Minimax strategies for a predator—Prey game

Suppose prey are distributed in patches. The predator knows the fraction of patches containing 0, 1, 2,… prey, but not how many prey a particular patch contains. It searches each patch randomly, at constant speed. It leaves a patch when the intercapture times satisfy a formula designed to maximize the number of prey eaten per unit time. We show that, if the prey distribution is Poisson, the predator should stay in each patch for the same time, regardless of what happens there. Accordingly, the prey can minimize the predator's maximum intake by choosing the Poisson distribution, and the predator can maximize its minimum intake (against a “smart” prey) by choosing the constant-time strategy.     

Optimal Bayesian foraging policies and prey population dynamics-some comments on Rodriguez-Girones and Vasquez

In this paper we show the density-dependent harvest rates of optimal Bayesian foragers exploiting prey occurring with clumped spatial distribution. Rodríguez-Gironés and Vásquez (1997) recently treated the issue, but they used a patch-leaving rule (current value assessment rule) that is not optimal for the case described here. An optimal Bayesian forager exploiting prey whose distribution follows the negative binomial distribution should leave a patch when the potential (and not instantaneous) gain rate in that patch equals the best long-term gain rate in the environment (potential value assessment rule). It follows that the instantaneous gain rate at which the patches are abandoned is an increasing function of the time spent searching in the patch. It also follows that the proportion of prey harvested in a patch is an increasing sigmoidal function of the number of prey initially present. In this paper we vary several parameters of the model to evaluate the effects on the forager's intake rate, the proportion of prey harvested per patch, and the prey's average mortality rate in the environment. In each case, we study an intake rate maximizing forager's optimal response to the parameter changes. For the potential value assessment rule we find that at a higher average prey density in the environment, a lower proportion of the prey is taken in a patch with a given initial prey density. The proportion of prey taken in a patch of a given prey density also decreases when the variance of the prey density distribution is increased and if the travel time between patches is reduced. We also evaluate the effect of using predation minimization, rather than rate maximization, as the currency. Then a higher proportion of the prey is taken for each given initial prey density. This is related to the assumption that traveling between patches is the most risky activity. Compared to the optimal potential value assessment rule, the current value assessment rule performs worse, in terms of long-term intake rate achieved. The difference in performance is amplified when prey density is high or highly aggregated. These results pertain to the foraging patch spatial scale and may have consequences for the spatial distribution of prey in the environment.     

Optimal Bayesian Foraging Policies and Prey Population Dynamics—Some Comments on Rodríguez-Gironés and Vásquez

In this paper we show the density-dependent harvest rates of optimal Bayesian foragers exploiting prey occurring with clumped spatial distribution. Rodríguez-Gironés and Vásquez (1997) recently treated the issue, but they used a patch-leaving rule (current value assessment rule) that is not optimal for the case described here. An optimal Bayesian forager exploiting prey whose distribution follows the negative binomial distribution should leave a patch when the potential (and not instantaneous) gain rate in that patch equals the best long-term gain rate in the environment (potential value assessment rule). It follows that the instantaneous gain rate at which the patches are abandoned is an increasing function of the time spent searching in the patch. It also follows that the proportion of prey harvested in a patch is an increasing sigmoidal function of the number of prey initially present. In this paper we vary several parameters of the model to evaluate the effects on the forager's intake rate, the proportion of prey harvested per patch, and the prey's average mortality rate in the environment. In each case, we study an intake rate maximizing forager's optimal response to the parameter changes. For the potential value assessment rule we find that at a higher average prey density in the environment, a lower proportion of the prey is taken in a patch with a given initial prey density. The proportion of prey taken in a patch of a given prey density also decreases when the variance of the prey density distribution is increased and if the travel time between patches is reduced. We also evaluate the effect of using predation minimization, rather than rate maximization, as the currency. Then a higher proportion of the prey is taken for each given initial prey density. This is related to the assumption that traveling between patches is the most risky activity. Compared to the optimal potential value assessment rule, the current value assessment rule performs worse, in terms of long-term intake rate achieved. The difference in performance is amplified when prey density is high or highly aggregated. These results pertain to the foraging patch spatial scale and may have consequences for the spatial distribution of prey in the environment.     

