Emergent Effects of Multiple Predators on Prey Survival: the Importance of Depletion and the Functional Response
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Ecology Letters, (2012) 15: 1449–1456 doi: 10.1111/ele.12005 LETTER Emergent effects of multiple predators on prey survival: the importance of depletion and the functional response Abstract Michael W. McCoy,1,2* Adrian C. The combined effects of multiple predators often cannot be predicted from their independent effects. Stier2 and Craig W. Osenberg2 Emergent multiple predator effects (MPEs) include risk enhancement, where combined predators kill 1 more prey than predicted by their individual effects, and risk reduction, where fewer prey are killed than Department of Biology, East predicted. Current methods for detecting MPEs are biased because they assume linear functional Carolina University Greenville, NC, responses and/or no prey depletion. As a result, past studies overestimated the occurrence of risk 27858, USA enhancement for additive designs, and tended to overestimate the occurrence of risk reduction for sub- 2Department of Biology, University stitutive designs. Characterising the predators’ functional responses and accounting for prey depletion of Florida Gainesville, FL, 32611- 8525, USA reduces biases in detection, estimation, interpretation and generalisation of the emergent effects of preda- tor diversity on prey survival. These findings have implications beyond MPE’s and should be considered *Correspondence: E-mail: in all studies aimed at understanding how multiple factors combine when demographic rates are density [email protected] dependent. Keywords Additivity, density dependence, handling time, MPE, predation, Roger’s random predator model. Ecology Letters (2012) 15: 1449–1456 in the presence of combinations of predators to expected survival pre- INTRODUCTION dicted from the independent effects of each predator species in Traditionally, ecological systems have been studied as subsets of monoculture (Soluk & Collins 1988; Billick & Case 1994; Sih et al. pairwise interactions, with the hope that these can then be assem- 1998; Griffen 2006). Early studies of MPEs misinterpreted results by bled to predict the spatial and temporal patterns of intact communi- using incorrect models to calculate expected effects (see critiques by ties (e.g. Oksanen et al. 1981; Wootton 1994). If pairwise Billick & Case 1994; Wootton 1994), or by ignoring prey losses in the interactions are independent of other members of the community, absence of predators (see clarifications by Sih et al. 1998; Vonesh & then community dynamics can be assembled piecemeal. However, if Osenberg 2003). Indeed, considerable debate in the literature focused interaction strengths are not independent of other players in the on understanding how statistical models used to make predictions system, then observed community dynamics will depart from simple about the expected effects of multiple predators are linked to the predictions based on pairwise interactions (Wootton 1994; Bolker underlying biological models assumed to drive prey survival (Soluk & et al. 2003; Werner & Peacor 2003). Such departures can reveal the Collins 1988; Billick & Case 1994; Sih et al. 1998; Vonesh & Osenberg action of complex and potentially novel forms of species interac- 2003; Griffen 2006). A consensus approach emerged (Vonesh & tions, which have been referred to as higher order interactions, trait Osenberg 2003; Vance-Chalcraft & Soluk 2005; Griffen 2006). Specif- mediated indirect interactions or non-consumptive predator effects ically, if two predators have independent effects, then expected pro- (Wootton 1994; Bolker et al. 2003; Werner & Peacor 2003). As portion of prey surviving (hereafter prey survival) in the presence of ^ predator–prey interactions comprise the foundation of food web both predators, S1;2 can be calculated based on prey survival in the dynamics, many studies have focused on examining possible interac- presence of each predator species in monoculture, S1 and S2, corrected tions among multiple predator species and a shared prey (Polis & for background mortality (i.e. survival in no predator control treat- Holt 1992; Sih et al. 1998; Ives et al. 2005; Vance-Chalcraft & Soluk ment Sctl) (also see Table 1): 2005; Griffen 2006; Schmitz 2009). In general, these studies show Á ^ ¼ S1 S2 ð Þ that the effects of multiple predators are often not independent, S1;2 1 Sctl suggesting that a better understanding of these higher order interac- tions is needed to fully appreciate food web dynamics. Equation 1 is a corrected version of the ‘Multiplicative Risk Model’ Interactions between predators (e.g. cooperation, competition or of Soluk & Collins (1988) based on an additive design (i.e. where intraguild predation), as well as anti-predator responses by prey, can the combined effects of predator species 1 and 2, at densities C1 lead to emergent ‘multiple predator effects’ (MPEs), where prey con- and C2, are predicted based on their isolated effects, also evaluated sumption rates by