Size dependence, facilitation, and microhabitats mediate space competition between coral and crustose coralline algae in a spatially explicit model

Size dependence, facilitation, and microhabitats mediate space competition between coral and crustose coralline algae in a spatially explicit model

Ecological Modelling 237–238 (2012) 23–33 Contents lists available at SciVerse ScienceDirect Ecological Modelling journal homepage: www.elsevier.com...

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Ecological Modelling 237–238 (2012) 23–33

Contents lists available at SciVerse ScienceDirect

Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel

Size dependence, facilitation, and microhabitats mediate space competition between coral and crustose coralline algae in a spatially explicit model Kate E. Buenau ∗ , Nichole N. Price 1 , Roger M. Nisbet Department of Ecology, Evolution, and Marine Biology, University of California, Santa Barbara, Santa Barbara, CA 93106, United States

a r t i c l e

i n f o

Article history: Received 21 September 2011 Received in revised form 3 March 2012 Accepted 11 April 2012 Keywords: Coral Crustose coralline algae Space competition Facilitation Size dependence Stochastic simulation Spatial refuge

a b s t r a c t Coral interacts both positively and negatively with different types of crustose coralline algae (CCA) throughout the coral life cycle. These interactions range from settlement cues and facilitation by “promoter” CCA species to settlement inhibition, preemptive competition for space, and overgrowth of smaller coral colonies by “inhibitor” CCA species. Corals coexist with CCA in healthy coral reefs despite appearing to be weaker space competitors than inhibitor CCA. We use spatially explicit stochastic simulations of size dependent interactions between individual coral colonies and CCA patches to explore how CCA affects the recovery of corals after disturbance in homogenous and heterogeneous habitat. Specifically, we look at whether positive or negative interactions have a larger effect on coral growth and survival and whether events during recruitment or interactions between CCA and established colonies have larger impacts on coral cover and persistence. We find that competition for space through preemption and overgrowth is the primary factor driving coral dynamics, overshadowing settlement processes. Coexistence of coral and CCA is difficult if not impossible to achieve in homogenous landscapes unless corals are more effective than CCA at preempting space. Microhabitats that protect coral settlers from overgrowth allow vulnerable coral to persist and replace refuge coral that has died, but additional mechanisms such as competitive reversals or patchy CCA mortality are required for coral persistence outside of protected microhabitats. Through these models we identify mechanisms that have been rarely studied but are potentially critical for the survival of coral in areas where CCA is a dominant competitor. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Competition for space is an important driver of the dynamics and distribution of sessile marine organisms, whose survival depends on both obtaining a site for settlement and retaining occupancy of that space (Connell, 1983; Jackson and Buss, 1975; Muko et al., 2001). For many scleractinian corals, the ability to grow laterally and occupy more space is important for maturity and reproduction as well as survival (Crowley et al., 2005). The distribution and abundance of a species can depend, to varying extents, both upon processes that occur during the initial occupancy of space and upon the ability of established individuals to maintain and increase the space they control (Chesson, 1998).

∗ Corresponding author at: Marine Sciences Laboratory, Pacific Northwest National Laboratory, 1529 W. Sequim Bay Rd., Sequim, WA 98382, United States. Tel.: +1 360 681 4590; fax: +1 360 681 3681. E-mail address: [email protected] (K.E. Buenau). 1 Present address: Center for Marine Biodiversity and Conservation, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0202, United States. 0304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ecolmodel.2012.04.013

The relative contribution of pre- and post-settlement processes to the dynamics of open populations is a lasting question in marine ecology (Caley et al., 1996; Connell, 1985; Hunt and Scheibling, 1997). While questions about the roles of settlement, recruitment, and competition have been explored extensively in fish (Anderson et al., 2007; Hixon, 1998; Schmitt et al., 1999) and intertidal invertebrates (Jenkins, 2005), they are difficult to study in long-lived, slow-growing taxa such as coral. Long-term studies that track the growth and fate of coral colonies (e.g. Hughes and Tanner, 2000) generally must operate at a spatial and temporal resolution that cannot resolve the early dynamics of coral settlement and recruitment. Attempts to resolve early dynamics, in turn, require a frequency and intensity of monitoring that limits the studies to short time spans (Roth and Knowlton, 2009). Models can allow for the simultaneous exploration of both finescale settlement dynamics and long-term dynamics of coral and their competitors, though most existing models are either not spatially explicit (Connolly and Muko, 2003; Gonzalez-Rivero et al., 2011) or operate on scales broader than individuals (Mumby and Dytham, 2006; Melbourne-Thomas et al., 2011). In this study we use a spatially explicit model of coral and two crustose coralline algae (CCA) functional types that interact with coral both positively and negatively throughout the coral life cycle. While our

