MARINE ECOLOGY PROGRESS SERIES Vol. 328: 285–293, 2006 Published December 20 Mar Ecol Prog Ser NOTE Prey size refugia and trophic cascades in marine reserves Marissa L. Baskett* Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544, USA Present address: National Center for Ecological Analysis and Synthesis, 735 State St., Suite 320, Santa Barbara, California 93101, USA ABSTRACT: After the establishment of marine reserves, trophic cascades, with an increase in top predators, decrease in herbivores and increase in producers, are often expected but not consistently observed. Recent empirical results suggest that the lack of cascades in a Caribbean coral reef reserve may be due to larger herbivores escaping predation. To explore the potential for such prey size refu- gia to prevent trophic cascades after reserve establishment, I construct a simple trophic model with and without herbivore size refugia and determine the conditions necessary for herbivorous fish to decrease after the elimination of harvest mortality. Generally, cascades do not occur and herbivores increase if the effect of harvest on herbivores before reserve establishment is greater than the effect of predation after reserve establishment. The parameter space where herbivores increase is much greater when accounting for size refugia. The potential for prey size refugia to prevent cascades makes it an important dynamic to consider in community-level approaches to reserve design and monitoring. KEY WORDS: Marine reserves · Trophic cascades · Size refugia · Predation · Model Resale or republication not permitted without written consent of the publisher INTRODUCTION recurring trophic cascades (Halpern 2003). This has many possible explanations, such as cascades being Trophic cascades occur frequently in coastal, hard- restricted to a subset of a given marine community, substratum marine ecosystems (Pinnegar et al. 2000). variable recruitment, the influence of pathogens and Cascading effects often result from fisheries, as these food web complexity (Polis & Strong 1996, Pinnegar tend to target top predators (Pauly et al. 1998), whose et al. 2000, Halpern 2003). In a study of a Caribbean subsequent decline can lead to an increase in herbi- coral reef marine reserve, where larger herbivores vores and decrease in producers. Therefore, as marine increased along with piscivores after reserve esta- reserves, or no-take zones, are established to protect blishment, Mumby et al. (2006) suggest that the reason biodiversity and ecosystem structure (Allison et al. for the lack of trophic cascades is the existence of 1998), there is an expectation that predators will in- prey size refugia, i.e. larger herbivores escape pre- crease after reserve establishment, leading to cascades dation from piscivorous fish. In theoretical support of with herbivores decreasing and producers increasing. the potential for size refugia to prevent cascades, Accordingly, large-scale simulations of marine com- one model indicates that prey size refugia reduce munities predict that trophic cascades are likely to the effects of top-down predator control in high- occur in marine reserves (Walters 2000). productivity environments (Chase 1999). However, a meta-analysis of empirical studies of Trophic cascades after reserve establishment may marine reserves failed to find evidence for consistently not be a desirable outcome in the case of marine *Email: [email protected] © Inter-Research 2006 · www.int-res.com 286 Mar Ecol Prog Ser 328: 285–293, 2006 ecosystems such as Caribbean coral reefs, where a μ decrease in herbivores could increase the potential Mortality P h for algal overgrowth of corals after disturbances such P as hurricanes (Mumby 2006). Therefore, predicting Piscivores whether trophic cascades will occur is important to P deciding whether marine reserves are an appropriate β management strategy, as well as determining appro- P Reproduction priate expectations for reserve monitoring. To assess μ μ Mortality H δ H Mortality the extent to which prey size refugia may prevent hH P Predation hH trophic cascades after reserve establishment, I explore Small Growth Large a simple resource-based trophic model with and with- herbivores γ herbivores out prey size refugia. β HS H HL Reproduction β METHODS H δ Predation δ The model below takes the most basic form possible H H for generality and analytical tractability; this approach Input Resource Flow out allows determination of the potential importance of D RIN R D incorporating size refugia in more detailed studies across marine ecosystems. In the model, the resource R Fig. 1. Outline of the size refugia model (Eqs. 1 to 4) (e.g. algae) has input RIN and flow rate D, analogous to classic chemostat models. Herbivores consume the resource at rate δH, which is converted into reproduc- reserve establishment on expected population sizes. tion with efficiency βH. Herbivores are divided into 2 Specifically, whether the expected herbivore popula- size classes, HS and HL, where piscivores prey