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Roles of Alternative Prey for Mesopredators on Trophic Cascades in Intraguild Predation Systems: A Theoretical Perspective. Author(s): Shota Nishijima, Gaku Takimoto, and Tadashi Miyashita Source: The American Naturalist, Vol. 183, No. 5 (May 2014), pp. 625-637 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/10.1086/675691 . Accessed: 08/05/2014 12:02 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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vol. 183, no. 5

the american naturalist

may 2014

Roles of Alternative Prey for Mesopredators on Trophic Cascades in Intraguild Predation Systems: A Theoretical Perspective Shota Nishijima,1,* Gaku Takimoto,2 and Tadashi Miyashita1 1. Laboratory of Biodiversity Science, School of Agricultural and Life Sciences, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo 113-8657, Japan; 2. Department of Biology, Faculty of Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan Submitted June 10, 2013; Accepted December 27, 2013; Electronically published March 31, 2014 Online enhancements: appendixes, zip file.

abstract: Declines of apex predators can cause dramatic increases of smaller predators and ensuing collapses of their prey. However, recent empirical evidence finds that the disappearance of apex predators does not reduce but can increase prey populations. This poses a great challenge in managing species interactions involving mesopredator release. Here we analyze a mathematical model to explain variable consequences of apex predator loss and to develop management guidelines for prey conservation. The model formulates an intraguild predation system (apex predators, mesopredators, and their shared prey) with mesopredators supplied with additional alternative prey. We show that apex predator loss causes only negative effects on shared prey without alternative prey but has either negative or positive effects with alternative prey. Moreover, when alternative prey is highly abundant, apex predator loss causes strong mesopredator release and reduces shared prey greatly. Finally, the model suggests that a viable management strategy to restore shared prey under much uncertainty about a target system is to allocate a limited control effort not only to both predators but also to alternative prey. Alternative prey for mesopredators may be a crucial ingredient that controls the cascading dynamics of intraguild predation systems and should be considered as an important management target. Keywords: apparent competition, exploitative competition, invasive alien species, log-response ratio, management strategy, resource subsidy.

Introduction Concern is growing over unexpected outbreaks of mesopredators and the ensuing collapses of their prey (Prange and Gehrt 2004; Prugh et al. 2009; Ritchie and Johnson 2009; Brashares et al. 2010). Mesopredators are medium-sized predators preyed on by larger-sized intraguild predators (apex predators). The rise of mesopred* Corresponding author; e-mail: [email protected]. Am. Nat. 2014. Vol. 183, pp. 625–637. 䉷 2014 by The University of Chicago. 0003-0147/2014/18305-54729$15.00. All rights reserved. DOI: 10.1086/675691

ators can be initiated by the decline or extinction of apex predators that suppress mesopredators through intraguild predation or resource competition (Litvaitis 1996; Courchamp et al. 1999; Prugh et al. 2009; Brashares et al. 2010). This phenomenon is called “mesopredator release” (Soule et al. 1988). Human activities are a major cause of the decline of apex predators and the subsequent release of mesopredators. For instance, habitat destruction has decimated mammalian carnivores (e.g., coyotes), resulting in increase of mesopredators (cats), which jeopardize their prey (birds; Crooks and Soule 1999). Moreover, the eradication of introduced apex predators (e.g., cats or largemouth bass) can lead to undesirable outcomes, because it releases invasive mesopredators (rats or crayfish), which causes more damage to the native prey species (Courchamp et al. 1999; Maezono and Miyashita 2004; Rayner et al. 2007). However, apex predator loss does not always cause prey collapse through mesopredator release; it can have a positive effect on prey species, even in the presence of mesopredators (Wright et al. 1994; Rodrı´guez et al. 2006; Lloyd 2007; Rayner et al. 2007; Hughes et al. 2008; Bonnaud et al. 2010; Watari et al. 2011). For example, on Port-Cros Island, eradicating feral cats (apex predator) enhanced the abundance of small yelkouan shearwater (Puffinus yelkouan; shared prey) despite increased predation pressure on the shearwater from introduced rats (mesopredator; Bonnaud et al. 2010). Positive or negative response of prey populations to apex predator loss may reflect the dynamics inherent in intraguild predation systems in which intraguild predators (apex predators) can have direct negative effects on both intraguild prey (mesopredators) and their shared prey while potentially having an indirect positive effect on the shared prey (Prugh et al. 2009). These dual effects of intraguild predator on shared prey, however, have not been fully integrated in

