Diversity stability relationships in multitrophic systems: an empirical exploration PRIYANGA AMARASEKARE

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1 Ecology , Diversity stability relationships in multitrophic systems: Blackwell Publishing Ltd. an empirical exploration PRIYANGA AMARASEKARE Department of Ecology and Evolution, University of Chicago, 1101 East 57th Street, Chicago, IL 60637, USA Summary 1. The relationship between diversity and stability is crucial in understanding the dynamics of multitrophic interactions. There are two basic hypotheses about the causal link between diversity and stability. The first is that fluctuations in resource abundance allow consumer coexistence, thus increasing diversity at the consumer trophic level (resource variability hypothesis). The second is that interactions between coexisting consumer species reduce consumer efficiency and dampen population fluctuations, thus increasing consumer resource stability (consumer efficiency hypothesis). 2. The two hypotheses lead to three comparative predictions: (i) fluctuations should be greater (resource variability) or smaller (consumer efficiency) in resource populations with coexisting consumer species, compared to those invaded only by the consumer species superior at resource exploitation; (ii) average resource abundance should be greater (resource variability) or smaller (consumer efficiency) in resource populations with greater fluctuations; and (iii) removal of the consumer species inferior at resource exploitation should increase or not affect resource population fluctuations (resource variability), or always increase them (consumer efficiency). 3. I tested these predictions with data from a host multiparasitoid community: the harlequin bug (Murgantia histrionica) and two specialist parasitoids (Trissolcus murgantiae and Ooencyrtus johnsonii) that attack the bug s eggs. 4. Local host populations with coexisting parasitoids exhibited smaller fluctuations and greater average abundance compared to those with just Trissolcus, the species superior at host exploitation. Local populations that lost Ooencyrtus, the species inferior at host exploitation, exhibited an increase in host population fluctuations compared to those that did not. 5. The results contradict the expectations of the resource variability hypothesis, suggesting that host population fluctuations are unlikely to be driving parasitoid coexistence. They are consistent with the consumer efficiency hypothesis, that interactions between coexisting parasitoid species dampens host population fluctuations. I discuss the implications of these results as well as possible caveats. Key-words: coexistence, diversity, exploitative competition, host parasitoid, interference, multitrophic interactions, stability. Ecology (2003) 72, Ecological Society Introduction The relationship between species diversity and community stability is a central issue in both basic and applied ecology. Whether diversity begets stability or stability begets diversity is key to understanding community function and persistence. It is also crucial in understanding and predicting the impact of species additions Correspondence: amarasek@uchicago.edu due to invasions by exotics, and species losses due to habitat destruction and fragmentation. Theory suggests that the cause and effect relationship between diversity and stability can work both ways. For example, fluctuations in resource abundance can allow multiple consumers to coexist on a common resource (Levins 1979; Armstrong & McGehee 1980; Sommer 1985; Huisman & Weissing 1999, 2001). Thus, instability in the resource trophic level can increase diversity at the consumer trophic level. On the other

2 714 P. Amarasekare hand, interactions between consumer species that exploit a common resource can dampen the fluctuations inherent in strongly coupled consumer resource systems (McCann & Hastings 1997; Huxel & McCann 1998; McCann, Hastings & Huxel 1998). Thus, diversity at the consumer trophic level can stabilize the interaction between consumer and resource trophic levels. Although the link between diversity and stability is straightforward in theory, elucidating it in practice remains a challenge. Empirical data are scarce, particularly for multitrophic interactions. The difficulty lies in separating the effects of competitive interactions within the consumer trophic level from the effects of interactions between consumer and resource trophic levels. This separation is crucial in distinguishing between the two hypotheses suggested by theory. Here I present an empirical test of the relationship between diversity and stability. I begin with a summary of the theory and hypotheses. I test comparative predictions for the two hypotheses with data from an insect host parasitoid system and then discuss the results in light of their relevance to multiconsumer food webs in patchy environments. Theory and hypotheses It is important to note that diversity (e.g. species richness) is an outcome rather than a mechanism. The mechanisms that produce diversity are those by which interacting species coexist. Hence, the important relationship to consider is that between coexistence and stability. The concept of stability itself needs to be defined explicitly. Stability in the mathematical sense refers to a population s ability to return to equilibrium following a perturbation (May 1974; Murray 1993). Investigations of diversity stability relationships (e.g. McCann 2000) use a broader definition of stability, the tendency for populations to move away from extremes of low or high densities. Because densities are bounded, this definition of stability implies reduced population variability. It is also the mathematical equivalent of transitioning from complex (e.g. chaotic or cyclic) to more regular and simple dynamics (Hastings 1993; Doebeli 1995). Because empirical studies typically quantify stability in terms of population variability, this definition provides a way to reconcile both mathematical and ecological notions of stability. Diversity stability relationships in multitrophic systems result from the interplay between competition and consumer resource dynamics. The cause and effect relationship between diversity and stability can take two forms. The first I term the resource variability hypothesis: stability/instability in resource dynamics determines whether multiple consumer species can coexist on a common resource. The second I term the consumer efficiency hypothesis: mechanisms by which multiple consumers coexist on a common resource increase or decrease overall consumer efficiency, and hence the stability/instability of consumer resource dynamics. Below I describe the two hypothesis and the resulting comparative predictions. RESOURCE VARIABILITY HYPOTHESIS It is well known that consumer species interacting indirectly via exploitative competition for a biotic resource (i.e. a resource that grows and reproduces typically on the same time scale as its consumers; MacArthur & Levins 1964; Armstrong & MeGehee 1980) cannot coexist at a point attractor. The species that can maintain a positive growth rate at