better predictive tools to increase our understanding of the responses of corals to an anthropogenically-mediated ∗ Corresponding author. Tel.: +44-24-76523523. E-mail address: [email protected] (C. Sheppard).

changing environment. Prediction of coral communities is vital to provide direction and support for their conservation and management, and the motivation of this work is to provide answers to many current questions about possible reef recovery, and build a thorough foundation for future research into effects of disturbance on reefs. Understanding the relationship between corals and natural disturbances is a fundamental step towards the prediction of corals under shifting regimes of numerous human induced dis-

0304-3800/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2003.10.019

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turbances, but is one which has not been adequately addressed to date in a quantitative sense. Natural disturbance is an important process that structures coral communities. However, comparatively little is known about rates of natural background disturbance; the literature is dominated by reports of rare catastrophic events (e.g. hurricanes; Bythell et al., 1993; Woodley et al., 1981) or anthropogenic disturbances (review by Dubinsky and Stambler, 1996), while few workers have measured natural rates of background disturbance (e.g. Bak and Luckhurst, 1980; Hughes, 1984). This is because background disturbance is difficult to measure due to the wide ranging spatial and temporal scales over which it operates, and also because visible effects, manifest as coral mortality, are variable and transient (e.g. corals regenerate lost tissue at different rates; Bak, 1983; Meesters et al., 1997a). It is clear that natural disturbances affect corals according to their colony size; small corals are more vulnerable to whole colony death than large ones that, in turn, are vulnerable to partial mortality (Bak and Meesters, 1998; Hughes, 1984; Hughes and Jackson, 1985). Also some species are more susceptible than others, due to a combination of morphological (e.g. fragile colony structure) and physiological (e.g. regeneration capacity) characteristics (Bak and Luckhurst, 1980; Hughes and Jackson, 1985; Meesters et al., 1997b). This is reflected by the marked contrast in composition between juvenile and adult coral populations (Bak and Engel, 1979; Rylaarsdam, 1983). This implies that post-settlement mortality processes are important in shaping the adult coral community. The role of natural background disturbance and its importance in maintaining coral communities was examined using a spatially explicit simulation model. This approach was selected as some life history processes (e.g. growth, recruitment) are limited by availability of free space on the reef (Hughes and Jackson, 1985; Roughgarden et al., 1985), and it also allows the effects of distribution of the disturbances in space to be explored. Specifically, this model represents a coral community on a Caribbean fore-reef slope. This was selected primarily because of the low species diversity of this region compared with the Indopacific biogeographical region; many Caribbean coral communities are composed of <20 scleractinian species (Goreau, 1959). These communities are also amongst

the best studied in the world, with records spanning 4 decades in some areas (e.g. Jamaica, Goreau, 1992), so that many parameters can be taken from the literature. The taxonomy of these corals is relatively well understood, and many aspects of their biology have been established, for example reproductive strategies (Szmant, 1986), dynamics along environmental gradients such as depth (Bak and Luckhurst, 1980; Bak and Nieuwland, 1995) and wave exposure (Geister, 1977; Witman, 1992). This means that for the most part, corals can be modelled at species level, without necessity to artificially categorise them into functional groups and thereby degrading resolution of predictions and, secondly, adequate information is available on which to base parameters. Central to the simulation model is a cellular automaton (CA). These temporally discrete, spatially explicit mathematical systems constructed from many identical components, mimic the colonial structure of corals particularly well. Each component is simple and behaves according to preset rules, but the cooperative effect of many components acting together can generate complex behaviour. This was considered an appropriate approach for a system that is composed of modular organisms, and CAs can accommodate complex clonal processes such as indeterminate growth, colony fission, fusion and partial mortality, which would be difficult to simulate with other demographic modelling techniques. Specific aims of this research were to develop the CA-based model and apply it to the dynamics of a Caribbean coral community and, in doing so, investigate ongoing natural disturbance processes affecting such communities. Secondly the model performance is evaluated by comparing emergent properties of the modelled coral community with real coral communities.

2. Methods 2.1. Model structure The model represents a two-dimensional plot (homogeneous reef substratum) of 300 × 300 cells. Each cell can exist as bare substratum or as one of 10 coral species. (Other aspects, such as algae occupation, are considered in later studies, Langmead and Sheppard, submitted). The spatial resolution of the model is sug-

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Fig. 1. Schematic diagram of model showing ordering of modules and position of CA.