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626 The American Naturalist the theory of trophic cascades through apex predator loss and mesopredator release. Previous models could explain only negative (Courchamp et al. 1999; Fan et al. 2005) or positive (Russell et al. 2009) effects of apex predator loss on prey populations. An integrative theoretical framework that can explain both negative and positive effects of apex predator loss on shared prey is necessary for appropriately managing intraguild predation systems including apex predators, mesopredators, and shared prey. To resolve the variable consequences of apex predator loss, we should take into account the omnivorous nature of mesopredators. Mesopredators tend to have a wide dietary breadth (Brashares et al. 2010) and can feed on alternative prey that is not utilized by apex predators (fig. 1). In island ecosystems, for example, invasive rats (i.e., mesopredator) not only prey on animals such as birds (shared prey) but also eat plant materials (alternative prey; Rayner et al. 2007; Caut et al. 2008; Russell et al. 2009; Norbury et al. 2013). Midsized mammals (mesopredator), such as foxes, cats, and raccoons, prey on both forestbreeding birds (shared prey) and anthropogenic resources (alternative prey) (Litvaitis 1996; Prange and Gehrt 2004; Bino et al. 2010; Rodewald et al. 2011; Fischer et al. 2012). In freshwater ponds, invasive crayfish, a mesopredator reducing the abundance of benthic invertebrates (shared prey), are sustained by allochthonous litter inputs (alternative prey; Kobayashi et al. 2011). The presence of alternative prey for mesopredators affects the dynamics of intraguild predation systems and the impact of mesopredators on shared prey. Without alternative prey, the standard theory of intraguild predation predicts that for coexistence, mesopredators must be superior to apex predators at suppressing shared prey, and intraguild predation on mesopredators by apex predators will increase the abundance of shared prey (Holt and Polis 1997). However, recent theory suggests that alternative prey helps the persistence of competitively inferior mesopredators that would otherwise be excluded by apex predators (Briggs and Borer 2005; Daugherty et al. 2007; Holt and Huxel 2007). In such a case, suppression of shared prey by apex predators is stronger than that by mesopredators, and apex predator loss would benefit the shared prey. Thus, we expect that by promoting the coexistence of weak mesopredators with stronger apex predators, alternative prey generates conditions in which apex predator loss has a positive effect on shared prey in the coexistence state. On the other hand, increasing the availability of alternative prey is predicted to augment the impact of intraguild prey on shared prey through apparent competition (Briggs and Borer 2005). Thus, we also anticipate that apex predator loss substantially decreases the

Figure 1: Modeled interactions between the apex predator, the mesopredator, the shared prey, and alternative prey.

abundance of shared prey when alternative prey is highly abundant. Using a mathematical model including alternative prey as a dynamic variable, we address the following two main points. First, we consider how (a) the ability of the mesopredator to suppress the shared prey, (b) the ability of the apex predator to suppress the shared prey, and (c) the availability of alternative prey change the cascading effect of apex predator loss in intraguild predation systems. Existing models have not simultaneously explored the effects of these components on the consequences of apex predator loss (Courchamp et al. 1999; Fan et al. 2005; Russell et al. 2009). Second, we look for effective management strategies for conserving shared prey populations by examining how a given control effort should be allocated to apex predator, mesopredator, and alternative prey. Earlier works did not incorporate the trade-off between allocated efforts toward multiple control targets nor considered the reduction of alternative prey for mesopredators as a management method (Courchamp et al. 1999; Fan et al. 2005). It is important to know the effectiveness of reducing alternative prey because mesopredators are often resilient to eradication programs (Prugh et al. 2009) and decreasing the availability of alternative prey can be effective for reducing overabundant predators (Kennedy et al. 2005; Didham et al. 2007; Bino et al. 2010).

Model Our model describes the dynamics of the densities of shared prey (S), alternative prey (A), mesopredator (M),

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Trophic Cascades in Intraguild Predation 627 and apex predator (P; fig. 1). Although previous models of intraguild predation have commonly used the terms “intraguild prey” and “intraguild predator” (e.g., Holt and Polis 1997; Holt and Huxel 2007; Takimoto et al. 2007), we instead adopt “mesopredator” and “apex predator” because these terms are more familiar in studies of mesopredator release (e.g., Prugh et al. 2009; Ritchie and Johnson 2009). The mesopredator consumes the shared and alternative prey, whereas the apex predator consumes the shared prey and the mesopredator. We assume that the shared prey population shows logistic growth with the intrinsic growth rate (r) and the carrying capacity (K) in the absence of predation. On the other hand, we assume that the alternative prey is supplied at a constant rate (I) and is removed or becomes inaccessible to the mesopredator at a density-independent loss rate (e). This is because empirical examples of alternative prey for mesopredators include anthropogenic garbage for midsized mammals (Litvaitis 1996; Prange and Gehrt 2004; Fischer et al. 2012), wildlife carcasses for coyotes (Berger et al. 2008), plant materials (e.g., fruits, seeds, and leaves) for rats (Rayner et al. 2007; Caut et al. 2008; Russell et al. 2009; Norbury et al. 2013), and terrestrial leaf litter for freshwater crayfish (Kobayashi et al. 2011). These examples suggest that consumption by mesopredators is not likely to have strong influence on the supply rate of alternative prey and thus that the supply rate of alternative prey can be adequately modeled as donor controlled. The model equations are

