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Object-oriented simulation of coral competition in a coral reef community
Ecological Modelling 245 (2012) 111–120
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Object-oriented simulation of coral competition in a coral reef community Tze-wai Tam, Put O. Ang ∗,1 Biology Programme, School of Life Sciences, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong Special Administrative Region, China
a r t i c l e
i n f o
Article history: Available online 21 April 2012 Keywords: Coral reef model Object-oriented simulation Alternative stable states Coral competition 3-Dimensional individual-based model
a b s t r a c t A 3-dimensional individual-based model, the ReefModel, was developed to simulate the dynamical structure of coral reef community using object-oriented techniques and Smalltalk/V language. Interactions among six functional groups of reef organisms: tabular coral, foliaceous coral, massive coral, macroalga, corallivorous gastropod and herbivorous fish were examined. Results from the simulation of interaction among the three coral groups are presented here. The behaviours of the coral groups were described with simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms) observed in natural coral reef communities. All corals were allowed to grow in a 3-dimensional spatial environment. The model was implemented to explore the competitive mechanisms governing coral community structure. Simulation results suggest that a fast-growing habit with overtopping competitive mechanism is probably the most effective strategy for corals to gain spatial dominance in a coral community under stable environmental conditions. In addition, multimodality exists in the final states of individual coral group as a result of small random spatial events that occurred during the early stages of interactions among the corals in the community. This suggests that alternative stable states may exist in a coral community as a result of inter-specific coral competition. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Simulation models are powerful tools to study the dynamics of coral population and communities. They have been applied in the scientific study of coral reef ecosystem and the development of strategies to manage it (Andres and Rodenhouse, 1993; Fong and Glynn, 1998; Lirman, 2003). Various models have since been developed in the past 20 years to investigate reef dynamics (Tam and Ang, 2009). These have provided insights on the possible effects of biological and physical disturbances on reef ecosystem (Andres and Rodenhouse, 1993; McClanahan, 1995; Stone, 1995; Stone et al., 1996; Tanner et al., 1996; Fong and Glynn, 1998; Hughes and Tanner, 2000; Lirman, 2003; Langmead and Sheppard, 2004). However, most of the coral models developed so far are based on the assumptions that all individuals are identical and behave similarly, and that there is no spatial interaction among individuals simulated within the model. Such assumptions violate two basic tenets in biology–individual variation and local interaction (Huston et al., 1988) and may limit the applicability of the models to effectively simulate the dynamical structure of coral reef communities. Such structure has arisen from diverse
∗ Corresponding author. E-mail addresses: [email protected] (T.-w. Tam), [email protected] (P.O. Ang). 1 Tel.: +852 3943 6133; fax: +852 2603 5391. 0304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2012.03.023
and complicated spatial interactions identified among many reef organisms (Stimson, 1985; Lang and Chornesky, 1990; Sorokin, 1993; Tanner, 1995; Adjeroud, 1997; River and Edmunds, 2001). In addition, only a few models extend their focus from the dynamical behaviour of the coral assemblage to that of a more complicated coral reef community (e.g. McClanahan, 1995; Tanner et al., 1996). Understanding how ecological pattern of reef ecosystems can arise from complex interactions among organisms is still limited (Pastorok and Bilyard, 1985; Done, 1992; Sorokin, 1993; Tanner, 1995; Knowlton, 2001; Lesser, 2004) and awaits exploration by using holistic ecological modelling approach (Hatcher, 1997). In order to address the issues raised above, object-oriented programming (OOP) can be one of the effective approaches to develop a more realistic coral reef model. OOP is based on the idea that programs should represent the interaction between abstract representations of real objects. According to this approach, each object can be modelled as an independent computer programme. The behaviour of each object, including its interaction with other objects and its environment, can be specified within the entity itself. There is no overall controlling programme or agent in the model, other than an action scheduler and defined virtual space within which the agents interact. The overall behaviour of the system emerges from local interactions among the objects simulated. OOP has been demonstrated as a useful modelling technique to address the concern about realistic representation of an ecosystem in terms of spatial interaction and individual variability (Sekine
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et al., 1991; Sequeira et al., 1991; Silvert, 1993; Ferreira, 1995; Olson and Sequeira, 1995; Baskent et al., 2001; Bian, 2003; Tam and Ang, 2009). More detailed descriptions of OOP and its use in ecological modelling are provided by Sequeira et al. (1991), Silvert (1993), Ferreira (1995), Bian (2003) and (Tam and Ang, 2009). In this paper, we present a 3-dimensional individual-based model, ReefModel, that we developed using object-oriented technique to simulate the dynamical structure of a coral reef community (Tam and Ang, 2009). Interactions among six functional groups of reef organisms: tabular coral, foliaceous coral, massive coral, macroalga, corallivorous gastropod and herbivorous fish, have been developed in the model and interaction among the three coral groups were simulated in the present study. The coral groups simulated were allowed to grow in a 3-dimensional spatial environment. The behaviours of the coral groups were described with simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms, response to physical disturbance) observed in natural coral reef communities and were based on data obtained from a detailed monitoring study of two coral communities located in A Ma Wan and A Ye Wan, in Tung Ping Chau Marine Park, Hong Kong (Tam, 2006; Tam and Ang, 2008). Furthermore, we have searched extensively through the relevant coral reef literature to ensure that all the interaction terms and functions we used are within the recorded norms, and hence are as close as possible to what could be happening in reality in the coral reef system. Functional groups (i.e. meta-species), instead of individual species, were modelled in ReefModel as the interactions among numerous individual species in a coral reef community are very sophisticated and therefore, are not yet fully understood. This makes it impossible or unrealistic to model individual species. Besides, the coral groups simulated are all known to have their own distinct biological characteristics (Sorokin, 1993), competitive mechanisms (Hughes and Jackson, 1985; Lang and Chornesky, 1990) and response to physical disturbance (Woodley et al., 1981). Their interactions with other functional groups are also considered as one of the important controlling factors of reef community structure (Hughes et al., 1987; Done, 1992; Coyer et al., 1993; Tanner, 1995; Miller, 1998; McCook, 1999; Ostrander et al., 2000). The model was used to simulate the effects of physical disturbances on the dynamical structure of the communities and the results suggested that alternative stable states and catastrophic regime shifts may exist in a coral community under unstable physical environment (Tam and Ang, 2009). Based on the model constructed, we have further investigated the effects of various types of interspecific coral competition on the dynamical structure of coral communities. We have identified the existence of alternative stable states in the communities and provided some suggestions on its cause.
2. The model The model was developed using the Smalltalk/V language (ParcPlace Systems, Inc., U.S.A.), which is one of the representative OOP languages in the Personal Computer (PC). The software used for the model is Visual Smalltalk Enterprise 3.11 (ParcPlace-Digitalk, Inc., U.S.A.), which has a programming environment for describing objects and the interactions among them. We followed the standard protocol proposed by Grimm et al. (2006) to describe the model in this paper. However, as only part of the model was used to simulate the dynamical structure of a 3-coral community in the present study, only description of the basic system unit, simulating environment and the relevant behaviour of the organism (coral) groups of the model used for the simulation is given here. More detailed description of the complete model can be found in Tam (2006) and Tam and Ang (2009).
2.1. Purpose The purpose of the model is to simulate the population dynamics of and spatial interactions among tabular, foliaceous and massive corals in order to investigate the effects of various types of inter-specific coral competition on the dynamical structure of coral communities.
2.2. State variables and scales The model is consisted of three hierarchical levels: individual, system sub-unit and environment. Individuals (class Organism) are characterized by state variables such as developmental stage, moving speed, position, various kinds of tolerance level, and various ranges of active temperature for food searching. More detailed descriptions of these variables are given in Appendix A. System sub-unit (class EcoUnit) is a cubic grid cell and represents a 3-dimensional micro-environment inside the simulated environment for the organisms to interact with. System sub-unit is characterized by state variables such as position, size, available space for organisms to inhabit, and the environmental conditions (Appendix A). The highest hierarchical level in ReefModel is the abiotic environment (class ReefSystem). It is a spatially explicit environment and a collection of system sub-units arranged in 3-D lattice. The environment has variables to store the list of system subunits and the rate of transmission of various physical factors (e.g. sediment, oxygen, etc.) inside the simulated environment (Appendix A). The environment in the present study was set to have 37 system subunits at both of its width and length, and 10 system subunits at its height. Length of each subunit is equal to one arbitrary unit and each subunit was set to allow one individual to grow into. The maximum resulting space that the corals could grow in the simulated environment is 13,690 arbitrary units.
