vol. 170, no. 6 the american naturalist december 2007 ൴
Spatial Dynamics of Communities with Intraguild Predation: The Role of Dispersal Strategies
Priyanga Amarasekare*
Department of Ecology and Evolutionary Biology, University of 2004, 2005). This interplay is well established for com- California, Los Angeles, California 90095 munities with one or two trophic levels (e.g., resource, consumer; Levin 1974; Holt 1985; Murdoch et al. 1992; Submitted November 1, 2006; Accepted July 11, 2007; Electronically published October 16, 2007 Amarasekare and Nisbet 2001; Jansen 2001; Abrams and Wilson 2004) but not for the more common situation of Online enhancements: appendixes. communities with multiple trophic levels (e.g., resource, consumer, natural enemy). Multitrophic communities present quite a challenge for spatial ecology. Studies of spatial coexistence typically fo- abstract: I investigate the influence of dispersal strategies on in- cus on one type of species interaction (nontrophic or pair- traguild prey and predators (competing species that prey on each wise trophic interactions) and situations where species other). I find an asymmetry between the intraguild prey and predator cannot coexist in the absence of dispersal (e.g., competitive in their responses to each other’s dispersal. The intraguild predator’s dominance, predator overexploitation, Allee effects in- dispersal strategy and dispersal behavior have strong effects on the duced by the absence of a mutualistic partner). Dispersal intraguild prey’s abundance pattern, but the intraguild prey’s dis- can allow coexistence, given spatial variation in the persal strategy and behavior have little or no effect on the intraguild predator’s abundance pattern. This asymmetry arises from the dif- strength of species interactions (Levin 1974; Holt 1985; ferent constraints faced by the two species: the intraguild prey has Amarasekare and Nisbet 2001; Codeco and Grover 2001; to acquire resources while avoiding predation, but the intraguild Amarasekare 2004; Leibold et al. 2004). Multitrophic com- predator only has to acquire resources. It leads to puzzling distri- munities do not fit this mold, and not merely because they bution patterns: when the intraguild prey and predator both move contain both trophic and nontrophic interactions. It is away from areas of high density, they become aggregated to high- because they involve situations where species within a density habitats, but when they both move toward areas of high resource productivity, they become segregated to resource-poor and trophic level can coexist in the absence of dispersal, but resource-rich habitats. Aggregation is more likely when dispersal is the operation of such coexistence mechanisms varies over random or less optimal, and segregation is more likely as dispersal space and time. The influence of dispersal on diversity is becomes more optimal. The crucial implication is that trophic con- therefore fundamentally different. There is now the po- straints dictate the fitness benefits of using dispersal strategies to tential for simultaneous operation of local and spatial co- sample environmental heterogeneity. A strategy that affords greater existence mechanisms, and for emergent properties to arise benefits to an intraguild predator can lead to a more optimal outcome for both the intraguild predator and prey than a strategy that affords from the interaction between the two classes of mech- greater benefits to an intraguild prey. anisms. Two examples of natural multitrophic interactions serve Keywords: competition, dispersal strategies, intraguild predation, life- to illustrate these differences. Intraguild predation (IGP) history trade-offs, multitrophic communities, productivity. occurs when species that compete for a common resource also prey on or parasitize one another (e.g., Polis et al. 1989; Arim and Marquet 2004); selective predation (SP) It is widely appreciated that diversity maintenance in spa- occurs when species that compete for a common resource tially structured environments results from the interplay also share a natural enemy (e.g., Sih et al. 1985; Navarrete between species interactions and dispersal (Leibold et al. and Menge 1996). In both cases, the two consumer species
* E-mail: [email protected]. can coexist via a trade-off that allows for resource parti- Am. Nat. 2007. Vol. 170, pp. 819–831. ᭧ 2007 by The University of Chicago. tioning. In IGP, the trade-off is such that the inferior re- 0003-0147/2007/17006-42191$15.00. All rights reserved. source competitor gains a second resource by preying on DOI: 10.1086/522837 its competitor; in SP, the inferior competitor gains more 820 The American Naturalist of the common resource by being less susceptible to the inhabited by invertebrate communities (Chase and Leibold predator. A key feature of these trade-offs is that their 2002; Chase 2003; Chase and Ryberg 2004). I consider expression depends on species occupying other trophic spatial heterogeneity in habitat quality to be permanent, levels within the community. In IGP, it is the common as would be the case with differences in soil, nutrient resource; in SP, it is the common resource and/or natural availability, or moisture content that make some ponds or enemy. In the absence of dispersal or other ameliorating host plant patches more productive than others. The spa- factors, spatial variation in resource productivity or pred- tial scale on which such heterogeneity occurs is within the ator mortality can eliminate the trade-off and cause ex- dispersal ranges of the organisms that occupy these hab- clusion of the species that has the overall disadvantage. itats. For instance, a set of ponds (host plant patches) in For instance, when resource productivity is low (predator a given area may vary in quality but occur in sufficiently mortality is high), exploitative competition dominates, and close proximity to allow dispersal between ponds (host the inferior resource competitor is excluded; when re- plant patches). source productivity is high (predator mortality is low), Each habitat patch supports a local community with predation dominates, and the species more susceptible to unidirectional IGP: two species compete for the same lim- predation is excluded (Holt and Polis 1997; Diehl and iting resource, but one species (“IGPredator”) can prey on Feissel 2000; Noonburg and Abrams 2005). Thus, the or parasitize its competitor (“IGPrey”). Unidirectional IGP trade-off between competition and predation operates commonly occurs in aquatic invertebrates (Wissinger et only at intermediate productivity/mortality levels. This il- al. 1996; MacNeil et al. 2004) and insect parasitoids (Zwol- lustrates another feature that distinguishes multitrophic fer 1971; Polis et al. 1989; Amarasekare 2000, 2003; Arim interactions. In nontrophic or pairwise trophic interac- and Marquet 2004). Coexistence is possible within a given tions, environmental variability in species’ traits