Oecologia 9 Springer-Verlag1989

Oecologia (1989) 79:76-82

Predation risk and the structure of freshwater zooplankton communities* Craig E. Williamson, Mark E. Stoeckel, and L. Jane Schoeneck Department of Biology 31, Lehigh University, Bethlehem, PA 18015, USA

Summary. Many predators inflict substantial mortality on their prey. The prey respond to these selective pressures with changes in their spatial and temporal overlap with the predator (density risk responses), or with changes in their vulnerability to the predator (prey vulnerability responses). Here we develop a simple predation model that permits quantification of the basic response types of the prey in nature. We then test the hypothesis that prey response will be proportional to the intensity of the predation mortality relative to all other sources of mortality and decreased natality acting on the prey. A significant regression relationship is obtained for the prey vulnerability response but not for any of the density risk responses. The individual response values and regression statistics are used to interpret the relative importance of the different response types and to assess the predator's influence on prey community structure. Key words: Predation risk - Community structure - Zooplankton

Predation is a potent force in the ecology and evolution of animal communities. Predators may cause either an increase (Paine 1966) or a decrease (Addicott 1974) in prey species richness depending on system-specific characteristics. Experimental manipulations in the field have shown that birds can have a significant impact on insect prey communities (Holmes et al. 1979). The importance of predation has been particularly well demonstrated in freshwater zooplankton communities where the presence or absence of vertebrate predators can induce major shifts in the sizefrequency distributions of the whole community (Hrbacek et al. 1961; Brooks and Dodson 1965). Invertebrate predators may also be a potent force in freshwater zooplankton communities. Striking evidence of this comes from the direct induction of morphological and behavioral defenses in the prey by specific chemical substances released by invertebrate predators (Gilbert 1966, 1967; Folt and Goldman 1981; Grant and Bayly 1981; Krueger and Dodson 1981; Gilbert and Stemberger 1984; Stemberger and Gilbert 1984), and from either the dramatic reduction or even total exclusion of the more vulnerable prey species or morphs * Supported by Lehigh University Environmental Studies Center Offprint requests to: C.E. Williamson

from systems, or portions of systems, where invertebrate predation intensity is high (Dodson 1972, 1974; Kerfoot 1975; O'Brien and Vinyard 1978; Lynch 1979; O'Brien and Schmidt 1979; Kerfoot and Peterson 1980; Neill and Peacock 1980). These prior studies demonstrate that predators place substantial selective pressures on individual prey species to respond to predation. Other factors such as food limitation, interference competition, parasites, and pathogens may, however, place additional, and often conflicting, selective pressures on these prey. The ecological and evolutionary responses of the prey to this array of selective pressures will ultimately determine prey community structure, i.e. the distribution and abundance of prey in space and time. A central theme in ecology has involved attempts to separate the role of predation from these other environmental factors in the ecology and evolution of species in natural communities. The simplest way to examine the impact of predation on prey communities is to look for inverse correlations between prey and predator populations in space and time. Simple correlation analyses between predator and prey populations do not, however, demonstrate causality: other environmental variables may be confounding (e.g. Frank and Leggett 1985). Analysis of prey birth and death rates and predator densities have vastly improved our ability to interpret the contribution of predation to observed fluctuations in prey populations (Edmondson 1960, 1968; Hall 1964; Cooper and Smith 1982; Threlkeld 1981; Magnien 1983). A second limitation of the correlation approach involves the interpretation of the correlations (Sih 1984). Predator and prey exhibit conflicting responses to predator-prey interactions: the prey's response is to minimize spatial and temporal overlap with the predator, while the predator's response is to maximize this overlap. Thus, when predation pressures are strong, either a positive, a negative, or no correlation between predator and prey population densities may be observed depending on the relative dominance of the predator and prey responses. Prey may also respond to predation pressures by reducing their vulnerability to predators. For example, a wide range of plant and animal prey exhibit inducible polymorphisms such as spines, armor, and chemical defenses that reduce their vulnerability to predators (Havel 1987). The potential for prey to exhibit vulnerability responses to predation creates an additional problem in the interpretation

77 of correlations between predator and prey population densities. The selective pressures on prey to exhibit population density responses may be reduced or eliminated in the presence of prey vulnerability responses. This trade-off between vulnerability and density responses in prey is driven by the cost of defense against predation. In the current paper we present a simple predation model that incorporates both population density-overlap (density risk) and prey vulnerability responses of the prey to increased predation pressures. We use this model to assess the magnitude of the two types of prey responses to increases in predation pressure. The prey responses are then regressed against the pre-impact predation risk values across the whole community to estimate the relative importance of density risk versus prey vulnerability responses across the community.

