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The Strength of Trophic Cascades Across Ecosystems: 74, 1029–1038 Predictions from Allometry and Energetics

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The Strength of Trophic Cascades Across Ecosystems: 74, 1029–1038 Predictions from Allometry and Energetics Journal of Animal Blackwell Publishing, Ltd. Ecology 2005 The strength of trophic cascades across ecosystems: 74, 1029–1038 predictions from allometry and energetics JONATHAN B. SHURIN*† and ERIC W. SEABLOOM* *Department of Zoology and Centre for Biodiversity Research, University of British Columbia, 6270 University Blvd, Vancouver, BC V6T 1Z4, Canada; and †Department of Zoology, Oregon State University, Corvallis, OR 97331–2914, USA Summary 1. Top-down control of trophic structure is often highly variable both within and among ecosystems. We explored the roles of relative body sizes of predators and prey, their metabolic types, the production-to-biomass ratio (P : B) of plants, and system pro- ductivity in determining the strength of the indirect effects of predators on plants. 2.We used a well-studied food chain model with three trophic levels that is parameterized based on allometric relationships for rates of ingestion and metabolic efficiency. The model predicts that invertebrate and ectotherm predators and herbivores should propagate cascades to a greater degree than vertebrates and endotherms because of their higher metabolic efficiency. 3. Increasing the herbivore-to-plant body-size ratio strengthened the effects of cascades, while predator body-size was predicted to have no effect. Increasing system productivity or plant P : B magnified cascades. Because herbivore : plant body size ratios and plant P : B are both generally greater in aquatic than terrestrial systems (especially those with uni- cellular producers), the model predicts stronger cascades in water than on land. This predic- tion is supported by a recent cross-system comparison of trophic cascade experiments. 4. We discuss features of natural systems that are not incorporated into the model and their implications for the intensity of trophic cascades across ecosystems. Key-words: allometry, cross-system comparison, indirect effects, metabolic rate, popu- lation dynamic equations, production, top-down control, trophic structure. Journal of Animal Ecology (2005) 74, 1029–1038 doi: 10.1111/j.1365-2656.2005.00999.x magnitudes of their effects are often quite variable both Introduction within and among systems (Wootton et al. 1996; The importance of trophic cascades in regulating the Leibold et al. 1997; Persson 1999; Polis 1999; Shurin abundance of organisms has long been a controversial et al. 2002). Several hypotheses have been proposed to topic in ecology (Hairston et al. 1960; Murdoch 1966; explain variability in the strength of cascades based on McQueen et al. 1986; Polis 1991; Power 1992; Strong factors such as life history, organism size and edibility, 1992; Carpenter & Kitchell 1993; Polis & Strong 1996; productivity, adaptive behaviour, nutrient recycling and Holt 2000). Evidence for cascades has been found in non-equilibrium dynamics (Leibold 1989; DeAngelis systems as disparate as grasslands, lakes, streams, kelp 1992; Abrams 1993; Chase 1996, 1998, 1999; Polis 1999; beds, forests and marine pelagia (Power 1990; McClaren Peacor & Werner 2001). However, the processes that & Peterson 1994; Brett & Goldman 1996, 1997; Estes regulate the expression of trophic cascades in natural et al. 1998; Micheli 1999; Pace et al. 1999; Post et al. systems, and their variability among systems, remain 1999; Schmitz et al. 2000; Halaj & Wise 2001). Although largely unknown. trophic cascades may be prevalent in nature, the Four features of food webs that may be important for determining the strength of cascades are (1) the relative body sizes of consumers and their resources, (2) the Correspondence: Jonathan B. Shurin, Department of Zool- metabolic types of organisms (e.g. ectotherms vs. endo- ogy and Centre for Biodiversity Research, University of Brit- therms), (3) the turnover time (the biomass-to-production © 2005 British ish Columbia, 6270 University Blvd, Vancouver, BC V6T ratio) of the species and (4) system productivity. For Ecological Society 1Z4, Canada. E-mail: [email protected] instance, in the pelagic zones of lakes, body-size ratios 1030 between planktivorous fish and zooplankton are generally of plants and herbivores) influence the strength of J. B. Shurin & on the order of 106, while the ratio between zoop- top-down control. E. W. Seabloom lankton and phytoplankton is around 105 (Cohen et al. Our modelling approach is clearly a great simplifica- 2003). Ungulate herbivores in grasslands are generally tion of natural food webs. We ignore many important of similar size to their predators, and around 104 larger aspects of real communities, such as omnivory, inter- than the plants they consume. The majority