( )

dS S p rS 1 ⫺ ⫺ d M fSM(S)M ⫺ d P fSP(S)P, dt K

(1a)

dA p I ⫺ eA ⫺ (1 ⫺ d M)fAM(A)M, dt

(1b)

dP p [d PbSP fSP(S) ⫹ (1 ⫺ d P)b MP f MP(M) ⫺ m P]P. dt

(1c) (1d)

The functional response of predator Y to a particular prey X, fXY (X) (XY p SM, SP, AM, MP), is assumed to be Holling type II: fXY(X) p

a XYX , 1 ⫹ a XYh XYX

dM p dP p

bSM fSM(S) , bSM fSM(S) ⫹ bAM fAM(A)

(3)

bSP fSP(S) , bSP fSP(S) ⫹ b MP f MP(M)

where bXY fXY (X) represents the amount of energy that an individual of predator Y can gain when it allocates all effort to prey X. An analogous approach has been applied to a model of suboptimal foragers in coarse-grained environments (van Baalen et al. 2001). The mesopredator spends more effort feeding on the shared prey if the potential energy gain from the shared prey is greater than that from the alternative prey, and vice versa. If the potential energy gain from the shared prey is the same as that from the alternative prey, the mesopredator allocates equal effort to the shared prey and the alternative prey. The apex predator adopts analogous diet choice when feeding on the shared prey and the mesopredator. This diet choice function multiplied by a Holling type II functional response produces a switching (as in Holling type III) functional response (van Baalen et al. 2001). Mortality rates of the mesopredator and the apex predator are mM and mP, respectively. Analysis Evaluating the Consequences of Apex Predator Loss

dM p [d MbSM fSM(S) ⫹ (1 ⫺ d M)bAM fAM(A) ⫺ m M] dt # M ⫺ (1 ⫺ d P)f MP(M)P,

and the conversion efficiency of consumed prey X into predator Y is bXY. To be realistic, we assume that the mesopredator and the apex predator change the allocation of their effort to each prey depending on the relative potential amount of energy obtained from each prey:

(2)

where aXY is the attack rate and hXY is the handling time. Predator Y devotes its effort (or time) to the shared prey instead of the alternative prey (if Y p M) or the mesopredator (if Y p P) with a proportion dY (Y p M, P),

We first examine the effect of apex predator loss on the shared prey density in the model without the alternative prey (i.e., A p 0). The effect of apex predator loss is examined in the case where the three species (apex predator, mesopredator, and shared prey) coexist, and also in the cases where either (or neither) predators can coexist with the shared prey. This is because, even in such cases, introduction of the alternative prey could allow these predators to persist and alter the consequences of apex predator loss. We analyze the system at locally stable equilibria, and assume that equilibrium densities of the model correspond to long-term average densities of real systems. The model without the alternative prey is studied analytically. We then analyze the model with the alternative prey to investigate how the alternative prey affects the consequences of apex predator loss. Because equilibrium densities of this model cannot be obtained analytically, we numerically integrate the model equations for a longenough time to reach a steady state (2,000 time steps for

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628 The American Naturalist our parameter setting) and then calculate the average densities in the latter half of simulation runs in order to remove initial transient dynamics. In “Results,” we present results under a default set of parameter values. These default parameter values are chosen so that the model has locally stable equilibria. To examine how different parameter values affect the results, we conducted an intensive parameter-sensitivity analysis. We generated 10,000 sets of randomly chosen parameter values around the default setting to run the model equations and confirmed that our general conclusions were broadly applicable to wide parameter ranges (app. A; apps. A–D available online). To evaluate strength of the effect of apex predator loss on the shared prey density, we use a log-response ratio: E⫺P p ln