2.3. Process overview and scheduling The model was set to proceed in monthly time steps. This time scale was based on the general growing and competitive behaviors of corals observed in the field (Connell, 1973; Lang and Chornesky, 1990). In brief, corals initially occupy space by the settlement of larvae or by the attachment of fragments or “buds”. They then grow two-dimensionally across the substratum by differentially oriented growth, or in three-dimensions into the overlying water column. When corals get close together they may affect one another directly or indirectly in competing for space. During direct competition, the adjacent corals come into physical contact with one another and utilize one or more competitive strategies to injure each other. In indirect competition, coral with an overtopping morphology expands above an underlying coral without touching it. As corals are generally slow-growing (e.g. <5 mm per year for foliaceous corals, Hughes and Jackson, 1985) and their larval recruitment occurs only once per year, the time step set in other modelling studies (e.g. Lirman, 2003) is one year. However, as the temporal scale of response in coral competition is generally shorter, i.e. from weeks to months (Lang and Chornesky, 1990), the time step in the present study was set at one month to reflect the general situation of coral competition observed in the field. Each individual (coral polyp) is triggered to act randomly during each time step. When initiated, each individual will carry out an “act”. The “act” method is specific for each particular coral group and allows a fair degree of variability in the behaviour of each individual. The execution of many functions is conditional upon the individual’s current state. The coral polyps were set to perform only
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some particular actions in the present study: they would only grow and then attack other coral polyps or die. 2.4. Design concepts This model was run with the following design concepts: Emergence: Population dynamics emerge from the behaviour of and the interaction among individuals. But the individual’s life cycle and behaviour are entirely determined by the initial inputs and empirical rules, e.g. the growth of individuals (coral polyps) will be in up to 10 directions only (i.e. eight horizontal directions, plus upward and downward directions). Adaptation and fitnessseeking are not modelled. Sensing: Individuals are assumed to know all of their own state variables, their position inside the simulated environment, and the environmental conditions (temperature, nutrient level, disturbance level, etc.) of the subunit that they inhabit. Interaction: Six types of interaction were originally developed for coral polyps: (i) competition for space among sessile organisms, (ii) attack between coral polyps, (iii) predation/feeding, (iv) avoidance of predators, (v) response to temperature changes and (vi) physical disturbance, but only interaction types (i) and (ii) were simulated in the present study. The behaviours of coral groups were determined by simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms) observed in a monitoring study on local coral communities in Hong Kong (Tam and Ang, 2008). Each coral polyp was set to grow radially (budding) and vertically to represent the natural growth pattern of corals. The former results in coral expanding two-dimensionally across the substratum; and the latter, in three dimensions into the overlying water column. Coral polyps perform these two growing behaviours at regular interval (i.e. with a specific growth rate) assigned for each functional coral group under suitable temperature. During vertical growth, each coral polyp detects whether there is any other sessile organism (i.e. polyps of other coral groups) just one unit space above itself. If there is, then the coral polyp will not reproduce. However, if there is none, the coral polyp will reproduce a new polyp of one unit height on top of itself. The coral polyp will also stop its vertical growth when it reaches the water surface of the reef environment. In general, only those coral polyps (budding polyps) along the margin of a coral colony will reproduce asexually by binary fission (budding). Each “budding polyp” first looks for a suitable free space around itself at one unit space distance in all eight directions – N, NE, E, SE, S, SW, W and NW. If there is/are suitable free spaces, then the polyp will randomly choose a suitable unit space in any direction and bud a new polyp into it. If no space is available, no polyp will be produced. More specific growth patterns are set for the coral polyps of different coral functional groups. The coral polyps of massive coral grow in such a way that all the newly formed polyps bud first. Only when there is no suitable free space around the polyps they would then start to grow vertically. In addition, the polyps of massive coral will bud a new polyp into a free space only when the space is at the bottom of the reef environment or when the space has other coral polyp just beneath it during budding. The new polyp exhibits an aggressive behaviour and will kill those polyps of other coral groups under it. By having such growing behaviour, the coral colony can normally attain a shape that is vertically high in the middle and low at the periphery. This is the common growth form of a massive coral observed in nature and resembles the overgrowing behaviour of massive corals occurring naturally in coral community (Lang and Chornesky, 1990) (Fig. 1a).
Fig. 1. (a) Massive coral (20-month old), (b) tabular coral (3-month old) and (c) foliaceous coral (6-month old) simulated in the ReefModel. Each coral polyp of the coral groups was set to perform radial and linear growth one time per month and to increase one unit space at each growing time if space is available (from Tam and Ang, 2009).
In comparison, coral polyps of tabular coral start to grow vertically once they are created. They do not require a free space to be present at the bottom of the reef environment nor to have other coral polyps just beneath the space to initiate budding. Therefore, this coral group can usually attain an “overtopping” growth form in the simulation, which resembles its naturally occurring form in a coral community (Lang and Chornesky, 1990). In addition, if the coral polyps die, they remain as dead polyps with skeleton that serve as the base for other newly reproduced polyps to grow vertically on top of them. This growth behaviour is usually observed in nature among tabular corals, with living tissue found mainly on the top part of the coral colony over dead skeleton underneath (Fig. 1b). Similarly, the coral polyps of foliaceous coral start to grow vertically once they are created. They do not require a free space to be present at the bottom of the reef environment, nor do they need to have other coral polyps beneath the space to initiate budding. However, these coral polyps do not die after their vertical growth. Furthermore, they bud new polyps in four directions only – N, E, S and W. In this regard, other than an “overtopping” growth form, this
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coral group can also attain the generally decussate growing pattern typical of many foliaceous corals observed in nature (Fig. 1c). Competition among coral colonies was simulated by allowing coral polyps to attack (kill) neighbouring coral polyps of other coral groups. This mimics the observed competitive mechanism exhibited by many corals (Lang and Chornesky, 1990). The maximum distance at which a coral polyp can reach to attack other coral polyps is defined by its coral group. For tabular and foliaceous corals, only their marginal polyps will attack other coral polyps. However, for massive coral, all its polyps will carry out attacking action. Overtopping is a competitive strategy available to tabular and foliaceous corals such that their polyps will not be attacked by other polyps that are directly in the space under them.
Table 1 Various combinations of coral groups in each simulation type and variation of the strength of their two major characteristics (growth rate and attacking distance) used in investigating the competitive mechanism governing their coral community structure. Shade tolerance level (month) for each coral group: tabular coral = 1, foliaceous coral = 2, massive coral = 3. Initial number of each coral group = 20. Simulation type
Coral group
Linear and radial growth ratesa (times/year)
Attacking distance (unit spaces)
TF 1
Tabular coral Foliaceous coral
12 12
1 1
TM 1
Tabular coral Massive coral
12 12
1 1
TM 2
Tabular coral Massive coral
12 12
1 2
TM 3
Tabular coral Massive coral
12 12
1 3
TM 4
Tabular coral Massive coral
12 10
1 3
TM 5
Tabular coral Massive coral
12 9
1 3
2.5. Initialization
TM 6
Tabular coral Massive coral
12 8
1 3
Each simulation began with 20 individuals of each coral group (Table 1). At the beginning of simulation, each individual was randomly distributed on the bottom of the simulated environment. The simulation was run for a period of 10 simulated years or was ended when the surface area of each coral group had leveled off or had fluctuated at a reasonable equilibrium level. Iteration period in the simulation equalled to one month time. Fifty simulations were run for each type of combination. However, those simulations that had any one coral group dying immediately after the simulation started were not further considered.
TM 7
Tabular coral Massive coral
12 6
1 3
FM 1
Foliaceous coral Massive coral
12 12
1 1
FM 2
Foliaceous coral Massive coral
12 12
1 2
FM 3
Foliaceous coral Massive coral
12 12
1 3
FM 4
Foliaceous coral Massive coral
12 10
1 3
FM 5
Foliaceous coral Massive coral
12 9
1 3
FM 6
Foliaceous coral Massive coral
12 8
1 3
FM 7
Foliaceous coral Massive coral
12 6
1 3
3Coral 1
Tabular coral Foliaceous coral Massive coral
12 12 12
1 1 3
3Coral 2
Tabular coral Foliaceous coral Massive coral
12 12 9
1 1 3
3Coral 3
Tabular coral Foliaceous coral Massive coral
12 12 8
1 1 3
3Coral 4
Tabular coral Foliaceous coral Massive coral
12 12 6
1 1 3
Stochasticity: Direction of growth to any available suitable space during the radial growth of any coral group in each time step is random. Observation: For model testing, spatial distribution of the individuals was observed process by process. For model analysis, only the coral cover of each coral group over time was recorded.