gested by coral biology; each cell nominally represents 1 cm2 , a median sized coral polyp. The CA at the centre of the model drives the processes of growth and aggression (Fig. 1). Spatial occupancy changes are generated temporally, depending on the state of any particular cell and its four immediate neighbours (Von Neuman neighbourhood) during the preceding time interval according to preset rules based on coral biology. Other processes such as recruitment and disturbance impact upon the CA. The time step is 1 year for some model processes, but the CA is iterated four times each model year. This is to reduce all growth rates to <1 (to cope with faster growing species) so implementation is entirely probabilistic and also to maintain a Von Neuman neighbourhood (larger neighbourhoods would compromise computational efficiency). Plot edges are wrapped (periodic boundary conditions). Model output is taken each year as percent cover, and at specified intervals is taken also as population size structure of each coral species. This is facilitated by a connected component analysis module integrated into the model that permits tracking of colonies through their naturally occurring complex processes of partial mortality, colony fission and colony fusion. 2.2. Life history processes Major known coral life history processes were incorporated into the model, and values for parameters taken from literature for each of the 10 coral species in-

cluded (some species were grouped into species complexes where it was necessary to maintain consistency with data sourced from earlier literature) (Table 1). 2.2.1. Recruitment Recruitment occurs at the start each year (8/11 Caribbean corals have one reproductive cycle per year; Szmant, 1986), and is assumed to originate from a regional pool of larvae. Each coral species was assigned a mean density based on larval settlement rates (Hughes, 1985; Rogers et al., 1984; Rylaarsdam, 1983; Smith, 1992; Tomascik, 1991), and the number of potential recruits was determined each year using Poisson probability distributions. Each potential recruit was placed in the plot using pseudorandom number generation to obtain their initial spatial coordinates. Recruitment success was limited both by the abundance of larvae in the pool and the amount of unoccupied space in the plot, as recruits could only settle on bare substratum. The species order was pseudorandomly allocated each year to prevent bias. 2.2.2. Growth and aggression Coral growth was implemented as radial expansion, with rates based on skeletal extension rates (Huston, 1985 and references therein). As the CA was iterated four times each year, all growth rates were <1, and implementation was probabilistic. Rules governing CA behaviour were based on coral competition: corals could only grow into adjacent cells if they

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Table 1 Parameter values assigned for key life history processes for 10 coral species Species

Aggressive rank (3–10, higher values indicating greater competitive ability)

Growth rate (radial increase in colony size) (cm per year)

Recruitment rate (larvae 9 m2 per year)

Montastraea cavernosa Stephanocoenia michellinii Agaricia spp.a Eusmilia fastigiata Meandrina meandrites Montastraea annularisb Colpophyllia natans Porites astreoides Madracis spp.c Siderastrea siderea

10 4 4 6 8 9 5 4 3 4

0.5 1 2 1 2 1 1 0.5 2 0.8

1 7.2 470 1.2 1.2 16 1.7 71 25 8.5

a b c

Agaricia spp. includes non-plating forms of this genus such as A. agaricites, A. tenuifolia and A. humilis. Montastraea annularis refers to the species complex including data from M. annularis, M. franksii, and M. faveolata. Madracis spp. refers to the complex including M. pharensis, M. decactis and M. formosa (Diekmann et al., 2001).

were either unoccupied (bare substratum) or occupied by a competitively subordinate species (Langmead, 2002). Species were ranked according to their aggressive capacity determined from field surveys in Utila, Honduras undertaken for this purpose (Langmead, 2002). 2.2.3. Background disturbance Biotic and abiotic processes that cause coral mortality, such as sedimentation, sand scouring, dislodgement and predation occur naturally. Within the model this is simulated by setting pseudorandomly-placed circular patches to bare substratum. The influence of two key parameters of disturbance, namely spatial extent of background disturbance (proportion of the plot disturbed) and size of disturbed patches were investigated. 2.2.3.1. Spatial extent of disturbance. The spatial extent of disturbance (proportion of the plot disturbed each year) was varied: 0, 0.1, 0.2, 0.4 and 0.6. The size of disturbed patches was initially kept constant at 5 cm radii. Starting conditions for all simulations were bare substratum, and 10 replicates were made of each simulation (as the model is probabilistic, inbuilt stochasticity means there are varying outcomes). This number was selected as preliminary trials showed species compositions converged over the relatively long temporal scale, due to a combination of the high spatial resolution of the plot and species-specific life history characteristics. Simulations were run

for 500 years (complete cycles of the model) and percent cover of each species was taken each year. Multivariate techniques were used to quantify differences in community structure at the end of simulations, namely diversity indices and Bray–Curtis similarity matrices. Diversity (Shannon and Weaver, 1948) was calculated from percent cover at 500 years:
H = − pi (ln pi ) (1) where pi indicates the proportion of the total cover of the ith species. A Bray–Curtis similarity matrix (Bray and Curtis, 1957) was constructed from untransformed cover data from 500 years using all 10 replicates at each disturbance level, and this was plotted as a multidimensional scaling (MDS) ordination. Differences in community structure between disturbance levels were analysed using a one-way analysis of similarity (ANOSIM; Clarke, 1993). At the end of each simulation, the number and size of colonies was taken. To assess how mortality was distributed amongst different sized colonies, and the nature of this mortality (total or partial colony mortality), coral populations were examined before and after disturbance at 500 years. Colonies undergoing partial or total mortality were recorded, and using the formula as follows:   Ts,c Ms,c = log10 (2) Ps,c