Bayesian foraging with only two patch types

I model the optimal Bayesian foraging strategy in environments with only two patch qualities. That is, all patches either belong to one rich type, or to one poor type. This has been a situation created in several foraging experiments. In contrast, previous theories of Bayesian foraging have dealt with prey distributions where patches may belong to one out of a large range of qualities (binomial, Poisson and negative binomial distributions). This study shows that two‐patch systems have some unique properties. One qualitative difference is that in many cases it will be possible for a Bayesian forager to gain perfect information about patch quality. As soon as it has found more than the number of prey items that should be available in a poor patch, it “knows” that it is in a rich patch. The model generates at least three testable predictions. 1) The distribution of giving‐up densities, GUDs, should be bimodal in rich patches, when rich patches are rare in the environment. This is because the optimal strategy is then devoted to using the poor patches correctly, at the expense of missing a large fraction of the few rich patches available. 2) There should be a negative relation between GUD and search time in poor patches, when rich patches are much more valuable than poor. This is because the forager gets good news about potential patch quality from finding some food. It therefore accepts a lower instantaneous intake rate, making it more resistant against runs of bad luck, decreasing the risk of discarding rich patches. 3) When the energy gains required to remain in the patch are high (such as under high predation risk), the overuse of poor patches and the underuse of rich increases. This is because less information about patch quality is gained if leaving at high intake rates (after short times). The predictions given by this model may provide a much needed and effective conceptual framework for testing (both in the lab and the field) whether animals are using Bayesian assessment.     

Optimal patch residence time of a sit-and-wait forager

This paper addresses optimal giving-up time of a sit-and-waitforager by a rate maximization model. It was assumed that aforager takes at most only one prey item in a patch in one trial,that is, the forager leaves a patch with a prey item (if itattacks it) or without prey (if it gives up). Some kinds ofsit-and-wait foragers, like owls, hunt in this manner. The followingassumptions were made: (1) A forager recognizes the habitattype of patches (e.g., forest type or grassland type). (2) Spatialor temporal heterogeneity generates the uncertainty of the environmentin each habitat type. It was assumed that in a patch (in habitattype i), prey encounter rate (X) is fixed during the trial andencounter with prey depends on a Poisson process. However, preyencounter rate varies across trials within each habitat typeaccording to _i-(). Thus the forager does not know the prey encounterrate that is assigned to each patch in the type, but it knowsthe probability density function, _i-(). (3) The forager encounterseach habitat type randomly in the environment. The patch residencetime for each habitat type was considered as the only decisionparameter. Considering stochastic change of prey encounter ratein patches of a habitat type, information limitation for theforaging animal can be treated. Patch residence time was influencedby the pattern of the stochasticity. When the forager knowsperfectly the encounter rate of prey in each patch (i.e., nostochasticity), the optimal giving-up time is infinite or zero(reject the patch). With the limited information (stochasticenvironment), the condition for a finite, nonzero optimal giving-uptime in patches of a habitat depends on how far the worst caseis below the average among patches of the habitat and how badthe worst case is compared to the average of the whole environment.In a negatively skewed habitat, these conditions tend to holdeasily. The optimal forager should perform pessimistically ordoubt whether the patch contains prey, that is, set a finitegiving-up time. In a positively skewed habitat, the optimalforager should perform optimistically, that is, set an infinitegiving-up time. The expected gain is higher in the positivelyskewed habitat than in the negatively skewed habitat. When theforager must choose between the two habitats, it should choosethe positively skewed habitat. [Behav Ecol 1991;2:283–294]     

Response of predators to prey abundance: separating the effects of prey density and patch size

