Current Biology 24, 1000–1005, May 5, 2014 ª2014 Elsevier Ltd All rights reserved
http://dx.doi.org/10.1016/j.cub.2014.03.026
Report Vulnerability of Coral Reef Fisheries to a Loss of Structural Complexity Alice Rogers,1,2,* Julia L. Blanchard,3 and Peter J. Mumby1,2,* 1Marine Spatial Ecology Lab, School of Biological Sciences and ARC Centre of Excellence for Coral Reef Studies, University of Queensland, St Lucia, QLD 4072, Australia 2College of Life and Environmental Sciences, University of Exeter, Exeter, EX4 4PS, UK 3Department of Animal and Plant Sciences, University of Sheffield, Alfred Denny Building, Western Bank, Sheffield S10 2TN, UK
Summary Coral reefs face a diverse array of threats, from eutrophication and overfishing to climate change. As live corals are lost and their skeletons eroded, the structural complexity of reefs declines. This may have important consequences for the survival and growth of reef fish because complex habitats mediate predator-prey interactions [1, 2] and influence competition [3–5] through the provision of prey refugia. A positive correlation exists between structural complexity and reef fish abundance and diversity in both temperate and tropical ecosystems [6–10]. However, it is not clear how the diversity of available refugia interacts with individual predator-prey relationships to explain emergent properties at the community scale. Furthermore, we do not yet have the ability to predict how habitat loss might affect the productivity of whole reef communities and the fisheries they support. Using data from an unfished reserve in The Bahamas, we find that structural complexity is associated not only with increased fish biomass and abundance, but also with nonlinearities in the size spectra of fish, implying disproportionately high abundances of certain size classes. By developing a size spectrum food web model that links the vulnerability of prey to predation with the structural complexity of a reef, we show that these nonlinearities can be explained by size-structured prey refugia that reduce mortality rates and alter growth rates in different parts of the size spectrum. Fitting the model with data from a structurally complex habitat, we predict that a loss of complexity could cause more than a 3-fold reduction in fishery productivity. Results and Discussion Given that vulnerability to predation and refuge availability are highly dependent on body size (reviewed in [11]), our empirical analyses and trophic models focus on the size structure of coral reef fish assemblages and answer four questions: (1) how does structural complexity on coral reefs influence the size spectra of predatory and herbivorous fish, (2) can we explain the observed fish size spectra by explicitly incorporating size-structured prey refugia into a trophic model of the ecosystem, (3) how do changes in the diversity and density of refugia (e.g., crevices) influence reef fish assemblages,
*Correspondence: (P.J.M.)
[email protected]
(A.R.),
[email protected]
and (4) what are the implications for reef fishery productivity of transitioning from a high- to low-complexity reef? The model we present is parameterized for a Caribbean coral reef. However, the framework we introduce quantitatively links the function of structural complexity to the production of biomass and could easily be adapted for use in other ecosystems ranging from mangroves [12, 13] to African savannah [14, 15], where habitat structure also influences competition and predation risk. Effect of Structural Complexity on Observed Size Spectra of Reef Fish The Exuma Cays Land and Sea Park (ECLSP) is one of the most successful marine reserves in the Caribbean and has been free from fishing effects since at least 1985. The antecedent morphology of reefs in the ECLSP has created two contrasting habitats within the same linear stretch of forereef (Figure 1A). Areas of structurally complex Orbicella reef (herein referred to as high-complexity reefs; Figure 1B), are interspersed with extensive areas of relatively flat, hard substratum that is typically colonized with a low density of gorgonians (herein referred to as low-complexity reefs; Figure 1C). Using the Pareto distribution, which takes into account every individual and incorporates a high degree of variation from the data (see the Supplemental Experimental Procedures available online), we show that the size spectra of fish assemblages from these two contrasting habitats are distinctly different (see the Supplemental Experimental Procedures for details of data collection). Though the slopes of the relationships do not differ significantly, both predatory and herbivorous fish assemblages from high-complexity habitats exhibit more nonlinearities, or lumps, in their size spectra that indicate disproportionately high abundances of certain size classes (predators: F = 19.23, df = 10, p < 0.01; herbivores: F = 13.7, df = 10, p < 0.01, Figure 2). At low complexity, the size spectra are smooth and lack such nonlinearities. In most cases, the nonlinearities in size spectra correspond to high abundances of small- to medium-sized fish ranging from w30 to 500 g or w15 to 40 cm. Relationships between size spectra and habitat structural complexity have not been studied extensively for coral reef fish, though the literature is burgeoning. Graham et al. [16] found that the slopes of size spectra became shallower in response to reduced structural complexity in the Seychelles, and both Wilson et al. [17] and Alvarez et al. [18] found similar patterns in Fiji and Cozumel, all indicating that high complexity was associated with higher abundances of small-bodied fish. Here, we show that size spectra from high-complexity habitats also exhibit a marked series of nonlinearities, implying that some size classes are disproportionately more abundant than others. This nonlinear feature of size spectra has not been previously described, though the textural discontinuity hypothesis of Holling [19] suggests that such a pattern is likely when habitats exhibit structural discontinuities. Our finding is, however, consistent with several studies that relate the size distributions of reef fish to the sizes of refugia on the reef [20–22]. Given experimental evidence that fish use appropriately sized crevices as prey refugia and improve their survival by doing so [1, 23, 24], we hypothesize that by modeling
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Figure 1. Location and Appearance of High- and Low-Complexity Reefs in the Exuma Cays Land and Sea Park Locations (A) and appearance of patches of high-complexity Orbicella reef (B) and patches of low-complexity gorgonian plane (C) in the Exuma Cays Land and Sea Park, Bahamas. Panel (A) courtesy of Google Inc. All rights reserved ª 2013 DigitalGlobe, U.S. Geological Survey.