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where Ms,c indicates an index of mortality for coral species s, size class c, Ts,c indicates the number of colonies that underwent total colony mortality or death (from species s, size class c), while Ps,c indicates the number of colonies that underwent partial mortality or shrinkage (same species and size class), at 500 years. Colony size classes were defined on a log scale, after Bak and Meesters (1998). Mortality processes were examined in this way for four species that were sufficiently abundant at each disturbance level to enable comparison. The modal size class for each species at each disturbance level was obtained from log transformed colony size frequency distributions. 2.2.3.2. Size of disturbed patches. Simulations were run as above, but in this case, the total proportion of the plot disturbed each year was kept constant at 0.2, and the size of disturbed patches were varied: 1, 3, 5, 10 and 20 cm radii. Starting conditions, runtime and model output were as before.

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Table 2 Differential mortality probabilities for 10 coral species Coral species

Mortality probability

Montastraea cavernosa Stephanocoenia michellinii Agaricia spp. Eusmilia fastigiata Meandrina meandrites Montastraea annularis Colpophyllia natans Porites astreoides Madracis spp. Siderastrea siderea

0.7 0.1 1.0 0.5 0.7 0.6 0.3 0.2 0.1 0.1

Mortality probabilities correspond to the chance of mortality during disturbance if impacted by a disturbed patch. Probabilities were based on colony size, and rates of tissue regeneration were known.

(3)

1.75 and 2.0. In each case the spatial extent of disturbance (as proportion of the plot) was held constant at 0.15, while the spatial distribution of disturbed space was adjusted by using different values for a. One further parameter was introduced, Rmax (maximum patch size) which was set at 100 cm radius to prevent the entire plot from being obliterated. While this can happen in nature, in this model of 300 × 300 cells it merely ‘resets’ the plot to its initial starting condition. For each simulation, 10 replicates were run, each to 200 years, at which point the species abundance and population size structure was taken. These data were used to construct Bray–Curtis similarity matrices as previously, which were plotted as a MDS ordination, and mortality indices were calculated (Eq. (2)).

where r is patch size (radius), R0 is minimum patch size (1 cm as dictated by the spatial resolution of the model), a is a constant controlling the shape of the curve (this is tested below), and P is the probability of obtaining that patch size. This was implemented by calculating the mean patch size, from which the number of patches required to disturb a preset proportion of the plot was calculated. Then, during the disturbance routine, this preset number of patches would be created, using pseudorandom number generation to obtain P and assign a radius to each patch. These patches were then placed in the plot as before. The constant a, controlling the shape of the curve required testing to determine the optimal value for use in this model. Simulations were run with a at 1.25, 1.5,

2.2.3.4. Differential mortality. Because corals vary in their susceptibility to disturbances, each coral species was assigned a probability of mortality if impacted by a disturbance patch (Table 2). It is known that Agaricia spp. have the highest tissue turnover rates (Bak and Luckhurst, 1980; Hughes and Jackson, 1985) so this group was assigned a probability of 1 (i.e. death always occurs after disturbance). All other species had probabilities of mortality based on two aspects of coral life history, colony size (Meesters et al., 2001) and tissue regeneration rate (Bak and Steward van Es, 1980; Bak et al., 1977; Guzman et al., 1994; Meesters and Bak, 1993; Nagelkerken et al., 1999). Each coral was ranked on an ordinal scale (1–5) according to these two characters, and differential mortality probabilities were based on mean ranks.

2.2.3.3. Power law model. A power law model was introduced to the coral community model to distribute disturbed space into different sized patches, based on the assumption that cleared patches on a reef occur at different scales of time and space; small patches occur frequently and very large patches are more rare (Connell and Keough, 1985). This was implemented using the equation: r = R0 P (−1/a)