Predation is a life or death proposition for both parties involved: the predators must eat to live, and the prey will die if eaten. From the predator's perspective, the goal is to maximize the efficiency with which it can locate, capture, and ingest its prey. From the prey's perspective, the goal is how to minimize mortality due to predation. The following model looks at predation from the prey's perspective, and how prey can reduce their chances of being ingested by a predator. In a three dimensional aquatic environment the instantaneous predation rate of a predator on prey species i (G~, prey predator- 1 time 1) is a function of the volume of water cleared of prey per unit time (F0, and the prey density (ni, Vanderploeg and Scavia 1979, 1983): (1)

If either prey or predator populations, or both, are randomly distributed in a common three dimensional environment, the predation rate of all N predators on the ith prey species (G'i) is: G'i = Fi ni N,

G;' = F~ n~ NO~.

(3)

Spatial overlap can be estimated as: (Nz n i~) m

z-- 1 z--1

(5)

This quantity is a mortality rate coefficient that represents the predation risk of the ith prey species (PRO. Two of the variables in this equation (N and Oi) are density terms that can be combined to give the density risk (DRi) of the ith prey species to predation: (N~ niz) DR,-

~= 1

(6)

~, (ni z) Z--1

P R i = P Vi D R i .

(7)

Density risk is defined as the risk per prey individual averaged over the whole population, and not the risk experienced by any single individual in response to locally high predator densities. It is strictly defined as a function of predator density and overlap between predator and prey populations. Prey vulnerability includes all of the prey-specific characteristics that influence the ability of the predator to detect, subdue, and eventually kill or ingest they prey. Predation risk as defined here provides us with an estimate of the probability that an average individual of the ith prey species will be killed by a predator in some given time period. From an evolutionary perspective this quantity is useful because it looks at the predation process at the level of the individual, the unit of natural selection. Because it is simply a mortality rate coefficient, predation risk can also be interpreted at the population level. This definition provides a mathematical expression and precise biological interpretation of predation risk, a term that is frequently and variously used in the literature.

(2)

where N is the average predator density. When both prey and predator populations are patchily distributed in the environment, the spatial overlap of the predator and prey populations (Oi) must also be incorporated into the predation rate estimate:

Oi --

P R i = Fi N O i .

Predation risk can thus be defined as a product of two primary components, prey vulnerability, and density risk:

The predation risk model

G i -- f i n i.

The proportion of the prey population removed per unit time can be estimated by dividing Eq. 3 through by ni to get:

(4) z=l

where z is the unit of patch size, and m is the number of patches sampled. When either prey or predator populations, or both, are randomly distributed O5 will equal one. When both prey and predator populations are patchily distributed Oi values of greater or less than one are likely depending on whether the distributions of the prey and predator populations are positively or negatively correlated respectively.

The prey response

Temporal fluctuations in predator populations have the potential to play a major role in the seasonal shifts observed in the structure of plankton communities (see introduction). In a system where there is a seasonal increase in the density of some predator, there will be a corresponding increase in the selective pressures on the prey to respond to that predator. The prey can respond to this increase in predator density in a number of ways. The rate of removal of the ith prey species from a population (G~', prey time-l) is a function of four variables: prey vulnerability, prey density, predator density, and overlap. This can be seen more clearly by rewriting Eq. 3 as follows: G'i' = P Vi ni N Oi.

(8)

As predator density increases, prey can minimize the increase in G~' by reducing their prey vulnerability (prey vulnerability responses), or by reducing their own population density or spatial overlap with the predator (density risk responses). Reductions in prey density as predator density increases will reduce temporal overlap with the predator, and thus reduce the total annual density risk of the prey.