structural complexity as the availability of size-structured prey refugia in a trophic food web, we will generate nonlinearities in size spectra akin to those observed in the field. Modeling Structural Complexity to Reproduce Observed Size Spectra Several studies have developed food web models for coral reefs [25–28], but the impacts of size-structured prey refugia on trophic dynamics have not been considered explicitly. Given that predation mortality and refuge availability are highly size dependent [11], we developed a size-structured food web model to address this gap. Its foundation stems from the functional group and size-structured benthic-pelagic food web model originally developed by Blanchard et al. [29]. The model includes three functional groups: predatory fish, herbivorous fish, and benthic invertebrates (see the schematic in Figure 3A). Predators feed from all three size spectra in a size-dependent manner, whereas herbivores and invertebrates compete for an unstructured pool of algae and detritus. Structural complexity was modeled by the inclusion of a vulnerability function (Figures 3B–3E), defined as the proportion of the population at a given weight that is vulnerable to predation. When the function has a value of one, all prey are vulnerable, but vulnerability can decline in two dimensions as structural complexity increases. A deepening of the vulnerability function along the y axis allows a higher proportion of fish of a given size to experience a refuge, thereby representing an overall increase in the density of crevices on the reef (Figure 3B). A widening of the x axis represents a higher diversity of refugia (i.e., a larger range of crevice sizes) such that fish from a wider range of body sizes can seek refuge from predators (Figure 3C). Examples of vulnerability functions associated with habitats with low and high complexity are shown in Figures 3D and 3E, respectively, and the lower panels in Figure 3A demonstrate how declining structural complexity increases the vulnerability of some size classes to predation. The Supplemental Information provides more detailed model descriptions, equations (Table S1), and parameters (Table S2). The fit between predicted predatory fish size spectra and those observed in the ECLSP was calculated both for the base model without structural complexity and for the model that explicitly included the density and diversity of
prey refugia. Specifically, we tested the hypothesis that, with all else being equal, the inclusion of size-structured prey refugia in a trophic model of coral reefs would improve its fit to observed data from reef locations with high structural complexity. The base model, parameterized for coral reefs but lacking refugia, generated linear size spectra of a form that characterizes those in open-ocean pelagic systems [30] and benthicpelagic systems that lack structure [29]. It provided a good fit to predatory fish size spectra data from low-complexity habitats of the ECLSP (sum of squared errors of 0.2, coefficient of determination of 0.99; Figure 4A), but a poorer fit to data from high-complexity habitats (error of 2.06, coefficient of determination of 0.90). When crevice density, Vmin, and diversity, s, were included in the model, predicted size spectra exhibited nonlinearities or lumps, the locations and size of which were determined by the parameter values. Given that these parameters were not known for complex habitats of the ECLSP, we explored a broad range of possible combinations (see the Experimental Procedures) and asked whether the inclusion of the function could allow for an improved fit of the model to the data. Using grid search and minimizing the sum of squared errors between predicted and observed data, we found that the best fit was achieved when Vmin = 0.1 and s = 1,000. With the inclusion of these two additional parameters, we improved the model fit to complex data by 6%, reducing the sum of squared errors from 2.06 to 0.84 and increasing the coefficient of determination from 0.9 to 0.96 (Figure 4B) when compared with the base model lacking prey refugia. The estimated best-fit parameters of the vulnerability function suggest that highcomplexity habitats in the ECLSP provide refugia for a diversity of fish body sizes up to 1,000 g and leave only 10% of the population within this size range vulnerable to predation. Our modeling results lead to a conclusion that the mediating effects of refugia on predation and competition within a food web can result in nonlinear size spectra consistent with those observed from habitats with high structural complexity. Inclusion of size-structured refugia in coral reef food web models will therefore allow for improved model fits to data and provides a framework that can be used to explore the impacts of declining structural complexity on coral reef communities. We provide additional support for this conclusion with sensitivity analyses, which confirm that variation