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Tissue regeneration rates were not known for Eusmilia fastigiata and Madracis spp., and so to prevent them from becoming extinct, their mortality probability was decreased. The mortality probability was increased for Meandrina meandrites as these corals are known to be highly susceptible (Bak and Luckhurst, 1980), and indeed, without this adjustment, this species would swamp the plot. Results from this simulation are given together with the evaluation of model performance. 2.3. Parameter sensitivity The modelled coral community was tested for sensitivity to changes in their allocated coral life history parameters. Growth, recruitment, mortality and competitive rank were varied individually for each species, within and beyond the ranges that these variables are known to operate on reefs, both above and below the initial value. Simulations were run for 100 years using disturbance parameters as previously (a = 1.5, Rmax = 100, R0 = 1, 0.15 of the plot affected per year), and again each simulation was replicated 10 times. Output was taken as percent cover, number and size of colonies at the end of the simulation. To enable comparison across parameters, sensitivities were normalised relative to each other by converting values to ranks. A rank of ‘1’ indicated a relative change in cover of 0–5%, ‘2’ a change of 5–10% and ‘3’ indicated a change of >10%. Comparisons were made for two-fold increases in growth and recruitment and increases of 0.1 and 1 for differential mortality probabilities and competitive rank, respectively. 2.4. Model performance The model was critically evaluated in terms of its success in predicting coral dynamics at population level by comparing its predictions to field observations. Unlike coral cover, which is typically highly variable over a scale of metres on a reef (Bythell et al., 2000), the size structure of coral populations is remarkably stable within species, and can be considered a species character (Meesters et al., 2001; Soong, 1993). Thus, in terms of testing the model, comparisons of population size structure are a much more rigorous test of predictive power than are cover estimations.

Simulations were run with increasing levels of background disturbance: 0.05, 0.1, 0.15 and 0.2 of the plot disturbed each year, and 20 replicates were made at each level. Other parameters of disturbance were as used previously (a = 1.5, Rmax = 100, R0 = 1), and maintained constantly through these simulations. Each simulation was run for 200 years, with output taken as percent cover each year and the size-frequency distribution of colonies at the end of the simulation. Colonies were divided into broad size classes on a log scale (1–10, 11–100, 101–1000, 1001–10,000 and >10,000), using all replicates combined by species. Relative proportions of the population within each size class were calculated to enable comparison of populations with different sizes. Wherever possible these were compared to published size structures as planar area, but for many species this was not possible as colony sizes have been reported in other forms, so it was necessary to transform model output. For example, Meesters et al. (2001) recorded data as three-dimensional surface area. Model output was transformed to the same scale by assuming colonies were hemispherical: planar area was multiplied by 2. Foliose corals were not treated in the same way, as the relationship between planar and three-dimensional surface area is more complicated (see Eq. (4)). The few species found to be markedly different in population size structure from field measurements were further tested by varying recruitment rates. This parameter is the one in which least confidence exists due to the enormous variability in natural recruitment across space and time (Hughes et al., 1999). Also earlier trials testing parameter sensitivity suggested that changes in recruitment could influence colony size structure in certain species. Simulations were run to 200 years with the proportion of background disturbance held at 0.1, and 5 replicates were made at each setting. Results were taken as before. For Montastraea annularis, colony size frequency was taken in two forms: (1) size of individual colonies and (2) size of genetic colonies (i.e. all the fragments from the same original genetic individual). The reason for this was that M. annularis is long lived and frequently undergoes fission and, when measured in the field, an obvious genetic individual with a common skeleton is generally considered a single colony even if the tissue is divided into separate patches (Bak and Meesters, 1998; Meesters et al., 2001).

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3. Results and discussion 3.1. Background disturbance

Fig. 2. Effect of spatial extent of disturbance on coral community structure. MDS ordination of Bray–Curtis similarity matrix of percent cover at 500 years. Numbers denote proportion of the plot disturbed each year. Minimum stress for best two-dimensional ordination is 0.01.

3.1.1. Spatial extent of disturbance Increasing amounts of disturbance drove the coral community into significantly distinct structures (one-way ANOSIM: r = 0.999, P < 0.001, Fig. 2). Under conditions of no disturbance, the entire plot becomes occupied with the competitively dominant species, Montastraea cavernosa. This would be the end point of a succession process that began with a peak in Agaricia spp. within a decade of initiating the simulation, followed by a peak in M. annularis at around 50 years, which in turn was displaced by the competitively dominant M. cavernosa after 272 years. A similar pattern was seen under conditions of

Fig. 3. Effect of spatial extent of disturbance on coral community composition. Mean percent cover at 500 years for the most abundant species (Mc, Montastraea cavernosa; Ma, Montastraea annularis; Mm, Meandrina meandrites; Ag, Agaricia spp.) and bare substratum (BS).

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Fig. 4. Effect of spatial extent of disturbance on distribution of total and partial mortality across colony size classes (on a log scale), and modal colony size class. (a, b) Montastraea cavernosa, (c, d) Agaricia spp., (e, f) Meandrina meandrites, and (g, h) Montastraea annularis (distribution of mortality and modal size class, respectively).