78 Prey vulnerability and density risk responses are defined here on a strictly functional basis, and do not imply discrete evolutionary adaptations by the prey. These responses are measured empirically and may be due to evolutionary aptations of the prey in the broader sense (Gould and Vrba 1982). The aptations may be either specific responses to predation pressures (adaptations), or responses to selective pressures other than predation that function fortuitously in reducing predation pressures (exaptations). The predator may also contribute to these responses. The presence or absence of alternative foods, and changes in predator hunger levels or foraging behavior may influence prey vulnerability, density, or overlap values by inducing clonal succession or altering predator selectivity (Kerfoot and Peterson 1980; Pastorok 1980; Williamson 1980; Williamson and Vanderploeg in press). Environmental factors such as light, temperature, and oxygen profiles may also influence the feeding rates, density, and overlap of the predator and prey. For this reason response, as defined here, refers to an "apparent response" that is specific to a given prey type. The responses of each individual prey type may be due to a variety of factors (prey, predator, environment). It is only the regression of the apparent responses on the predator-specific predation risk that allows separation of the contribution of prey, predator, and other factors to the observed response. There are many good examples of individual prey species responding to predators by reducing their density risk or their prey vulnerability. Density risk responses have been observed in animal prey ranging from zooplankton (Williamson and Magnien 1982; Ohman et al. 1983; Hairston 1987; Johnsen and Jakobsen 1987) and insects (Sih 1982; Feltmate 1987) to salamander larvae (Holomuzki 1986; Semlitsch 1987), fish (Stein and Magnuson 1976; Werner et al. 1983), and juvenile moose (Edwards 1983). Prey vulnerability responses have been observed in many species of both plant and animal prey (reviewed by Havel 1987). Our interest here is in examining the potential for more subtle, community-wide responses by a variety of prey species. Here we test the hypothesis that the intensity of a prey's response to a given predator will increase with an increase in the predator-specific predation risk. We expect that the intensity of a prey's response to a given predator will be a function of the intensity of the predation-induced mortality (predation risk) relative to the intensity of all other existing sources of mortality and decreased natality on that prey. By regressing prey response on predation risk across the entire community we can sort out the predation effects from the residual effects of other environmental variable such as competition, food limitation, tolerance limits to temperature or oxygen concentration, and other predators. Because the two variables being regressed (prey response and predation risk) are 1) being examined across the whole community, 2) defined in terms of a single predator, and 3) not just population densities, a significant pattern is likely to be indicative of the importance of predation, and other variables are unlikely to be confounding. Due to the predatorspecific nature of prey defense mechanisms (Gilbert and Williamson 1978; Williamson and Gilbert 1980), it is unlikely that the vulnerability of all prey in a community will be similar for two different predators: the most likely situation that might lead to confounding. In the unlikely case that

two predators are extremely similar, they can and should be treated as a single source of predation pressure.

A test of the predation risk model

Most invertebrate predators of freshwater zooplankton in temperate lakes are characterized by seasonal fluctuations in population density. Cyclopoid copepods of the genus Mesocyclops, for example, have seasonal peaks in abundance during the warmer months, and are rare or absent during the winter months. Seasonal increases in predation pressures are accompanied by fluctuations in other biotic and abiotic environmental factors, often making it difficult to identify clear patterns of prey response to these observed fluctuations in predator density. The predation risk model provides us with a predator specific, community wide regression technique that separates the prey responses to a given predator from their responses to all other factors. In addition, this model permits us to separate prey responses into density risk or prey vulnerability responses. Here we use the predation risk model to examine the response of a zooplankton community to a seasonal population increase in the cyclopoid predator Mesocyclops edax. Intensive sampling and experiments were carried out during two periods: 1) when Mesocyclops was just becoming established in the reservoir, and 2) after Mesocyclops had become well established and reached high density. Prey responses were then regressed on the pre-impact predation risk values of the prey to assess how the prey community responded to the increase in predation pressures. Methods

Hellertown Reservoir is a small ( < 1 ha surface area, Zmax = 10 m) mesotrophic body of water located in a wellprotected watershed in Northampton County, PA. The reservoir is fed by underground springs, has no stream inlets, and only a minor outlet which is dry for much of the summer so that flow-through rates are very low. The dominant invertebrate predator during the summer is the cyclopoid copepod Mesocyclops edax. In 1986, the predatory stages of Mesocyclops first appeared in the reservoir in June, became established in early to mid July, and reached peak densities in August (Fig. 1). While average water column densities peaked at about 8 predators L-1, densities of up to 40 L - 1 occurred in some strata of the water column. Midge larvae (Chaoborus flavicans and C. punctipennis) and Diacyclops bicuspidatus are present but rare in the reservoir. Asplanchna is abundant in the spring, but decreases to densities of < 1 L - 1 during the summer months. Intensive 24 h sampling was carried out to estimate prey densities, predator densities, overlap, and density risk on 9 July and 5 August, 1986. Duplicate zooplankton samples were collected at odd-metered depths from surface to bottom (10 m) every 3 h with an 8.2 L Van Dorn bottle. Samples were strained through a 48 gm mesh rotifer cone (Likens and Gilbert 1970), narcotized with carbonated water (Gannon and Gannon 1975), and preserved in cold sucrose formalin (Prepas 1978). Small rotifers and nauplii were counted in a Sedgwick-Rafter cell, while Asplanchna and crustaceans were counted in a Bogorov chamber (Gannon 1971). Prey and predator densities (number liter - t ) and overlap (Eq. 4, unitless) with the predator (Mesocyclops