the lowest resource level will exclude all other species (R* rule; Tilman 1982). If, however, the resource fluctuates in abundance such that average resource abundance exceeds that required for the inferior competitor to invade and establish itself, then multiple consumers can coexist on a common resource (Armstrong & McGehee 1976, 1980; Kemp & Mitsch 1979; Levins 1979; Powell & Richardson 1985; Huisman & Weissing 1999). Coexistence occurs via a form of niche partitioning: one consumer exploits the resource more efficiently at low resource abundances and the other at high resource abundances (Yodzis 1989). Implicit in this model, therefore, is a difference between coexisting consumer species in their resource exploitation efficiency. Resource fluctuations could arise due to exogenous factors (e.g. seasonal or random fluctuations in weather; Kemp & Mitsch 1979; Levins 1979) or as a result of overexploitation by consumers (Armstrong & McGehee 1976, 1980; Huisman & Weissing 1999). In the latter case, an increase in resource productivity (via an increase in per capita resource production or resource carrying capacity) should increase fluctuations and hence the possibility of consumer coexistence. This is because an increase in productivity weakens resource self-limitation relative to consumer efficiency, thus increasing the potential for resource overexploitation (the paradox of enrichment, Rosenzweig 1971). CONSUMER EFFICIENCY HYPOTHESIS As discussed above, two consumer species engaging in exploitative competition for a biotic resource cannot coexist unless the resource itself fluctuates in abundance. In nature, however, negative effects of exploitative competition may be ameliorated by other species interactions. For instance, consumers that share a predator may be subject to keystone predation (Paine 1966; Sih et al. 1985; Navarrete & Menge 1996) or apparent competition (Holt 1977; Holt & Lawton 1993, 1994; Abrams 1998). Alternatively, consumer species themselves may engage in interactions other than pure exploitative competition. Examples include interference competition (Rice 1974; Harper 1977; Walls 1990; NiIsson 1994; Kennedy & White 1996; Ridenour &

3 715 Coexistence and stability in multitrophic systems Callaway 2001) and intraguild predation/parasitism (i.e. two consumer species exploit the same resource but one consumer also preys on or parasitizes the other; Polis, Myers & Holt 1989; Rosenheim et al. 1995). Theory shows that consumer species engaging in interactions besides exploitative competition can coexist on a non-fluctuating biotic resource provided these interactions reduce overall consumer efficiency and increase resource abundance above that required for an inferior competitor to invade (Hochberg & Holt 1990; Briggs 1993; Holt & Polis 1997). Moreover, the reduction in consumer efficiency reduces the potential for resource overexploitation, thus dampening population fluctuations in both resource and consumer species (McCann & Hastings 1997; McCann et al. 1998). In this view, coexistence and stability both result from an overall decline in consumer efficiency. Hence, coexisting consumer species should exhibit an interspecific trade-off such that the species superior at resource exploitation should be inferior at interference competition or intraguild predation, or be more vulnerable to a shared predator (Hochberg & Holt 1990; Briggs 1993; Holt & Polis 1997; McCann et al. 1998). Resource productivity determines whether coexistence is possible via such a trade-off (Holt & Polis 1997). Only the superior resource exploiter can persist at low productivity, while only the inferior resource exploiter can persist at high productivity. Coexistence is possible at intermediate productivity. Although increased productivity itself can increase resource fluctuations, reduced consumer efficiency at productivity levels that allow coexistence and beyond should counteract this tendency. This in turn should allow for greater stability at higher levels of productivity, the opposite of what one would expect under the resource variability hypothesis. COMPARATIVE PREDICTIONS ABOUT THE RELATIONSHIP BETWEEN DIVERSITY AND STABILITY The two hypotheses about the diversity stability relationship lead to three comparative predictions (Table 1). Prediction 1: resource population fluctuations and invasibility If stability/instability in resource population dynamics drives consumer coexistence, then resource populations invaded by both superior and inferior competitors should exhibit greater fluctuations in abundance (and hence greater average abundance) compared to resource populations invaded only by the superior competitor. (The superior competitor is the species more efficient at exploiting the resource at low resource abundances.) This is because the inferior resource competitor can invade only when fluctuations are sufficiently large that average resource abundance exceeds that required for it to maintain a positive growth rate (Armstrong & McGehee 1976, 1980). This prediction holds regardless of whether resource fluctuations are exogenous (e.g. due to weather) or endogenous (e.g. due to feedback between consumers and the resource). If, on the other hand, consumer efficiency drives stability/instability, resource populations invaded by both superior and inferior competitors should exhibit smaller fluctuations in abundance compared to resource populations invaded only by the superior resource exploiter. These outcomes are robust to changes in resource productivity in time or space. Increased productivity will increase fluctuations and increase invasibility under the resource variability hypothesis, while increased productivity will increase invasibility and reduce fluctuations under the consumer efficiency hypothesis. Prediction 2: average resource abundance Coexistence requires that consumer species maintain a positive growth rate at the ambient level of resources (R* rule; Tilman 1982). If consumer coexistence results from resource fluctuations, average resource abundance should be greater in resource populations with fluctuations large enough to allow invasion of both superior and inferior resource exploiters compared to those invaded only by the superior resource exploiter. If reduced consumer efficiency dampens resource fluctuations, average resource abundance should be greater Table 1. Comparative predictions for the two hypotheses about the link between coexistence and stability Resource variability Consumer efficiency 1. Resource fluctuations Greater in populations invaded Smaller in populations invaded by both consumers 1 by both consumers 1 2. Average resource Greater in populations with Greater in populations with abundance larger fluctuations that with smaller fluctuations as allow invasion of both a result of invasion by both consumers 1 consumers 1 3. Removal of inferior Does not affect 2 or increases 3 Increases resource resource exploiter resource fluctuations population fluctuations 1 Compared to resource populations invaded only by the superior resource exploiter; 2 if fluctuations are exogenously driven; 3 if fluctuations are endogenously driven.