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low-level disturbance (0.1), where M. cavernosa also dominated the plot (Fig. 3a) and diversity was low (H  = 0.58 ± 0.02 (mean ± S.D.), n = 10). At intermediate disturbance levels (0.2), the resulting plot was more diverse (H  = 1.26±0.01), in which Meandrina meandrites, M. annularis and Agaricia spp. were abundant. The amount of bare substratum remaining was considerably greater (36.4 ± 0.5%). This level of disturbance generated a temporal mosaic, whereby different patches of the plot were in different phases of succession, and the monopolisation of M. cavernosa was broken by the frequent creation of openings that were initially colonised by other species, notably Agaricia spp. Disturbance levels greater than 0.2 of the plot lead to development of entirely different communities (Figs. 2 and 3) dominated by M. meandrites, together with low abundances of Agaricia spp. Other species were present at very low abundances or absent, and consequently diversity was low (0.84±0.03 and 0.79±0.02 for disturbance levels 0.4 and 0.6, respectively). Only species with extremely high colonisation rates were able to survive in this highly unstable environment, and this is because of their fast turnover. Diversity patterns across increasing spatial extents of disturbance support the long-held hypothesis that highest diversity occurs at intermediate levels of disturbance (Connell, 1978). The relative importance of total colony mortality to partial colony mortality changed with colony size class (Fig 4a, c, e and g). Total colony mortality was more important for small colonies, and partial colony mortality more important for large ones. This pattern was consistent across all spatial extents of disturbance. The threshold between predominantly total and predominantly partial mortality fell in approximately the same position for all species investigated, namely between size classes of 3–6 and 7–19 cm2 . The modal size class of colonies on a log scale also showed little response to increasing spatial extent of disturbance, though variance in the results obscures interpretation to a certain extent (Fig 4b, d, f and h). In general though, the modal size class appeared to be one to two classes larger than the threshold (between predominately total colony mortality and predominantly partial colony mortality). These results support hypotheses developed by Bak and Meesters (1998) that modal colony size on a log scale is related to the type of mortality (total

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or partial) that affects the population. However, these results show that the modal size is greater than the mortality threshold, thus the relationship between size and age in corals is likely to be decoupled at smaller sizes than previously thought, as size classes below the modal size are susceptible to partial mortality. 3.1.2. Size of disturbed patches Disturbed patch size clearly had a strong influence on coral community structure (one-way ANOSIM: r = 0.999, P < 0.001, Fig. 4). Under a disturbance regime of many small patches (1 cm radius), the coral community was markedly similar to that without disturbance; the competitively dominant species, M. cavernosa, monopolised almost all space (Fig. 5). This is because small patches were rapidly in-filled by lateral growth of surviving colonies, and space was not available for recolonisation via recruitment. This also meant that diversity was very low (H  = 0.13±0.01, mean±S.D.). A similar pattern was seen with patches of 3 cm radius, although M. meandrites was also present at a low abundance (<10%), and diversity was greater (0.8 ± 0.01). Intermediate sized patches (5–10 cm) acted to increase diversity (H  = 1.26 ± 0.12 and 1.20 ± 0.02, respectively), as abundances of Agaricia spp., Meandrina meandrites, Montastraea annularis and Montastraea cavernosa increased (Fig. 6). As seen with intermediate levels of disturbance, intermediate sized patches created a temporal mosaic, with patches at different phases of succession, and broke the spatial monopoly of the competitively dominant

Fig. 5. Effect of disturbed patch size on community structure. MDS ordination of Bray–Curtis similarity matrix of percent cover at 500 years. Numbers denote radii of disturbed patches (cm). Minimum stress for best two-dimensional ordination is 0.01.

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Fig. 6. Effect of disturbed patch size on community composition. Mean percent cover at 500 years for the most abundant species (Mc, Montastraea cavernosa; Ma, Montastraea annularis; Mm, Meandrina meandrites; Ag, Agaricia spp.) and bare substratum (BS).

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Fig. 7. Effect of disturbed patch size on distribution of total and partial mortality across colony size classes (on a log scale), and modal colony size class. (a, b) Montastraea cavernosa, (c, d) Agaricia spp., (e, f) Meandrina meandrites and (g, h) Montastraea annularis (distribution of mortality and modal size class, respectively).

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Fig. 8. Effect of varying distribution of disturbed patches using a power law function, on coral community structure. MDS ordination of Bray–Curtis similarity matrix for percent cover at 200 years. Four levels of a were tested, with 10 replicates of each. Minimum stress for the best two-dimensional ordination is 0.07.