79 edax copepodite IV-adult females) were estimated from these counts and averaged over each 24 h period. Males were excluded from the analysis due to their different migration patterns and reduced feeding rates (Williamson and Magnien 1982; Gilbert and Williamson 1983; Williamson 1986). Density risk (predators liter-i) was calculated as the product of Oi and the mean predator density over the 24 h period. Experiments were performed on these same two dates to estimate prey vulnerability (liters predator-1 day-1) for each prey from clearance rates with the entire zooplankton assemblage. Whole water samples were collected from oddmetered depths (excluding the anoxic 9 m depth), combined in a large tub, and used to fill twelve 1 L narrow-necked bottles. Twenty M. edax predators were added to each of six of these jars. All twelve jars were rotated at 1 rpm in a controlled environment chamber that simulated the temperature (20 ~ C), light intensity (5400 lux) and photoperiod (16:8, L : D cycle) conditions at intermediate depths in the reservoir. At the end of the 24 h incubation the contents of each jar were collected on a 48 pm mesh, narcotized with carbonated water, and preserved in cold sucrose formalin. All prey species and predators were counted and clearance rates calculated with the standard exponential equations (Gauld 1951; D o d s o n 1975) and regression analysis (Lehman 1980; Landry and Hassett 1982). Predation risk (proportion of prey population removed per day by all predators) was estimated as the product of prey vulnerability and density risk for each species in the initial (July) community. Four types of responses (prey vulnerability, density, overlap, and density risk; see Eqs. 7 and 8) were estimated for each prey species during the period of predator increase from July to August with the following equation:

8.0 7.0 6.0 L5.O 04.0 z 3.0

2.0 J.O

O0 9

--

I

-

22

i

i

i

4

19

3

MAY

Species

Month

Asplanchna girodi

J A J A J A J A J A J A J A J A J A J A J A J A J A J A

Daphnia parvula (<0.75 mm) Polyarthra remata Keratella crassa Polyarthra vulgaris

X value at low predator density (July) - X value at high predator density (August)

Conochilus unicornis

Average predator densities differed by a factor of 2.54 between the July 9 (2.29 L -1) and August 5 (5.81 L i) sampling date (Fig. 1). Most of the prey species in the lake showed substantial changes in density, and somewhat

T

I

14 26 AUGUST

Table 1. Mean 24 h density (hi), overlap (Oi), density risk (DRI) and prey vulnerability (PE,) values used in calculating responses of prey to increase in predator density in Hellertown Reservoir

Tropocyclops prasinus

Results

JULY

I

31

Fig. 1. Density of the predator Mesocyclops edax (CIV, CV and adult females) in Hellertown Reservoir during the summer of 1986

X response

where X represents the mean 24 h value of the response type being estimated. The range of these responses is from zero (negative response) to infinity (positive response), where a value of 1 represents no response. Next we tested the hypothesis that the intensity of the prey response increased with an increase in the intensity of the predation-induced mortality during the given period. This hypothesis was tested by separately regressing each prey response type on the corresponding initial (pre-impact) July predation risk values across the whole community. The coefficients of determination and significance levels of the regressions were used to estimate the relative importance of the different response types within the community. Prey vulnerability and total responses could not be calculated for four species due to either the low population densities (three species) or zero clearance rate values (one species) observed during the August sampling and experiments (Table 1).

JUNE

I

16

Gastropus stylifer nauplii Polyarthra euryptera copepodites Ascomorpha ovalis Daphnia parvula (>0.75 mm) KelIicottia bostoniensis

nl 38.0 0.6 24.0 4.4 407.0 174.0 15.0 236.0 150.0 87.0 14.0 15.0 353.0 1.4 84.0 21.0 239.0 206.0 60.0 26.0 33.0 66.0 33.0 3.4 64.0 18.0 76.0 38.0