is gen- habitat patch if the IGPrey and IGPredator exhibit a trade- erally conducive to coexistence (Leibold et al. 2004). In off that allows resource partitioning, as would occur if multitrophic interactions, environmental variability that the IGPrey is the superior resource competitor but the affects the resource or predator trophic level can constrain IGPredator’s ability to prey on the IGPrey gives it an ad- coexistence at the intermediate consumer trophic level. ditional resource (Holt and Polis 1997). Coexistence, how- Diversity maintenance therefore depends crucially on ever, is not guaranteed. The trade-off is expressed only at whether dispersal by intermediate consumers can coun- intermediate resource productivity; if productivity changes teract the diversity-reducing effects of spatial variation that such that it becomes too low or too high, one species gains act through a shared resource or natural enemy. an overall advantage and excludes the other (Holt and Here I investigate this issue using IGP, a multitrophic Polis 1997). Coexistence in variable environments thus interaction that occurs in a wide variety of taxa from mi- requires additional mechanisms besides the competition- crobes to mammals (Polis et al. 1989; Arim and Marquet IGP trade-off. 2004). I consider the worst-case scenario for coexistence: These features define a landscape that is patchy and there is spatial variation in resource productivity but no spatially heterogeneous, and in which local coexistence spatial variation in the consumers’ life-history traits. How- within a habitat patch is determined by the ambient level ever, the consumer species can sample spatial variation in of resource productivity. Here I consider the simplest productivity by adopting different dispersal strategies. This mathematical representation of such a system, a three- study is novel in two respects. First, it presents a theoretical patch model with each patch exhibiting a level of resource framework for spatial dynamics of multitrophic com- productivity that leads to a qualitatively different outcome: munities, an area of spatial community ecology that has (1) resource productivity is too low for the IGPredator to hitherto received little attention. Second, it investigates the invade when rare, (2) resource productivity is too high for impact of dispersal strategies on species that interact via the IGPrey to invade when rare, and (3) resource pro- competition and predation, an aspect of spatial dynamics ductivity is within the range that allows both species to that has not been studied. invade when rare and coexist via a competition-IGP trade- off (Holt and Polis 1997). I consider a situation in which the resource species is The Model sedentary. In nature, this corresponds to communities in I consider a spatially structured environment in which which the basal resource is a plant species or an immobile suitable habitat patches are separated by an inhospitable life stage of insects and aquatic invertebrates (e.g., eggs, matrix. Common examples of such spatial environments immobile adult stages of Coccinellids). The two consumers include host plant patches inhabited by insect herbivore (IGPrey and IGPredator) do disperse, and they can adopt guilds and their natural enemies (Harrison et al. 1995; Lei dispersal strategies that sample the spatial variation in re- and Hanski 1998; Amarasekare 2000) and pond systems source productivity in different ways. I consider four basic Intraguild Predation and Dispersal Strategies 821 types of dispersal strategies. At one extreme is random I nondimensionalize equation (1) using scaled quanti- dispersal, where emigration and immigration are inde- ties. Nondimensional analysis not only reduces the num- pendent of species’ or habitat characteristics. At the other ber of parameters but also highlights the biologically sig- extreme is dispersal in response to spatial variation in local nificant scaling relations between parameters (Nisbet and (i.e., within-patch) fitness, where individuals move in the Gurney 1982; Murray 1993). direction of increasing fitness (Holt 1983; Armsworth and ˆ p ˆ p I use the following substitutions:RjjR /KC , ij Roughgarden 2005b). Dispersal in the direction of increas- p p p ˆ p Cij/eK i,, rˆˆ jr j /da1 iiiieaK/d ,aˆ e 22aK/d ,biiib /d , ing fitness is obviously the best strategy. Adopting it, how- ˆf p ef/e ,d p d /d , andt p dt (where d ( 0 , i p ever, requires that individuals have complete information 12 21 1 i 1, 2, andj p 1, 2, 3 ) to transform the original variables on spatial variance in fitness across the landscape. In re- into nondimensional quantities. The advantage of these ality, individuals often have to make dispersal decisions quantities is that the units used in the analysis are un- based on incomplete information. I therefore consider two important, and the expressions “small” and “large” have nonrandom strategies that rely on partial information on fitness differences: dispersal in response to density and clear relative meaning (Murray 1993). The dimensionless dispersal in response to habitat quality. time metric t expresses time in terms of the IGPrey’s death These ideas are formalized by the following dynamical rate. This time scaling allows for comparing systems that equations: differ in their natural timescales. Resource abundance is expressed as a fraction of the resource carrying capacity and varies from 0 to 1. While a particular value of the dRjjp ϪϪ R Ϫ rRjj1 aRC1 j 1j aRC2 j 2j , carrying capacity may not be all that informative, knowing dt() K whether the resource abundance is close to carrying ca- K dC j pacity is. For example,R 1 indicates that the resource 1 p eaRC Ϫ dC Ϫ aCC dt 11 j 1j 11j 1j 2j abundance is well below the carrying capacity and that resource self-limitation is weak, whileR r 1 indicates the Ϫ b E (m )C ϩ b I (m ), (1) 1 j 11j 1 j 1 opposite. The consumers’ abundances are scaled by their