of predator : specific heterogeneity in edibility within trophic levels, prey body-size ratios fall within the range of 101−103 nutrient fluxes and recycling, population structure and (Cohen et al. 1993). Relative plant and herbivore body adaptive behaviour (Polis 1991; Strong 1992; Abrams sizes are also a major feature distinguishing terrestrial 1993; Polis & Strong 1996; Leibold et al. 1997). Although and aquatic (especially planktonic) food webs (Hairston these factors clearly influence the expression of cascades, & Hairston 1993). Many aquatic systems are dominated it is not obvious that they differ systematically among by unicellular producers (phytoplankton and periphy- habitats (e.g. aquatic vs. terrestrial; Chase 2000). The ton) that are much smaller than their grazers, whereas model we use can be considered the most simplified herbivores on land range from much larger (e.g. ungulates) representation of food chains that captures many to much smaller (e.g. arthropods) than the plants factors known to vary among ecosystems. The model they consume. Differences in relative body size may be therefore provides a more appropriate basis for cross- important for regulating the intensity of trophic cascades system comparisons of the intensity of cascades than a because body size is related closely to metabolic, growth null-model that there will be no differences. Deviations and demographic rates (Peters 1983). In addition, physio- between the model predictions and empirical data may logical rates such as feeding and respiration are related point to other critical features that distinguish different to an organism’s metabolic type, with endotherms, system types. vertebrate ectotherms and invertebrates showing distinct scaling relations (Peters 1983; Yodzis & Innes Models 1992). The production-to-biomass ratio (P : B) of plants is also related to the fraction of primary produc- - tion consumed by herbivores, and is greatest in aquatic systems and lowest with woody plants (Cyr & Pace The model of a three-species food chain presented by 1993; Nielsen et al. 1996; Cebrian 1999). Finally, pro- McCann & Yodzis (1994) was based on Yodzis & Innes’s ductivity may play a role in determining the number (1992) model of predators and prey. It can be written as of trophic levels and the strength of top-down con- follows: trol (Oksanen et al. 1981; McQueen et al. 1986; Power 1992; Sarnelle 1992; Wootton & Power 1993; Chase dR R HR 3 =−R 1 333− xy et al. 2000). 3 HH −+δ dt K fRRHH()()1 3 o Here we use a well-studied approach to modelling food chain dynamics to examine the influence of relative dH R PH 3 = xH y 3 −1 − xy 33 HH3 + PP −+δ body sizes, metabolic types, plant P : B and system pro- dt RR3 o fHHPP()()1 3 o ductivity on the strength of trophic cascades. Yodzis & Innes (1992) developed a model of parameterized dP H 3 = xP y 3 −1 eqn 1 PP3 + consumer-resource dynamic equations using empirical dt HH3 o relations among body size, metabolic type and rates of ingestion, metabolism and biomass production (see where R3, H3 and P3 are the biomass densities of the also McCann & Yodzis 1994; Huxel & McCann 1998; resources (plants), herbivores and predators, respec- McCann et al. 1998; Post et al. 2000). The form of tively, in the three trophic level system, and K is the the model is the same as Rosenzweig & MacArthur’s carrying capacity of the plant trophic level. The con- (1963) equations; however, the parameter values are version efficiencies of the predator and herbivore are constrained based on empirical relations between described by δ, the fraction of ingested energy lost to metabolic rates and body size. The model is therefore egestion and excretion, and f, the proportion of prey biologically plausible; however, it retains the generality biomass consumed. The form of the model is somewhat that comes from having relatively few parameters. In unusual in that these terms appear in the denominator addition, it can be used to make predictions about the of the loss term for the prey, rather than the growth behaviour of systems with different types of organisms term for the consumer; however, the same model could because it converts all fluxes into units of biomass easily be written in the more traditional way without rather than population density. We use Yodzis & Innes’ changing any of its properties. The parameter xi is the model to ask how predator impacts on the abundance mass specific metabolic rate of species i measured of their prey, and their indirect effects on the prey’s relative to the production-to-biomass ratio of the © 2005 British resources, vary with plant P : B and the body sizes and plant (for full derivation, see Yodzis & Innes 1992). Ecological Society, Journal of Animal metabolic types of organisms. Our goal is to ask how Note that the metabolic rate determines rate at which Ecology, 74, two features that distinguish aquatic and terrestrial
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