2.6. Input Only two major characteristics (growth rate and attacking distance) of the corals were investigated in this study as Lang and Chornesky (1990) concluded that relative growth rate may have a profound effect on the resolution of some competitive interactions among corals. In addition, it is reasonable to expect that the ability of a coral polyp to inflict injuries on other coral polyps over a greater distance could influence its competitive dominance. Table 1 summarizes the various combinations of coral groups and variation in the growth rate and attacking distance of each coral group used in the simulation investigating the competitive mechanism governing the coral community structure. The relative growth rate of each coral group was set based on the generalization of the results found by Barnes (1973), Buddemeier and Maragos (1974), Baker and Weber (1975), Gladfelter et al. (1978), Hubbard and Scaturo (1985), Hughes and Jackson (1985), Guzmàn and Cortés (1989) and Sorokin (1993). In general, the growth rate of tabular corals (e.g. many coral species of Family Acroporidae) and foliaceous corals (e.g. Pavona decussata) was much faster than that of massive corals (e.g. most coral species of Family Faviidae). In addition, the relative attacking distance assigned for each coral group in the present study represents the general spatial characteristics of direct killing behaviour of each coral group reviewed by Lang and Chornesky (1990). Tabular corals have been observed to utilize histoincompatibility to injure the soft tissues of other corals that they come into contact with. Histoincompatibility is also known to be used by foliaceous corals (e.g. Pavona sp.) for competition. However, histoincompatibility was observed to occur only when the attacking coral is touching other corals (<5 mm separation). Therefore, these two coral groups were set in the
a For each growing coral polyp, the unit is referred to as the number of times the polyp will carry out growing behaviour per year. The polyp will increase 1 unit space at each time of growing if space is available.
simulating environment to have very short effective ranges of attack. In contrast, massive corals usually have aggressive killing activities brought about by their sweeper tentacles or mesenterial filaments, which can be deployed over a range of 10 cm or more. This coral group was thus set to have a relatively long attacking distance in the simulation. The relative shade-tolerance level of each coral group was based on the findings of Stimson (1985) and our own observation in the field (data not shown). In general, massive corals were found to
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Table 2 Final area cover and number of times for being dominant in each coral group at the end of each type of simulation under various combinations of coral groups and variation of the strength of their growth rate and attacking distance. Refer to Table 1 for more detailed characteristics of the coral groups used in the simulations. n = 50. Coral group
No. of times for being dominant (out of 50)
Final area cover (arbitrary units)
Range
Mean ± 1 SEM
TF 1
Tabular coral Foliaceous coral
34 16
201–468 199–393
339.8 ± 9.4* 295.4 ± 6.3
TM 1
Tabular coral Massive coral
50 0
494–785 19–247
672.9 ± 9.0* 72.6 ± 6.5
TM 2
Tabular coral Massive coral
34 16
175–461 127–543
343.2 ± 9.4* 294.7 ± 11.7
TM 3
Tabular coral Massive coral
0 50
20–206 437–775
112.7 ± 6.6* 589.5 ± 10.6
TM 4
Tabular coral Massive coral
1 49
26–339 304–739
165.0 ± 9.6* 508.1 ± 12.7
TM 5
Tabular coral Massive coral
16 34
129–460 103–636
266.8 ± 11.2* 348.7 ± 17.0
TM 6
Tabular coral Massive coral
37 13
132–559 87–608
366.7 ± 12.1* 259.3 ± 16.4
TM 7
Tabular coral Massive coral
50 0
643–900 0–28
886.0 ± 6.1* 1.3 ± 0.8
FM 1
Foliaceous coral Massive coral
50 0
354–542 198–357
440.7 ± 6.0* 280.6 ± 5.6
FM 2
Foliaceous coral Massive coral
0 50
65–307 395–695
160.5 ± 7.4* 561.6 ± 9.0
FM 3
Foliaceous coral Massive coral
0 50
3–150 605–846
60.8 ± 4.9* 717.0 ± 8.3
FM 4
Foliaceous coral Massive coral
0 50
15–241 463–830
108.7 ± 7.8* 641.3 ± 11.2
FM 5
Foliaceous coral Massive coral
0 50
56–312 344–696
181.0 ± 8.9* 533.9 ± 13.1
FM 6
Foliaceous coral Massive coral
4 46
87–372 288–687
236.2 ± 10.7* 464.4 ± 13.8
FM 7
Foliaceous coral Massive coral
50 0
724–900 0–109
875.2 ± 6.6* 7.6 ± 3.2
3Coral 1
Tabular coral Foliaceous coral Massive coral
0 0 50
39–284 11–204 429–939
161.6 ± 8.6† 94.1 ± 6.4† 700.0 ± 14.5
3Coral 2
Tabular coral Foliaceous coral Massive coral
15 4 31
145–598 103–355 188–711
279.0 ± 11.5† 214.0 ± 8.7† 366.6 ± 16.1
3Coral 3
Tabular coral Foliaceous coral Massive coral
36 10 4
208–673 129–486 44–484
408 ± 15† 269 ± 12† 199 ± 14
3Coral 4
Tabular coral Foliaceous coral Massive coral
26 24 0
222–797 259–872 0–24
545.4 ± 20.6N 507.4 ± 19.6N 0.5 ± 0.5 †
* † N
Significantly different from the other coral group (p ≤ 0.0083). Significantly different from the other two coral groups (p ≤ 0.004). Not significantly different from each other (p = 0.3131).
be more shade-tolerant than foliaceous corals, which in turn were more tolerant than tabular corals. All the other factors (e.g. food requirements, heat tolerance, etc.), which are incorporated in ReefModel, were set at an extreme value in the present study such that these factors would not affect the survivorship nor the competitive mechanism of the corals during simulations. For instance, the life span of each coral group was set as 100 years; no food was required for each coral polyp and that the coral did not spawn during the period of simulation.
2.7. Data analysis The coral community structures resulted from the simulations were analysed by calculating the area cover (in arbitrary units) of each coral group. This refers to the area of their canopy layers in the simulated environment. Statistical analyses using the Wilcoxon Signed Rank test were carried out to compare the mean area covers among the coral groups under the same type of simulations (Townsend, 2002). Shapiro–Wilk test was carried out to check for multimodality, a hint on catastrophic regime shift (Scheffer and
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Fig. 2. Changes in the mean area cover of each coral group in the simulations of 3-coral interaction with massive coral having attacking distance 3 times longer than that of the other two coral groups and (a) with growth rate being the same for all three coral groups; or with tabular and foliaceous corals growing (b) 1.33 times, (c) 1.5 times and. (d) 2 times faster than the massive coral. Note different scales of Y-axis in different plots. n = 50 for each simulation.
Carpenter, 2003), in the frequency distribution of the area cover of each coral group. Multidimensional scaling (MDS) analysis, based on Bray–Curtis similarity measures using double square-root transformations of the area cover of each coral group, was also carried out to determine if there was any outlier or distinct grouping in the coral community structure under the same type of simulations. 3. Results A distinct dominance effect brought about by different competitive mechanisms and degrees of competitive strength of the coral groups was observed in the simulations (Table 2). Firstly, it was found that the mean final abundance of tabular coral was significantly higher than that of foliaceous coral (Wilcoxon Signed Rank test, p = 0.0013) and the number of times it was dominant was much greater than that of foliaceous coral in the simulation when these two corals had the same growth rates and attacking distances (TF 1). Such results indicate that the radial growing pattern of tabular coral dominated over the decussating growing pattern of foliaceous coral.
Secondly, direct killing of nearby coral polyps over long distances was also observed as an effective mechanism for a coral to gain dominance in interspecific competition. Massive coral lost out completely to both tabular and foliaceous corals when its growth rate and attacking distance were the same as those of these two corals (TM 1 and FM 1; Wilcoxon Signed Rank test, both p < 0.0001). However, when its attacking distance increased to three times greater than that of tabular and foliaceous corals, massive corals were found to completely dominate over the other two coral groups in either one-to-one interaction (TM 3 and FM 3) or one-to-two interaction (3Coral 1) (Wilcoxon Signed Rank test, all p < 0.0001). Nevertheless, it was demonstrated that fast-growing habit is also an effective mechanism for a coral group to compete for space. Tabular coral was found to dominate over massive coral when its growth rate was set at 1.5 times higher than that of massive coral in TM 6 (Wilcoxon Signed Rank test, p = 0.0003) even if the attacking distance of massive coral was three times greater than that of tabular coral in the simulation. Similarly, foliaceous coral was also found dominating over massive coral when it was set to grow two
Table 3 Results of the Shapiro–Wilk test for normality in the frequency distribution of the final area cover of each coral group in each type of simulation under various combinations of coral groups and variation of the strength of their growth rate and attacking distance. Only those with significant level less than 0.05 are shown. Refer to Table 1 for more detailed characteristics of the coral groups used in the simulations. n = 50. Simulation type
Tabular coral Statistic value (W)
TM TM TM TM FM FM FM
1 2 6 7 3 4 7
– – – 0.38 – – –
Foliaceous coral Sig. level – – – <0.0001 – – –
Massive coral
Statistic value (W)
Sig. level
Statistic value (W)
Sig. level
– – – – 0.94 0.95 0.60
– – – – 0.018 0.030 <0.0001
0.85 0.93 0.94 0.25 – – 0.39
<0.0001 0.006 0.021 <0.0001 – – <0.0001
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Fig. 3. Some examples showing clear multimodal distribution of the final area cover of coral group under different combinations of coral groups and variation of the strength of their two major charateristics (growth rate and attacking distance). Refer to Table 1 for detailed characteristics of the coral groups used in the simulations. Note different X- and Y-axis scales among plots. n = 50 for each simulation.