dC j respective conversion efficiencies and the resource carrying 2 p Ϫ ϩ eaRC22 j 2j dC22j faCC1j 2j capacity. Large and small (p ( ) mean dt CCiik, k 1, 2; i k that for any given resource carrying capacity, consumer i Ϫ ϩ b2Ej(m 22)C j b2Ij(m 2), has a lower conversion efficiency than consumer k. The scaled attack rates (aˆ ) depend on the resource carrying whereRC is the resource abundance in patch j and is i jijcapacity and the consumer death rate (d ); the scaled in- the abundance of consumer species i in patch j (i p i p terference parameteraˆ shows that the per capita inhibitory 1, 2;j 1, 2, 3 ). The parameterrj is the per capita rate of resource production in patch j, and K is the resource car- effect of the IGPredator on the IGPrey depends on the rying capacity. Resource productivity varies spatially, while IGPredator’s conversion efficiency and mortality rate as ˆ the resource carrying capacity remains invariant across well as the resource carrying capacity. The parameterbi is the per capita emigration rate of consumer i relative to its patches. The parameteraeii is consumer i’s attack rate, is the number of its offspring resulting from resource con- within-patch mortality rate. While a particular value of sumption, anddi is its background mortality rate. The the consumer emigration rate may not be meaningful, parameter a is consumer 2’s attack rate on consumer 1, knowing whether the emigration rate approaches or ex- ˆˆr 1 and f is the number of consumer 2 offspring resulting ceeds the local mortality rate (i.e.,bii1 orb 1 , re- from intraguild predation. Consumer 1, therefore, is the spectively) is important in understanding how emigration IGPrey, and consumer 2 is the IGPredator. Although nei- affects coexistence. The other important parameter is the ther consumer species exhibits spatial variation in their efficiency metricˆf . On their own, the efficiency parameters vital rates, each can sample spatial variation in productivity ei and f have little meaning, but as a composite, they reveal by adopting different dispersal strategies. The functions important scaling relationships between conversion effi- bijE (m i)C ijandb ijI (m i) represent the patch-specific emi- ciencies for resource consumption and IGP. For instance, ˆ k gration and immigration rates of the two consumers, large values offef imply that for any value of12 ,e ; that wherebi is the intrinsic or potential dispersal rate of con- is, the IGPredator obtains a greater benefit from the IGPrey sumer i andmi is the dispersal strategy it employs. Dis- than from the basal resource. persal strategies are species specific but not habitat specific; I substitute the nondimensional quantities into equation that is, all individuals of a given species adopt the same (1) and drop the hats for convenience. This yields the strategy. nondimensional system 822 The American Naturalist
dRj differences between habitat patches. In reality, most or- p rR(1 Ϫ R ) Ϫ aRC Ϫ daRC , dt jj j 1 j 1j 2 j 2j ganisms make dispersal decisions in the absence of com- plete information on such differences. I therefore consider dC j 1 p Ϫ Ϫ two suboptimal but biologically realistic strategies that rely aRC1 j 1j C1j daCC1j 2j dt on incomplete information on fitness differences. I also Ϫ b E (m )C ϩ b I (m ), (2) consider random dispersal as an extreme case of subop- 1 j 11j 1 j 1 timal dispersal. The term “optimal” is typically used to dC j imply that organisms are behaving in an ideal free manner 2 p d[aRC Ϫ C ϩ faCC dt 2 j 2j 2j 1j 2j (e.g., Krˇivan 1996). Here I use it to mean movement in the direction of increasing fitness. I make this distinction Ϫ b ϩ b 2Ej(m 22)C j 2Ij(m 2)]. because in models of species interactions, dispersal in the direction of increasing fitness does not necessarily lead to Unless otherwise noted, all variables and parameters from ideal free distributions (Abrams 2007). this point on are expressed as nondimensional quantities. The first biologically realistic strategy is one where in- My goal is to understand the possible interplay between dividuals emigrate in response to the density of conspe- local and spatial coexistence mechanisms. I therefore focus cifics and heterospecifics in their resident patch, but they on the situation where local coexistence via a competition- immigrate in a random manner. This strategy reflects the IGP trade-off is possible in at least one patch. The trade- information limitation faced by dispersing individuals: it off is such that the IGPrey is superior in resource com- ∗ is relatively easy to assess the strength of competition and petition; that is, it has a lowerR ; Tilman 1982), but the predation in the habitat patch one occupies, but it is much IGPredator has the advantage of being able to prey on the harder to assess these factors from afar when immigrating 1 ∗ IGPrey (a 0 ). From equation (2),R in the absence of to a new habitat patch. In this situation, random immi- dispersal is 1/ai, and hence the IGPrey’s competitive su- gration provides a bet-hedging opportunity by allowing periority translates into having a higher attack rate than individuals to sample spatial variation in density. A strategy the IGPredator. I use ai as the measure of competitive of density-dependent emigration and random immigra- ability and a as a measure of the strength of IGP while tion is also consistent with empirical evidence. A large keeping the mortality ratio (d) and conversion efficiency number of studies on a wide variety of taxa show that ( f ) fixed. emigration is density-dependent (i.e., emigration rate in- I focus in particular on the influence of dispersal strat- creases with increasing density; Denno et al. 1991; Herzig egies on the relationship between abundance and resource 1995; Fonseca and Hart 1996; Aars and Ims 2000; Al- productivity. I do so for two reasons. First, resource pro- brectsen and Nachman 2001; Rhainds et al. 1998), but no ductivity is a parameter that is amenable to experimental studies show a relationship between density and the im- manipulation, and abundance is a variable that is easily migration rate (Sutherland et al. 2002). measured, which enables model predictions to be readily The second biologically realistic strategy is one where translated into empirical investigations. Second, while the emigration and immigration both occur in response to mechanisms underlying the abundance-productivity re- habitat quality. This strategy arises when organisms can lationship have been studied from the perspective of local use cues other than conspecifics to assess habitat quality. species interactions (Holt et al. 1994; Holt and Polis 1997; For instance, most insect herbivores and parasitoids use Diehl and Feissel 2000; Bonsall and Holt 2003), they have yellow flowers as a cue to locate suitable host plant patches not been studied from the perspective of dispersal and (Zwolfer 1971; Mills 1994; Amarasekare 2000). For brevity, spatial coexistence. I refer to dispersal in the direction of increasing fitness as fitness-dependent dispersal, dispersal in response to den- Dispersal Strategies sity as density-dependent dispersal, and dispersal in re- sponse to habitat quality as habitat-dependent dispersal. I consider four dispersal strategies. The first strategy is These dispersal strategies can be incorporated into the p dispersal in response to fitness differences, where individ- model as follows. For random dispersal,Eji(m ) 1 and p 3 uals disperse in the direction of increasing fitness. Follow- Iji(m ) (1/3) lp1 CC il, where il is the density of consumer ing previous studies (Holt 1983, 1985; Krˇivan 1996; Arms- i in patch l scaled by the resource carrying capacity worth and Roughgarden 2005b), I use the patch-specific (;i p 1, 2 j p 1, 2, 3 ). per capita growth rate in the absence of dispersal as the I use an exponential function to depict dispersal re- measure of local fitness. Dispersal in the direction of in- sponses to the various environmental cues. For habitat- creasing fitness is obviously the optimal strategy, but dependent dispersal, the emigration rate is a decreasing Ϫ p hrij adopting it requires organisms to accurately gauge fitness function of habitat quality; that is,Eji(m ) e , where Intraguild Predation and Dispersal Strategies 823