Oi

DR i

0.900 2.061 1.550 9.006 1.395 3.194 1.675 9.732 0.980 2.244 1.150 6.682 1.680 3.847 1.825 10.603 1.575 3.607 1.190 6.914 2.070 4.740 2.050 11.910 1.250 2.862 0.525 3.050 1.580 3.618 1.130 6.565 1.010 2.313 1.430 8.308 0.500 1.145 1.380 8.018 1.295 2.965 1.540 8.947 1.59 3.641 1.375 7.989 1.250 2.862 1.445 8.395 0 . 3 2 5 0.744 0.760 4.416

PVj 0.065 0.037 0.020 0.047 0.039 0.024 0.011 0.020 0.023 0.012 0.000 0.019 0.014 0.007 0.012 0.012 0.018 0.031 0.005 0.019 0.002 0.002 0.004 0.005 0.013

smaller changes in overlap and prey vulnerability over the same period (Table 1). When these changes were converted to responses by dividing the July values by the August values and arranging them in decreasing order of July predation risk, some interesting patterns emerged. Of the three basic response types, the population density responses were by far the most volatile, ranging from 0.06 to 252. Overlap responses ranged from 0.36 to 2.38, and prey vulnerability responses from

80

2.2

O

2.0

o

,,, 1.8 z

o

1.4 1.2 ~z 1.0 > 0.8 0. 0 . 6

0.4 0.2

0.0

I

i

i

t

0.00 0.02 0.04 0.06 0.08

I

i

O.lO 0.12

dULY PREDATION RISK

Fig. 2. Regression of prey vulnerability response on July predation risk showing the significant regression relationship with 95% confidence intervals 0.26 to 2.18. Of the two composite response types, the density risk responses ranged from 0.06 to 600, while the total responses ranged from 0.11 to 11.2. Each response type was regressed on the July predation risk values to test the hypothesis that higher predation risk species will be more likely to respond to predation pressures than lower predation risk species. These regressions also allowed comparison of the strength of the different types of response to the predator. The regression of prey vulnerability on predation risk was the only regression that resulted in a statistically significant (P < 0.05) relationship and a high coefficient of determination (Y-12.38X+0.45, P=0.012; Fig. 2). Predation risk accounted for 57% of the variation in the observed prey vulnerability responses, but only 1% or less of the variation in the density, overlap, and density risk responses. An intermediate r 2 value of 17% was obtained for the total response regression. All of the available data were used for each of the regressions. Prey vulnerability values were not available for four of the rarer species (Table 1). Density, overlap, and density risk regressions were repeated with the same 10 species that were used for the prey vulnerability and total regressions. This ensured that comparisons between response type regressions were not biased by the presence or absence of the four species for which prey vulnerability data were not available. None of these repeated regressions was significant (P=0.49, 0.27, 0.39 respectively). Although the r 2 values were higher (6%, 15%, 9% respectively) than for the regressions with all 14 species, they did not approach the 57% value obtained for the prey vulnerability regression.

Discussion

The predation risk model states that prey can respond to increases in predation pressures in either of two fundamental ways: they can reduce their density risk (spatial and temporal overlap with the predator), or they can reduce their prey vulnerability. Changes in the density risk and prey vulnerability are measured empirically at two time points during a period of increasing predator density. The hypothesis is that during this period of increasing predator density, prey will exhibit responses that will reduce their predation risk, and that the intensity of these responses