4 716 P. Amarasekare in resource populations that exhibit smaller fluctuations (as a result of being invaded by both superior and inferior competitors) compared to those that exhibit larger fluctuations (as a result of being invaded only by the superior resource exploiter). These outcomes are again robust to changes in resource productivity. Under the resource variability hypothesis, an increase in resource productivity will increase fluctuations and hence average resource abundance. Under the consumer efficiency hypothesis, an increase in resource productivity will increase resource abundance which, because it leads to consumer coexistence and reduced consumer efficiency, will counteract the tendency for increased fluctuations due to increased productivity. Prediction 3: consequences of removing the inferior competitor from a community of coexisting consumers The inferior competitor is the species less efficient at exploiting the resource at low resource abundances. Under the resource variability hypothesis, resource fluctuations enable consumer coexistence by allowing the inferior resource competitor to invade when rare. If resource fluctuations are generated by exogenous factors unrelated to the consumer resource interaction, removal of the inferior resource competitor should not affect their magnitude; if resource fluctuations are generated by feedback between consumers and the resource, removal of the inferior resource competitor can increase fluctuations (Armstrong & MeGehee 1980; Yodzis 1989). Under the resource variability hypothesis, therefore, removal of the inferior resource exploiter either increases resource population fluctuations or does not affect them. Under the consumer efficiency hypothesis, consumer coexistence dampens resource fluctuations by reducing overall consumer efficiency. Hence, removal of the inferior competitor should always increase resource population fluctuations. These outcomes are unchanged by variation in resource productivity. For both hypotheses, a reduction in productivity increases the likelihood that the inferior resource exploiter is eliminated while an increase in productivity has the opposite effect. Testing predictions 1 and 2 requires a spatial comparison between resource populations with coexisting consumers vs. those that cannot be invaded by the inferior resource exploiter. Testing prediction 3 requires a temporal comparison of the same set of resource populations before and after the removal of the inferior resource competitor. I make these comparisons using data from an insect host parasitoid system. Study system NATURAL HISTORY The system consists of the harlequin bug (Murgantia histrionica (Hahn); Hemiptera: Pentatomidae), a herbivore on bladderpod (Isomeris arborea (Nutt.); Capparaceae), and two specialist parasitoids (Trissolcus murgantiae (Ashm.); Hymenoptera: Scelionidae and Ooencyrtus johnsonii (How.); Hymenoptera: Eneyrtidae) that attack the bug s eggs. The host plant Isomeris is a coastal sage scrub endemic (Goldstein et al. 1991). The secondary compounds it produces (glucoisinolates) render it unpalatable (Nuss 1983). The only other insect species that inhabit Isomeris are the flea beetle and the pollen beetle, neither of which is a significant competitor for the harlequin bugs (Sjaarda 1989; Amarasekare 1998). The bug also lacks natural predators, which is probably due to sequestration of glucoisinolates from the host plant (Nuss 1983). The bugs are unpalatable to bird and lizard predators (Boyd Collier, personal communication). The two egg parasitoids T. murgantiae and O. johnsonii are the only known natural enemies of the bug (Walker & Anderson 1933; Huffaker 1941; Sjaarda 1989; Amarasekare 1998). Local dynamics therefore consist of the multiparasitoid single host interaction. O. johnsonii is both gregarious and engages in superparasitism (Sjaarda 1989; Amarasekare 1998, 2000a). One to three adults may emerge from one host egg (Walker & Anderson 1933). Superparasitism is absent in the solitary T. murgantiae (Sjaarda 1989; Amarasekare 1998, 2000a). Only one adult develops within a host egg. The bugs have three generations per year: spring, summer and autumn (Amarasekare 2000a) and the two parasitoids, about nine generations per year (Sjaarda 1989; Amarasekare 1998). I have been studying harlequin bugs within a protected area of the Crystal Cove State Park in western Orange County, California. The study site occurs along exposed coastal bluffs m above the Pacific ocean, and provides a closed system bounded by residential areas and the ocean (Amarasekare 1998, 2000a). Isomeris is naturally patchily distributed, which creates a hierarchical spatial structure. Individual bushes are aggregated into discrete patches separated by an uninhabitable matrix of annual grasses and weeds. I used a combination of mark recapture experiments and spatial variation in abundances to establish that a patch of host plants constitutes the local population for both bugs and parasitoids (Amarasekare 1998, 2000b). The study site contains two types of host plant patches. In six patches only Trissolcus is present. In the remaining nine patches both Trissolcus and Ooencyrtus coexist on the host. The one-parasitoid patches are smaller in size (mean number of bushes ± SE: oneparasitoid patches = 8 ± 1; two-parasitoid patches = 21 ± 4; n = 15 patches, t-test, P = ; Amarasekare 1998) and have lower maximum bug densities (mean ± SE: one-parasitoid patches = 1 ± 0 3 bugs/m 2 ; twoparasitoid patches = 4 ± 0 9 bugs/m 2 ; n = 15 patches, t- test, P = 0 04; Amarasekare 2000a). The system has several features that make it ideal for testing hypotheses about coexistence and stability. First, the community consists of a small number of specialist species and hence its dynamics can be easily