hi is a positive constant that determines the strength of ican Naturalist for details), andrmax is the maximum re- habitat selection,rj is the resource productivity in patch j, source productivity. The patch-specific r values determine 33Ϫ p hrilp hr ij hr il andIji(m ) I Cijlp1 eC il , where I C ij e / lp1 e the strength of spatial variation in productivity; that is, r r determines habitat selection during immigration (i.e., in- r13max0 andr r mean strong spatial variation, while r r dividuals are more likely to immigrate into habitats of r1 rrC21and3 rC mean weak spatial variation. The base- p higher resource productivity). The maximum dispersal line spatial variation in productivity was set to r1 r r p ϩ p ϩ rate isbijji (i.e., asr 0 ,E (m ) 1 , and the per capita rC2211/2,r2 (rCCr )/2 , andr3 (rC rmax)/2 . r dispersal ratebijE (m i) b i ). Since my focus is on the interplay between IGP and For fitness- and density-dependent dispersal, the emi- dispersal, I consider the two consumer species as differing gration rate is an increasing function of fitness and density, in their attack rates (ai ) and dispersal traits (bi, si, hi, gi) p p respectively. I use the scaled dispersal function Eji(m ) but having similar background mortality rates (i.e., d e XX/(1 ϩ e ) (where X depicts fitness- or density-depen- 1). The equal mortality rate assumption is biologically re- dence in dispersal), which also leads to a maximum dis- alistic, given that competitors within a guild are often sub- r ϱ r persal rate ofbiji (i.e., asX ,E (m ) 1 , and the per ject to the same density-independent mortality factors r capita dispersal ratebijE (m i) b i ). (Zwolfer 1971; Mills 1994; Amarasekare 2000). It allows 2 p sik()S p1Ckj For density-dependent dispersal, Eji(m ) e / all important life-history traits to be scaled relative to the 2 ϩ sik()S p1Ckj (1 e ), wheresi determines the strength of density- common mortality rate. 2 dependent emigration,kp1 Ckj is the total consumer den- sity in patch j, andI (m ) p (1/3) 3 (E (m )C ) (i p jilp1 liil Results 1, 2;j p 1, 2, 3 ). For fitness-dependent dispersal, 3 Ϫ Ϫ p gi(w ilw ij) ϩ g i(w ilw ij) p Eji(m ) l(j [e /(1 e )] and I ji(m ) Figure 1 depicts the abundance-productivity relationships 3 Ϫ Ϫ giijil(w w ) ϩ g iijil(w w ) l(j [e /(1 e )]Cgil, where i is a positive con- of the IGPrey and the IGPredator for the four dispersal stant that determines the ability to detect fitness differences strategies. Fitness-dependent dispersal leads to interspe- p Ϫ Ϫ between patches,w1j aR1 j 1 daC 2j is the IGPrey’s cific segregation, with the IGPrey being restricted to the fitness (per capita growth rate in the absence of dispersal) low-productivity habitats and the IGPredator being re- p Ϫ ϩ in patch j, andw2j d(aR2 j 1 faC1j) is the IGPred- stricted to the high-productivity habitats. Habitat-depen- ator’s fitness in patch j. dent dispersal yields an outcome similar to that of fitness- dependent dispersal. Density-dependent dispersal yields an outcome quite different from that of fitness-dependent Model Analyses dispersal: it leads to interspecific aggregation with both Because the three-patch model with dispersal is analytically species concentrated in the higher-productivity habitats. intractable, I used numerical methods to investigate the Aggregation results because density-dependent dispersal conditions for invasibility and coexistence. I obtained induces a qualitative change in the IGPrey’s abundance long-term abundances by numerically integrating equation pattern: the IGPrey’s abundance increases rather than (2) for 25,000 time steps and calculating the average abun- decreases with increasing productivity. The effect on the dance over the last 1,000 time steps. The large number of IGPredator is quantitative: its abundance continues to in- parameters makes an exhaustive exploration of the param- crease with increasing productivity, the only difference be- eter space difficult. Instead, I focused on two situations ing a nonzero abundance in low-productivity habitat that are biologically relevant: where the trade-off between (where it cannot persist when sedentary). Random dis- k ≥ competition and IGP is strong (i.e.,a12a , a a 2 ) or persal yields an outcome similar to that of density-depen- Ӎ ! weak (i.e.,a12a , a a 2 ). A strong trade-off means that dent dispersal. coexistence via local niche partitioning can occur for a The abundance-productivity relationships (fig. 1) high- broad range of resource productivities, while a weak trade- light several counterintuitive outcomes. When both species off means the opposite. move toward areas of high resource productivity (habitat- I introduced spatial variation by setting the patch- dependent dispersal), they become segregated into low- specific resource productivity to levels that yield the three productivity and high-productivity habitats. When both scenarios observed in the absence of dispersal: (1) patch species move away from areas of high density (density- ! ! ⇒ ! ! 1:0 r1 rCC22IGPrey only, (2) patch 2: r r2 dependent dispersal), they become aggregated in to areas ⇒ ! ! ⇒ rCC1 coexistence, and (3) patch 3: r 1 r3maxr of high density, a tendency that increases with increasing
IGPredator only. The quantitiesrrCC12 and are, respectively, dispersal ratebi . When compared to fitness-dependent dis- the threshold resource productivities required for the persal, therefore, density-dependent dispersal leads to a IGPrey and IGPredator to invade when rare in the absence less optimal outcome than habitat-dependent dispersal. of dispersal (see app. A in the online edition of the Amer- This result is puzzling, because one would expect density Figure 1: Long-term abundances of the intraguild prey (IGPrey) and the intraguild predator (IGPredator) in the low, medium, and high resource productivity patches when the competition–intraguild predation trade-off is strong. Note that low productivity refers to the range of r values that is too low for the IGPredator to invade, high productivity refers to the range of r values that is too high for the IGPrey to invade, and medium productivity refers to the range of r values that allows coexistence (see app. A in the online edition of the American Naturalist for details). Parameter p p p p p p values used are as follows:g12g 20 (fitness-dependent dispersal),h 1h 25 (habitat-dependent dispersal),s 12s 5 (density-dependent p p p p p p p dispersal), andb12b 1.0 for all four dispersal strategies. Other parameter values used area1210 ,a 2 ,a 2 ,f 2 , andd 1 . Intraguild Predation and Dispersal Strategies 825 to be a better indicator of fitness differences between any given dispersal strategy, variation in the IGPredator’s patches than resource