times faster than massive coral in FM 7 (Wilcoxon Signed Rank test, p < 0.0001). Similar results were also observed during the threecoral-group interaction when the growth rate of both tabular and foliaceous corals was 1.5 times or more than that of massive coral (Fig. 2 and Table 2). In these simulations, tabular and foliaceous corals dominated over massive coral in the three-coral community simulated even if the attacking distance of massive coral was three times greater than that of these two coral groups (Wilcoxon Signed Rank test, all p ≤ 0.004). Shift in dynamic regime was found occasionally in the dynamics of individual coral group and the coral community structure during both two-coral-group and three-coral-group interactions. Shapiro–Wilk test for normality showed that the frequency distribution of the final area cover of massive coral was clearly multimodal in some of its one-to-one interaction with the other coral groups (TM 1–2, TM 6–7 and FM 7) (Fig. 3 and Table 3; all W ranged between 0.25 and 0.94 and all p ≤ 0.021). It can be noted that in these five types of simulations, massive coral generally
lost out to the corals it interacted with, but could occasionally out-compete these corals in some simulation runs in TM 2 and TM 6 (Table 2). Significant multimodal frequency distribution of the final area cover of foliaceous coral was also found in some of its interaction with massive coral (FM 3–4 and FM 7, all W ranged between 0.60–0.95 and all p ≤ 0.030). In addition, MDS ordination plots based on Bray–Curtis similarity measures of the final area cover of the coral groups showed that there was distinct outlier in the three-coral community structure when growth rate of both tabular and foliaceous corals was 1.33 or two times more than that of massive coral (Fig. 4). 4. Discussion The 3-dimensional individual-based model (ReefModel) developed in this study provides important insights into the mechanisms governing coral community structure. Although only 50 simulation runs were carried out in each simulation, in a broad sense, several
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Fig. 4. MDS ordination plots based on Bray–Curtis similarity measures of area cover of the coral groups in the simulations of 3-coral interaction with massive coral having attacking distance 3 times longer than that of the other two coral groups and with tabular and foliaceous corals growing (a) 1.33 times and (b) 2 times faster than the massive coral. Distinct outlier is circled in the plots. Each symbol represents the coral community composition at the end of each simulation run. Refer to Table 1 for detailed characteristics of the coral groups used in the simulations. n = 50 for each simulation.
aspects of the effects of competitive mechanisms on coral community structure and the potential presence of alternative stable states could already be identified. The results from the simulations of interspecific coral competition suggest that a fast-growing habit with overtopping competitive mechanism is probably one of the most effective strategies for corals to gain spatial dominance in a coral community under stable environmental conditions. A fastgrowing habit with overtopping characteristics has the advantages of allowing the coral to colonize space faster, not to be limited by “available hard substratum” in radial growth and to allow overtopping to kill other sessile organisms (corals) indirectly. Indeed, in nature, coral species with such biological characteristics are usually found dominating in shallow water coral communities (Sorokin, 1993). Besides unravelling some mechanisms in structuring coral community, the present modelling study reveals that alternative stable states can exist in a coral community under the same environmental regime. Multimodal distribution was observed occasionally in the frequency distribution of the final area cover of the coral groups in some of the simulations of two-coral interaction. This reflects the potential existence of alternative stable states of the coral groups under such interaction (Scheffer and Carpenter, 2003). The survivorship of the coral group was set to be unaffected by environmental changes in the simulating environment and no temporal changes (e.g. spawning and recruitment of larvae, natural mortality due to aging) were also set to affect the dynamics of the coral group. Therefore, the alternative states of the coral groups observed in the simulations should have resulted mainly from the influence of small random spatial events that occurred during the early interaction among coral groups. These events included initial distances between colonies of the different coral groups at the beginning of the simulation. Massive coral may be used as an example to clarify this point. Massive coral was a relatively slowgrowing coral group with no overtopping competitive mechanism. This coral group relied on its more aggressive behaviour (relative long attacking distance) to compete for space with the other two fast-growing coral groups, tabular and foliaceous corals. However, this competitive strategy would no longer be effective once the massive coral colony was overtopped by the colonies of tabular and foliaceous corals as the overtopped massive coral polyps were not set in the simulation to be able to attack from underneath any other polyps that directly overtopped them. As a result, the only opportunity for massive coral to win over tabular and foliaceous corals in the simulation was to cause mortality of the whole colonies of the other two coral groups as much as possible when the colonies were still within its effective range of attack at the beginning of
the simulation. Missing this opportunity, the massive coral colony would not be able to induce mortality on the colonies of the other two coral groups again and would subsequently be overtopped by them. The polyps of the slow-growing massive coral would not be able to catch up with the other fast-growing colonies and would be unable to reach and inflict damage on them. Such possible all-ornone scenario for a massive coral colony to out-compete the coral colonies of the other coral groups indicated that a little difference in the initial number of the other coral colonies that was within its effective range of attack, hence the initial distance among them, would lead to diverse outcomes on the final states of the massive coral during its interaction with other coral groups. The ReefModel developed here represents a more realistic model to simulate the population dynamics and spatial interactions in a coral community. The competitive mechanisms identified may be used to explain observable variations in existing coral community structures. Some coral communities, like those found in northeastern Hong Kong, are dominated by massive corals (mainly faviids) (Tam and Ang, 2008). Yet other communities nearby in eastern Hong Kong are dominated by tabular (mainly Acropora spp.) or foliaceous (Montipora spp.) corals (Ang et al., 2006). While historical developments of these coral communities were not closely followed and well documented, they nevertheless reflect different potential stable states. The mechanisms leading to these potential stable states could thus be deduced from those simulated in the present study. The model was also able to provide important insights in understanding the cause of alternative stable states in coral community during interspecific competition. Although direct results from field observations and experiments are not available in coral reef studies carried out so far to support this phenomenon, evidences from the field study of other sessile biological community are nonetheless available. Petraitis et al. (2009) showed that mussel bed (Mytilus edulis) and rockweed stands (Ascophyllum nodosum and Fucus vesiculosus) are multiple stable states on intertidal shores in the Gulf of Maine, USA and suggests that the development of either community depends on which species becomes established first. The present results obtained from ReefModel described here show the potential utilities of this model. Further refinements could certainly be done to provide deeper insights and understanding into other critical mechanisms that contribute to the structuring of coral as well as other benthic communities. Acknowledgements This study was partly funded by NSFC/RGC Joint Research Scheme Project no. N CUHK457/09 and Research Committee of
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CUHK Group Research Scheme Project no. C001-3110042. We ˜ for their thank K.H. Chu, N.Y.S. Woo, J.W. McManus and P.M. Alino critical comments and advice. We would also like to thank J.H.M. Lee (Department of Computer Engineering, The Chinese University of Hong Kong) for his help with the use of programming techniques in Smalltalk V for the development of the Reef Model. Critical comments from the reviewers and editor are also most helpful.