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model, like any model, contains many simplifications including a limited number of organism types, it allows us to study both shortterm settlement dynamics and extended space competition as coral colonies mature. Some field studies of the settlement dynamics of corals have focused on the distribution of coral across depths (Babcock and Mundy, 1996; Baird et al., 2003), while others focus on the role of larval supply in determining coral recovery (Arnold et al., 2010; Hughes et al., 2000). The composition of the existing community influences coral recruitment (Vermeij and Sandin, 2008) and the effects of foliose algae on coral settlement and early survival have been studied extensively (McCook et al., 2001). In some cases, algae damage or overgrow living coral (Jompa and McCook, 2003). In others, established coral colonies successfully compete with encroaching algae (Nugues and Bak, 2006; Nugues et al., 2004) but algae hinder or prevent coral recruitment through space preemption or microbial interactions (Birrell et al., 2008; Kuffner et al., 2006; Vermeij et al., 2009). Inhibition of coral settlement could lead to community shifts after disturbance if algae proliferate and prevent coral recovery (Ledlie et al., 2007; McManus and Polsenberg, 2004). Interactions between coral and CCA have received much less attention (Harrington et al., 2004) despite a broad range of potential positive and negative interactions throughout the coral life cycle. Certain species of CCA provide chemical cues that initiate metamorphosis and attachment in some corals (Heyward and Negri, 1999; Morse and Morse, 1996; Morse et al., 1994). Coral settling on “promoter” CCA may demonstrate increased survival or growth (Harrington et al., 2004), and thus the presence of CCA in a reef habitat can be a predictor of coral cover (Vermeij, 2005). Promoter CCA species tend to be thinner, faster-growing, and more shade tolerant than other types of CCA but also more susceptible to herbivory and overgrowth (Steneck et al., 1991). As a result, promoter CCA species are often rare (Harrington et al., 2004) and more prevalent in habitats that provide some protection from herbivores and reduced competition from species that require more light (Arnold et al., 2010; Caragnano et al., 2009; Price, 2010). Another group of CCA possesses defenses against fouling and actively inhibits coral settlement and survival (Harrington et al., 2004; Keats et al., 1997). The “inhibitor” functional type is generally thicker than promoter CCA, requires more light, is more resilient to herbivory and disturbance (Dethier and Steneck, 2001; Steneck et al., 1991), and is capable of overgrowing promoter CCA and coral (Antonius and Afonso-Carillo, 2001; Golbuu and Richmond, 2007; Vermeij and Sandin, 2008). Inhibitor species are generally strong competitors in habitats that are well-lit and more exposed to disturbance (Vermeij et al., 2011). Inhibitor CCA is most likely to overgrow coral colonies that are young and small, with a size dependent shift in competitive abilities possible as corals become large and develop more effective defenses (Golbuu and Richmond, 2007; Zilberberg and Edmunds, 2001). Empirical studies examining size dependence in competition between coral and CCA are limited. Previous modeling suggests that if CCA only overgrows coral colonies smaller than a threshold size, coral persistence can improve considerably if coral is competitive enough to reach the critical size (Buenau et al., 2011), though long-term coexistence remains highly unlikely if coral cannot compete for space occupied by CCA. In this study, we determine what mechanisms are minimally necessary for coral persistence. Mechanisms with the potential to promote coexistence between coral and CCA include competitive reversals, which could occur if larger corals not only defend themselves against overgrowth but overgrow CCA themselves (Hughes et al., 2000). This would be an example of a non-transitive competitive interaction (Buss and Jackson, 1979; Laird and Schamp, 2006). Most studies of non-transitive competition involve competitive “loops” of