species, as patches were large enough to allow recruitment and thus persistence of more ephemeral species. Very large patch sizes pushed the community into a lower diversity state (H  = 0.98 ± 0.06), composed mostly of Agaricia spp. with low abundances of Montastraea annularis and Meandrina meandrites (Fig. 6). As large patches killed entire colonies, surviving colony fragments were fewer and more dispersed and their regrowth was relatively less important in terms of recolonisation than of recruitment. Thus species with high rates of colonisation (recruitment and growth) such as Agaricia spp. and Meandrina meandrites were the only ones able to persist in this environment. The relative importance of total colony mortality to partial mortality shifted across colony size classes in response to the size of disturbed patches applied (Fig. 7), and responses were similar for each species investigated. Large disturbed patches killed off rela-

tively large corals, so the size classes affected by total colony mortality increased with disturbed patch size. This acted to drive the modal colony size into larger sizes classes. Consistent with the previous results investigating the spatial extent of disturbance, the modal size class was greater than the mortality type threshold (between predominantly total mortality and predominantly partial mortality). 3.1.3. Power law model The distribution of disturbed patches clearly had a strong effect on coral community structure (one-way ANOSIM; r = 0.49, P < 0.001, Fig. 8). With a at 1.25, a community developed that was distinct from all others (Table 3). This was composed of approximately equal abundances of Montastraea annularis and Agaricia spp. The community at a = 1.5 was also significantly different from those emergent at higher values of a, with greater abundances of Montastraea annularis. There were no detectible differences be-

Table 3 Comparisons of community structures run with contrasting disturbed patch size distributions (a), made from one-way ANOSIM a 1.5 1.25 1.5 1.75 ∗

Significant difference.

r = 0.74, P <

1.75 0.001∗

2.0 0.001∗

r = 0.955, P < r = 0.094, P = 0.071

r = 0.969, P < 0.001∗ r = 0.137, P = 0.042∗ r = −0.026, P = 0.581

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tween communities run with disturbance regimes of a = 1.75 and 2.0. Varying a also influenced the distribution of mortality through coral colony size classes. Total colony mortality affected the largest size classes when a was set at 1.25 (when the largest proportion of large patches were generated). Modal colony size class followed the same trends as the threshold between total and partial colony mortality. The relationship between patch size and modal colony size class was used to parameterise disturbance using the power law model. This was achieved by comparing the size structure of modelled populations of Agaricia spp., the coral with the highest tissue turnover, with those from the literature. When a was set at 1.5, modal colony size of Agaricia spp. was 7–19 cm2 planar area. This was converted to three-dimensional surface area to enable comparison to field observations from Curaçao (Meesters et al., 2001), using a specific formula for Agaricia agaricites (R. Bak, personal communication): √ sa = π3 lwh (4)

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(Meesters et al., 2001). From this point onwards in the study a value for a of 1.5 was used. 3.2. Parameter sensitivity Changes in competitive ranking resulted in a greater change in community composition than any other parameter (Table 4). Growth was the second most influential parameter, with changes in recruitment and mortality having least impact on the model. Species varied in their sensitivity to life history parameters, and broadly fell into two groups: (1) those that were sensitive to most parameters, e.g. Montastraea annularis, and (2) those that were resistant to changes in all parameters except competitive rank. The latter group was composed of subordinate species (all ranking below 5 in aggressive capacity, the midpoint of the hierarchy): Stephanocoenia michelinii, Agaricia spp. Porites astreoides, Madracis spp. and Siderastrea siderea. This again reflects the importance of spatial competition; even if rates of growth are changed but a species is low-ranking competitively, there is little impact on abundance.

where l, w and h are colony length, width and height (assumed to be equal and equivalent to colony diameter of a circular colony), respectively, and ‘sa’ is three-dimensional surface area. Three-dimensional surface area predicted by the model was 27–124 cm2 , highly comparable to published modal sizes of between 30 and 100 cm2 for Agaricia agaricites

3.3. Model performance Out of the 10 species modelled, 5 compared well with published observations, 2 species required further testing, 2 species could not be assessed due to lack of suitable field data for comparison, and 1 species was not accurately predicted.

Table 4 Relative sensitivity ranks by species to different life history traits Species

Growth

Recruitment

Relative mortality

Competitive rank

Average by species

Montastraea annularis Meandrina meandrites Colpophyllia natans Montastraea cavernosa Agaricia spp.

3 3 2 2 2

1 1 1 1 1

2 1 1 1 1

3 3 1 1 2

2.25 2.0 1.25 1.25 1.5

Stephanocoenia michelinii Eusmilia fastigiata Siderastrea siderea Porites astreoides Madracis spp.

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

3 2 3 3 3

1.5 1.25 1.5 1.5 1.5

Average by parameter

1.7

1

1.1

2.4

Sensitivity ranks were assigned according to changes in cover—1: 0–5% change; 2: 5–10% change; 3: >10% change. Results are given for value changes of two-fold for growth and recruitment rates, but 0.1 and 1 for differential mortality probability and competitive rank (as the latter response was non-linear, the largest increase in cover is given).

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Fig. 9. Comparison of modelled coral populations with field measurements. (a) Montastraea cavernosa, (b) Eusmilia fastigiata, (c) Meandrina meandrites, (d) Colpophyllia natans and (e) Porites astreoides. Bars indicate field measurements (a–d, Meesters et al., 2001; e, Soong, 1993), lines indicate model predictions (solid denotes disturbance level 0.05; long dash, 0.1; dash, 0.15; and dot, 0.2).