productivity. This is because density dispersal trait (b2, s2, h2, g2) has very little effect on itself is a consumer attribute that reflects the strength of com- but a much larger effect on the IGPrey. For instance, the petition and IGP within a patch, while productivity is a IGPrey’s abundance-productivity relationship at low val- resource attribute that provides no information about ues of the IGPredator’s dispersal traits is qualitatively dif- competition or IGP. ferent from that at high values. Such qualitative differences Resolving this puzzle requires understanding how the are not observed in the IGPredator (fig. 2). different dispersal strategies influence each species’ fitness Figure 3 illustrates the impact of the IGPrey’s dispersal (per capita growth rate in the absence of dispersal). Con- on the IGPredator. Now the IGPredator’s dispersal is ran- sider first the situation where both species move in re- dom, but the IGPrey adopts different dispersal strategies. sponse to density. The highest overall density is in the Again, there are two key points. First, the IGPrey’s dis- most productive habitat patches. Hence, dispersal in re- persal strategy has a small effect on its own abundance sponse to density involves a net movement of each species pattern but no effect on the IGPredator’s abundance pat- from areas of higher to lower resource productivity. For tern. Second, for any given dispersal strategy, variation in the IGPrey, this is optimal because there is a net move- the IGPrey’s dispersal trait (b1, s1, h1, g1) has a small effect ment from areas of lower to higher fitness (because on itself but no effect on the IGPredator (fig. 3). higher-productivity areas lead to greater mortality via These results illustrate a strong asymmetry between the IGP). However, for the IGPredator, it is suboptimal be- IGPrey and the IGPredator in their responses to each cause there is a net movement from areas of higher to other’s dispersal strategy and dispersal trait values. The lower fitness (because higher-productivity areas lead to IGPredator’s dispersal has a strong effect on the IGPrey, greater reproduction). The key point is that when dis- but the IGPrey’s dispersal has little or no effect on the persal is optimal for the IGPrey but suboptimal for the IGPredator. This asymmetry helps explain the puzzling re- IGPredator, the overall outcome is suboptimal for both sults that we see (fig. 1). Dispersal in response to density is species (i.e., the abundance-productivity relationships of optimal for the IGPrey and suboptimal for the IGPredator. both species deviate strongly from those obtained under Because the IGPredator’s dispersal has a disproportionately fitness-dependent dispersal). Now consider the situation large effect on the IGPrey, when the IGPredator moves where both species move in response to resource pro- suboptimally it imposes a large fitness cost on the IGPrey, ductivity. This results in a net movement of both species despite the fact that its own dispersal occurs in the optimal into areas of high resource productivity. This means that direction. Thus, when both species move in response to the IGPrey’s net movement is from areas of higher to density, a suboptimal outcome ensues for both species. In lower fitness, while the IGPredator’s net movement is contrast, dispersal in response to resource productivity is from areas of lower to higher fitness. Thus, when dis- suboptimal for the IGPrey but optimal for the IGPredator. persal is suboptimal for the IGPrey but optimal for the Because the IGPrey’s dispersal has little or no effect on IGPredator, we get a more optimal outcome for both the IGPredator, when the IGPrey moves suboptimally it species (i.e., the abundance-productivity relationships imposes no fitness cost on the IGPredator. Thus, when of both species closely approximate that obtained under both species move in response to resource productivity, a fitness-dependent dispersal). more optimal outcome ensues for both species. These observations suggest an asymmetry between the The above results for density-dependent dispersal ensue IGPrey and the IGPredator in their responses to each when emigration is dependent on the density of both con- other’s dispersal. The IGPredator’s dispersal appears to specifics and heterospecifics within a patch, and immi- have a strong effect on the IGPrey but not vice versa. We gration is random. This raises the question of whether a can investigate this potential asymmetry by looking more more optimal outcome would occur if the species use cues closely at how the dispersal strategy and dispersal traits of other than total consumer density, and when emigration one species affect the other species. and immigration are both density dependent. Appendix B Figure 2 illustrates the impact of the IGPredator’s dis- in the online edition of the American Naturalist provides persal on the IGPrey. The IGPrey’s dispersal is random, a detailed analysis of these issues. Here I highlight the key but the IGPredator adopts different dispersal strategies. points. There are two key points to note. First, the IGPredator’s Analysis of the different density responses under ran- dispersal strategy has a strong effect on the IGPrey’s abun- dom versus density-dependent immigration further con- dance patterns but a relatively small effect on its own firms the trophic asymmetry between the IGPrey and the abundance pattern. For instance, the four dispersal strat- IGPredator. The IGPredator’s dispersal traits determine egies of the IGPredator lead to four qualitatively different whether the two species’ abundance patterns conform to or abundance patterns in the IGPrey (fig. 2). Second, for deviate from fitness-dependent dispersal. Interestingly, it Figure 2: Long-term (equilibrium) abundances of the intraguild prey (IGPrey) and the intraguild predator (IGPredator) as a function of the p p p IGPredator’s dispersal traits when the competition–intraguild predation trade-off is strong. The IGPrey disperses randomly (g111h s 0 ), and the IGPredator adopts different dispersal strategies. Lines of increasing thickness respectively depict the abundances in the low-, intermediate-, and p p p high-productivity patches. For random dispersal,b1120.5 , whileb b 0.5 for all the nonrandom dispersal strategies. Other parameter values p p p p p used area1210 ,a 2 ,a 2 ,f 2 , andd 1 .
826 Figure 3: Long-term (equilibrium) abundances of the intraguild prey (IGPrey) and the intraguild predator (IGPredator) as a function of the IGPrey’s p p p dispersal traits when the competition–intraguild predation trade-off is strong. Now the IGPredator disperses randomly (g222h s 0 ), and the IGPrey adopts different dispersal strategies. Lines of increasing thickness respectively depict the abundances in the low-, intermediate-, and high- p p p productivity patches. For random dispersal,b2120.5 , whileb b 0.5 for all the nonrandom dispersal strategies. Other parameter values are as in figure 2.