5 717 Coexistence and stability in multitrophic systems understood. Secondly, there is clear evidence of competition between parasitoid species (Sjaarda 1989; Amarasekare 1998, 2000a,b), and the effects on host population dynamics are dramatic. Thirdly, the patchy distribution of the host plant yields multiple local populations of bugs and parasitoids in the same locality, with some containing both parasitoid species and others just one. This distribution allows direct comparison of resource fluctuations in populations with and without coexisting parasitoid species. BACKGROUND DATA Role of spatial processes in coexistence and stability Theory predicts that spatial processes can allow competing species to coexist (Levins & Culver 1971; Levin 1974; Hastings 1980; Nee & May 1992; Tilman et al. 1994; Amarasekare & Nisbet 2001) as well as stabilize host parasitoid dynamics (e.g. Murdoch & Oaten 1975; Reeve 1988; Murdoch et al. 1992; Taylor 1998). I conducted field experiments to test whether parasitoid coexistence occurred via a dispersal competition trade-off (Hastings 1980; Nee & May 1992; Tilman et al. 1994). I created experimental archipelagos with small and large interpatch distances (Near and Far treatments, respectively; Amarasekare 2000b) and measured the colonization ability and long-term persistence of each parasitoid species. Both parasitoid species took significantly longer to colonize the Far treatment than the Near treatment, suggesting that they have comparable dispersal abilities. In the long term (over 35 parasitoid generations) competitive exclusion did not occur even when interpatch distances were reduced below 30% of those observed in natural populations. These data suggest that parasitoid coexistence can occur in the absence of a dispersal advantage to the inferior competitor (Amarasekare 2000b), a result that also emerges in data from natural populations (Amarasekare 2000a). Because the Near and Far treatments did not differ in parasitoid composition, I next asked whether large interpatch distances could destabilize host parasitoid dynamics by restricting host dispersal. No local extinctions of bugs or parasitoids were observed. Bug populations in the Far treatment were no more variable than those in the Near treatment. In fact, temporal variability in the experimentally isolated patches was comparable to that observed in highly isolated natural populations (Amarasekare 2000b). These data argue against a strong effect of spatial dynamics on this host parasitoid system. They suggest that local processes drive both parasitoid coexistence as well as host parasitoid dynamics. Local mechanisms for parasitoid coexistence I have previously excluded several local mechanisms for parasitoid coexistence: alternative hosts, priority effects, predation and spatial niche partitioning via aggregation of attacks (Amarasekare 1998, 2000a). Available data are consistent with two hypotheses: coexistence via resource population fluctuations, and coexistence via a trade-off between resource exploitation and interference. Previous data suggest that Trissolcus is superior at exploitative competition. Laboratory experiments show that Trissolcus has a higher attack rate and parasitizes a significantly higher fraction of host eggs than Ooencyrtus over a wide range of temperatures (Sjaarda 1989). Two lines of field evidence also support this finding (Amarasekare 2000a). First, Trissolcus is able to persist at significantly lower egg densities than Ooencyrtus. This result is consistent with the prediction (Tilman 1982; Holt & Polis 1997) that the more efficient resource exploiter should be able to maintain itself at lower resource levels than a less efficient species. Second, when released from interference competition by Ooencyrtus, Trissolcus attains higher parasitism rates and inflicts greater egg mortality (mean annual parasitism ± SE: both parasitoids = 0 61 ± 0 03; Trissolcus alone = 0 71 ± 0 07; t-test, P = 0 09, n = 6 patches; Amarasekare 2000a), suggesting superior exploitation efficiency compared to Ooencyrtus. The absence of superparasitism (a form of intraspecific interference competition; van Alphen & Visser 1990) in Trissolcus may also contribute to its greater efficiency. Although Ooencyrtus is inferior in exploitative competition, it appears to have an advantage in interference competition. Interference occurs via multiparasitism. Laboratory experiments show that Trissolcus has zero success in parasitizing eggs that have been parasitized previously by Ooencyrtus, while the latter is able to multiparasitize about 50% of the eggs it encounters (Sjaarda 1989). Larvae of Ooencyrtus both kill and consume larvae of Trissolcus while developing inside the host egg. In fact, Ooencyrtus larvae can outcompete those of Trissolcus even when the latter has had a 5 9- day start in oviposition (Sjaarda 1989). If the parasitoids coexist via a trade-off between exploitation and interference, one expects to see the elimination of one species or the other along a gradient of host productivity (Polis et al. 1989; Holt & Polis 1997). For instance, only the efficient competitor should persist at low productivity, while coexistence is expected at higher productivity. In fact, patches occupied only by Trissolcus exhibit significantly lower per capita egg productivity compared to the two parasitoid patches (ANOVA contrast analysis, P < 0 05, n = 15 patches; Amarasekare 2000a), a pattern that is consistent across multiple years (Amarasekare 2000a). The existence of one-parasitoid patches with just Trissolcus is not due to a dispersal limitation by Ooencyrtus. Very small numbers of Ooencyrtus (e.g. < 1% parasitism) were observed in these patches at the time it typically emerges (April May) but not thereafter (Amarasekare 2000a). This suggests that Ooencyrtus is able to find these patches, but fails to invade and establish because of low egg productivity.