in other uncertain parameters in this model do not result in nonlinearities in size spectra, nor do they allow for better fits of the model to data from high-complexity habitats (see Figure S1 and the Supplemental Experimental Procedures). Implications of Habitat Loss for Reef Fishery Productivity Productivity is captured in our model by the flux of biomass through fish size classes (g m23 y21; see the Supplemental Experimental Procedures for equations). To explore the potential implications of habitat degradation on fishery productivity in the Caribbean, we asked two questions. First, we asked how each dimension of the vulnerability function—crevice density (Vmin) and crevice diversity (s)—influenced the productivity of predatory and herbivorous fish assemblages. Second, we asked how a profound decline in reef habitat quality, such as might occur under intense stress or disturbance [31], might influence the overall fishery productivity of the system. Exploring a broad range of possible parameter combinations, we found that a loss of crevice density led to nonlinear declines in the productivity of both predatory and herbivorous fish (Figures 4C and 4D, respectively). The response to a loss
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Figure 2. Fish Size Spectra Differences between High- and Low-Complexity Habitats of the Exuma Cays Land and Sea Park Differences in nonlinearities in size spectra of predatory (1) and herbivorous (2) fish from highand low-complexity reef habitats in the Exuma Cays Land and Sea Park. Shown are size spectra and linear model fits for example sites from highand low-complexity habitats (A; top and bottom, respectively), the associated autocorrelation in residuals (B), and greater autocorrelation and nonlinearity in high-complexity sites overall (C; ANOVA, F = 13.7, df = 10, p < 0.01).
of crevice diversity was more complex, exhibiting a quadratic (convex) function indicating that productivity was low when crevice diversity was low, increased as diversity increased, but then reduced again as crevice diversity became high. Increased productivity in response to an increasing density of prey refugia and, initially an increasing diversity of refuge sizes, is not surprising. Small-bodied fish, which are highly vulnerable to predation, benefit from refugia by experiencing reduced mortality, and their abundance increases as a result. Because small-bodied fish comprise both prey species and the juveniles of larger predators, the increased survival and abundance results in greater fish productivity. Although the proportion of vulnerable prey fish declines with increasing structural complexity, the total availability of prey may increase because of the overall increase in population size [6, 8, 32]. Further, a reef with high habitat complexity may allow for not only an increased abundance of small-bodied fish inside refugia, but also an increased abundance of subordinates that are excluded from those refugia through competition [33, 34]. These fish are available to predators and also contribute to an increase in productivity. We interpret the quadratic association between productivity and crevice diversity as a tradeoff between reduced mortality rates and reduced growth rates. Initially, as crevice diversity increases, the mechanism for increased productivity follows that described above (i.e., higher fish abundance and competition). However, when crevice diversity is high, a wide range of fish body sizes are unavailable as prey. Some of the largest predators in the system then have to supplement their diet by feeding from the benthic community. If the benthic community does not provide sufficient energy to meet a large predator’s demand, its growth rate declines. In these scenarios, the negative impacts of reduced growth outweigh the benefits from avoiding predation and, as a result, there is a maximum refuge size beyond which productivity declines. Thus, the model has generated a new hypothesis that could be tested in the field; i.e., do we find evidence of increased prey
switching away from piscivory when the diversity of crevices on the reef becomes high? Modeling ecosystem functions has become a central concern of ecology, motivated in part by the need to value ecosystem services [35–37]. Yet, production functions for many ecosystems remain unknown [38]. While trophic models have been used to estimate total fish production (e.g., [39]), they do not yet attempt to predict how changes in ecosystem function caused by declining structural complexity might influence the food web and alter ecosystem services such as fishery productivity. To shed some light on this question, we contrast the fishery productivity from our model of a complex reef in the ECLSP with one that lacks structural complexity. Habitat loss reduced the productivity of predatory fish by almost half, from 285 g m23 yr21 to 159.3 g m23 yr21, and of herbivorous fish by more than two and a half times, from 45 to 16.9 g m23 yr21. Moreover, if we assume that a reef fishery ignores smaller-bodied individuals (e.g., X) wx) were plotted on double-log axes for each reef site (n = 12; four high complexity, eight low complexity). We specifically asked