S⫺P

( ) S⫹P

,

(4)

where S⫹P and S⫺P are the average densities of the shared prey in the presence and absence of the apex predator. Previous empirical and theoretical studies have adopted this measure in order to characterize the strength of trophic cascades (Shurin et al. 2002; Shurin and Seabloom 2005; Hall et al. 2007; Leroux and Loreau 2008) and to determine whether and how the removal (or addition) of an apex predator decreases or increases the shared prey in intraguild predation systems (Vance-Chalcraft et al. 2007). In our model, E⫺P ! 0 indicates that apex predator loss reduces the shared prey density, while E⫺P 1 0 indicates that the apex predator loss increases the shared prey density. If apex predator loss does not change the shared prey density, E⫺P p 0. Management Strategy We analyze whether and how human controls on the apex predator, the mesopredator, and the alternative prey are useful to restore the shared prey population. To incorporate human controls in the model (1), we redefine parameters of the predator mortality rates and the alternative prey supply rate: m P p m P0(1 ⫹ r P D)v P, m M p m M0(1 ⫹ r MD)v M, and I p I 0 /(1 ⫹ rAD)vA. The apex predator and the mesopredator experience natural death at rates of mP0 and mM0, respectively, and I0 is the default supply rate of the alternative prey. The control effort allocated to a particular target X (X p P, M, A) is expressed as the product of the total control effort D and the allocation rate rX (i.e., rXD; X p P, M, A). Because rP ⫹ rM ⫹ rA p 1, this model considers the trade-off between control efforts directed toward different target agents. The control efficiency for a target agent X is represented as vX (X p P, M, A). When the control efficiency is one (vX p 1), the mortality rates of the apex predator and the mesopredator increase

linearly with allocated control effort (rXD), and the supply rate of the alternative prey decreases hyperbolically with allocated control effort. The increase in the predator mortality rates and the decrease in the alternative prey supply rate are stronger as control efficiencies become larger than 1 (vX 1 1), whereas being more modest with control efficiencies smaller than 1 (vX ! 1). These parameters D, rX, and vX are dimensionless. To explore management strategies under situations closer to the reality in management programs, we set constraints on model parameters. We choose parameter values so that two predators suppress the shared prey density at low levels, since practical management actions are implemented in such situations. We also assume that the control efficiency for the mesopredator is lower than that for the apex predator (vM p 1/2, vP p 1), because apex predators are in general larger than mesopredators and relatively easily reduced by human controls, whereas smaller mesopredators are resilient to control programs (Palomares et al. 1995; Rodrı´guez et al. 2006; Prugh et al. 2009). Because the control efficiency for the alternative prey may differ among different target systems (Didham et al. 2007), we examine a range of control efficiencies for the alternative prey. This range was selected to encompass the control efficiencies for the mesopredator and the apex predator (0.25 ≤ vA ≤ 2). We set an upper limit of the total control effort such that the eradication of the mesopredator is impossible without controlling the alternative prey (0 ≤ D ≤ 50). We use 15,000 parameter sets under these constraints to compare effectiveness of potential management strategies (app. B). To seek effective management strategies, we take two complementary approaches. First, we compare seven simple strategies in terms of the shared prey density achieved under these strategies. These seven strategies are P, controlling only the apex predator (rP p 1); M, controlling only the mesopredator (rM p 1); A, controlling only the alternative prey (rA p 1); PM, controlling the apex predator and the mesopredator with equal effort (rP p rM p 1/2); PA, controlling the apex predator and the alternative prey with equal effort (rP p rA p 1/2); MA, controlling the mesopredator and the alternative prey with equal effort (rM p rA p 1/2); and PMA, controlling the apex predator, the mesopredator, and the alternative prey with equal effort (rP p rM p rA p 1/ 3). This approach is taken because high uncertainty in management of real systems prevents us from foreseeing the best proportion of rP, rM, and rA that can achieve the highest density of the shared prey. On the other hand, the second approach identifies such an optimal, idealistic strategy that achieves the highest density of the shared prey given a total control effort. Although it is almost impossible to take the optimal strategy before manage-

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Trophic Cascades in Intraguild Predation 629 ment implementation, finding the optimal strategy can be useful to gauge the effectiveness of seven simple strategies and to consider how to reallocate the total control effort if these simple strategies are not effective in restoring the shared prey population. We search the optimal management strategy by examining continuously many combinations of rP, rM, and rA. Results Without Alternative Prey Here we analyze the model under the conditions in which the alternative prey density is 0 (A p 0) and thus the mesopredator devotes all foraging effort to the shared prey (dM p 1). Abilities of the mesopredator and the apex predator to suppress the shared prey are described as * SM p

S P* p

mM , a SM(bSM ⫺ h SMm M)