6 718 P. Amarasekare Theory also predicts that a decline in productivity in patches where coexistence is observed typically should lead to elimination of the species inferior at host exploitation (Holt & Polis 1997). Elimination of Ooencyrtus in a subset of the two-parasitoid patches was associated with a significant decline in per capita egg productivity (mean ± SE) decline: patches that lost Ooencyrtus = 1 32 ± 0 29, patches that did not lose Ooencyrtus = 0 01 ± 0 07, paired t-test, P = , n = 9 patches; Amarasekare 2000a). Re-establishment of Ooencyrtus in these patches was correlated strongly with the degree to which egg productivity returned to preperturbation levels (r = 0 82 ± 0 08, P = 0 03, n = 6 patches; Amarasekare 2000a). These results suggest that parasitoid coexistence could occur via an interspecific trade-off between exploitation and interference. However, coexistence could occur even in the absence of such a trade-off, if the host fluctuates in abundance such that Trissolcus is superior at host exploitation at low host abundances while Ooeneyrtus is superior at high abundances. Methods PREDICTIONS 1 AND 2: RESOURCE POPULATION FLUCTUATIONS AND AVERAGE RESOURCE ABUNDANCE Testing these predictions involves a spatial comparison between host patches with coexisting parasitoids vs. host patches invaded only by Trissolcus. If the parasitoids coexist because fluctuations in bug abundance allow the species inferior at resource exploitation (Ooencyrtus) to invade and establish itself (resource variability hypothesis), one would expect greater fluctuations in bug abundance in patches in which Ooencyrtus coexists with Trissolcus compared to patches with just Trissolcus. One would also expect average bug abundance to be greater in patches that exhibit greater population fluctuations. On the other hand, if the parasitoids coexist because the species inferior at resource exploitation (Ooencyrtus) is superior at interference competition (consumer efficiency hypothesis), then one would expect bug population fluctuations to be lower, and average bug abundance to be higher, in patches with coexisting parasitoids compared to patches with just Trissolcus. I tested these predictions with time series data. I conducted monthly surveys of all 15 patches at the Crystal Cove site from April 1994 to December This period covered 12 bug generations and about 35 parasitoid generations. I surveyed all bushes within a patch if the number of bushes 10, or sampled 10 bushes (using stratified random sampling to obtain spatially representative data for the larger patches) if the number of bushes > 10. I counted the number of eggs and adult harlequin bugs on each bush. I quantified the density of each life-history stage as the number of individuals of that stage on the bush divided by the canopy surface area (calculated by approximating the surface area to that of a spheroid). Each month I marked all newly laid egg clusters on the I. arborea bushes being censused. I collected all marked egg clusters after 30 days, which allowed sufficient time for all eggs of the cohort to have hatched. Eggs were examined under a dissecting microscope. The fact that the bugs and parasitoids had distinct methods of emergence made it possible to score the fate of all hatched eggs accurately (see details in Amarasekare 2000a,b). The monthly parasitism rate for each species was quantified as the number of eggs parasitized by that species divided by the total number of eggs. PREDICTION 3: DYNAMIC CONSEQUENCES OF REMOVING THE SPECIES INFERIOR AT RESOURCE EXPLOITATION Testing this prediction requires a temporal comparison of the same set of two-parasitoid patches before and after the removal of the inferior resource exploiter (Ooencyrtus). A natural experiment allowed me to test this prediction. In 1995 Ooencyrtus failed to establish itself in six of the nine two-parasitoid patches (Amarasekare 2000a). This effectively converted the six two-parasitoid patches to Trissolcus-only patches. The two-parasitoid patches that lost Ooencyrtus and those that did not are comparable in size and plant quality (Amarasekare 2000a). The fact that they are not segregated in space discounts the possibility of an intrinsic difference due to soil or plant quality (Amarasekare 1998, 2000a). I measured adult bug density in the twoparasitoid patches both before and after the loss of Ooencyrtus, and quantified population fluctuations as described below. QUANTIFYING POPULATION FLUCTUATIONS Temporal variability in population fluctuations is measured typically as the standard deviation (SD) of the logarithm of consecutive population censuses (SD[log(N)]; cf. Murdoch & Walde 1989; Murdoch et al. 1996). Logarithmic transformation creates problems when zero values are observed in the data, which is rectified by adding a constant to the zero observations (Stewart-Oaten, Walde & Murdoch 1995). The corrected measure, however, is biased because it underestimates the variability in populations that are rare (McArdle, Gaston & Lawton 1990). An alternative measure that shares some of the advantages of SD[log(N)] but is not affected by zeros is the coefficient of variation ( CV SD( N = ) ). The coefficient of variation has the added N advantage that it provides for direct comparison of variability among populations that differ in their mean abundances (McArdle et al. 1990). I quantified the magnitude of resource population fluctuations using both SD[log(N)] and CV. Stewart- Oaten et al. (1995) suggest several methods for dealing

7 719 Coexistence and stability in multitrophic systems with zeros when calculating SD (see also Murdoch et al. 1996). I chose the option of adding a constant (one-sixth of the smallest density or fraction parasitized) to the zero observations. This is the method that appears to have the fewest drawbacks (Stewart-Oaten et al. 1995). Because I am interested in the relative variability across treatments rather than in the absolute variability of any particular treatment, choice of this particular method over any other is unlikely to pose a problem. I quantified resource fluctuations both in terms of egg density fluctuations (the resource that the parasitoids compete for) and adult bug density fluctuations. While it is possible that egg density fluctuations may allow parasitoid coexistence, any effects the parasitoids have on the host have to be translated into an effect at the level of adult host population dynamics (Briggs 1993). Hence, it is important to investigate the causes or consequences of resource fluctuations both at