The species that had similar population size structures to observed corals were: Montastraea cavernosa, Eusmilia fastigiata, Meandrina meandrites, Colpophyllia natans and Porites astreoides (Fig. 9). In all cases, the proportion of corals in the smallest size

class (1–10 cm2 ) was over represented. There are two possible explanations for this, either small corals are frequently underestimated during field censuses due to their size and preference for cryptic habitats, or mortality rates for the earliest post-settlement stage were

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Table 5 Effect of increasing levels of background disturbance on coral size structure Species Montastraea cavernosa Stephanocoenia michellinii Agaricia spp. Eusmilia fastigiata Meandrina meandrites Montastraea annularis Colpophyllia natans Porites astreoides Madracis spp. Siderastrea siderea

χ2

P

Direction of change

71.7 51.1 6.3 5.19 10.9 5.8 17.6 116.3 10.7 40.4

<0.001∗

CS decreasing with increasing disturbance CS increasing with increasing disturbance

<0.001∗ 0.390 0.520 0.282 0.421 0.039 <0.001∗ 0.097 <0.001∗

CS increasing with increasing disturbance CS increasing with increasing disturbance

χ2 was carried out on all data from all replicates combined for colonies in broad log-scale size classes. CS: colony size. ∗ Significant difference.

underestimated within the model. Interestingly, the population size structure of some species was highly resistant to increasing levels of disturbance (e.g. Eusmilia fastigiata and Meandrina meandrites, Table 5), while other species were sensitive to increasing levels of disturbance, with competitively dominant species being forced into smaller size classes (Montastraea cavernosa) or subordinate species able to expand into larger size classes (Colphophyllia natans and Porites astreoides). Montastraea annularis and Agaricia spp. both had smaller sized colonies than populations in Curaçao (Meesters et al., 2001) (Fig. 10a and c). Both species had population structures that resisted disturbance (Table 5). Further simulations with decreased recruitment rates acted to increase colony sizes (Fig. 10b and d), and optimal values for recruitment were 100 larvae 9 m2 for Agaricia spp. and 0.6 larvae 9 m2 for Montastraea annularis (using genetic colonies, see Methods). In the case of Agaricia spp. it is possible that the extraordinarily high levels of post-settlement mortality measured on reefs (Hughes and Jackson, 1985) was not accounted for in the model, and decreasing the recruitment rate of this species compensated for this. With M. annularis, the case is more readily explained. A spuriously high field observation of 36 larvae 9 m2 pushed up the average recruitment rate used as model input from 0.3 to 15.6 larvae m2 (Tomascik, 1991). This anomalous result was possibly made during a ‘mast’ year of unusually high recruitment (sensu Hughes and Tanner, 2000). When this value was removed, the input value for recruitment for M. annularis was

0.3 larvae 9 m2 , close to the derived value of 0.6 larvae 9 m2 . No field data was found with which to compare Madracis spp. and Stephanocoenia michellinii, but both species had realistically distributed size structures. The former showed resistance in population structure to increasing levels of disturbance, while S. michellinii colonies increased in size with increasing levels of disturbance (Table 5). S. siderea was the only species not predicted accurately by this model. Colonies were consistently smaller than those measured in the field (Meesters et al., 2001) (Fig. 10e). Changes in recruitment rate did not bring the colonies into larger size classes (Fig. 10f). Small sized S. siderea colonies were not entirely unexpected from the attributes of this species, they have low rates of recruitment and growth, are susceptible to mortality, and possess minimal competitive proficiency. This does lead to further questions regarding how this species persists on reefs in large numbers, forming large colonies. A possible answer relates to substrate heterogeneity, and utilisation of spatial refuges. S. radians, a congener, is extremely tolerant of silty conditions and can even survive unattached, rolling freely across sandy lagoonal habitats. This suggests high resource investment in sediment removal and tissue regeneration, possibly at the expense of reproduction and growth. S. siderea may use a similar strategy, growing in marginal areas of the reef, e.g. adjacent to unconsolidated substratum. There is no evidence available to suggest that this is the case, but this hypothesis is worth further consideration.

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Fig. 10. Comparison of modelled coral populations with field measurements. (a, b) Agaricia spp., (c, d) Montastraea annularis and (e, f) Siderastrea siderea. Bars indicate field measurements (a and b, Hughes, 1984; c–f, Meesters et al., 2001). Lines indicate model predictions—for (a), (c) and (e) the solid denotes disturbance level 0.05; long dash, 0.1; dash, 0.15; and dot, 0.2. For (b) lines indicate results from simulations using a recruitment rate of 100 larvae 9 m2 per year. For (d) lines indicate results from simulations using a recruitment rate of 0.6 larvae 9 m2 per year, solid line shows all colonies measured as individuals, broken line shows colonies grouped as genetic individuals. In (f) lines show results of simulations with different recruitment rates (ranging from 1 to 68 larvae 9 m2 per year).