Modeling The first step in the modeling process was to extend and parameterize the generic dynamical coupled size spectrum model lacking prey refugia [29] for a coral reef ecosystem, creating a base model. To do this, we added a spectrum of herbivorous fish and set parameters based on coral reef specific values where possible. The Supplemental Experimental Procedures provide detailed model descriptions and information about model parameterization. The Supplemental Information lists all model equations (Table S1) and parameter values (Table S2). The second step in the process was to add into the base model a vulnerability function (described in the main text above) that represented the effects of size-structured prey refugia on trophic dynamics. This required the inclusion of just two additional parameters: Vmin, the minimum proportion of the population vulnerable to predation, and s, the maximum refuge size. We did not have empirical data to estimate these parameters, and so we selected values for them by minimizing the residual sum of squared errors RSS (Equation 1) between the predatory fish size spectrum
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predicted by the model and that observed in high-complexity habitats of the ECLSP: Xn RSS = ðyi 2 fðxi ÞÞ2 ; Equation 1 i=1 where yi is the ith value of the observed log10 (prob(x > X)) in the Pareto distribution of predatory fish size spectra and f (xi) is the equivalent predicted value from the model. The selection of best-fit parameters was carried out using a method of grid search across a broad range of possible parameter combinations (Vmin: 0.1–0.95; s: 1–1,500). Utilizing our base model and the plausible refugia model resulting from step two, we asked the question of whether, all else being equal, the addition of the vulnerability function to describe size-structured refugia improved the model fit to size spectra data from high-complexity habitats of the ECLSP. This comparison was made by examination of the difference in both the residual sum of squared errors from each model fit (Equation 1) and the coefficient of determination, R2 (Equation 2), that describes the amount of variation in the data that is explained by the model R2 = 1 2
RSS ; TSS
Equation 2
where TSS =
Xn i=1
2
ðyi 2 yÞ ;
where y is the mean log10 (prob(x > X)) in the pooled data from sites with high structural complexity. Supplemental Information Supplemental Information includes one figure, two tables, and Supplemental Experimental Procedures and can be found with this article online at http://dx.doi.org/10.1016/j.cub.2014.03.026. Acknowledgments
D
We thank Adrian Stier for information on body masses of reef fish recruits, Alastair Harborne and Yves-Marie Bozec for insightful discussions on predator-prey interactions, and Iliana Chollett for comments on a previous version of the manuscript. This work was funded by the Natural Environment Research Council (NERC), a Pew Fellowship, and an ARC Laureate Fellowship to P.J.M. Received: November 12, 2013 Revised: January 30, 2014 Accepted: March 10, 2014 Published: April 17, 2014 References 1. Hixon, M.A., and Beets, J.P. (1993). Predation, prey refuges, and the structure of coral-reef fish assemblages. Ecol. Monogr. 63, 77–101. 2. Syms, C., and Jones, G.P. (2000). Disturbance, habitat structure, and the dynamics of a coral-reef fish community. Ecology 81, 2714–2729. 3. Macarthur, R., and Levins, R. (1967). The limiting similarity, convergence, and divergence of coexisting species. Am. Nat. 101, 377–385. 4. Hixon, M.A., and Menge, B.A. (1991). Species diversity: prey refuges modify the interactive effects of predation and competition. Theor. Popul. Biol. 39, 178–200. 5. Buchheim, J.R., and Hixon, M.A. (1992). Competition for shelter holes in the coral-reef fish Acanthemblemaria spinosa Metzelaar. J. Exp. Mar. Biol. Ecol. 164, 45–54.
Figure 4. Model Predictions for the Shape of Size Spectra and the Productivity of Reef Fish for Coral Reefs with Varying Degrees of Habitat Structural Complexity (A and B) Comparisons of predicted and observed size spectra of predatory reef fish from contrasting low- and high-complexity reef habitats. Lines
show predictions from size-structured models lacking prey refugia (A) and providing refugia for 90% of fish up to 1,000 g in body size (B). Points show respective observed size spectra data from low-complexity reefs (A) and high-complexity reefs (B) in the Exuma Cays Land and Sea Park. (C and D) Model outputs showing how declining habitat structural complexity influences predatory (C) and herbivorous (D) fish productivity (g m23 yr21; measured as the rate at which biomass fluxes through fish size classes). See also Figure S1.