the particular life-history stage that the parasitoids utilize (eggs) as well the adult host stage. STATISTICAL ANALYSES Predictions 1 and 2: resource abundance and fluctuations I used temporal variability in resource population fluctuations as the dependent variable in a two-way ANOVA with patch type (Trissolcus-only vs. two-parasitoid) and year ( ) as independent variables. If resource fluctuations are driving coexistence (resource variability hypothesis) or coexistence is dampening resource population fluctuations (consumer efficiency hypothesis), one patch type should exhibit greater resource fluctuations than the other. Hence, one should expect a significant effect of patch type but not a year patch type interaction. An interaction effect would suggest that resource fluctuations are greater in one patch type in some years and in the other patch type in other years, which is inconsistent with a cause and effect relationship between coexistence and stability. If there is no statistically distinguishable year patch type interaction, linear contrast analysis (Winer, Brown & Michaels 1991; Sokal & Rohlf 1995) can be used to distinguish between whether resource fluctuations are greater in the two-parasitoid patches than in the Trissolcus-only patches (resource variability hypothesis) or vice versa (consumer efficiency hypothesis). The two hypotheses about coexistence and stability both predict that average resource abundance should be greater in the patches with coexisting parasitoids. This prediction can also be tested with a two-way ANOVA design with patch type and year as independent variables. As with resource fluctuations, one should expect a significant patch type effect and a non-significant patch type year interaction. If these expectations are realized, then linear contrast analysis can reveal whether or not average resource abundance is greater in fluctuating resource populations compared to nonfluctuating ones (resource variability hypothesis) or vice versa (consumer efficiency hypothesis). Prediction 3: dynamic consequences of removing the inferior resource competitor If the parasitoid species coexist by virtue of fluctuations in the host population (resource variability hypothesis), removal of the species inferior at resource exploitation (Ooencyrtus) should either increase bug population fluctuations (if fluctuations result from feedback between bugs and parasitoids) or not affect them (if fluctuations result from factors external to the bug parasitoid interaction). If the parasitoids coexist because the species inferior at resource exploitation is superior at interference (consumer efficiency hypothesis), removal of the inferior resource exploiter should always increase bug population fluctuations. I used a paired t-test to ask whether the perturbation (loss of Ooencyrtus) likely to have caused the impact (increase in resource population fluctuations) is greater in the patches that lost Ooencyrtus compared to patches that did not change status. As I am interested in the population dynamic consequences of removing the inferior competitor, I used adult bug population fluctuations as the dependent variable in the analysis. One disadvantage of the natural experiment was that treatments were not randomized among patches. Hence, one cannot eliminate the possibility that bug population fluctuations were affected by other factors besides the loss of Ooencytus (see Discussion). Results PREDICTION 1: RESOURCE POPULATION FLUCTUATIONS The two-way ANOVA on adult bug population fluctuations revealed a non-significant patch type year interaction (P = 0 17, n = 15 patches), suggesting that population fluctuations are consistently greater/ smaller in one patch type as opposed to the other. This was confirmed by a significant patch type effect in the overall ANOVA (P < 0 001, n = 15 patches) and by linear contrasts of the two patch types within each year (P < in 1994, 1996 and 1997, P = 0 08 in 1995). The contrast analysis shows that bug population fluctuations are consistently greater in the single parasitoid patches with just Trissolcus, compared to the two-parasitoid patches (Fig. 1). It is interesting to note that the difference in temporal variability between patch types is only marginally significant in 1995, the year when the failure of Ooencyrtus to establish itself in a subset of the twoparasitoid patches was associated with an increase in bug population fluctuations in these patches (see below). The year effect was marginally significant (P = 0 07). Fluctuations in egg density showed a similar pattern, with a statistically indistinguishable patch type year interaction (P = 0. 1, n = 15 patches), and a highly

8 720 P. Amarasekare Fig. 1. Temporal variability (mean CV + SE) in egg (top panel) and adult (bottom panel) bug density for the two patch types. Open bars represent the two-parasitoid patches and the black bars, the Trissolcus-only patches. Fluctuations in egg and adult bug density are consistently greater in the Trissolcusonly patches compared to the two-parasitoid patches. significant patch type effect (P < 0 001). Linear contrast analysis showed that egg density fluctuations are consistently greater in the Trissolcus-only patches (P < in 1994 and 1997, P = 0 03 in 1995 and P = in 1996; Fig. 1). The year effect was significant (P = 0 002). Two-way ANOVA of egg and adult bug density fluctuations quantified as SD[log(N)] gave qualitatively similar results. These results show that fluctuations in both egg and adult bug density are consistently greater in the Trissolcus-only patches compared to the two-parasitoid patches. PREDICTION 2: AVERAGE RESOURCE ABUNDANCE Two-way ANOVA for adult bug density showed that both year (P = 0 28, n = 15 patches) and patch type year interaction (P = 0 52) effects were statistically indistinguishable. The patch type effect, however, is highly significant (P < ). Contrast analysis shows that average adult bug density is consistently greater in the two-parasitoid patches compared to the Trissolcusonly patches (P < 0 004; Fig. 2). Fig. 2. Average abundance (+ SE) of eggs (top panel) and adult harlequin bugs (bottom panel) in the two-parasitoid (open bars) and Trissolcus-only (black bars) patches. Both egg and adult bug abundance are consistently greater in the twoparasitoid patches compared to the Trissolcus-only patches. Egg density shows a similar pattern with a nonsignificant patch type year interaction (P = 0 84) and a highly significant patch type effect (P < ). Again, contrast analysis shows average egg density to be consistently greater in the two parasitoid patches compared to patches with just Trissolcus (P < ; Fig. 2). Unlike adult bug density, the year effect is significant (P = 0 03), with total egg density declining over time regardless of patch type (Fig. 2). Results of predictions 1 and 2 show that host populations with coexisting parasitoid species have higher host abundance and exhibit fewer fluctuations compared to those that contain only Trissolcus. This outcome is consistent with the hypothesis of coexistence via a trade-off between exploitation and interference (consumer efficiency), but not with that of coexistence via resource population fluctuations (resource variability). PREDICTION 3: DYNAMIC CONSEQUENCES OF REMOVING THE INFERIOR COMPETITOR Under the resource variability hypothesis, host population fluctuations allow the two parasitoid species to coexist via a form of niche partitioning, such that Trissolcus is more efficient at host exploitation at low