multiple species (e.g. Frean and Abraham, 2001), though Buss (1980) observed non-hierarchical competition between three encrusting marine species in which competitive outcomes between each species varied depending upon the size of individual crusts. Connolly and Muko (2003) modeled reversal competition between an understory coral and an overtopping coral, but their nonspatial models did not account for the space required for the overtopping species to mature. Patchy CCA mortality would also allow coral to regain space occupied by CCA; while information on CCA mortality is limited, disease (Vargas-Angel, 2010), grazing (O’Leary and McClanahan, 2010), and bleaching (Anthony et al., 2008) might, in some locations and circumstances, contribute to patchy CCA mortality. Coral larvae have been observed to actively choose the depth, type, and orientation of substrate on which they settle (Baird et al., 2003; Raimondi and Morse, 2000; Vermeij, 2006). Preferential settlement on sheltered surfaces of settlement tiles, where predation, sedimentation, and competition with algae is limited, can result in higher survival of coral recruits (Arnold et al., 2010; Raimondi and Morse, 2000), though growth rates may be limited (Vermeij, 2006). On more complex substrates, coral larvae preferentially seek cracks and crevices that also allow for increased survival until coral are larger and less vulnerable to predation and overgrowth (Nozawa, 2008), though habitat preferences do not always correlate with improved outcomes for coral (Babcock and Mundy, 1996; Edmunds et al., 2004) and some species demonstrate preference for exposed convex surfaces (Roth and Knowlton, 2009). Since promoter CCA is most often found in sheltered habitats where other algal species cannot grow (Price, 2010), it may act as an indicator of habitat that could protect coral recruits and provide an evolutionary benefit for using promoter CCA as a settlement cue. We use small-scale simulation models that track individual coral colonies to examine how interactions with different types of CCA throughout the coral life cycle might impact the distribution and abundance of corals and their recovery after disturbance. In a previous study (Buenau et al., 2011) we showed that size-dependent competition was an insufficient mechanism for long-term coexistence of coral with competitively dominant CCA. Here, we explore size-dependent competition with an inhibitor CCA and positive interactions with a promoter CCA to determine what mechanisms are necessary and/or sufficient for the long-term recovery of coral after disturbance. We ask the following questions: (1) What are the relative contributions of settlement processes and space competition to the recovery of coral after disturbance? (2) Does coral benefit from preferential settlement on promoter CCA and facilitation of survival and growth? (3) How does the supply of coral settlers affect inter- and intra-specific competition? (4) Do protected settlement microhabitats increase the cover of mature coral in open habitat? (5) Are competitive reversals or patchy CCA mortality realistic mechanisms for competition between mature coral and CCA?

2. Model description Our model focuses on the interactions between small coral colonies and CCA during the early years after settlement, using a high-resolution lattice-based simulation. We use a 240 × 240 grid of 1 mm2 cells. Each cell can be classified as empty or occupied by coral, promoter, or inhibitor CCA. Coral overgrows promoter CCA and inhibitor CCA overgrows both coral and the promoter (Fig. 1); cells can therefore have multiple layers of occupancy which may affect the growth or mortality rates of the dominant occupant. The lattice boundaries are reflecting to the movement of coral settlers and absorbing for growth. In the following paragraphs we describe

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Refuge coral

overgrowth

Inhibitor CCA

maturaon

selement overgrowth

selement overgrowth

Vulnerable coral

Promoter CCA

selement survival facilitaon growth facilitaon

Table 1 Parameters. Description

Default values

Flux of coral (# larvae/mm2 /time) Flux of inhibitor (# propagules/mm2 /time) Flux of promoter (# propagules/mm2 /time) Area covered by coral larva (mm2 ) Area covered by CCA propagule (mm2 ) Mortality of coral settlers (time−1 ) Mortality of coral settlers on promoter (time−1 ) Mortality of vulnerable coral (time−1 ) Mortality of refuge coral (time−1 ) Mortality of inhibitor (time−1 ) Mortality of promoter (time−1 )

0.001* 0.001†† 0.001†† 1 1 0.2† 0.1† 0.14* , † [0–0.8] 0.01* , † [0–0.1] 0.1†† 0.1††

Linear expansion (mm/time)

Size refuge threshold diameter

Slow coral 1† , ** [0–2.7] 2†† 3†† 2†† 1†† 30

unbiased, memoryless random walk of specified maximum length from a random starting position and moving via eight nearest neighbors. All coral in a simulation replicate are assigned one of three settlement strategies: seek promoter CCA, avoid inhibitor, or no strategy (ignores substrate). Upon selection of an initial cell and during the random walk a settler tests the substrate at each step, stopping once they reach their goal or run out of steps. If a coral settler runs out of steps while on the inhibitor or coral, it dies. Settlers with no settlement strategy stop as soon as they have located a cell not already occupied by coral. The order in which the model groups settle does not affect the results.

2.2. Growth

Fig. 1. Interactions between model groups. Solid lines indicate interactions that are always included. Dashed lines indicate interactions that are included when specified.

Coral on empty cell Coral facilitated by promoter Promoter on empty cell Inhibitor on empty cell Inhibitor on coral or promoter

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Fast coral 2 3 3 1 1 24

Parameters given (mean with [range] when multiple sources indicated) are for a two month time step, in order to accommodate the spatial resolution of the simulation model. Two sets of parameters are provided for linear expansion rates and the size refuge threshold diameter: one set where coral grows slowly relative to inhibitor CCA on empty cells (“slow coral”) and one set where coral grows quickly relative to inhibitor CCA (“fast coral”). * Vermeij (2006). ** Edmunds (2007). † Price (2010). †† Price unpublished (dissertation).