Class
Instance variable
Description
activeTempAdult
Stores the range of temperature that an adult organism will search for food Stores the number of simulation days that a larva or a spore will change to adult organism Stores the number of simulation days that an adult organism can tolerate for feeling cold Stores the disturbance level that an adult organism can tolerate
changeAdultTime
coldToleranceAdult
Appendix A. disturbTolerance Adult
Description of some basic instance variables of the three major classes developed in the ReefModel for storing the states of the objects created during the simulation (from Tam and Ang, 2009). Class
Instance variable
Description
ReefSystem
tickCount
Stores no. of tick received from the timer of the simulation system so as to keep track of system time Stores the width of the ecosystem Stores the length of the ecosystem Stores the height of the ecosystem Stores a list of sub-units (instances of class EcoUnit) created inside the ecosystem Stores the month that the simulation system encounters Stores the time interval for retrieval of data during the simulation
systemWidth systemLength systemHeight ecoUnitList
monthCount dataInterval
EcoUnit
Length
Ecosystem Position Various physical factor names or abbreviations (e.g. temp, nutrient) exposedAdult
hiddenAdult
Organism
tickCount
ecoUnit Ecosystem Stage Position maxSpeed lifeSpanAdult foodReqAdult delayFeedingTimeAdult
hungryCount
hungry Tolerance Adult
Stores the length of a sub-unit (instance of Class EcoUnit) inside the ecosystem Stores the kind of ecosystem that the sub-unit belongs to Stores its 3-dimensional position inside the ecosystem Stores the physical factors (e.g. temperature, nutrient) of a sub-unit of the ecosystem
Stores a list of adult organisms that are exposed inside a sub-unit of the ecosystem Stores a list of adult organisms that are hidden inside a sub-unit of the ecosystem Stores no. of tick received from the timer of the simulation system so as to keep track of the life time (i.e. age) of an organism in the system Stores the sub-unit that an organism inhabits Stores the kind of ecosystem that an organism inhabits Stores the developmental stage (adult, larva or spore) of an organism Stores the 3-dimensional position of an organism inside the ecosystem Stores the maximum moving speed of an adult organism Stores the maximum life span of an adult organism Stores the amount of food required for an adult organism Stores the number of simulation days that the adult organism will search food once Stores the no. of tick that an organism receives from the timer of the simulation system when the organism is being hungry (not able to obtain the amount of food that meets its required level) continuously Stores the number of simulation days that an adult organism can tolerate for being hungry
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Object-oriented simulation of coral competition in a coral reef community Tze-wai Tam, Put O. Ang ∗,1 Biology Programme, School of Life Sciences, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong Special Administrative Region, China
a r t i c l e
i n f o
Article history: Available online 21 April 2012 Keywords: Coral reef model Object-oriented simulation Alternative stable states Coral competition 3-Dimensional individual-based model
a b s t r a c t A 3-dimensional individual-based model, the ReefModel, was developed to simulate the dynamical structure of coral reef community using object-oriented techniques and Smalltalk/V language. Interactions among six functional groups of reef organisms: tabular coral, foliaceous coral, massive coral, macroalga, corallivorous gastropod and herbivorous fish were examined. Results from the simulation of interaction among the three coral groups are presented here. The behaviours of the coral groups were described with simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms) observed in natural coral reef communities. All corals were allowed to grow in a 3-dimensional spatial environment. The model was implemented to explore the competitive mechanisms governing coral community structure. Simulation results suggest that a fast-growing habit with overtopping competitive mechanism is probably the most effective strategy for corals to gain spatial dominance in a coral community under stable environmental conditions. In addition, multimodality exists in the final states of individual coral group as a result of small random spatial events that occurred during the early stages of interactions among the corals in the community. This suggests that alternative stable states may exist in a coral community as a result of inter-specific coral competition. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Simulation models are powerful tools to study the dynamics of coral population and communities. They have been applied in the scientific study of coral reef ecosystem and the development of strategies to manage it (Andres and Rodenhouse, 1993; Fong and Glynn, 1998; Lirman, 2003). Various models have since been developed in the past 20 years to investigate reef dynamics (Tam and Ang, 2009). These have provided insights on the possible effects of biological and physical disturbances on reef ecosystem (Andres and Rodenhouse, 1993; McClanahan, 1995; Stone, 1995; Stone et al., 1996; Tanner et al., 1996; Fong and Glynn, 1998; Hughes and Tanner, 2000; Lirman, 2003; Langmead and Sheppard, 2004). However, most of the coral models developed so far are based on the assumptions that all individuals are identical and behave similarly, and that there is no spatial interaction among individuals simulated within the model. Such assumptions violate two basic tenets in biology–individual variation and local interaction (Huston et al., 1988) and may limit the applicability of the models to effectively simulate the dynamical structure of coral reef communities. Such structure has arisen from diverse
∗ Corresponding author. E-mail addresses: [email protected] (T.-w. Tam), [email protected] (P.O. Ang). 1 Tel.: +852 3943 6133; fax: +852 2603 5391. 0304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2012.03.023
and complicated spatial interactions identified among many reef organisms (Stimson, 1985; Lang and Chornesky, 1990; Sorokin, 1993; Tanner, 1995; Adjeroud, 1997; River and Edmunds, 2001). In addition, only a few models extend their focus from the dynamical behaviour of the coral assemblage to that of a more complicated coral reef community (e.g. McClanahan, 1995; Tanner et al., 1996). Understanding how ecological pattern of reef ecosystems can arise from complex interactions among organisms is still limited (Pastorok and Bilyard, 1985; Done, 1992; Sorokin, 1993; Tanner, 1995; Knowlton, 2001; Lesser, 2004) and awaits exploration by using holistic ecological modelling approach (Hatcher, 1997). In order to address the issues raised above, object-oriented programming (OOP) can be one of the effective approaches to develop a more realistic coral reef model. OOP is based on the idea that programs should represent the interaction between abstract representations of real objects. According to this approach, each object can be modelled as an independent computer programme. The behaviour of each object, including its interaction with other objects and its environment, can be specified within the entity itself. There is no overall controlling programme or agent in the model, other than an action scheduler and defined virtual space within which the agents interact. The overall behaviour of the system emerges from local interactions among the objects simulated. OOP has been demonstrated as a useful modelling technique to address the concern about realistic representation of an ecosystem in terms of spatial interaction and individual variability (Sekine
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et al., 1991; Sequeira et al., 1991; Silvert, 1993; Ferreira, 1995; Olson and Sequeira, 1995; Baskent et al., 2001; Bian, 2003; Tam and Ang, 2009). More detailed descriptions of OOP and its use in ecological modelling are provided by Sequeira et al. (1991), Silvert (1993), Ferreira (1995), Bian (2003) and (Tam and Ang, 2009). In this paper, we present a 3-dimensional individual-based model, ReefModel, that we developed using object-oriented technique to simulate the dynamical structure of a coral reef community (Tam and Ang, 2009). Interactions among six functional groups of reef organisms: tabular coral, foliaceous coral, massive coral, macroalga, corallivorous gastropod and herbivorous fish, have been developed in the model and interaction among the three coral groups were simulated in the present study. The coral groups simulated were allowed to grow in a 3-dimensional spatial environment. The behaviours of the coral groups were described with simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms, response to physical disturbance) observed in natural coral reef communities and were based on data obtained from a detailed monitoring study of two coral communities located in A Ma Wan and A Ye Wan, in Tung Ping Chau Marine Park, Hong Kong (Tam, 2006; Tam and Ang, 2008). Furthermore, we have searched extensively through the relevant coral reef literature to ensure that all the interaction terms and functions we used are within the recorded norms, and hence are as close as possible to what could be happening in reality in the coral reef system. Functional groups (i.e. meta-species), instead of individual species, were modelled in ReefModel as the interactions among numerous individual species in a coral reef community are very sophisticated and therefore, are not yet fully understood. This makes it impossible or unrealistic to model individual species. Besides, the coral groups simulated are all known to have their own distinct biological characteristics (Sorokin, 1993), competitive mechanisms (Hughes and Jackson, 1985; Lang and Chornesky, 1990) and response to physical disturbance (Woodley et al., 1981). Their interactions with other functional groups are also considered as one of the important controlling factors of reef community structure (Hughes et al., 1987; Done, 1992; Coyer et al., 1993; Tanner, 1995; Miller, 1998; McCook, 1999; Ostrander et al., 2000). The model was used to simulate the effects of physical disturbances on the dynamical structure of the communities and the results suggested that alternative stable states and catastrophic regime shifts may exist in a coral community under unstable physical environment (Tam and Ang, 2009). Based on the model constructed, we have further investigated the effects of various types of interspecific coral competition on the dynamical structure of coral communities. We have identified the existence of alternative stable states in the communities and provided some suggestions on its cause.
2. The model The model was developed using the Smalltalk/V language (ParcPlace Systems, Inc., U.S.A.), which is one of the representative OOP languages in the Personal Computer (PC). The software used for the model is Visual Smalltalk Enterprise 3.11 (ParcPlace-Digitalk, Inc., U.S.A.), which has a programming environment for describing objects and the interactions among them. We followed the standard protocol proposed by Grimm et al. (2006) to describe the model in this paper. However, as only part of the model was used to simulate the dynamical structure of a 3-coral community in the present study, only description of the basic system unit, simulating environment and the relevant behaviour of the organism (coral) groups of the model used for the simulation is given here. More detailed description of the complete model can be found in Tam (2006) and Tam and Ang (2009).
2.1. Purpose The purpose of the model is to simulate the population dynamics of and spatial interactions among tabular, foliaceous and massive corals in order to investigate the effects of various types of inter-specific coral competition on the dynamical structure of coral communities.
2.2. State variables and scales The model is consisted of three hierarchical levels: individual, system sub-unit and environment. Individuals (class Organism) are characterized by state variables such as developmental stage, moving speed, position, various kinds of tolerance level, and various ranges of active temperature for food searching. More detailed descriptions of these variables are given in Appendix A. System sub-unit (class EcoUnit) is a cubic grid cell and represents a 3-dimensional micro-environment inside the simulated environment for the organisms to interact with. System sub-unit is characterized by state variables such as position, size, available space for organisms to inhabit, and the environmental conditions (Appendix A). The highest hierarchical level in ReefModel is the abiotic environment (class ReefSystem). It is a spatially explicit environment and a collection of system sub-units arranged in 3-D lattice. The environment has variables to store the list of system subunits and the rate of transmission of various physical factors (e.g. sediment, oxygen, etc.) inside the simulated environment (Appendix A). The environment in the present study was set to have 37 system subunits at both of its width and length, and 10 system subunits at its height. Length of each subunit is equal to one arbitrary unit and each subunit was set to allow one individual to grow into. The maximum resulting space that the corals could grow in the simulated environment is 13,690 arbitrary units.