(5)

mP , a SP(bSP ⫺ h SPm P)

respectively. These two quantities are the solutions of (1/ * S)(dS/dt) p 0 in the equation (1a) where P p 0 for S M * and M p 0 for S P. Notice that the ability of the mesopredator (apex predator) to exploit the shared prey in* creases with decreasing S M (S P* ). The relative magnitudes of these two quantities and the carrying capacity of the shared prey (K) are the key that defines the persistence of the intraguild predation system (Holt and Polis 1997; Takimoto et al. 2007). Below we show the consequences of apex predator loss on the shared prey density, classified into three cases: (1) both predators have weak abilities to * suppress the shared prey (K ! S M , S P* ), (2) the mesopredator is superior to the apex predator at exploitative com* petition for the shared prey (S M ! S P* , K), and (3) the apex predator is superior to the mesopredator at exploitative * competition for the shared prey (S P* ! S M , K). The conditions for these cases are summarized in figure 2, along with the consequences of apex predator loss as functions of the mortality rates of the mesopredator and the apex predator because these parameters may be artificially controllable and could therefore have practical implications for management. The higher mortality rates of the mesopredator and the apex predator would weaken their abilities to suppress the shared prey. * , S P* ), apex predator loss has no effect In case I (K ! S M on the shared prey (E⫺P p 0) since the apex predator cannot persist in this system in the first place. Case II * (S M ! S P* , K) can be further classified according to whether or not the apex predator can invade the system with the mesopredator. When the apex predator cannot invade (de-

fined as case IIa), apex predator loss has no influence on the share prey density (E⫺P p 0), as in case I. When the apex predator can invade (case IIb), on the other hand, apex predator loss decreases the shared prey density (E⫺P * ! 0; see app. C for a proof). In case III (S P* ! S M , K), the mesopredator cannot invade the system with the shared prey and the apex predator, and apex predator loss increases the shared prey density (E⫺P 1 0). This is because * the condition for this case (S P* ! S M , K) means that the shared prey density at the equilibrium with the apex predator (i.e., S P*) is smaller than that without the apex pred* * ator: S M (if SM* ! K; defined as case IIIa) or K (if K ! S M ; case IIIb). In a limited parameter space (shadowed area in fig. 2), the model generates alternative stable states (details in app. D). This parameter space is divided into four areas (cases IIa, IIb, IIIa, and IIIb) depending on which combination of equilibria forms alternative stable states. Effects of apex predator loss on the shared prey density differ between alternative stable states except in case IIb. However, apex predator loss always decreases the shared prey density in the alternative stable states where both predators coexist without the alternative prey.

With Alternative Prey Increasing the supply of alternative prey changes the consequences of apex predator loss for the shared prey through promoting the persistence and increases of the mesopredator and/or the apex predator (fig. 3).1 In cases I and IIa, E⫺P decreases from 0 as the alternative prey supply rate increases (fig. 3a, 3b). Increasing the alternative prey supply rate allows the apex predator to persist, which suppresses the mesopredator density. The presence of the apex predator weakens (in case I), or even reverses (in case IIa), the negative impact of increasing the alternative prey supply rate on the shared prey density. When the apex predator is lost, however, larger supplies of the alternative prey increases the mesopredator density, which lowers the shared prey density. Thus, apex predator loss reduces the shared prey density for high supply rates of the alternative prey. In case IIb, E⫺P is always negative irrespective of the alternative prey supply rate, and increasing the alternative prey supply rate further decreases E⫺P (fig. 3c). In this case, the alternative prey does not affect the persistence of two predators, but increases in the alternative prey enhance the apex predator density, which strengthens top-down 1 Mathematica code for producing figures 3 and 4 is available in a zip file online. Code that appears in The American Naturalist is provided as a convenience to the readers. It has not necessarily been tested as part of the peer review.

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630 The American Naturalist

Figure 2: Structures at equilibrium and consequences of apex predator loss for the shared prey density (E⫺P) in five cases (I, IIa, IIb, IIIa, and IIIb). MS* is the mesopredator density at equilibrium without the apex predator: MS* p (r/aSM)(1 ⫺ SM* /K)(1 ⫹ aSMhSMSM* ). Alternative stable states occur in the shadowed area, where consequences of apex predator loss for the shared prey are E⫺P p 0 or E⫺P ! 0 in case IIa, E⫺P ! 0 in case IIb, E⫺P 1 0, or E⫺P ! 0 in case IIIa and E⫺P 1 0 or E⫺P p 0 in case IIIa (details in app. D). Parameters used are r p 1, K p 10, aSM p 0.1, aSP p aMP p 0.2, hSM p hSP p 0.1, hMP p 0.2, bSM p bMP p 0.2, and bSP p 0.1.