the basic simulation model as well as variations that allow us to explore alternative competitive mechanisms. 2.1. Settlement Due to the limited spatial scale of the model and the pelagic life stages of coral larvae and algal spores, we assume that all settlers arrive from outside our model domain at a constant rate (Table 1). Each propagule occupies a single 1 mm2 cell. CCA settlement occurs first, during which CCA propagules land on random cells and survive if the cell is empty. The inhibitor can settle on top of the promoter, but not on coral. Promoter CCA may only settle on empty cells. If settlement is not allowed on the selected cell, the settler dies. As coral settlers have been observed to sample the substrate and exercise some choice over landing sites (Harrington et al., 2004; Raimondi and Morse, 2000), we model settlers as taking an

Growth of coral or CCA occurs through colonization of cells adjacent to occupied cells. During each time step, all cells on the lattice are visited in a random order newly generated that time step. If a cell occupied by CCA or coral that was present in the previous time step shares an edge with at least one cell that species can occupy, the occupant expands outward into available cells for as many steps as are allowed by a growth parameter. Promoter CCA can only grow into empty cells. Coral can grow into empty cells or onto the promoter, at an increased rate if growth facilitation is included. Inhibitor CCA can overgrow vulnerable coral and the promoter. If the growth rate (g) is 1, expansion will occur to each available cell of the 4 nearest neighbors. The growth rate indicates how many times the expansion process repeats for each newly occupied cell. If neighboring cells are always empty, growth from a single originating cell results in a diamond shaped patch that is 2g + 1 cells wide. Once the growth process is complete for the originating cell, the next cell on the randomly ordered list is checked. If that cell has not been overgrown during the current time step, the growth process occurs again. As coral colonies expand, each newly occupied cell receives an ID number from the originating cell, which allows each coral cell to be attributed to a specific colony. Adjacent coral colonies are considered separate. Inhibitor CCA can grow into empty cells, or onto promoter CCA or vulnerable coral at a rate that may be reduced from its growth into empty cells. We define two scenarios of growth rates for coral and inhibitor CCA, “slow coral” and “fast coral”, as described in Table 1. If coral or inhibitor CCA grows from one substrate onto another (e.g. from promoter CCA to empty cells), growth rates may change. The occupancy of a cell determines the rate of growth originating from that cell for the dominant occupant. If, during the growth process, the substrate changes from that of the originating cell, additional growth steps may be added or removed for remaining growth to match the growth rate on the new substrate. For this process to work correctly, overgrown occupants are recorded as present in cells to determine the future growth of the overgrowing species, but are not considered in measurements of cover. We assume that upon attaining a critical size (area), coral colonies have matured to the point where CCA can no longer overgrow them. Such coral colonies are regarded as being in a “size refuge”. For ease of comparison with empirical studies of coral growth and maturity, we parameterize the size refuge threshold in terms of the diameter of a symmetrical colony and consider irregularly-shaped colonies of equivalent area to be in the size refuge. The default interaction between inhibitor CCA and coral in the size refuge is standoff competition. When we model competitive reversal, inhibitor CCA still overgrows vulnerable coral, but refuge coral overgrows the inhibitor.

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2.3. Mortality Mortality of CCA occurs on a cell-by-cell basis in the basic model. Each cell occupied by CCA has a constant probability per time step of becoming empty. When an inhibitor cell dies, any overgrown occupant of that cell is also considered dead. To implement patchy mortality of inhibitor CCA, we model mortality in patches larger than a 1 mm2 cell. Randomly chosen squares of the specified size are cleared of inhibitor until the total area of inhibitor lost reaches the proportion specified by the mortality parameter. By contrast, coral colonies are assumed to have a constant probability of mortality during a time step: if mortality occurs, the entire colony is removed. Coral mortality occurs at different rates for vulnerable and refuge corals. There is evidence that smaller coral colonies are unable to survive partial mortality of the colony following predation or physical injury, while larger colonies may regenerate and survive smaller injuries (Bythell et al., 1993; Meesters et al., 1997). We do not explicitly model partial mortality, but rather incorporate it into lower mortality rates for coral colonies that have attained the size refuge. Coral settlers in their first time step have a separate mortality probability from other vulnerable coral, and that probability is reduced upon the promoter if survival facilitation is enabled. If a settler on promoter CCA dies during the first time step, the promoter CCA survives, otherwise CCA underneath coral is presumed to die and the cell becomes empty when the coral dies.