will be proportional to the magnitude of the prey's predation risk during the initial (pre-impact) period of low predator density. These prey responses are referred to as "apparent responses" because they may be the result of changes in characteristics of either the prey, the predator, or the environment. The assumption is that a significant regression relationship of the apparent response on predation risk will occur only when the predator-prey interaction has a relatively stronger effect on community structure compared to all other variables. While environmental variables may effect prey morphology and distribution, there is no reason to expect that the strength of these effects will be correlated with predation risk across the prey community. The regression in the predation risk model thus serves to separate the variance due to a specific predator from the variance due to all "other" factors. The effects of other dissimilar predators (such as fish) are unlikely to be confounding due to the different vulnerabilities of prey species to these predators. In the current study the significant regression of the prey vulnerability responses on predation risk (Fig. 2) suggests that Mesocyclops predation contributed significantly to the community-wide prey vulnerability responses. The coefficient of determination indicates that 57% of the variation in this response was attributable to predation risk, and the rest to "other" factors such as environmental changes. This is consistent with previous studies that show that spine length in rotifers and crustaceans are inducible not only by predators, but also by changes in food supply or abiotic factors such as light, temperature, and turbulence (Brooks 1947; Jacobs 1961, 1962; Hebert 1978; Pejler 1980). The lack of a consistent regression relationship between the density risk responses and predation risk across the community suggests that factors other than predation by Mesocyclops were responsible for most of these changes in prey density and overlap. The lack of a significant regression relationship does not imply that certain individual prey species did not exhibit any responses to predation. The component data that lead to the regression analysis can be used to identify relationships that deserve further investigation. For example, the two species with the highest predation risk (Asplanchnaand juvenile Daphnia) also had two of the higher density and density risk responses in the community, suggesting that these species may be influenced by Mesocyclopspredation. In a similar manner, the individual responses leading to significant regressions can be used to identify outliers: prey species that exhibit responses that diverge substantially from significant community responses. In the current study Gastropus exhibited an exceptionally strong prey vulnerability response relative to its predation risk. The predation risk model has several limitations that should be recognized when interpreting the results. First, the method used to estimate prey vulnerability combines all prey species in a single vessel over 24 h and is thus artificial when compared to the situation in nature where the prey and predators are heterogeneously distributed. Second, the predation risk model examines predator-prey interactions from the perspective of the prey: it assumes that the prey response dominates and that there will thus be an inverse relationship between prey response and predation risk. This may be a reasonable assumption for polyphagous predators that are unlikely to exhibit strong responses to any single prey species. The assumption may be less valid

81 however, for oligophagous predators, and the model is not applicable to m o n o p h a g o u s predators. Another limitation of the model is that in habitats where environmental conditions or multiple predators have a strong influence on prey distribution and abundance, the effects of a single important predator may be masked. The predation risk model examines the importance of predation, by a single predator, relative to all " o t h e r " factors, and does not sort out interactive effects. In addition, the assumption of linearity of the regression was chosen parsimoniously. More information on the relationship between predation risk and prey responses is necessary to define the precise shape of the expected curve. The two-component structure of the predation risk model presented here (Eq. 8) is closely analagous to that of Holling's earlier models. Our approach diverges from that of Holling in that we examine the predation process from the prey's perspective, whereas Holling examined predation from the predator's perspective. Holling (1959, 1961) divided predation into its "universal" components and its "subsidiary" components. Prey and predator densities were considered to be "universal" components in that they are important to all predator-prey systems. The subsidiary components included characteristics of the prey (e.g. prey defense mechanisms, reactions to predators, stimulus detected by predator), characteristics of the predator (e.g. food preferences, efficiency of attack), and characteristics of the environment (e.g. density and quality of alternate foods available to the predator). In our model, density risk accounts for the universal components of predation, while prey vulnerability accounts for the subsidiary components (Eq. 8). Density risk and prey vulnerability responses are fundamentally different in their modes of action, and as a result, they have profoundly different implications for the ecology and evolution of the prey species involved. Prey that exhibit density risk responses to predation may be restricted to habitats where food, temperature, oxygen, or other environmental factors are suboptimal for survival, growth, or reproduction (Stein and M a g n u s o n 1976; Sih 1980, 1982; Edwards 1983; Werner et al. 1983; Abrams 1984; Holomuzki 1986; Johnsen and Jakobsen 1987). Prey that exhibit prey vulnerability responses to predation may be limited to body shapes, sizes, or swimming modes that are suboptimal for feeding, reproduction, or other basic physiological processes (Zaret 1972; Kerfoot 1977; O'Brien and Vinyard 1978; Zaret and Kerfoot 1980; D o d s o n 1984; Riessen 1984; Havel and D o d s o n 1987). Prey that exhibit both density risk and prey vulnerability responses may experience both types of restrictions. The presence of restrictions placed on prey that utilize these responses to reduce predation pressures suggests that defense against predation may have an associated cost, and indicates the need to examine the type and magnitude of prey responses to predation more carefully in nature. The predation risk model may also be a valuable management tool in understanding the dynamics of predators in biological control programs. In order to be successful as a biological control agent, a predator must be able to overcome both density risk and prey vulnerability mechanisms of defense in the target pest. If a pest evades predation due to a low density risk, manipulation of predator densities through release programs to increase the densities of the predators in the microhabitat in which the prey are most abundant will be most effective at decreasing pest densities. On the other hand, if a pest evades predation due to a

low prey vulnerability, manipulation of predator densities is likely to have little effect on the control program, and a new control agent should be sought.

Acknowledgements. We thank Bruce Hargreaves and Henry Vanderploeg for valuable comments and discussion in several stages of this project, and David Cundall for his comments on an earlier draft of the manuscript.

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