trophic cascades. Interestingly, small increases in the alternative prey supply rate slightly decrease the densities of both the mesopredator and the shared prey. This result is because prey switching by the mesopredator from the shared to alternative prey lowers the mesopredator density, which in turn causes prey switching by the apex predator from the mesopredator to the shared prey. In cases IIIa and IIIb, E⫺P starts positive but eventually becomes negative as the alternative prey supply rate increases (fig. 3d, 3e). Increasing the alternative prey supply rate allows the mesopredator to persist, but the apex predator suppresses the mesopredator density and keeps the shared prey density at certain levels. However, when the apex predator is removed, the mesopredator density increases, which greatly reduces the shared prey density especially when the alternative prey is highly abundant. As a result, increasing the alternative prey supply rate changes the effect of apex predator loss on the shared prey density

from positive to negative. Importantly, apex predator loss increases the shared prey when moderate supply rates of the alternative prey allow the coexistence of the apex predator and the mesopredator at equilibrium. Alternative stable states that emerge without the alternative prey disappear at relatively low supplies of the alternative prey (fig. D2; figs. A1, B1–B3, D1, D2 available online). Once the alternative stable state disappear, qualitative consequences of apex predator loss in cases IIa, IIb, IIIa and IIIa become the same as those in corresponding cases without alternative states (i.e., IIa, IIb, IIIa, and IIIa, respectively). Therefore, alternative stable states do not have major influences on the outcomes of apex predator loss. In summary, inclusion of the alternative prey alters the predictions of the model in the following aspects. First, apex predator loss can increase the shared prey density where the apex predator and the mesopredator coexist in

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b)

c) d)

e)

Figure 3: Effects of the alternative prey supply rate on densities of the apex predator, the mesopredator and the shared prey, and on consequences effect of apex predator loss for the shared prey density (E⫺P). Black solid and gray dashed lines represent the presence and absence, respectively, of the apex predator. Parameters used are e p 1; aAM p 0.5; hAM p 0.3; bAM p 0.2; and (mM, mP) p (0.2, 0.2) for a, (0.1, 0.15) for b, (0.05, 0.1), for c, (0.1, 0.05) for d, and (0.2, 0.05) for e. Other parameter settings are the same as in figure 2. Mathematica code for producing this figure is available in a zip file online.

a)

632 The American Naturalist the steady state (fig. 3d, 3e). This is because the alternative prey promotes the persistence of the mesopredator that is inferior to the apex predator in competition for the shared prey. Second, if the alternative prey is sufficiently abundant, apex predator loss substantially reduces the shared prey density regardless of competitive superiority between the mesopredator and the apex predator (fig. 3). The reason is that large amounts of the alternative prey strengthen the impact of the mesopredator on the shared prey through apparent competition. Sufficiently large inputs of alternative prey may thus cause severe mesopredator release and reduce the shared prey density to such low levels that it could be driven into stochastic extinction, although this is unlikely to occur when the mesopredator is supported only by the shared prey. Management Strategy Among the seven simple strategies we considered, controlling all three targets (PMA) becomes the best (fig. 4) in most cases across broad parameter settings (app. B). Controlling the mesopredator and/or the alternative prey without controlling the apex predator (M, A, MA) cannot increase the shared prey density because prey switching by the apex predator from the mesopredator to the shared prey cancels out the positive effects of mesopredator reductions on the shared prey. On the other hand, controlling the apex predator (P), controlling the apex predator and the mesopredator (PM), and controlling the apex predator and the alternative prey (PA) can enhance the shared prey density at low levels of effort. This is because the apex predator can persist at low densities under moderate controls of the apex predator, which prevents overabundance of the mesopredator and reduces the total predation pressure on the shared prey. Yet, further increases in the control effort reduce the shared prey density due to mesopredator release. Controlling all three targets (PMA) can also lead to such reductions in the shared prey density. However, the shared prey density at intermediate levels of control effort is higher than for the other strategies, even if the control efficiency for the alternative prey is less than or equal to that for the mesopredator (fig. 4a, 4b). This result suggests that controlling all three targets is a good strategy to avoid the negative effect of mesopredator release. In addition, when the control efficiency for the alternative prey is similar to that for the apex predator, increasing the control effort at high levels can again enhance the shared prey density (fig. 4c). When the control efficiency for the alternative prey is the highest, shared prey reduction at intermediate levels of the control effort is trivial, and further increases of the control effort can enhance the shared prey density up to its carrying ca-