rapid coral exclusion (∼36 months) and medium- to long-term coral persistence (>36 months, but finite). These outcomes result from varying the coral and inhibitor growth rates and the coral size refuge threshold (Table 1), which primarily determine the qualitative dynamics. When coral grows more slowly than the inhibitor (“slow coral” parameters), inhibitor CCA excludes coral before any colonies enter the size refuge. When coral growth rates are increased and the inhibitor growth rate and size refuge threshold are decreased (“fast coral” parameters), some colonies enter the size refuge and inhibitor CCA and refuge coral coexist until the colonies die and are not replaced. The addition of promoter CCA does not change these fundamental outcomes. Other parameters influence the quantitative results for persistence times or cover, but do not produce distinct outcomes unless set to values that depart from the biology of the system (e.g. extremely high mortality of inhibitor CCA such that all inhibitor cover turns over multiple times within the course of one year). We use these two biologically reasonable scenarios as a basis to explore the roles of settlement and post-settlement processes. We begin by determining the relative importance of settlement and post-settlement processes, including coral substrate selection, facilitation of coral growth and/or settler survival, and settlement supply in order to determine where barriers to persistence occur. We then examine additional mechanisms that affect coral persistence and cover: heterogeneous habitat, competitive reversal and patchy inhibitor mortality.

2.4. Simulation process

3. Results

Simulations start with all cells empty, as in the aftermath of an intense disturbance. To accommodate the slow growth rates of corals on a 1 mm resolution grid, we use a bimonthly time step and estimate all parameters accordingly. The percent covers of inhibitor CCA, promoter CCA, vulnerable coral, and refuge coral are recorded after the mortality phase and prior to settlement. Only occupants that are not overgrown are counted as cover. Coral is considered excluded if total coral cover drops below the cover provided by one time step’s settlement, which represents the case where the only coral in the system is new settlers that are overgrown within a single time step. All results shown are summaries of multiple model replicates, with the number of replicates varying dependent upon the inherent uncertainty in the model scenarios being run and specified in the figure legends.

3.1. Effects of promoter CCA and settlement processes

2.5. Protected settlement habitats To include protected microhabitats for coral settlement, we divide the lattice into a coarser grid using the specified minimum size of microhabitats as a grain size. For each simulation replicate we randomly select a proportion of the resulting blocks of cells to be protected microhabitats. We assume that inhibitor CCA is unable to settle within the microhabitats and dies if it grows into the microhabitat. All other parameters remain the same across habitat types. 2.6. Parameterization We parameterize the model with empirical estimates when possible (Table 1). Most parameters were estimated in situ by photographing individual corals or patches of CCA on standardized settlement substrata and using image analysis to quantify expansion and survival rates over several years (Price, unpublished). Limited information is available about the demographics of CCA on tropical reefs, leaving us with a range of potential growth and mortality parameters. In previous work (Buenau et al., 2011) we identified two parameter sets that demonstrate the non-trivial outcomes of a coral-inhibitor model in homogenous space: relatively

When coral grows too slowly to reach the size refuge, persistence times (Fig. 2a) are determined by the growth rate of the inhibitor and show little variation. The only mechanism improving coral persistence is a decrease in the inhibitor’s growth rate when overgrowing another occupant. In that case, the presence of an additional CCA functional type benefits coral, but whether the second type facilitates coral does not affect coral persistence. A settlement strategy of avoiding the inhibitor leads to a slight increase in persistence, but seeking the promoter or neutral CCA does not. Limiting the effect of the promoter is its short persistence time, roughly 24 months, with cover peaking before 12 months. When coral grows rapidly enough for some colonies to reach the size refuge, the promoter improves coral persistence if it increases the coral growth rate while present (Fig. 2b), thus increasing the number of colonies reaching the size refuge. Settlement strategies have negligible effects on coral persistence time or on the number of colonies that mature. 3.2. Effects of coral larval supply on colony maturation High settlement fluxes limit the number of colonies reaching refuge size (Fig. 3). The effect is most pronounced when the mortality rates of coral settlers and vulnerable coral are reduced, in which case the lowest settlement flux results in the highest number of colonies reaching the size refuge. When mortality is higher, there is an optimal level of settlement above the lowest level. Removing the settlement cue has a very small effect on the number of adults observed. When the supply of settlers is low, there is a slight advantage in preferential settlement on promoter CCA, but at higher fluxes the advantage is reversed. 3.3. Protected microhabitats for coral settlement Providing protected microhabitats for coral to settle without competition with the inhibitor guarantees the persistence of coral

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Fig. 2. (a) Mean persistence time for coral over 100 replicate simulations using “slow coral” parameters, except overgrowth of inhibitor over coral = 2 for fast overgrowth conditions. Labels indicate whether coral (C), inhibitor CCA (I), promoter CCA (P), and neutral CCA (N; no facilitation) are present, and whether coral settlers seek or avoid a specified substrate or settle at random. Error bars are 95% confidence intervals. (b) Persistence time distributions for “fast coral” parameters, 500 replicate simulations capped at 1000 months. Solid line indicates median, dashed line indicates mean. In one case the promoter only facilitates growth (“CIP growth only”) and in another case the promoter only facilitates settlement survival (“CIP settlement only”).