9 721 Coexistence and stability in multitrophic systems host abundances while Ooencyrtus is more efficient at high host abundances. Under this hypothesis, removal of Ooencyrtus should either increase bug population fluctuations (if fluctuations are driven by feedback between bugs and parasitoids) or not affect them (if fluctuations are driven by exogenous factors such as weather or disturbances). Under the consumer efficiency hypothesis, interference by Ooencyrtus reduces Trissolcus exploitation efficiency, which in turn should lead to a dampening of host population fluctuations. In this case, parasitoid coexistence drives host fluctuations and not vice versa. Hence, removal of Ooencyrtus should always increase bug population fluctuations. The results show a large increase in adult bug population fluctuations in patches that lost Ooencyrtus compared to patches that stayed the same (mean change in CV (± SE) from 1994 to 1995: patches that lost Ooencyrtus = 38 9 ± 9 0, patches that did not lose Ooencyrtus = 17 7 ± 8 2, n = 8 patches, paired t-test, P = 0 06). The marginal significance is due to the low statistical power (i.e. the probability of rejecting the null hypothesis when it is false; Zar 1995). A post-hoc power analysis shows that the power of the test given the available number of patches is only 50%, and that at least eight patches per treatment are necessary to increase the power to 90%. In fact, if the Trissolcusonly patches are included in the control group (which makes for a conservative test as these patches exhibit greater fluctuations), the observed increase in variability is highly significant (mean change in CV (± SE) from 1994 to 1995: patches that lost Ooencyrtus = 38 9 ± 9 0, patches that did not change status = 4 7 ± 11 2, n = 14 patches, paired t-test, P = 0 005) despite the greater variability among patches in the control group. If the increase in bug population fluctuations is in fact a result of the loss of Ooencyrtus in 1995, one would expect population fluctuations to decrease in magnitude upon recolonization by Ooencyrtus. I found a significant negative correlation between bug population fluctuations and re-establishment of Ooencyrtus in 1996 (r = 0 78 ± 0 12, P < 0 05, n = 6 patches). For example, patches in which Ooencyrtus re-established itself and approached typical parasitism levels showed a 30 70% decline in temporal variability from 1995 to 1996, while patches in which Ooencyrtus re-established but did not reach typical parasitism levels the decline in temporal variability was less than 25%. The negative correlation was less strong in 1997 (r = 0 50 ± 0 17, P = 0 09, n = 6 patches), because of the variation among patches in their degree of recovery in (These results for prediction 3 are unaltered when the analysis is repeated with SD rather than CV.) The correlation between recovery of Ooencyrtus and the decline in bug population fluctuations in subsequent years suggests strongly that the loss of Ooencyrtus was responsible for the increase in population fluctuations observed in the two-parasitoid patches in Taken together, the results for the three predictions are inconsistent with the resource variability hypothesis. All results are consistent with the consumer efficiency hypothesis. Discussion Understanding the link between diversity and stability is critical to understanding the dynamics and persistence of multitrophic interactions. Although there is a great deal of theory on the cause and effect relationship between diversity and stability, empirical investigations of the causal link have been few. The two hypotheses about diversity stability relationships in multitrophic systems lead to a set of comparative predictions. I tested these predictions with data from a naturally occurring host multiparasitoid system. The data are inconsistent with the hypothesis that host population fluctuations enable parasitoid coexistence. All data are consistent with the hypothesis that the mechanism of parasitoid coexistence (a tradeoff between resource exploitation and interference) reduces parasitoid efficiency and dampens host population fluctuations. The data, however, are observational and hence does not constitute proof of the consumer efficiency hypothesis. Field experiments that investigate diversity stability relationships are few, for the good reason that it is exceedingly difficult to conduct species removals and other required manipulations at the spatial scales on which population dynamics occur (McCann 2000). In the absence of experimental evidence, observational studies can provide some insights into how diversity stability relationships operate in nature. The issue is to identify possible confounding factors that could also lead to the pattern observed. In the host parasitoid system I studied, resource abundance (egg and adult bug density) and resource productivity (per capita egg production) are consistently lower in patches with just Trissolcus (the species superior at resource exploitation) compared to patches in which Trissolcus and Ooencyrtus coexist. These results are consistent with the R* rule (Tilman 1982), that only the superior resource exploiter should persist at low resource abundances, and also with the prediction from intraguild predation theory (Holt & Polis 1997) that only the superior resource exploiter should be able to invade areas of low resource productivity. The second observation that resource population fluctuations are consistently higher in the Trissolcusonly patches is consistent with predictions from consumer resource theory (Rosenzweig & MacArthur 1963; Rosenzweig 1971; Gurney & Nisbet 1998): an efficient consumer that maintains itself at low resource abundances can overexploit the resource, leading to large fluctuations in resource and consumer abundance. If the differences between patches in resource abundance and variability result from random environmental fluctuations or some other factor unrelated to