pacity because both predators are eradicated (fig. 4d). Thus, controlling not only the apex predator and the mesopredator but also the alternative prey is an effective management strategy for conserving shared prey populations. The optimal management strategy depends on the total control effort and the control efficiency for the alternative prey (fig. 4). When the control effort is extremely low, controlling only the apex predator is optimal, but the allocation of effort to the apex predator decreases as the total control effort increases. When the control efficiency for the alternative prey is less than or equal to that of the mesopredator, more effort should be allocated to the mesopredator (fig. 4a, 4b). However, these optimal strategies can only slightly elevate the shared prey density with moderate to high levels of the control effort because the mesopredator density cannot be effectively reduced due to the low control efficiencies for the mesopredator and the alternative prey. When the control efficiency for the alternative prey is equal to that for the apex predator, but higher than that for the mesopredator, the allocation of effort to the alternative prey is slightly higher than that to the mesopredator (fig. 4c). When the control efficiency for the alternative prey is the highest, the allocation of effort to the apex predator increases as the total control effort increases from moderate to high levels (fig. 4d). This is because the high control efficiency for the alternative prey enables the eradication of the mesopredator, which generates situations where complete removal of the apex predator increases the shared prey density due to there being no risk of mesopredator release. Discussion Empirical evidence suggests that apex predator loss can decrease or increase the abundance of shared prey by affecting mesopredators. However, what governs the occurrence and strength of trophic cascades in intraguild predation systems has remained poorly understood. Using a mathematical model, we found that the consequences of apex predator loss on shared prey depended not only on the competitive abilities of mesopredators and apex predators but also on the presence and availability of alternative prey for the mesopredators. Our model also demonstrated that controlling alternative prey as well as mesopredators and apex predators was an effective management strategy for conserving shared prey populations. Below we discuss implications of the results. Our model showed that when mesopredators were superior to apex predators at exploitative competition for shared prey, apex predator loss reduced the shared prey density. This prediction is supported by empirical examples. Vance-Chalcraft et al. (2007) conducted a meta-anal-

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b)

c)

d)

Figure 4: Effects of seven simple strategies (solid lines) and optimal strategy (gray dashed lines) on the shared prey density (upper panels) and optimal allocation rates of the total control effort to the apex predator (P), the mesopredator (M), and the alternative prey (A) (lower panels). In the lower panels, lengths of vertical lines from y p 1 to the upper gray lines represent the allocation rate of the total control effort to the apex predator, lengths from the upper to the lower gray lines represent that to the mesopredator, and lengths from the lower gray lines to y p 0 represent that to the alternative prey. Parameters used are mM0 p mP0 p 0.05; I0 p 100; vM p 0.5; vP p 1; and vA p 0.25 for a, 0.5 for b, 1 for c, and 2 for d. Other parameter settings are the same as in figures 2 and 3. Mathematica code for producing this figure is available in a zip file online.

a)

634 The American Naturalist ysis of experiments examining intraguild predation and found that, in general, intermediate predators were more effective at suppressing shared prey than apex predators, and removal (or addition) of apex predators decreased (increased) the shared prey density. In Australia, red foxes (mesopredator) appeared to suppress the density of mammalian prey (shared prey) more effectively than dingoes (apex predator; Cupples et al. 2011; Letnic and Dworjanyn 2011). Removal of dingoes induced the collapse of mammalian prey populations through release of foxes throughout Australia, suggesting that trophic cascades are ubiquitous in ecosystems with dingoes and foxes (Johnson et al. 2007; Letnic et al. 2009, 2011). In our model, alternative prey facilitated the persistence of mesopredators that were inferior to apex predators at exploitative competition and created the conditions under which apex predator loss could increase the shared prey density in the coexistence state (fig. 3d, 3e). This suggests that removal of introduced apex predators may lead to the recovery of prey species even in the presence of invasive mesopredators. For island ecosystems, Courchamp et al. (1999) predicted that eradicating introduced cats (apex predator) will extirpate bird populations (shared prey) through release of invasive rats (mesopredator). However, recent evidence showed that the removal of cats had a positive effect on seabird populations even in the presence of alien rats (Rodrı´guez et al. 2006; Rayner et al. 2007; Hughes et al. 2008; Bonnaud et al. 2010). In light of our study, this observation implies that, compared with cats, rats are a less effective predator of avian prey. Eradicating cats, even in the presence of rats, would lead to bird recoveries if the availability of alternative prey (e.g., plants) is not high. When alternative prey was abundant, apex predator loss greatly decreased the shared prey density regardless of the competitive abilities of mesopredators and apex predators (fig. 3), suggesting that human-derived subsidies may set the stage for apex predator loss to lead to strong trophic cascades through mesopredator release. For example, the disappearance of coyote (apex predator) severely affected the persistence of their avian prey (shared prey) through increases in populations of midsized mammals (mesopredator; Crooks and Soule 1999), which were highly subsidized by anthropogenic resources, such as organic refuse, in urban landscapes (Prange and Gehrt 2004; Rodewald et al. 2011; Fischer et al. 2012). In forests, the extirpation of wolves (apex predator) induced a high abundance of coyotes (mesopredator) and strong predation of coyotes on pronghorns; these coyotes also consumed large numbers of elk carcasses generated by human activities (Berger et al. 2008). Nonindigenous pasture plants with high seed production (alternative prey) strengthened mesopredator release of introduced mice, which diminished endangered