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http://dx.doi.org/10.1016/j.cub.2014.03.026
Report Vulnerability of Coral Reef Fisheries to a Loss of Structural Complexity Alice Rogers,1,2,* Julia L. Blanchard,3 and Peter J. Mumby1,2,* 1Marine Spatial Ecology Lab, School of Biological Sciences and ARC Centre of Excellence for Coral Reef Studies, University of Queensland, St Lucia, QLD 4072, Australia 2College of Life and Environmental Sciences, University of Exeter, Exeter, EX4 4PS, UK 3Department of Animal and Plant Sciences, University of Sheffield, Alfred Denny Building, Western Bank, Sheffield S10 2TN, UK
Summary Coral reefs face a diverse array of threats, from eutrophication and overfishing to climate change. As live corals are lost and their skeletons eroded, the structural complexity of reefs declines. This may have important consequences for the survival and growth of reef fish because complex habitats mediate predator-prey interactions [1, 2] and influence competition [3–5] through the provision of prey refugia. A positive correlation exists between structural complexity and reef fish abundance and diversity in both temperate and tropical ecosystems [6–10]. However, it is not clear how the diversity of available refugia interacts with individual predator-prey relationships to explain emergent properties at the community scale. Furthermore, we do not yet have the ability to predict how habitat loss might affect the productivity of whole reef communities and the fisheries they support. Using data from an unfished reserve in The Bahamas, we find that structural complexity is associated not only with increased fish biomass and abundance, but also with nonlinearities in the size spectra of fish, implying disproportionately high abundances of certain size classes. By developing a size spectrum food web model that links the vulnerability of prey to predation with the structural complexity of a reef, we show that these nonlinearities can be explained by size-structured prey refugia that reduce mortality rates and alter growth rates in different parts of the size spectrum. Fitting the model with data from a structurally complex habitat, we predict that a loss of complexity could cause more than a 3-fold reduction in fishery productivity. Results and Discussion Given that vulnerability to predation and refuge availability are highly dependent on body size (reviewed in [11]), our empirical analyses and trophic models focus on the size structure of coral reef fish assemblages and answer four questions: (1) how does structural complexity on coral reefs influence the size spectra of predatory and herbivorous fish, (2) can we explain the observed fish size spectra by explicitly incorporating size-structured prey refugia into a trophic model of the ecosystem, (3) how do changes in the diversity and density of refugia (e.g., crevices) influence reef fish assemblages,
*Correspondence: (P.J.M.)
[email protected]
(A.R.),
[email protected]
and (4) what are the implications for reef fishery productivity of transitioning from a high- to low-complexity reef? The model we present is parameterized for a Caribbean coral reef. However, the framework we introduce quantitatively links the function of structural complexity to the production of biomass and could easily be adapted for use in other ecosystems ranging from mangroves [12, 13] to African savannah [14, 15], where habitat structure also influences competition and predation risk. Effect of Structural Complexity on Observed Size Spectra of Reef Fish The Exuma Cays Land and Sea Park (ECLSP) is one of the most successful marine reserves in the Caribbean and has been free from fishing effects since at least 1985. The antecedent morphology of reefs in the ECLSP has created two contrasting habitats within the same linear stretch of forereef (Figure 1A). Areas of structurally complex Orbicella reef (herein referred to as high-complexity reefs; Figure 1B), are interspersed with extensive areas of relatively flat, hard substratum that is typically colonized with a low density of gorgonians (herein referred to as low-complexity reefs; Figure 1C). Using the Pareto distribution, which takes into account every individual and incorporates a high degree of variation from the data (see the Supplemental Experimental Procedures available online), we show that the size spectra of fish assemblages from these two contrasting habitats are distinctly different (see the Supplemental Experimental Procedures for details of data collection). Though the slopes of the relationships do not differ significantly, both predatory and herbivorous fish assemblages from high-complexity habitats exhibit more nonlinearities, or lumps, in their size spectra that indicate disproportionately high abundances of certain size classes (predators: F = 19.23, df = 10, p < 0.01; herbivores: F = 13.7, df = 10, p < 0.01, Figure 2). At low complexity, the size spectra are smooth and lack such nonlinearities. In most cases, the nonlinearities in size spectra correspond to high abundances of small- to medium-sized fish ranging from w30 to 500 g or w15 to 40 cm. Relationships between size spectra and habitat structural complexity have not been studied extensively for coral reef fish, though the literature is burgeoning. Graham