Fig. 4. Maximum percent of exposed habitat occupied by coral in the size refuge, using “slow” coral growth: (a) with standoff competition between refuge coral and inhibitor, (b) with refuge coral able to overgrow inhibitor, and (c) with standoff competition and inhibitor mortality in 100 mm2 patches. Coral colonies require 421 mm2 of space to enter the size refuge. Data are averages of 20 replicate simulations for each parameter combination, each run for 120 time steps.

Fig. 3. Maximum number of colonies entering size refuge for “fast” coral parameters over a range of settlement fluxes. Mortality was varied by increasing or decreasing mortality rates for settlers and vulnerable coral by 33% as compared to other two cases. Data are maximum number of colonies in size refuge over 50 time steps, averaged over 100 simulations. Error bars indicate standard error.

within the microhabitats. The presence of refuge coral outside microhabitats (Fig. 4) depends upon having protected areas large enough for corals to mature to refuge size within a microhabitat, which can be achieved through high proportions of sheltered habitat, large minimum microhabitat size, or an intermediate combination of the two (Fig. 4a). Expansion of coral outside of protected habitat is very slow and coral occupy only a small fraction of exposed habitat.

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Coral cover in exposed habitat increases dramatically if refuge coral overgrows the inhibitor rather than being in a standoff (Fig. 4b). Coral success in these cases still requires microhabitats of sufficient size for corals to mature. When the proportion of sheltered habitat is high, coral expands to cover most of the exposed habitat, though cover fluctuates with colony mortality. Patchy inhibitor mortality increases the time needed for the inhibitor to regenerate and therefore increases coral cover, though not to the extent that reversal does (Fig. 4c). In this case, refuge coral expansion relies on CCA mortality adjacent to the coral colony, resulting in less coral cover than produced by competitive reversal but more than with cell-based CCA mortality. The structure of microhabitats that leads to increased coral cover outside the microhabitat also depends on the mechanisms of competition. A greater ratio of edge to area (small minimum microhabitat size) increases the odds of patchy disturbance occurring adjacent to a refuge colony, but the reverse is true for competitive reversal where larger microhabitats promote the establishment of more mature coral colonies.

facilitation of the survival of settlers alone, but evidence suggests that facilitation is restricted to the smaller life stages (Price, 2010).

4. Discussion

4.4. Protected settlement habitats

4.1. Relative importance of settlement and post-settlement processes

Microhabitats for coral settlement allow slow-growing corals to coexist indefinitely with CCA, but coexistence in separate habitats is not surprising. We wish to explain the persistence of coral in habitats where inhibitor CCA grows well, but our basic model with microhabitats results in very low coral cover in exposed habitats. Experiments suggest that coral species that settle on and survive at higher rates on the undersides of settlement tiles, due to decreased levels of predation and algal growth, will eventually grow out into the open even if growth rates are decreased in shaded habitats (Babcock and Mundy, 1996). In our model habitat quality is binary, with a direct interface between habitats where coral does and does not compete with the inhibitor, limiting the ability of coral to expand from the protected habitat into space available to the dominant competitor. The utility of microhabitats depends on whether coral colonies can both mature within that habitat (i.e. microhabitats themselves are of sufficient size) and expand into open space as they are found on healthy reefs (mature corals have access to additional space through preemption or overgrowth).

Competition for space among young coral colonies and competitively dominant CCA functional types drives coral dynamics in this three species model and overshadows events that occur during and shortly after settlement, limiting the importance of settlement strategies and recruitment facilitation. If coral persistence depends on the ability of colonies to reach a minimum size, the growth rates of coral and inhibitor CCA determine whether or not coral escapes overgrowth. Mechanisms that increase colony growth and size, such as growth facilitation, can improve persistence. Once space is filled, coral persistence depends on the ability of existing colonies to survive. At that point recruitment is negligible, as are the impacts of processes that affect recruitment. These findings agree with empirical studies such as described by Vermeij (2006) and Arnold and Steneck (2011) that found that adaptive substrate selection is only useful until space begins to fill, after which more competitive organisms overwhelm coral recruits.

4.3. Settler supply Whether or not facilitation or settlement cues are present, our model suggests that establishment of a mature coral population can be limited by high settlement fluxes due to crowding. Mortality for settlers and recruits may be high (Vermeij and Sandin, 2008) and some supply of settlers is required for establishing a population, but the optimal level of recruitment following disturbance may be relatively low to reduce competition between recruits and thus time spent in vulnerable life stages. Aggregation of coral recruits on promoters or in protected microhabitats can further limit the maturation of corals. An exception to this pattern would be seen in cases where juvenile coral colonies are able to fuse rather than compete with each other (Amar et al., 2008; Raymundo and Maypa, 2004), a mechanism which increases the rate at which colonies enter the size refuge (Buenau et al., 2011).