Table 6 Properties of some previous spatial models for sessile communities from marine and terrestrial systems Maguire and Reichelt et al. Porter (1977) (1985)

25 × 25 to 500 × 500 Area simulated 1.2 m × 1.2 m 5 m × 5 m Spatial resolution 2 cm 1, 2, 5, 10 (size of cells) and 20 cm Time step (per years 1 generation 1 year iterations) (=1 year) Temporal scale (per 250 20 iterations run) Taxonomic resolution Species Species Array size

No. of groups Output Boundary conditions Neighbourhood System modelled

a b c

60 × 60

2 No. of ramets Periodic 12 Herbaceous perennial plants

6 % Cover ? ? Eastern Pacific coral community

Crimp and Braddock (1993)

Karlson and Jackson (1981)

Burrows and Hawkins (1998)

Johnson and Preece (1992), Preece and Johnson (1993)

This model

120 × 60

100 × 100

40 × 40

25 × 25

33 × 120

300 × 300

12 m × 6 m 10 cm

5m × 5m 5 and 10 cm

? ?

25 m × 25 m 1m

165 km × 600 km 5 km

3m × 3m 1 cm

?

1 year

?

?

?

240

500

25

230

?

4 × year and 1 × yeara 100–500

Functional groups Functional groups ?

Community states Coral cover states

5 % Cover ? 4 Coral reef community (3 corals, soft coral and algae)

5

5 % Cover Zero flux ? Great Barrier Reef coral community (all groups represent corals)

10 % Cover ? ? Sessile benthic community (non-scleractinian)

Growth was iterated four times each year, recruitment and mortality were iterated once each year. Some species complexes. CSS: colony size structure.

5 Mean state Periodic ? ? 8 Temperate rocky Great Barrier Reef shore community coral communities (low resolution)

Predominately speciesb 10 % Cover, CSSc Periodic 4 Caribbean coral community

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Inghe (1989)

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Out of 10 coral species, 7 had negatively skewed colony size distributions on a log scale, indicating fewer small colonies relative to larger ones. Exceptions were Porites astreoides, Madracis spp. and Siderastrea siderea. This is a comparable result to a field study by Meesters et al. (2001), who found 48/52 coral populations measured were negatively skewed. Those authors also found a positive relationship between mean colony size and degree of negative skewness, which is consistent with these results as the three species with positively skewed populations formed the smallest colonies.

4. Conclusions The input data for this model was gathered from various sources in the literature, ranging in geographical location, collector, and in some cases collection technique (namely recruitment data, for which there appears to be no standard protocol for basing estimations). In view of this, the fact that the model was able to accurately predict coral population size structures in 7 out of 10 species tested is extremely encouraging (possibly this figure is 9 out of 10, but data are not currently available to compare a further 2 species). As noted earlier, population size structure is a much more rigorous test of the predictive abilities of the model than simply comparing coral cover, an intrinsically variable property of reefs (Bythell et al., 2000). In reaching this result, other interesting and important characteristics of disturbance emerged. Firstly, the relationship between the threshold of partial and total colony mortality and modal colony size on a log-scale demonstrates that size and age may be decoupled at an earlier stage than previously thought (Bak and Meesters, 1998). Increasing our understanding of mortality processes structuring coral populations also yields insight into the pattern of other size dependant processes, namely fecundity, which is strongly correlated with colony size (Soong, 1993). Secondly the size of disturbed patches appears to be as important in structuring coral communities as the overall amount of disturbance. The distribution of cleared substratum in space is rarely measured in the field, and is instead usually deduced by differences in coral cover. This has important implications for recovery mechanisms of reefs, given the differences be-

tween species in recolonisation of space, which depends on patch size and the relative speed of recruitment compared with in-filling of cleared patches by vegetative growth of surviving colony fragments. Thirdly the power law model appears to be highly realistic in generating disturbed patches, and thus assumptions regarding disturbed patch distribution appear to hold. This model has several advantages over its CA predecessors (Table 6). It is much larger, and is run for much longer, to the extent that initial starting conditions which previously have been important, become unimportant. A major benefit comes also from the fact that the size structures of coral populations are accounted for, and output is not restricted to simple estimations of cover. This is likely to be in part a reflection of the advances in computers over the last decade, that allow plots to be constructed at this high level of resolution. In fact, this model yields information of a similar quality to that of a size structured transition matrix type model (e.g. Done, 1987, 1988; Hughes, 1984) but has the advantage of being spatially explicit and containing multiple interacting species.

Acknowledgements The authors thank Dr. M. Keeling and B. Barnes of the University of Warwick, and Professor R.P.M. Bak (NIOZ) and the University of Warwick Graduate School for financial support to O.L.

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