lizard populations (shared prey) in grassland and shrubland ecosystems (Norbury et al. 2013). In farm ponds, the removal of exotic largemouth bass (apex predator) extirpated a number of odonate species (shared prey) through an outbreak of invasive crayfish (mesopredator; Maezono and Miyashita 2004); the abandonment of traditional coppicing in riparian secondary forests has increased the amount of allochthonous litter inputs (Kobori and Primack 2003), which supports high densities of the crayfish (Kobayashi et al. 2011). Interacting effects of apex predator declines and increased resource subsidies, both due to human activities, could result in substantial mesopredator release and unwanted collapses of animal prey. In our model, a strategy that allocated control effort equally to apex predators, mesopredators, and alternative prey was the best among the simple strategies we examined (fig. 4). A lower control allocation to apex predators and higher control allocations to mesopredators and alternative prey decreased the risk of mesopredator release and increased the maximum shared prey density compared to the other strategies. This suggests that increasing the control allocation to alternative prey (e.g., anthropogenic subsidies or allochthonous litter inputs) is crucial not only to protect shared prey but also to extirpate harmful apex predators (e.g., dingoes or largemouth basses). On Amami-Oshima Island, Japan, for instance, the decrease in the invasive mongoose (apex predator) by the eradication project resulted in the recovery of endangered endemic vertebrates (shared prey; Watari et al. 2013), but an alien rat (mesopredator) responded positively to habitat alternation, probably due to increased agricultural crops and rubbish (alternative prey; Fukasawa et al. 2013). Hence, further urbanization may lead to strong mesopredator release of the nonnative rat, which could pose negative influences on endemic species. Protecting forests from urbanization will be important for the achievement of both endemic species recovery and mongoose eradication. It is worth noting that the effectiveness of our proposed strategy allocating the control effort equally to two predators and alternative prey is robust across a broad range of parameter settings (app. B). This simple strategy can be a fundamental management guideline widely applicable in various conservation programs. This strategy is nevertheless not a panacea; moderate or high levels of control effort cannot increase the shared prey when the control efficiency for the alternative prey is low. Thus, management should begin with a low control effort, and then the control effort should be gradually increased while monitoring shared prey populations. We propose two ways to handle the situations when increasing the control effort fails to enhance shared prey density. First, the control effort should be reallocated from apex predators to mesopredators, alternative prey, or both so as to

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Trophic Cascades in Intraguild Predation 635 approximate the optimal strategy. However, this strategy can do little to elevate shared prey density when the control efficiency for alternative prey is less than or equal to that for mesopredators (fig. 4a, 4b). Therefore, a second effective strategy would be to reduce the total control effort to low levels, which can lower the management cost. A crucial part of this strategy is ensuring that apex predators do not become extinct. Beyond simple intraguild predation systems, the effective strategies that we have presented may be applicable to the management of more complex systems with two or more invasive predators. Many ecosystems have now been transformed from their original state by the introduction of multiple invasive species (Tompkins and Veltman 2006; Ramsey and Norbury 2009; Wallach et al. 2010; Miyake and Miyashita 2011; Ruscoe et al. 2011). Such systems are called “novel ecosystems” (Hobbs et al. 2006, 2009). Managing novel ecosystems is generally difficult due to a high likelihood of mesopredator or competitor release (Tompkins and Veltman 2006; Ramsey and Norbury 2009; Ruscoe et al. 2011). However, previous studies aimed to reduce invasive predator numbers intensively, not to control predators moderately or suppress prey availability. Our model suggests that small reductions of apex predators or removal of alternative prey sustaining invasive predators could be effective for restoring endangered prey populations that suffer from multiple invaders. In conclusion, our model highlights the importance of alternative prey for mesopredators in predicting and managing top-down trophic cascades in intraguild predation systems. We revealed two roles of alternative prey in the consequences of apex predator loss. First, through facilitating the persistence of mesopredators that are inferior to apex predators at exploiting shared prey, alternative prey creates the conditions in which apex predator loss has a positive impact on shared prey in the coexistence state. Second, a large amount of alternative prey strengthens mesopredator release and consequent shared prey collapse resulting from apex predator loss. Importantly, human activities are a major source of highly abundant alternative prey (Oro et al. 2013). Reducing alternative prey such as anthropogenic resource subsidies, in addition to managing invasive mesopredators and apex predators, might be an effective approach for conserving prey species that would be threatened by mesopredator release.

Acknowledgments We appreciate two anonymous reviewers for helpful comments on the manuscript. This study was supported by a Grant-in-Aid for Japan Society for the Promotion of Science Fellows (KAKENHI 22-4267) to S.N.

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ators keystone species in Neotropical forests? the evidence from Barro Colorado Island. Oikos 71:279–294. Associate Editor: James Elser Editor: Susan Kalisz

The small Indian mongoose (Herpestes auropunctatus), an apex predator introduced into Amami-Oshima Island, Japan. Photo credit: Amami Wildlife Conservation Center.

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