et al. [16] found that the slopes of size spectra became shallower in response to reduced structural complexity in the Seychelles, and both Wilson et al. [17] and Alvarez et al. [18] found similar patterns in Fiji and Cozumel, all indicating that high complexity was associated with higher abundances of small-bodied fish. Here, we show that size spectra from high-complexity habitats also exhibit a marked series of nonlinearities, implying that some size classes are disproportionately more abundant than others. This nonlinear feature of size spectra has not been previously described, though the textural discontinuity hypothesis of Holling [19] suggests that such a pattern is likely when habitats exhibit structural discontinuities. Our finding is, however, consistent with several studies that relate the size distributions of reef fish to the sizes of refugia on the reef [20–22]. Given experimental evidence that fish use appropriately sized crevices as prey refugia and improve their survival by doing so [1, 23, 24], we hypothesize that by modeling
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Figure 1. Location and Appearance of High- and Low-Complexity Reefs in the Exuma Cays Land and Sea Park Locations (A) and appearance of patches of high-complexity Orbicella reef (B) and patches of low-complexity gorgonian plane (C) in the Exuma Cays Land and Sea Park, Bahamas. Panel (A) courtesy of Google Inc. All rights reserved ª 2013 DigitalGlobe, U.S. Geological Survey.
structural complexity as the availability of size-structured prey refugia in a trophic food web, we will generate nonlinearities in size spectra akin to those observed in the field. Modeling Structural Complexity to Reproduce Observed Size Spectra Several studies have developed food web models for coral reefs [25–28], but the impacts of size-structured prey refugia on trophic dynamics have not been considered explicitly. Given that predation mortality and refuge availability are highly size dependent [11], we developed a size-structured food web model to address this gap. Its foundation stems from the functional group and size-structured benthic-pelagic food web model originally developed by Blanchard et al. [29]. The model includes three functional groups: predatory fish, herbivorous fish, and benthic invertebrates (see the schematic in Figure 3A). Predators feed from all three size spectra in a size-dependent manner, whereas herbivores and invertebrates compete for an unstructured pool of algae and detritus. Structural complexity was modeled by the inclusion of a vulnerability function (Figures 3B–3E), defined as the proportion of the population at a given weight that is vulnerable to predation. When the function has a value of one, all prey are vulnerable, but vulnerability can decline in two dimensions as structural complexity increases. A deepening of the vulnerability function along the y axis allows a higher proportion of fish of a given size to experience a refuge, thereby representing an overall increase in the density of crevices on the reef (Figure 3B). A widening of the x axis represents a higher diversity of refugia (i.e., a larger range of crevice sizes) such that fish from a wider range of body sizes can seek refuge from predators (Figure 3C). Examples of vulnerability functions associated with habitats with low and high complexity are shown in Figures 3D and 3E, respectively, and the lower panels in Figure 3A demonstrate how declining structural complexity increases the vulnerability of some size classes to predation. The Supplemental Information provides more detailed model descriptions, equations (Table S1), and parameters (Table S2). The fit between predicted predatory fish size spectra and those observed in the ECLSP was calculated both for the base model without structural complexity and for the model that explicitly included the density and diversity of
prey refugia. Specifically, we tested the hypothesis that, with all else being equal, the inclusion of size-structured prey refugia in a trophic model of coral reefs would improve its fit to observed data from reef locations with high structural complexity. The base model, parameterized for coral reefs but lacking refugia, generated linear size spectra of a form that characterizes those in open-ocean pelagic systems [30] and benthicpelagic systems that lack structure [29]. It provided a good fit to predatory fish size spectra data from low-complexity habitats of the ECLSP (sum of squared errors of 0.2, coefficient of determination of 0.99; Figure 4A), but a poorer fit to data from high-complexity habitats (error of 2.06, coefficient of determination of 0.90). When crevice density, Vmin, and diversity, s, were included in the model, predicted size spectra exhibited nonlinearities or lumps, the locations and size of which were determined by the parameter values. Given that these parameters were not known for complex habitats of the ECLSP, we explored a broad range of possible combinations (see the Experimental Procedures) and asked whether the inclusion of the function could allow for an improved fit of the model to the data. Using grid search and minimizing the sum of squared errors between predicted and observed data, we found that the best fit was achieved when Vmin = 0.1 and s = 1,000. With the inclusion of these two additional parameters, we improved the model fit to complex data by 6%, reducing the sum of squared errors from 2.06 to 0.84 and increasing the coefficient of determination from 0.9 to 0.96 (Figure 4B) when compared with the base model lacking prey refugia. The estimated best-fit parameters of the vulnerability function suggest that highcomplexity habitats in the ECLSP provide refugia for a diversity of fish body sizes up to 1,000 g and leave only 10% of the population within this size range vulnerable to predation. Our modeling results lead to a conclusion that the mediating effects of refugia on predation and competition within a food web can result in nonlinear size spectra consistent with those observed from habitats with high structural complexity. Inclusion of size-structured refugia in coral reef food web models will therefore allow for improved model fits to data and provides a framework that can be used to explore the impacts of declining structural complexity on coral reef communities. We provide additional support for this conclusion with sensitivity analyses, which confirm that variation in other uncertain parameters in this model do not result in nonlinearities in size spectra, nor do they allow for better fits of the model to data from high-complexity habitats (see Figure S1 and the Supplemental Experimental Procedures). Implications of Habitat Loss for Reef Fishery Productivity Productivity is captured in our model by the flux of biomass through fish size classes (g m23 y21; see the Supplemental Experimental Procedures for equations). To explore the potential implications of habitat degradation on fishery productivity in the Caribbean, we asked two questions. First, we asked how each dimension of the vulnerability function—crevice density (Vmin) and crevice diversity (s)—influenced the productivity of predatory and herbivorous fish assemblages. Second, we asked how a profound decline in reef habitat quality, such as might occur under intense stress or disturbance [31], might influence the overall fishery productivity of the system. Exploring a broad range of possible parameter combinations, we found that a loss of crevice density led to nonlinear declines in the productivity of both predatory and herbivorous fish (Figures 4C and 4D, respectively). The response to a loss
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Figure 2. Fish Size Spectra Differences between High- and Low-Complexity Habitats of the Exuma Cays Land and Sea Park Differences in nonlinearities in size spectra of predatory (1) and herbivorous (2) fish from highand low-complexity reef habitats in the Exuma Cays Land and Sea Park. Shown are size spectra and linear model fits for example sites from highand low-complexity habitats (A; top and bottom, respectively), the associated autocorrelation in residuals (B), and greater autocorrelation and nonlinearity in high-complexity sites overall (C; ANOVA, F = 13.7, df = 10, p < 0.01).
of crevice diversity was more complex, exhibiting a quadratic (convex) function indicating that productivity was low when crevice diversity was low, increased as diversity increased, but then reduced again as crevice diversity became high. Increased productivity in response to an increasing density of prey refugia and, initially an increasing diversity of refuge sizes, is not surprising. Small-bodied fish, which are highly vulnerable to predation, benefit from refugia by experiencing reduced mortality, and their abundance increases as a result. Because small-bodied fish comprise both prey species and the juveniles of larger predators, the increased survival and abundance results in greater fish productivity. Although the proportion of vulnerable prey fish declines with increasing structural complexity, the total availability of prey may increase because of the overall increase in population size [6, 8, 32]. Further, a reef with high habitat complexity may allow for not only an increased abundance of small-bodied fish inside refugia, but also an increased abundance of subordinates that are excluded from those refugia through competition [33, 34]. These fish are available to predators and also contribute to an increase in productivity. We interpret the quadratic association between productivity and crevice diversity as a tradeoff between reduced mortality rates and reduced growth rates. Initially, as crevice diversity increases, the mechanism for increased productivity follows that described above (i.e., higher fish abundance and competition). However, when crevice diversity is high, a wide range of fish body sizes are unavailable as prey. Some of the largest predators in the system then have to supplement their diet by feeding from the benthic community. If the benthic community does not provide sufficient energy to meet a large predator’s demand, its growth rate declines. In these scenarios, the negative impacts of reduced growth outweigh the benefits from avoiding predation and, as a result, there is a maximum refuge size beyond which productivity declines. Thus, the model has generated a new hypothesis that could be tested in the field; i.e., do we find evidence of increased prey