827 828 The American Naturalist
is the IGPredator’s dispersal rate (b2 ) rather than the den- relationship but not vice versa (app. B). Random dispersal sity response that drives the abundance patterns, with low yields a similar outcome (app. C). dispersal rates leading to interspecific segregation and high dispersal rates leading to interspecific aggregation (app. Discussion B; fig. B1). Segregation is most pronounced when the IGPredator responds to heterospecific (i.e., the IGPrey’s) A great deal is known about how random dispersal influ- density. Density-dependent emigration and immigration ences the outcome of species interactions (e.g., Levin 1974; lead to qualitatively similar results except that the tendency Holt 1985; Murdoch et al. 1992; Bolker and Pacala 1999; for segregation is greater overall and is most pronounced Jansen 2001; Abrams and Wilson 2004; Amarasekare 2006). when the IGPredator responds to heterospecific density Very little, however, is known about how nonrandom dis- (app. B; fig. B2). Thus, density-dependent emigration and persal strategies influence the outcome of species interac- random immigration provide a bet-hedging strategy that tions (Abrams 2007). This is particularly true for com- works quite well when organisms are unable to gauge the munities characterized by both competitive and strength of competition and predation in patches they have predator-prey interactions. And yet, such multitrophic in- yet to colonize. teractions are the basic building blocks of all natural Overall, density-dependent dispersal leads to a less op- communities. timal outcome compared to fitness-dependent dispersal, Here I have presented what is to my knowledge the first even when one considers cues other than total consumer comparative analysis of dispersal strategies for a multi- density. Interspecific segregation does not occur unless the trophic community characterized by competition and pre- IGPredator has extremely low vagility. Even in this case, dation. I have focused on intraguild predation as a rep- complete segregation (with the IGPrey absent from the resentative multitrophic interaction both because it is high-productivity patch and the IGPredator absent from widespread in nature (Polis et al. 1989; Arim and Marquet the high-productivity patch) occurs rarely, if at all (app. 2004) and because it allows for local coexistence via a B). competition-predation trade-off, thus allowing investiga- tions of the interplay between local and spatial mecha- nisms of coexistence. A second novel contribution is the Sensitivity of Results to Key Biological Parameters analysis of how dispersal strategies influence the relation- The above results ensue when the trade-off between com- ship between population abundance and resource pro- petition and IGP is relatively strong and, in the case of ductivity. Despite the importance of abundance-produc- fitness- and habitat-dependent dispersal, when the two tivity relationships to diversity maintenance and ecosystem p species have equal dispersal propensities (b12b ). There- functioning (Kinzig et al. 2001), the impact of spatial dy- fore, it is important to investigate the robustness of these namics, particularly dispersal strategies, on the nature of results to variation in trade-off strength and unequal dis- the relationship has not previously been investigated. persal rates. Here I summarize the key effects of such The most significant finding is an asymmetry between parameter variation. Details are given in appendix C in the IGPrey’s and the IGPredator’s responses to each other’s the online edition of the American Naturalist. dispersal. The IGPrey’s abundance-productivity relation- ship depends crucially on the dispersal strategy and dis- persal behavior (dispersal rate, strength of density depen- Strength of the Competition-IGP Trade-Off dence and habitat preference, fitness detection ability) of The asymmetry between the IGPrey and the IGPredator the IGPredator, but the IGPredator’s abundance-produc- in their response to each other’s dispersal is largely un- tivity relationship is unaffected by the dispersal strategy affected by the strength of the competition-IGP trade-off. or behavior of the IGPrey. For instance, the IGPredator’s A weak trade-off can in some situations enhance the abundance increases monotonically with increasing re- trophic asymmetry (app. C). source productivity regardless of the IGPrey’s dispersal strategy or behavior, while the IGPrey’s abundance can increase, decrease, or become hump shaped with increas- Strength of Dispersal Propensity ing productivity, depending on the IGPredator’s dispersal With fitness- and habitat-dependent dispersal, dispersal strategy and behavior. Thus, the IGPredator’s dispersal rates (bi ) have no effect on abundance-productivity re- strategy and behavior determine the spatial distributions lationships, except when the fitness detection ability (gi ) of both species. and habitat selection ability (hi ) are weak (app. C). With A key issue in the study of dispersal strategies is the cues density-dependent dispersal, the IGPredator’s dispersal rate that organisms use in making dispersal decisions. Here I has a large effect on the IGPrey’s abundance-productivity have considered two cues commonly used by real organisms: Intraguild Predation and Dispersal Strategies 829 density and habitat quality. One would expect density to be IGPredator moves optimally, both species experience a more more informative than habitat quality about fitness differ- optimal outcome than when the IGPrey moves optimally. ences between patches because density is a consumer at- The asymmetry between the IGPrey and the IGPredator tribute that reflects the strength of competition and pre- arises because they interact via both competition and pre- dation within a patch, whereas productivity is a resource dation. The IGPredator has a doubly negative effect on the attribute that provides no information about competition IGPrey (as a competitor and predator), while the IGPrey or predation. However, when the IGPrey and the IGPredator has both a negative (as a competitor) and a positive (as both move in response to density, they become aggregated a prey item) effect on the IGPredator. Because of its greater to high-density habitats (except when the IGPredator has negative impact on the IGPrey via competition and pre- extremely low vagility). In contrast, when both species move dation, the IGPredator’s dispersal has a much stronger in response to resource productivity they become segregated effect on the IGPrey’s fitness than if they engaged in com- to resource-poor and resource-rich habitats. Thus, we have petition or