10 722 P. Amarasekare the host parasitoid interaction, then one would not expect patches with coexisting parasitoids to considently exhibit higher resource abundance and lower resource variability compared to patches with just Trissolcus. While this does not eliminate the possibility that other factors may be driving the observed pattern, it makes it less likely than if patterns of resource abundance and variability did not show an exact match with patterns of parasitoid coexistence. The loss of Ooencyrtus from a subset of the twoparasitoid patches and the subsequent increase in host population fluctuations occurred in a natural experiment. As I had no control over which patches lost Ooencyrtus and which patches did not, it is possible that some factor other than the elimination of Ooencyrtus caused the increase in host population fluctuations. However, the fact that Ooencyrtus elimination was accompanied by a large reduction in per capita egg productivity, and that the re-establishment of Ooencyrtus in subsequent years was associated with egg productivity returning to preperturbation levels, support the prediction from intraguild predation theory (Holt & Polis 1997) that the inferior resource exploiter should not be able to persist at low resource productivities. The data are consistent, therefore, with the hypothesis that the parasitoids coexist via a tradeoff between exploitation and interference. The increase in host population fluctuations in patches that lost Ooencyrtus and the subsequent decrease in fluctuations with the re-establishment of Ooencyrtus, are also consistent with the prediction that two consumer species engaging in exploitation and interference should reduce overall consumer efficiency and dampen resource population fluctuations (McCann & Hastings 1997; McCann et al. 1998). The increase in fluctuations, despite a large reduction in productivity, is strong evidence that Ooencyrtus reduces overall consumer efficiency; the increase in consumer efficiency that accompanied the loss of Ooencyrtus overwhelmed the stabilizing effect of reduced productivity predicted by pairwise consumer resource models such as the paradox of enrichment. While the congruence between parasitoid coexistence and host population variability is consistent with the expectation from theory that consumer coexistence drives consumer resource stability, a clear demonstration of the causal link between diversity and stability requires species removals and monitoring of population fluctuations under more controlled conditions. As mentioned above, this is a tall order for most field systems. Species removals require caging, which can itself be a confounding factor because caging can aflect population dynamics by altering the abiotic environment as well by preventing the natural emigration response of species. One alternative is to remove species by increasing or decreasing resource productivity. If species coexist via a trade-off between exploitation and interference, a reduction in resource productivity should eliminate the species inferior at resource exploitation, while an increase in resource productivity should achieve the opposite. If species eliminations occur as expected, then a comparison of host population fluctuations before and after the productivity manipulation should reveal whether or not elimination of the efficient vs. aggressive competitor leads to a decrease vs. an increase of host population fluctuations. The experiment, however, has to be conducted in a locality isolated sufficiently from other populations in order to prevent immigration from counteracting local competitive exclusion. This study has several broader implications. The first concerns the applicability of theoretical predictions and empirical results to complex communities with many species at each trophic level. With regard to the resource variability hypothesis, both theory and data show that resource fluctuations can allow many species to coexist on a few limiting resources (Armstrong & McGehee 1976, 1980; Kemp & Mitsch 1979; Powell & Richardson 1985; Huisman & Weissing 1999, 2001). In these studies resource fluctuations arise exogenously via random fluctuations in weather, or endogenously via overexploitation by consumers. Fluctuations driven by periodic disturbances constitute another exogenous factor that can allow large numbers of species to coexist on few limiting resources (Wootton 1998). With regard to the consumer efficiency hypothesis it is well known, both theoretically and empirically, that trade-offs between competitive ability and other life-history traits can allow multiple consumer species to coexist on multiple resources (Tilman & Pacala 1993). Whether multispecies coexistence via trade-offs other than exploitation and interference can stabilize consumer resource dynamics requires further investigation. The link suggested by this study between parasitoid coexistence and host population stability has practical implications for both conservation and biological control. In the case of biological control, the desired outcome is to reduce and maintain pest populations below some economic threshold (Murdoch 1990). Natural enemy coexistence via a trade-off between exploitation and interference is undesirable because interference tends to increase equilibrium pest density (Briggs 1993; Holt & Polis 1997). In such a situation it is better to release only the species that is efficient at resource exploitation. However, such an interaction is likely to exhibit large fluctuations in both pest and natural enemy abundance due to overexploitation. This in turn could cause local extinction of the natural enemy, leading to pest outbreaks. Hence, in biological control, the benefits of reducing pest abundance have to be weighed against the costs of an unstable pest enemy interaction. While the stabilizing effect of coexisting consumers may be undesirable in biological control, it is highly desirable from the viewpoint of conservation biology. Reduced consumer efficiency provides for increased consumer diversity and a more stable interaction between consumers and resources. The stabilizing effects of diversity that arise due to interactions between consumer