4.5. Competitive reversal 4.2. Effects of facilitation Promoter CCA only improves coral persistence in our model if it accelerates coral growth; there is no significant benefit to its presence as a settlement cue. In fact, a settlement cue can be detrimental if it intensifies intraspecific competition; corals that are obligate settlers on CCA would need to have low settlement rates or some selective advantage that counteracts competition between recruits. Also note that in our model, growth facilitation only improves persistence if coral already grows rapidly enough that some colonies reach the refuge without facilitation. While this may not hold for all possible combinations of coral and CCA growth rates, it suggests facilitation cannot necessarily compensate for a lack of intrinsic competitive ability. Increased success of coral settlers on specific CCA types has been attributed to decreased competition from other algae types (Harrington et al., 2004) or to decreased accumulation of sediments as compared to substrates such as turf algae (Babcock and Mundy, 1996). Most studies are limited to observing whether coral preferentially settles on promoter CCA (Baird and Morse, 2004; Heyward and Negri, 1999; Negri et al., 2001) and short-term survival benefits (Golbuu and Richmond, 2007). Less is known about whether benefits to coral recruits continue through juvenile stages or beyond, which would have greater effects than

We explored two mechanisms for expansion of coral from protected settlement habitat into open habitat: competitive reversal and patchy inhibitor mortality. Either mechanism results in coexistence in open habitat, with reversal leading to notably higher coral cover. Little is known about direct interactions between coral and CCA, and whether and to what extent competitive reversals may occur. The high coral cover in open habitats exhibited in our model with competitive reversal may in fact be unrealistically high; mechanisms that allow for partial success in reversals or reversals only under certain conditions may lead to more realistic predictions. Competitive networks in cryptic coral communities can lead to coexistence (Buss and Jackson, 1979) and the introduction of additional space competitors (e.g. turfing algae, macro-algae, sponges, other coral species) may lead to partial or relative reversals in competitive hierarchies. For instance, the interaction zone in which competitive stand-offs occur between corals and CCA appears to be less “toxic” than interaction zones between corals and turfing or macro-algae, which are hypoxic and associated with coral tissue damage (Barott et al., 2009). Foliose algae can overgrow CCA, but in general the relative dominance among sessile functional groups on reefs is context dependent (Littler et al., 2006). To understand if size-dependent competitive reversal or interactions with other species allows coral to compete with competitively dominant CCA,

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more information about the sizes and conditions under which these interactions occur is needed. 4.6. Patchy inhibitor mortality Little is also known about the sources of mortality for thick, slow-growing inhibitor CCA on coral reefs. If grazing produces patches of bare substrate that are available for coral growth, the same level of total inhibitor mortality per time step in fewer, larger patches led to improved outcomes for corals. In temperate regions, CCA species with thick thalli (Dethier and Steneck, 2001; Steneck et al., 1991) are not always grazed down to the substrate, allowing regeneration from below rather than growth inward from the edges. In such cases, the impact of the patchy mortality we modeled may be too fleeting to be an opportunity for slow-growing corals. Other potential sources of CCA mortality include disease (Vargas-Angel, 2010) or sedimentation, which has been linked to lower CCA cover (Fabricius and De’ath, 2001). Our scenario would require that CCA suffers mortality at levels of sedimentation that do not affect corals. Corals and CCA have been observed to be differentially affected by ocean acidification and warming: Porolithon onkodes, an inhibitor CCA used in our model, bleach more, photosynthesize less, and even dissolve when exposed to low carbonate saturation state and high temperatures and are affected to a greater extent than some coral species (Anthony et al., 2008). Thus, there is limited empirical evidence of scenarios in which inhibitor CCA experience patchy or complete mortality and corals do not, because of disparate tolerance limits. 4.7. Effects of dimension and spatial scale Our two-dimensional model cannot account for the range of morphologies of corals, only some of which require continual expansion across the substrate in order to grow. However, even corals that primarily grow upward must survive early stages in which they are small and susceptible to overgrowth. In addition, our model operates on small scales, where disturbance is either entire or extremely limited in scope and settlement fluxes are constant. We initiated simulations in an empty grid, as after complete disturbance, as we found this to be the most interesting case. Initial partial cover of disturbance-resistant inhibitor CCA accelerates coral exclusion and generally limits the entrance of coral into the size refuge. Partial cover of promoter CCA, aside from being less likely, has little effect due to the limited impact of the presence of that species as shown above. We can extrapolate how the dynamics of our model would fit into a larger mosaic of disturbed and undisturbed patches, a common pattern on reefs (Connell et al., 1997). In such cases, the size of the disturbance and the