predation. Similarly, because of its weaker neg- the counterintuitive result that dispersal in response to den- ative effect on the IGPredator via competition and pre- sity yields a less optimal outcome than dispersal in response dation, the IGPrey’s dispersal has a weaker effect on the to resource productivity. IGPredator than if they were to engage solely in a com- The key to this puzzle lies in the different constraints petitive interaction. In fact, a dispersal asymmetry between faced by the two species: density is a more useful cue for species is not observed in spatial models of pure resource the IGPrey, who has to acquire resources in the face of predation pressure, while resource productivity is a more competition or apparent competition (Holt and Barfield useful cue for the IGPredator, whose only priority is re- 2003; Abrams and Wilson 2004; Amarasekare et al. 2004). source acquisition. The crucial consequence of this dif- These results have significant implications for both spa- ference is that if the two species use the same cues for tial community ecology and the evolution of dispersal. dispersal, as is likely with members of the same guild, From the perspective of community ecology, the most im- dispersal is necessarily optimal for one and suboptimal for portant insight is the existence of keystone dispersers, spe- the other. For instance, density-dependent dispersal results cies whose dispersal strategy and behavior have a dispro- in the net movement of both species from higher to lower portionately large effect on the spatial distributions of productivity habitats regardless of whether the species re- other species in a community. Such species are likely to spond to conspecific, heterospecific, or total consumer have a significant impact on both natural and agricultural density. For the IGPrey, this constitutes a net movement ecosystems. For instance, maintenance of biodiversity may from areas of lower fitness to areas of higher fitness, while depend crucially on the dispersal strategies that predators, for the IGPredator, it is the opposite. Paradoxically, how- rather than intermediate consumers, adopt in response to ever, the IGPrey suffers a large fitness cost despite the fact habitat fragmentation; similarly, control of invasive pests that its own dispersal is optimal. This occurs because of may depend crucially on whether the dispersal strategies the asymmetry between the IGPrey and the IGPredator: adopted by their natural enemies increase or decrease the the IGPredator’s dispersal induces a qualitative change in fitness of the pest species. the IGPrey’s abundance pattern, causing it to increase rather The asymmetry between IGPrey and IGPredators has im- than decrease with increasing productivity. In contrast, the portant implications for the evolution of dispersal. While IGPrey’s dispersal has no effect on the IGPredator’s abun- this topic has received a great deal of attention lately, most dance, which continues to increase with increasing pro- of the work focuses on single-species populations (e.g., ductivity. Density-dependent dispersal thus leads to inter- McPeek and Holt 1992; Travis et al. 1999; Mathias et al. specific aggregation. (The only exception to this occurs 2001; Parvinen 2002; Armsworth and Roughgarden 2005a) when the IGPredator has extremely low vagility.) Dispersal or competitive interactions with an implicit resource (Arm- in response to resource productivity leads to a more optimal outcome. This is because both species experience a net sworth and Roughgarden 2005a). Investigating the evolu- movement from areas of lower productivity to areas of tion of dispersal in communities with competition and pre- higher productivity, which causes a fitness loss for the dation is an essential next step. On the basis of the above IGPrey but not for the IGPredator. Because the IGPrey’s findings, one would expect trophic position to have a sig- dispersal has little effect on the IGPredator, greater move- nificant impact on evolutionary dynamics. The IGPredators ment of the IGPrey to higher productivity areas simply should evolve a strategy that best facilitates resource ac- results in greater mortality for the IGPrey without adverse- quisition. The strategy evolved by IGPrey is likely to be ly affecting the IGPredator. Habitat-dependent dispersal contingent on whether the IGPredator’s dispersal strategy thus leads to interspecific segregation. The crucial conse- strengthens or ameliorates the antagonistic interaction be- quence of the asymmetry between species is that when the tween them. 830 The American Naturalist
Acknowledgments gradient of resource supply: a microbial experimental model. American Naturalist 157:300–315. This research was supported by National Science Foun- Denno, R. F., G. K. Roderick, K. L. Olmstead, and H. G. Dobel. dation grant DEB-0717350. I thank four anonymous re- 1991. Density-related migration in planthoppers (Homoptera:Del- viewers for many helpful comments on the manuscript. phaciadea): the role of habitat preference. American Naturalist 138: 1513–1541. Diehl, S., and M. Feissel. 2000. Effects of enrichment on three-level Literature Cited food chains with omnivory. American Naturalist 155:200–218. Aars, J., and R. A. Ims. 2000. Population dynamic and genetic con- Fonseca, D. M., and D. D. Hart. 1996. Density-dependent dispersal sequences of spatial density-dependent dispersal in patchy pop- of black fly neonates is mediated by flow. Oikos 75:49–58. ulations. American Naturalist 155:252–265. Harrison, S., C. D. Thomas, and T. M. Lewinsohn. 1995. Testing a Abrams, P. A. 2007. Habitat choice in predator-prey systems: spatial metapopulation model of coexistence in the insect community of instability due to interacting adaptive movements. American Nat- ragwort (Senecio jacobea). American Naturalist 145:546–562. uralist 169:581–594. Herzig, A. L. 1995. Effects of population density on long-distance Abrams, P. A., and W. G. Wilson. 2004. Coexistence of competitors dispersal in the goldenrod beetle Trirhabda virgata. Ecology 76: in metacommunities due to spatial variation in resource growth 2044–2054. rates: does R∗ predict the outcome of competition? Ecology Letters Holt, R. D. 1983. Optimal foraging and the form of the predator 7:929–940. isocline. American Naturalist 122:521–541. Albrectsen, B., and G. Nachman. 2001. Female-biased density- ———. 1985. Population dynamics in two-patch environments: dependent dispersal of a tetripid fly in a fragmented habitat and some anomalous consequences of an optimal habitat distribution. its implication for population regulation. Oikos 94:263–272. Theoretical Population Biology 28:181–208. Amarasekare, P. 2000. Coexistence of competing parasitoids on a Holt, R. D., and M. Barfield. 