on her- tion decreases with the elimination of harvest mortality bivores in the smaller size class HS at rate δP and herbi- indicates whether trophic cascades occur after reserve vores grow into the larger size class HL at rate γ. establishment. The ’expected’ population size is the Regardless of size, herbivores experience natural mor- locally stable equilibrium population size, given a set tality at rate μh and—before reserve establishment— of parameters, as determined by the Routh-Hurwitz constant effort harvest mortality at rate hH. Piscivores P criteria for the Jacobian matrix analyzed at the equilib- convert predation on herbivores into reproduction with rium; see Appendix 1 for local stability analysis. efficiency βP, experience natural mortality at rate μP, and experience harvest mortality at rate hP before reserve establishment. Given these parameters, the RESULTS dynamics are (Fig. 1): Basic model dR −−δ + = DR()()IN R H H S H L R (1) dt As shown in Appendix 1, possible equilibria are with dH S βδ+−+++ γ μ δ = HH()(HHR S L H h H P PH ) S (2) (1) the resource present and no herbivores or pisci- dt vores, (2) herbivores and the resource present and no dH L (3) piscivores, and (3) piscivores, herbivores and the = γμHhHSHHL−+() dt resource all present (Fig. 2). Only 1 equilibrium is dP βδ−+ μ = [()]PPHhP S P P (4) locally stable for a given set of parameters. I assume dt that the reproduction, growth, predation and natural The equivalent model without prey size refugia can mortality parameters have values such that the equi- be found by letting the herbivore growth rate into the librium with all 3 types of species present is the locally larger size class γ = 0. I take this approach—with stable equilibrium when there is no harvesting. In Type I (linear) functional response for the predation other words, the herbivore population size in the equi- dynamics, closed herbivore and predator dynamics, librium with the resource, herbivores and piscivores and resource-independent growth—for mathematical all present and with hH = hP = 0 is the expected herbi- simplicity. More biologically realistic versions of this vore population size after reserve establishment. The model warrant future study. locally stable equilibrium with hH, hP > 0, and therefore The effect of eliminating harvest mortality (hH, hP → 0) the expected herbivore density before reserve estab- on the equilibrium values approximates the effect of lishment, depends on the harvest mortality values. Baskett: Size refugia and cascades 287 Producers Fig. 2. Possible equilibria for the size refugia model as a function of the rate herbi- vores grow from the small to large size class (growth rate Small γ). Dotted lines: equilibrium herbivores with the resource but no her- bivores or piscivores; dashed lines: equilibrium with the re- source and herbivores but no piscivores; solid lines: equi- librium with all 3 types of Large species. Only one equilibrium herbivores is locally stable for a given set of parameter values. Note that the equilibrium with all 3 types does not exist at high growth rates because the her- bivores spend too little time in the smaller (available) size class to support the piscivores Piscivores 0 Growth rate Below are the criteria for local stability of each equilib- Second, when hH < h*H,dep, the opposite of the stabil- rium as well as the relevant criteria for herbivore ity criterion for the equilibrium without herbivores or increase (no trophic cascades), with and without size piscivores, and hP > h*P,dep,SR, where: refugia, given the expected herbivore population size bbPH[(−+μ H h H )] after reserve establishment. h*P,dep,SR = − μP (8) μγ++h To simplify the presentation of the model analysis, HH let bH be the maximum herbivore birth rate: the equilibrium with the resource and herbivores but without piscivores exists biologically and is locally sta- b = β δ R (5) H H H IN ble. The above value can be interpreted as the pisci- and bP be the modified piscivore birth rate: vore harvest mortality being greater than the piscivore birth rate, given the herbivore population growth rate b = β δ D͞δ (6) P P P H and growth into the unavailable size class, minus their First, when hH > h*H,dep, where: natural mortality, or the piscivores are being fished to depletion. Note that this criterion depends on the her- h* = b – μ (7) H,dep H H bivore harvest rate as well as the piscivore harvest rate the equilibrium without herbivores or piscivores is the because of the potential to harvest herbivores at a rate locally stable equilibrium before reserve establish- such that they can persist but with a population too ment. The above value can be interpreted as the herbi- small to support piscivores, i.e. ecological overfishing. vore harvest mortality being greater than the herbi- When these criteria hold, herbivores will increase after vore population growth rate (births minus deaths) or reserve establishment (i.e. the herbivore density in the that the herbivores are being fished to depletion.