2.3. Process overview and scheduling The model was set to proceed in monthly time steps. This time scale was based on the general growing and competitive behaviors of corals observed in the field (Connell, 1973; Lang and Chornesky, 1990). In brief, corals initially occupy space by the settlement of larvae or by the attachment of fragments or “buds”. They then grow two-dimensionally across the substratum by differentially oriented growth, or in three-dimensions into the overlying water column. When corals get close together they may affect one another directly or indirectly in competing for space. During direct competition, the adjacent corals come into physical contact with one another and utilize one or more competitive strategies to injure each other. In indirect competition, coral with an overtopping morphology expands above an underlying coral without touching it. As corals are generally slow-growing (e.g. <5 mm per year for foliaceous corals, Hughes and Jackson, 1985) and their larval recruitment occurs only once per year, the time step set in other modelling studies (e.g. Lirman, 2003) is one year. However, as the temporal scale of response in coral competition is generally shorter, i.e. from weeks to months (Lang and Chornesky, 1990), the time step in the present study was set at one month to reflect the general situation of coral competition observed in the field. Each individual (coral polyp) is triggered to act randomly during each time step. When initiated, each individual will carry out an “act”. The “act” method is specific for each particular coral group and allows a fair degree of variability in the behaviour of each individual. The execution of many functions is conditional upon the individual’s current state. The coral polyps were set to perform only
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some particular actions in the present study: they would only grow and then attack other coral polyps or die. 2.4. Design concepts This model was run with the following design concepts: Emergence: Population dynamics emerge from the behaviour of and the interaction among individuals. But the individual’s life cycle and behaviour are entirely determined by the initial inputs and empirical rules, e.g. the growth of individuals (coral polyps) will be in up to 10 directions only (i.e. eight horizontal directions, plus upward and downward directions). Adaptation and fitnessseeking are not modelled. Sensing: Individuals are assumed to know all of their own state variables, their position inside the simulated environment, and the environmental conditions (temperature, nutrient level, disturbance level, etc.) of the subunit that they inhabit. Interaction: Six types of interaction were originally developed for coral polyps: (i) competition for space among sessile organisms, (ii) attack between coral polyps, (iii) predation/feeding, (iv) avoidance of predators, (v) response to temperature changes and (vi) physical disturbance, but only interaction types (i) and (ii) were simulated in the present study. The behaviours of coral groups were determined by simple mechanistic rules that were derived from their general behaviours (e.g. growing habits, competitive mechanisms) observed in a monitoring study on local coral communities in Hong Kong (Tam and Ang, 2008). Each coral polyp was set to grow radially (budding) and vertically to represent the natural growth pattern of corals. The former results in coral expanding two-dimensionally across the substratum; and the latter, in three dimensions into the overlying water column. Coral polyps perform these two growing behaviours at regular interval (i.e. with a specific growth rate) assigned for each functional coral group under suitable temperature. During vertical growth, each coral polyp detects whether there is any other sessile organism (i.e. polyps of other coral groups) just one unit space above itself. If there is, then the coral polyp will not reproduce. However, if there is none, the coral polyp will reproduce a new polyp of one unit height on top of itself. The coral polyp will also stop its vertical growth when it reaches the water surface of the reef environment. In general, only those coral polyps (budding polyps) along the margin of a coral colony will reproduce asexually by binary fission (budding). Each “budding polyp” first looks for a suitable free space around itself at one unit space distance in all eight directions – N, NE, E, SE, S, SW, W and NW. If there is/are suitable free spaces, then the polyp will randomly choose a suitable unit space in any direction and bud a new polyp into it. If no space is available, no polyp will be produced. More specific growth patterns are set for the coral polyps of different coral functional groups. The coral polyps of massive coral grow in such a way that all the newly formed polyps bud first. Only when there is no suitable free space around the polyps they would then start to grow vertically. In addition, the polyps of massive coral will bud a new polyp into a free space only when the space is at the bottom of the reef environment or when the space has other coral polyp just beneath it during budding. The new polyp exhibits an aggressive behaviour and will kill those polyps of other coral groups under it. By having such growing behaviour, the coral colony can normally attain a shape that is vertically high in the middle and low at the periphery. This is the common growth form of a massive coral observed in nature and resembles the overgrowing behaviour of massive corals occurring naturally in coral community (Lang and Chornesky, 1990) (Fig. 1a).
Fig. 1. (a) Massive coral (20-month old), (b) tabular coral (3-month old) and (c) foliaceous coral (6-month old) simulated in the ReefModel. Each coral polyp of the coral groups was set to perform radial and linear growth one time per month and to increase one unit space at each growing time if space is available (from Tam and Ang, 2009).
In comparison, coral polyps of tabular coral start to grow vertically once they are created. They do not require a free space to be present at the bottom of the reef environment nor to have other coral polyps just beneath the space to initiate budding. Therefore, this coral group can usually attain an “overtopping” growth form in the simulation, which resembles its naturally occurring form in a coral community (Lang and Chornesky, 1990). In addition, if the coral polyps die, they remain as dead polyps with skeleton that serve as the base for other newly reproduced polyps to grow vertically on top of them. This growth behaviour is usually observed in nature among tabular corals, with living tissue found mainly on the top part of the coral colony over dead skeleton underneath (Fig. 1b). Similarly, the coral polyps of foliaceous coral start to grow vertically once they are created. They do not require a free space to be present at the bottom of the reef environment, nor do they need to have other coral polyps beneath the space to initiate budding. However, these coral polyps do not die after their vertical growth. Furthermore, they bud new polyps in four directions only – N, E, S and W. In this regard, other than an “overtopping” growth form, this
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coral group can also attain the generally decussate growing pattern typical of many foliaceous corals observed in nature (Fig. 1c). Competition among coral colonies was simulated by allowing coral polyps to attack (kill) neighbouring coral polyps of other coral groups. This mimics the observed competitive mechanism exhibited by many corals (Lang and Chornesky, 1990). The maximum distance at which a coral polyp can reach to attack other coral polyps is defined by its coral group. For tabular and foliaceous corals, only their marginal polyps will attack other coral polyps. However, for massive coral, all its polyps will carry out attacking action. Overtopping is a competitive strategy available to tabular and foliaceous corals such that their polyps will not be attacked by other polyps that are directly in the space under them.
Table 1 Various combinations of coral groups in each simulation type and variation of the strength of their two major characteristics (growth rate and attacking distance) used in investigating the competitive mechanism governing their coral community structure. Shade tolerance level (month) for each coral group: tabular coral = 1, foliaceous coral = 2, massive coral = 3. Initial number of each coral group = 20. Simulation type
Coral group
Linear and radial growth ratesa (times/year)
Attacking distance (unit spaces)
TF 1
Tabular coral Foliaceous coral
12 12
1 1
TM 1
Tabular coral Massive coral
12 12
1 1
TM 2
Tabular coral Massive coral
12 12
1 2
TM 3
Tabular coral Massive coral
12 12
1 3
TM 4
Tabular coral Massive coral
12 10
1 3
TM 5
Tabular coral Massive coral
12 9
1 3
2.5. Initialization
TM 6
Tabular coral Massive coral
12 8
1 3
Each simulation began with 20 individuals of each coral group (Table 1). At the beginning of simulation, each individual was randomly distributed on the bottom of the simulated environment. The simulation was run for a period of 10 simulated years or was ended when the surface area of each coral group had leveled off or had fluctuated at a reasonable equilibrium level. Iteration period in the simulation equalled to one month time. Fifty simulations were run for each type of combination. However, those simulations that had any one coral group dying immediately after the simulation started were not further considered.
TM 7
Tabular coral Massive coral
12 6
1 3
FM 1
Foliaceous coral Massive coral
12 12
1 1
FM 2
Foliaceous coral Massive coral
12 12
1 2
FM 3
Foliaceous coral Massive coral
12 12
1 3
FM 4
Foliaceous coral Massive coral
12 10
1 3
FM 5
Foliaceous coral Massive coral
12 9
1 3
FM 6
Foliaceous coral Massive coral
12 8
1 3
FM 7
Foliaceous coral Massive coral
12 6
1 3
3Coral 1
Tabular coral Foliaceous coral Massive coral
12 12 12
1 1 3
3Coral 2
Tabular coral Foliaceous coral Massive coral
12 12 9
1 1 3
3Coral 3
Tabular coral Foliaceous coral Massive coral
12 12 8
1 1 3
3Coral 4
Tabular coral Foliaceous coral Massive coral
12 12 6
1 1 3
Stochasticity: Direction of growth to any available suitable space during the radial growth of any coral group in each time step is random. Observation: For model testing, spatial distribution of the individuals was observed process by process. For model analysis, only the coral cover of each coral group over time was recorded.