switching away from piscivory when the diversity of crevices on the reef becomes high? Modeling ecosystem functions has become a central concern of ecology, motivated in part by the need to value ecosystem services [35–37]. Yet, production functions for many ecosystems remain unknown [38]. While trophic models have been used to estimate total fish production (e.g., [39]), they do not yet attempt to predict how changes in ecosystem function caused by declining structural complexity might influence the food web and alter ecosystem services such as fishery productivity. To shed some light on this question, we contrast the fishery productivity from our model of a complex reef in the ECLSP with one that lacks structural complexity. Habitat loss reduced the productivity of predatory fish by almost half, from 285 g m23 yr21 to 159.3 g m23 yr21, and of herbivorous fish by more than two and a half times, from 45 to 16.9 g m23 yr21. Moreover, if we assume that a reef fishery ignores smaller-bodied individuals (e.g., X) wx) were plotted on double-log axes for each reef site (n = 12; four high complexity, eight low complexity). We specifically asked
Modeling The first step in the modeling process was to extend and parameterize the generic dynamical coupled size spectrum model lacking prey refugia [29] for a coral reef ecosystem, creating a base model. To do this, we added a spectrum of herbivorous fish and set parameters based on coral reef specific values where possible. The Supplemental Experimental Procedures provide detailed model descriptions and information about model parameterization. The Supplemental Information lists all model equations (Table S1) and parameter values (Table S2). The second step in the process was to add into the base model a vulnerability function (described in the main text above) that represented the effects of size-structured prey refugia on trophic dynamics. This required the inclusion of just two additional parameters: Vmin, the minimum proportion of the population vulnerable to predation, and s, the maximum refuge size. We did not have empirical data to estimate these parameters, and so we selected values for them by minimizing the residual sum of squared errors RSS (Equation 1) between the predatory fish size spectrum
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predicted by the model and that observed in high-complexity habitats of the ECLSP: Xn RSS = ðyi 2 fðxi ÞÞ2 ; Equation 1 i=1 where yi is the ith value of the observed log10 (prob(x > X)) in the Pareto distribution of predatory fish size spectra and f (xi) is the equivalent predicted value from the model. The selection of best-fit parameters was carried out using a method of grid search across a broad range of possible parameter combinations (Vmin: 0.1–0.95; s: 1–1,500). Utilizing our base model and the plausible refugia model resulting from step two, we asked the question of whether, all else being equal, the addition of the vulnerability function to describe size-structured refugia improved the model fit to size spectra data from high-complexity habitats of the ECLSP. This comparison was made by examination of the difference in both the residual sum of squared errors from each model fit (Equation 1) and the coefficient of determination, R2 (Equation 2), that describes the amount of variation in the data that is explained by the model R2 = 1 2
RSS ; TSS
Equation 2
where TSS =
Xn i=1
2
ðyi 2 yÞ ;
where y is the mean log10 (prob(x > X)) in the pooled data from sites with high structural complexity. Supplemental Information Supplemental Information includes one figure, two tables, and Supplemental Experimental Procedures and can be found with this article online at http://dx.doi.org/10.1016/j.cub.2014.03.026. Acknowledgments
D
We thank Adrian Stier for information on body masses of reef fish recruits, Alastair Harborne and Yves-Marie Bozec for insightful discussions on predator-prey interactions, and Iliana Chollett for comments on a previous version of the manuscript. This work was funded by the Natural Environment Research Council (NERC), a Pew Fellowship, and an ARC Laureate Fellowship to P.J.M. Received: November 12, 2013 Revised: January 30, 2014 Accepted: March 10, 2014 Published: April 17, 2014 References 1. Hixon, M.A., and Beets, J.P. (1993). Predation, prey refuges, and the structure of coral-reef fish assemblages. Ecol. Monogr. 63, 77–101. 2. Syms, C., and Jones, G.P. (2000). Disturbance, habitat structure, and the dynamics of a coral-reef fish community. Ecology 81, 2714–2729. 3. Macarthur, R., and Levins, R. (1967). The limiting similarity, convergence, and divergence of coexisting species. Am. Nat. 101, 377–385. 4. Hixon, M.A., and Menge, B.A. (1991). Species diversity: prey refuges modify the interactive effects of predation and competition. Theor. Popul. Biol. 39, 178–200. 5. Buchheim, J.R., and Hixon, M.A. (1992). Competition for shelter holes in the coral-reef fish Acanthemblemaria spinosa Metzelaar. J. Exp. Mar. Biol. Ecol. 164, 45–54.
Figure 4. Model Predictions for the Shape of Size Spectra and the Productivity of Reef Fish for Coral Reefs with Varying Degrees of Habitat Structural Complexity (A and B) Comparisons of predicted and observed size spectra of predatory reef fish from contrasting low- and high-complexity reef habitats. Lines
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