multiple predators foraging in concert cannot be at C1 and C2) (Vonesh & Osenberg 2003). An analogous null model predicted by knowing the independent effects of each predator on for a substitutive design (where total predator density is the same in prey survival (e.g. Polis & Holt 1992; Sih et al. 1998; Ives et al. 2005; both the monoculture and mixed species treatments) yields: Vance-Chalcraft & Soluk 2005; Griffen 2006; Schmitz 2009). Multiple S 0:5S 0:5 ^ ; ¼ 1 2 ð Þ predator species can combine: (1) independently, (2) synergistically S1 2 2 2 S ctl (leading to prey risk enhancement: Soluk & Collins 1988; Losey & Denno 1998; Sih et al. 1998) or (3) antagonistically (e.g. leading to Despite general consensus among ecologists on these calculations prey risk reduction: Sih et al. 1998; Vance-Chalcraft & Soluk 2005). of expected survival in combined predator treatments, the Studies of MPEs typically compare observed patterns of prey survival derivation (Table 1) and underlying assumptions of eqns 1 and 2 © 2012 Blackwell Publishing Ltd/CNRS 1450 M. W. McCoy, A. C. Stier and C. W. Osenberg Letter Table 1 Application of the Multiplicative Risk Model for additive and substitutive designs for predicting effects of two predators (1 and 2) from their effects quantified in isolation. These expressions assume both predators have a Type I functional response (so that mortality rates are constant and independent of prey number or density, N ). P is proportion of prey surviving from specific mortality sources, l is the per capita prey mortality rate from those sources, S is the proportion of prey surviving in a specific treatment and (Sˆ ) is predicted survival from the Multiplicative Risk Model for additive and substitutive experimental designs. Subscripts 1, 2 indicate predator identity (1 or 2) ctl indicates the control treatment (i.e. no predator) Absolute number surviving Proportion survival À ¼ uctl ¼ = Control Nctl Nctl N0C N0Pctl Sctl Pctl À À ¼ uctl u1 ¼ = Predator (1) N1 N1 N0C N0Pctl P1 S1 PctlP1 À À ¼ uctl u2 ¼ = Predator (2) N2 N2 N0C N0Pctl P2 S2 PctlP2 À À À ^ S S Additive (1 + 2) N N ; ¼ N C uctl u1 u2 ¼ N P P P S ; ¼ P P P ¼ 1 2 1,2 1 2 0 0 ctl 1 2 1 2 ctl 1 2 Sctl À : : À Àu2 u1 : : : : S 0 5S 0 5 + ¼ uctl ¼ 0 5 0 5 ^ ; ¼ 0 5 0 5 ¼ 1 2 Substitutive [(1 2)/2] N1,2 N1;2 N0C 2 N0Pctl P P S1 2 Pctl P P 1 2 2 1 2 Sctl (hereafter referred to as the Multiplicative Risk Model) are still not aNC F ¼ ð3Þ well appreciated. Most notably, the Multiplicative Risk Model is 1 þ ahN often assumed to account for prey depletion (Sih et al. 1998; Grif- fen 2006), ostensibly because it adjusts survival probabilities so that where F is the instantaneous feeding rate of one predator, C is they are conditional (i.e. prey cannot be eaten twice). However, the predator density, N is prey density, a is attack rate and h is handling Multiplicative Risk Model assumes that prey per capita mortality time (Holling 1959). Type II functional responses are thought to rates imposed by predators are constant over the course of the characterise the feeding rate of many types of predators (Jescheke experiment, which is only valid when predators have linear (i.e. et al. 2004). We also assumed that mortality of prey in the absence Type I) functional responses, when prey are continuously replen- of predators was negligible: that is, survival in the control treatment ished, or experimental durations are sufficiently short that depletion was 100% (Sctl = 1). As a result, prey survival, S, in the presence of is inconsequential (Collins et al. 1981; Juliano & Williams 1985; Juli- a predator assemblage with n predator species (with predator species ano et al. 2001). These assumptions are violated in most empirical i at density Ci), can be found by integrating the aggregate feeding studies, because most predators have nonlinear functional responses rates over the duration of the study (from time 0 to T ), as prey (Hassell et al. 1976, 1977; Jescheke et al. 2004) and because most density (Nt) declines: predation studies run sufficiently long that prey density declines R P appreciably from the start to end of trials. For example, we exam- T n ai Nt Ci ¼ þ dt ined 100 multiple predator studies reviewed by Vance-Chalcraft S ¼ 1 À 0 i 1 1 ai hi Nt ð4Þ et al. (2007) and found that on average prey were depleted by 70% N0 over the course of these experiments. Therefore, the assumption of We simulated foraging trials by solving eqn 4 numerically. First, constant instantaneous per capita feeding rates (i.e. temporally we did this for two predator species in monoculture, which yielded invariant mortality rates of prey) is probably severely violated in S1 and S2. Second, we generated the survival of prey in the presence studies of MPEs, and this could affect how we interpret and gener- of both predator species under the assumption of independence (i.e. alise the results of multiple predator studies. the true value of S1,2) using eqn 4 and the same parameters used to To our knowledge, no studies have examined explicitly how prey generate the monoculture results.