2003. Impacts of temporal variation patchily distributed host: local vs. spatial mechanisms. Ecology 81: on apparent competition and coexistence in open systems. Oikos 1286–1296. 101:49–58. ———. 2003. Diversity-stability relationships in multi-trophic sys- Holt, R. D., and G. A. Polis. 1997. A theoretical framework for tems: an empirical exploration. Journal of Animal Ecology 72:713– intraguild predation. American Naturalist 149:745–764. 724. Holt, R. D., J. Grover, and D. Tilman. 1994. Simple rules for inter- ———. 2004. Spatial dynamics of mutualistic interactions. Journal specific dominance in systems with exploitative and apparent com- of Animal Ecology 73:128–142. petition. American Naturalist 144:741–771. ———. 2006. Productivity, dispersal and the coexistence of intra- Jansen, V. A. A. 2001. The dynamics of two diffusively coupled pred- guild predators and prey. Journal of Theoretical Biology 243:121– ator-prey populations. Theoretical Population Biology 59:119–131. 133. Kinzig, A. P., S. W. Pacala, and D. Tilman. 2001. The functional Amarasekare, P., and R. Nisbet. 2001. Spatial heterogeneity, source- consequences of biodiversity. Princeton University Press, Prince- sink dynamics and the local coexistence of competing species. ton, NJ. American Naturalist 158:572–584. Krˇivan, V. 1996. Optimal foraging and predator-prey dynamics. The- Amarasekare, P., M. Hoopes, N. Mouquet, and M. Holyoak. 2004. oretical Population Biology 49:265–290. Mechanisms of coexistence in competitive metacommunities. Lei, G., and I. Hanski. 1998. Spatial dynamics of two competing American Naturalist 164:310–326. specialist parasitoids in a host metapopulation. Journal of Animal Arim, M., and P. Marquet. 2004. Intraguild predation: a widespread Ecology 67:422–433. interaction related to species biology. Ecology Letters 7:557–564. Leibold, M. A., M. Holyoak, N. Mouquet, P. Amarasekare, J. M. Armsworth, P. R., and J. E. Roughgarden. 2005a. Disturbance induces Chase, M. F. Hoopes, R. D. Hold, et al. 2004. The metacommunity the contrasting evolution of reinforcement and dispersiveness in concept: a framework for multi-scale community ecology. Ecology directed and random movers. Evolution 59:2083–2096. Letters 7:601–613. ———. 2005b. The impact of directed versus random movement in Leibold, M. A., M. Holyoak, and R. D. Holt. 2005. Metacommunities. population dynamics and biodiversity patterns. American Natu- University of Chicago Press, Chicago. ralist 165:449–465. Bolker, B. M., and S. W. Pacala. 1999. Spatial moment equations for Levin, S. A. 1974. Dispersion and population interactions. American plant competition: understanding spatial strategies and the ad- Naturalist 108:207–228. vantages of short dispersal. American Naturalist 153:575–602. MacNeil, C., J. Prenter, M. Briffa, N. J. Fielding, J. T. A. Dick, and Bonsall, M. B., and R. D. Holt. 2003. The effects of enrichment on G. Riddell. 2004. The replacement of a native freshwater amphipod the dynamics of apparent competitive interactions in stage-struc- by an invader: roles for differential environmental degradation and tured systems. American Naturalist 162:780–795. intraguild predation. Canadian Journal of Fisheries and Aquatic Chase, J. M. 2003. Strong and weak trophic cascades along a pro- Sciences 61:1627–1635. ductivity gradient. Oikos 101:187–195. Mathias, A., E. Kisdi, and I. Olivieri. 2001. Divergent evolution of Chase, J. M., and M. A. Leibold. 2002. Spatial scale dictates the dispersal in a heterogeneous landscape. Evolution 55:246–259. productivity-biodiversity relationship. Nature 416:427–430. McPeek, M. A., and R. D. Holt. 1992. The evolution of dispersal in Chase, J. M., and W. A. Ryberg. 2004. Connectivity, scale-dependence, spatially and temporally varying environments. American Natu- and the productivity-diversity relationship. Ecology Letters 7:676– ralist 140:1010–1027. 683. Mills, N. J. 1994. The structure and complexity of parasitoid com- Codeco, C. T., and J. P. Grover. 2001. Competition along a spatial munities in relation to biological control. Pages 397–417 in B. A. Intraguild Predation and Dispersal Strategies 831
Hawkins and W. Sheehan, eds. Parasitoid community ecology. Sih, A., P. Crowley, M. McPeek, J. Petranka, and K. Strohmeier. 1985. Oxford University Press, Oxford. Predation, competition and prey communities: a review of field Murdoch, W. W., C. J. Briggs, R. M. Nisbet, W. S. C. Gurney, and experiments. Annual Review of Ecology and Systematics 16:269– A. Stewart-Oaten. 1992. Aggregation and stability in metapopu- 311. lation models. American Naturalist 140:41–58. Sutherland, L. J., J. Gill, and K. Norris. 2002. Density-dependent Murray, J. D. 1993. Mathematical biology. Springer, New York. dispersal in animals: concepts, evidence, mechanisms and conse- Navarrete, S. A., and B. A. Menge. 1996. Keystone predation and quences. Pages 134–151 in J. M. Bullock, R. E. Kenward, and R. interaction strength: interactive effects of predators on their main S. Hails, eds. Dispersal ecology. Blackwell, Malden, MA. prey. Ecological Monographs 66:409–429. Tilman, D. 1982. Resource competition and community structure. Nisbet, L. M., and W. S. C. Gurney. 1982. Modelling fluctuating Princeton University Press, Princeton, NJ. populations. Wiley, Chichester. Travis, J. M., D. J. Murrell, and C. Dytham. 1999. The evolution of Noonburg, E., and P. A. Abrams. 2005. Transient dynamics and prey density-dependent dispersal. Proceedings of the Royal Society B: species coexistence with shared resources and predator. American Biological Sciences 266:1837–1842. Naturalist 165:322–335. Wissinger, S. A., G. B. Sparks, G. L. Rouse, W. S. Brown, and H. Parvinen, K. 2002. Evolutionary branching of dispersal strategies in Steltzer. 1996. Intraguild predation and cannibalism among larvae structured metapopulations. Journal of Mathematical Biology 45: of detritivorous caddisflies in subalpine wetlands. Ecology 77: 2421–2430. 106–124. Zwolfer, H. 1971. The structure and effect of parasite complexes Polis, G. A., C. A. Myers, and R. D. Holt. 1989. The ecology and attacking phytophagous host insects. Pages 405–418 in P. J. den evolution of intraguild predation: potential competitors that eat Boer and G. R. Gradwell, eds. Dynamics of populations. PUDOC, each other. Annual Review of Ecology and Systematics 20:297– Wageningen. 330. Rhainds, M., G. Gries, and A. Saleh. 1998. Density and pupation site of apterous female bagworms, Metisa plana (Walker) (Lepidoptera: Psychidae), influence the distribution of emergent larvae. Cana- Associate Editor: William F. Fagan dian Entomologist 130:603–613. Editor: Donald L. DeAngelis