2.6. Input Only two major characteristics (growth rate and attacking distance) of the corals were investigated in this study as Lang and Chornesky (1990) concluded that relative growth rate may have a profound effect on the resolution of some competitive interactions among corals. In addition, it is reasonable to expect that the ability of a coral polyp to inflict injuries on other coral polyps over a greater distance could influence its competitive dominance. Table 1 summarizes the various combinations of coral groups and variation in the growth rate and attacking distance of each coral group used in the simulation investigating the competitive mechanism governing the coral community structure. The relative growth rate of each coral group was set based on the generalization of the results found by Barnes (1973), Buddemeier and Maragos (1974), Baker and Weber (1975), Gladfelter et al. (1978), Hubbard and Scaturo (1985), Hughes and Jackson (1985), Guzmàn and Cortés (1989) and Sorokin (1993). In general, the growth rate of tabular corals (e.g. many coral species of Family Acroporidae) and foliaceous corals (e.g. Pavona decussata) was much faster than that of massive corals (e.g. most coral species of Family Faviidae). In addition, the relative attacking distance assigned for each coral group in the present study represents the general spatial characteristics of direct killing behaviour of each coral group reviewed by Lang and Chornesky (1990). Tabular corals have been observed to utilize histoincompatibility to injure the soft tissues of other corals that they come into contact with. Histoincompatibility is also known to be used by foliaceous corals (e.g. Pavona sp.) for competition. However, histoincompatibility was observed to occur only when the attacking coral is touching other corals (<5 mm separation). Therefore, these two coral groups were set in the
a For each growing coral polyp, the unit is referred to as the number of times the polyp will carry out growing behaviour per year. The polyp will increase 1 unit space at each time of growing if space is available.
simulating environment to have very short effective ranges of attack. In contrast, massive corals usually have aggressive killing activities brought about by their sweeper tentacles or mesenterial filaments, which can be deployed over a range of 10 cm or more. This coral group was thus set to have a relatively long attacking distance in the simulation. The relative shade-tolerance level of each coral group was based on the findings of Stimson (1985) and our own observation in the field (data not shown). In general, massive corals were found to
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Table 2 Final area cover and number of times for being dominant in each coral group at the end of each type of simulation under various combinations of coral groups and variation of the strength of their growth rate and attacking distance. Refer to Table 1 for more detailed characteristics of the coral groups used in the simulations. n = 50. Coral group
No. of times for being dominant (out of 50)
Final area cover (arbitrary units)
Range
Mean ± 1 SEM
TF 1
Tabular coral Foliaceous coral
34 16
201–468 199–393
339.8 ± 9.4* 295.4 ± 6.3
TM 1
Tabular coral Massive coral
50 0
494–785 19–247
672.9 ± 9.0* 72.6 ± 6.5
TM 2
Tabular coral Massive coral
34 16
175–461 127–543
343.2 ± 9.4* 294.7 ± 11.7
TM 3
Tabular coral Massive coral
0 50
20–206 437–775
112.7 ± 6.6* 589.5 ± 10.6
TM 4
Tabular coral Massive coral
1 49
26–339 304–739
165.0 ± 9.6* 508.1 ± 12.7
TM 5
Tabular coral Massive coral
16 34
129–460 103–636
266.8 ± 11.2* 348.7 ± 17.0
TM 6
Tabular coral Massive coral
37 13
132–559 87–608
366.7 ± 12.1* 259.3 ± 16.4
TM 7
Tabular coral Massive coral
50 0
643–900 0–28
886.0 ± 6.1* 1.3 ± 0.8
FM 1
Foliaceous coral Massive coral
50 0
354–542 198–357
440.7 ± 6.0* 280.6 ± 5.6
FM 2
Foliaceous coral Massive coral
0 50
65–307 395–695
160.5 ± 7.4* 561.6 ± 9.0
FM 3
Foliaceous coral Massive coral
0 50
3–150 605–846
60.8 ± 4.9* 717.0 ± 8.3
FM 4
Foliaceous coral Massive coral
0 50
15–241 463–830
108.7 ± 7.8* 641.3 ± 11.2
FM 5
Foliaceous coral Massive coral
0 50
56–312 344–696
181.0 ± 8.9* 533.9 ± 13.1
FM 6
Foliaceous coral Massive coral
4 46
87–372 288–687
236.2 ± 10.7* 464.4 ± 13.8
FM 7
Foliaceous coral Massive coral
50 0
724–900 0–109
875.2 ± 6.6* 7.6 ± 3.2
3Coral 1
Tabular coral Foliaceous coral Massive coral
0 0 50
39–284 11–204 429–939
161.6 ± 8.6† 94.1 ± 6.4† 700.0 ± 14.5
3Coral 2
Tabular coral Foliaceous coral Massive coral
15 4 31
145–598 103–355 188–711
279.0 ± 11.5† 214.0 ± 8.7† 366.6 ± 16.1
3Coral 3
Tabular coral Foliaceous coral Massive coral
36 10 4
208–673 129–486 44–484
408 ± 15† 269 ± 12† 199 ± 14
3Coral 4
Tabular coral Foliaceous coral Massive coral
26 24 0
222–797 259–872 0–24
545.4 ± 20.6N 507.4 ± 19.6N 0.5 ± 0.5 †
* † N
Significantly different from the other coral group (p ≤ 0.0083). Significantly different from the other two coral groups (p ≤ 0.004). Not significantly different from each other (p = 0.3131).
be more shade-tolerant than foliaceous corals, which in turn were more tolerant than tabular corals. All the other factors (e.g. food requirements, heat tolerance, etc.), which are incorporated in ReefModel, were set at an extreme value in the present study such that these factors would not affect the survivorship nor the competitive mechanism of the corals during simulations. For instance, the life span of each coral group was set as 100 years; no food was required for each coral polyp and that the coral did not spawn during the period of simulation.
2.7. Data analysis The coral community structures resulted from the simulations were analysed by calculating the area cover (in arbitrary units) of each coral group. This refers to the area of their canopy layers in the simulated environment. Statistical analyses using the Wilcoxon Signed Rank test were carried out to compare the mean area covers among the coral groups under the same type of simulations (Townsend, 2002). Shapiro–Wilk test was carried out to check for multimodality, a hint on catastrophic regime shift (Scheffer and
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Fig. 2. Changes in the mean area cover of each coral group in the simulations of 3-coral interaction with massive coral having attacking distance 3 times longer than that of the other two coral groups and (a) with growth rate being the same for all three coral groups; or with tabular and foliaceous corals growing (b) 1.33 times, (c) 1.5 times and. (d) 2 times faster than the massive coral. Note different scales of Y-axis in different plots. n = 50 for each simulation.
Carpenter, 2003), in the frequency distribution of the area cover of each coral group. Multidimensional scaling (MDS) analysis, based on Bray–Curtis similarity measures using double square-root transformations of the area cover of each coral group, was also carried out to determine if there was any outlier or distinct grouping in the coral community structure under the same type of simulations. 3. Results A distinct dominance effect brought about by different competitive mechanisms and degrees of competitive strength of the coral groups was observed in the simulations (Table 2). Firstly, it was found that the mean final abundance of tabular coral was significantly higher than that of foliaceous coral (Wilcoxon Signed Rank test, p = 0.0013) and the number of times it was dominant was much greater than that of foliaceous coral in the simulation when these two corals had the same growth rates and attacking distances (TF 1). Such results indicate that the radial growing pattern of tabular coral dominated over the decussating growing pattern of foliaceous coral.
Secondly, direct killing of nearby coral polyps over long distances was also observed as an effective mechanism for a coral to gain dominance in interspecific competition. Massive coral lost out completely to both tabular and foliaceous corals when its growth rate and attacking distance were the same as those of these two corals (TM 1 and FM 1; Wilcoxon Signed Rank test, both p < 0.0001). However, when its attacking distance increased to three times greater than that of tabular and foliaceous corals, massive corals were found to completely dominate over the other two coral groups in either one-to-one interaction (TM 3 and FM 3) or one-to-two interaction (3Coral 1) (Wilcoxon Signed Rank test, all p < 0.0001). Nevertheless, it was demonstrated that fast-growing habit is also an effective mechanism for a coral group to compete for space. Tabular coral was found to dominate over massive coral when its growth rate was set at 1.5 times higher than that of massive coral in TM 6 (Wilcoxon Signed Rank test, p = 0.0003) even if the attacking distance of massive coral was three times greater than that of tabular coral in the simulation. Similarly, foliaceous coral was also found dominating over massive coral when it was set to grow two
Table 3 Results of the Shapiro–Wilk test for normality in the frequency distribution of the final area cover of each coral group in each type of simulation under various combinations of coral groups and variation of the strength of their growth rate and attacking distance. Only those with significant level less than 0.05 are shown. Refer to Table 1 for more detailed characteristics of the coral groups used in the simulations. n = 50. Simulation type
Tabular coral Statistic value (W)
TM TM TM TM FM FM FM
1 2 6 7 3 4 7
– – – 0.38 – – –
Foliaceous coral Sig. level – – – <0.0001 – – –
Massive coral
Statistic value (W)
Sig. level
Statistic value (W)
Sig. level
– – – – 0.94 0.95 0.60
– – – – 0.018 0.030 <0.0001
0.85 0.93 0.94 0.25 – – 0.39
<0.0001 0.006 0.021 <0.0001 – – <0.0001
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Fig. 3. Some examples showing clear multimodal distribution of the final area cover of coral group under different combinations of coral groups and variation of the strength of their two major charateristics (growth rate and attacking distance). Refer to Table 1 for detailed characteristics of the coral groups used in the simulations. Note different X- and Y-axis scales among plots. n = 50 for each simulation.