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composition of neighboring areas will determine whether recolonization will primarily be from the expansion of survivors on the edge of the disturbance or from new recruits. Settlement also varies spatially and temporally for many species (Dunstan and Johnson, 1998; Hughes et al., 2000). If the supply of coral settlers reaching a given location varies over time, settlers may miss brief windows of space availability. Corals that brood larvae and release them more frequently may offset the geographical consolidation of their recruits by spreading their numbers more evenly over time and by releasing larvae that are more competent to settle, thus having higher larval fitness upon metamorphosis. In contrast, corals with annual pulses and wider dispersal may counter increased density and lower survival with the potential to settle areas of larger or more distant disturbance. 5. Conclusions Our results suggest that in a space competition system where survival and growth depends upon size, relative growth rates of competitors are far more important for the outcome of competition than mechanisms that determine the fate of individual settlers. For corals, the influences of larval substrate selection and factors affecting early survival, such as facilitation by CCA, may or may not translate into higher cover of adult coral; in fact, high levels of settlement, survival, or aggregation may reduce long term population persistence. Habitat complexity, combined with mechanisms that limit the ability of dominant CCA to retain space, allows for coexistence of even slow-growing corals with CCA. The logistics of linking these processes through field studies of coral are challenging, but we suggest that the influence of space competition is so strong that it should be included specifically in demographic studies. Understanding the details of competitive interactions with less-studied taxa such as CCA, which interact positive and negatively with corals at various points in coral life history, may help determine the strength of the link between settlement and population recovery and persistence. Acknowledgments We thank Peter Edmunds, Sally Holbrook, and Bruce Kendall for discussions and advice and Zachary Buenau for assistance with code. This is a contribution of the Moorea Coral Reef (MCR) Long Term Ecological Research site, and we thank many members of a MCR working group for comments. The research was supported by grants EF-074521 and DEB-0717259 from the US National Science Foundation to RMN.

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Appendix A. Simulation algorithm

// Initialization Specify all parameter values Initialize arrays to store species cover, temporal results and statistics If (heterogeneous habitat will be used) Initialize landscape array Calculate target number of protected cells or blocksof cells While (number of protected cells/blocks < target) Randomly assign cell or blocks to protected status End End // Run simulations For (time = 1 to length of simulation) // Settlement For (number of promoter CCA settlers) Select random cell If cell is empty, becomes occupied by promoter End For (number of inhibitor CCA settlers) Select random cell If cell is not occupied by coral, cell becomes occupied by inhibitor End For (number of coral settlers) Randomly select initial cells While (not on target substrate (promoter/not inhibitor) and steps remain) Randomly select one of eight neighbor cells, without leaving domain End If (on target substrate and site is not occupied by coral or previous settlers this time step) Coral settler occupies cell Else if (steps remain) Select additional neighbors until site not occupied by coral is found, but do not leave target substrate. If appropriate cell is located, coral settler occupies cell End End // Record statistics Calculate and record cover of vulnerable and refuge coral, inhibitor and promoter CCA Calculate number of coral colonies If (time > 3 and the number of cells occupied by coral < number of coral settlers during one time step) Coral is functionally extinct End

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// Growth Generate new randomly ordered list of cells For (each cell in list) If (any of four nearest neighbor cells can be overgrown by dominant occupant of cell) Available neighbor cells become occupied by dominant species in focal cell While (number of growth steps < growth rate for focalspecies) For (all newly occupied cells originating from focal cell) If (any offour nearest neighbor cells can be overgrown) Available cells become occupied by species in focal cell End End //Growth steps are added or removed if the occupant grows onto a //substrate on which it has a different growth rate from that of the focal cell End End End Calculate size of existing coral colonies // Mortality For (every coral colony) Check whether colony is in size refuge Determine fate of colony by vulnerable/ refuge mortality probability If (colony dies) Cells occupied by colony become empty End End For (every cell occupied by inhibitor CCA) If (inhibitor mortality is by patches of cells) While (number of inhibitor cells this time step that have become empty < probability of inhibitor mortality*inhibitor cover) Randomly select cell occupied by inhibitor CCA to be upper left or lower right corner of grazed square All sites occupied by inhibitor in squarebecome empty End Else //mortality is by individual cells Determine fate of cell by mortality probability If (inhibitor on cell dies) Cell becomes empty End End End For (every cell occupied by promoter CCA but not coral or inhibitor CCA) Determine fate of cell by mortality probability If (promoter on cell dies) Cell becomes empty End End End

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