times faster than massive coral in FM 7 (Wilcoxon Signed Rank test, p < 0.0001). Similar results were also observed during the threecoral-group interaction when the growth rate of both tabular and foliaceous corals was 1.5 times or more than that of massive coral (Fig. 2 and Table 2). In these simulations, tabular and foliaceous corals dominated over massive coral in the three-coral community simulated even if the attacking distance of massive coral was three times greater than that of these two coral groups (Wilcoxon Signed Rank test, all p ≤ 0.004). Shift in dynamic regime was found occasionally in the dynamics of individual coral group and the coral community structure during both two-coral-group and three-coral-group interactions. Shapiro–Wilk test for normality showed that the frequency distribution of the final area cover of massive coral was clearly multimodal in some of its one-to-one interaction with the other coral groups (TM 1–2, TM 6–7 and FM 7) (Fig. 3 and Table 3; all W ranged between 0.25 and 0.94 and all p ≤ 0.021). It can be noted that in these five types of simulations, massive coral generally
lost out to the corals it interacted with, but could occasionally out-compete these corals in some simulation runs in TM 2 and TM 6 (Table 2). Significant multimodal frequency distribution of the final area cover of foliaceous coral was also found in some of its interaction with massive coral (FM 3–4 and FM 7, all W ranged between 0.60–0.95 and all p ≤ 0.030). In addition, MDS ordination plots based on Bray–Curtis similarity measures of the final area cover of the coral groups showed that there was distinct outlier in the three-coral community structure when growth rate of both tabular and foliaceous corals was 1.33 or two times more than that of massive coral (Fig. 4). 4. Discussion The 3-dimensional individual-based model (ReefModel) developed in this study provides important insights into the mechanisms governing coral community structure. Although only 50 simulation runs were carried out in each simulation, in a broad sense, several
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Fig. 4. MDS ordination plots based on Bray–Curtis similarity measures of area cover of the coral groups in the simulations of 3-coral interaction with massive coral having attacking distance 3 times longer than that of the other two coral groups and with tabular and foliaceous corals growing (a) 1.33 times and (b) 2 times faster than the massive coral. Distinct outlier is circled in the plots. Each symbol represents the coral community composition at the end of each simulation run. Refer to Table 1 for detailed characteristics of the coral groups used in the simulations. n = 50 for each simulation.
aspects of the effects of competitive mechanisms on coral community structure and the potential presence of alternative stable states could already be identified. The results from the simulations of interspecific coral competition suggest that a fast-growing habit with overtopping competitive mechanism is probably one of the most effective strategies for corals to gain spatial dominance in a coral community under stable environmental conditions. A fastgrowing habit with overtopping characteristics has the advantages of allowing the coral to colonize space faster, not to be limited by “available hard substratum” in radial growth and to allow overtopping to kill other sessile organisms (corals) indirectly. Indeed, in nature, coral species with such biological characteristics are usually found dominating in shallow water coral communities (Sorokin, 1993). Besides unravelling some mechanisms in structuring coral community, the present modelling study reveals that alternative stable states can exist in a coral community under the same environmental regime. Multimodal distribution was observed occasionally in the frequency distribution of the final area cover of the coral groups in some of the simulations of two-coral interaction. This reflects the potential existence of alternative stable states of the coral groups under such interaction (Scheffer and Carpenter, 2003). The survivorship of the coral group was set to be unaffected by environmental changes in the simulating environment and no temporal changes (e.g. spawning and recruitment of larvae, natural mortality due to aging) were also set to affect the dynamics of the coral group. Therefore, the alternative states of the coral groups observed in the simulations should have resulted mainly from the influence of small random spatial events that occurred during the early interaction among coral groups. These events included initial distances between colonies of the different coral groups at the beginning of the simulation. Massive coral may be used as an example to clarify this point. Massive coral was a relatively slowgrowing coral group with no overtopping competitive mechanism. This coral group relied on its more aggressive behaviour (relative long attacking distance) to compete for space with the other two fast-growing coral groups, tabular and foliaceous corals. However, this competitive strategy would no longer be effective once the massive coral colony was overtopped by the colonies of tabular and foliaceous corals as the overtopped massive coral polyps were not set in the simulation to be able to attack from underneath any other polyps that directly overtopped them. As a result, the only opportunity for massive coral to win over tabular and foliaceous corals in the simulation was to cause mortality of the whole colonies of the other two coral groups as much as possible when the colonies were still within its effective range of attack at the beginning of
the simulation. Missing this opportunity, the massive coral colony would not be able to induce mortality on the colonies of the other two coral groups again and would subsequently be overtopped by them. The polyps of the slow-growing massive coral would not be able to catch up with the other fast-growing colonies and would be unable to reach and inflict damage on them. Such possible all-ornone scenario for a massive coral colony to out-compete the coral colonies of the other coral groups indicated that a little difference in the initial number of the other coral colonies that was within its effective range of attack, hence the initial distance among them, would lead to diverse outcomes on the final states of the massive coral during its interaction with other coral groups. The ReefModel developed here represents a more realistic model to simulate the population dynamics and spatial interactions in a coral community. The competitive mechanisms identified may be used to explain observable variations in existing coral community structures. Some coral communities, like those found in northeastern Hong Kong, are dominated by massive corals (mainly faviids) (Tam and Ang, 2008). Yet other communities nearby in eastern Hong Kong are dominated by tabular (mainly Acropora spp.) or foliaceous (Montipora spp.) corals (Ang et al., 2006). While historical developments of these coral communities were not closely followed and well documented, they nevertheless reflect different potential stable states. The mechanisms leading to these potential stable states could thus be deduced from those simulated in the present study. The model was also able to provide important insights in understanding the cause of alternative stable states in coral community during interspecific competition. Although direct results from field observations and experiments are not available in coral reef studies carried out so far to support this phenomenon, evidences from the field study of other sessile biological community are nonetheless available. Petraitis et al. (2009) showed that mussel bed (Mytilus edulis) and rockweed stands (Ascophyllum nodosum and Fucus vesiculosus) are multiple stable states on intertidal shores in the Gulf of Maine, USA and suggests that the development of either community depends on which species becomes established first. The present results obtained from ReefModel described here show the potential utilities of this model. Further refinements could certainly be done to provide deeper insights and understanding into other critical mechanisms that contribute to the structuring of coral as well as other benthic communities. Acknowledgements This study was partly funded by NSFC/RGC Joint Research Scheme Project no. N CUHK457/09 and Research Committee of
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CUHK Group Research Scheme Project no. C001-3110042. We ˜ for their thank K.H. Chu, N.Y.S. Woo, J.W. McManus and P.M. Alino critical comments and advice. We would also like to thank J.H.M. Lee (Department of Computer Engineering, The Chinese University of Hong Kong) for his help with the use of programming techniques in Smalltalk V for the development of the Reef Model. Critical comments from the reviewers and editor are also most helpful.
Class
Instance variable
Description
activeTempAdult
Stores the range of temperature that an adult organism will search for food Stores the number of simulation days that a larva or a spore will change to adult organism Stores the number of simulation days that an adult organism can tolerate for feeling cold Stores the disturbance level that an adult organism can tolerate
changeAdultTime
coldToleranceAdult
Appendix A. disturbTolerance Adult
Description of some basic instance variables of the three major classes developed in the ReefModel for storing the states of the objects created during the simulation (from Tam and Ang, 2009). Class
Instance variable
Description
ReefSystem
tickCount
Stores no. of tick received from the timer of the simulation system so as to keep track of system time Stores the width of the ecosystem Stores the length of the ecosystem Stores the height of the ecosystem Stores a list of sub-units (instances of class EcoUnit) created inside the ecosystem Stores the month that the simulation system encounters Stores the time interval for retrieval of data during the simulation
systemWidth systemLength systemHeight ecoUnitList
monthCount dataInterval
EcoUnit
Length
Ecosystem Position Various physical factor names or abbreviations (e.g. temp, nutrient) exposedAdult
hiddenAdult
Organism
tickCount
ecoUnit Ecosystem Stage Position maxSpeed lifeSpanAdult foodReqAdult delayFeedingTimeAdult
hungryCount
hungry Tolerance Adult
Stores the length of a sub-unit (instance of Class EcoUnit) inside the ecosystem Stores the kind of ecosystem that the sub-unit belongs to Stores its 3-dimensional position inside the ecosystem Stores the physical factors (e.g. temperature, nutrient) of a sub-unit of the ecosystem
Stores a list of adult organisms that are exposed inside a sub-unit of the ecosystem Stores a list of adult organisms that are hidden inside a sub-unit of the ecosystem Stores no. of tick received from the timer of the simulation system so as to keep track of the life time (i.e. age) of an organism in the system Stores the sub-unit that an organism inhabits Stores the kind of ecosystem that an organism inhabits Stores the developmental stage (adult, larva or spore) of an organism Stores the 3-dimensional position of an organism inside the ecosystem Stores the maximum moving speed of an adult organism Stores the maximum life span of an adult organism Stores the amount of food required for an adult organism Stores the number of simulation days that the adult organism will search food once Stores the no. of tick that an organism receives from the timer of the simulation system when the organism is being hungry (not able to obtain the amount of food that meets its required level) continuously Stores the number of simulation days that an adult organism can tolerate for being hungry
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