We tested the relative and combined effects of prey density and patch size on the functional response (number of attacks per unit time and duration of attacks) of a predatory reef fish (Cheilodactylus nigripes (Richardson)) to their invertebrate prey. Fish attacked prey at a greater rate and for longer time in large than small patches of prey, but large patches had naturally greater densities of prey. We isolated the effects of patch size and prey density by reducing the density of prey in larger patches to equal that of small patches; thereby controlling for prey density. We found that the intensity at which fish attacked prey (combination of attack rate and duration) was primarily a response to prey density rather than the size of patch they occupied. However, there was evidence that fish spent more time foraging in larger than smaller patches independent of prey density; presumably because of the greater total number of prey available. These experimental observations suggest that fish can distinguish between different notions of prey abundance in ways that enhance their rate of consumption. Although fish may feed in a density dependent manner, a critical issue is whether their rate of consumption outstrips the rate of increase in prey abundance to cause density dependent mortality of prey.     

Effects of resource distribution, patch spacing, and preharvest information on foraging decisions of northern bobwhites

We investigated patch assessment by northern bobwhites (Collinusvirginianus) in an experimental arena where the distributionof resources in patches, preharvest information about thesepatches, and spacing of patches varied. We found that preharvestinformation about patch quality and a bimodal distribution ofpatch rewards allowed birds to selectively exploit patches highin resources. In contrast, uniform distribution of patch qualitiesand lack of preharvest information caused birds to forage nonselectivelyamong patches. Birds distinguished among patches of differentquality when these patches were spaced 13 m apart, but failedto react to patch quality differences when patches were 0 or3 m apart We also found a strong effect of the level of patchdepletion on foraging decisions: as resources in die arena becamescarce, birds increasingly foraged selectively in die most profitablepatches. Foraging decisions of bobwhites are biased by die waythey experience and memorize a spatially and temporally variableenvironment. The relative cost of this cognitive bias (i.e.,lost opportunity) is nonlinearty related to die mean resourcedensity in die environment and to die difference between thismean density and die resource density in die exploited patch.Cognitive bias should be considered when evaluating patch assessmentcapabilities of foragers in complex environments.     

Rules to leave by: patch departure in foraging blue jays

Captive blue jays, Cyanocitta cristata, hunted for moths in projected images in a modified operant chamber. On each trial the jays could choose between two patches: (1) a non-depleting patch with a low, uniform prey density, and (2) a depleting patch that had a high initial prey density but depleted in a single step later in the session. The number of prey available in the depleting patch was varied across conditions. The jays typically started a bout in the depleting patch and finished in the non-depleting patch, obtaining close to the maximum number of total available prey. Efficiency declined when conditions changed, then recovered. Relative efficiency was greatest in the condition with the fewest prey. The decision to leave the depleting patch appeared to be a function of both the length of the ‘run-of-bad-luck’ and the number of prey found within the depleting patch.     

Invasion Waves in Populations with Excitable Dynamics

Whilst the most obvious mechanism for a biological invasion is the occupation of a new territory as a result of direct ingress by individuals of the invading population, a more subtle “invasion” may occur without significant motion of invading individuals if the population dynamics in a predator prey scenario has an “excitable” character. Here, “excitable” means that a local equilibrium state, either of coexistence of predator and prey, or of prey only, may, when disturbed by a small perturbation, switch to a new, essentially invaded state. In an invasion of this type little spatial movement of individuals occurs, but a wave of rapid change of population level nevertheless travels through the invaded territory. In this article we summarise and review recent modelling research which shows that the macroscopic features of these invasion waves depend strongly on the detailed spatial dynamics of the predator–prey relationship; the models assume simple (linear) diffusion and pursuit-evasion, represented by (non-linear) cross-diffusion, as examples. In the context of plankton population dynamics, such waves may be produced by sudden injections of nutrient and consequent rapid increase in plankton populations, brought about, for example, by the upwelling caused by a passing atmospheric low pressure system.     

Giving‐up densities and ideal pre‐emptive patch use in a predatory benthic stream fish

1. We used observational and experimental field studies together with an individual‐based simulation model to demonstrate that behaviours of mottled sculpin (Cottus bairdi) were broadly consistent with the expectations of Giving‐Up Density theory and an Ideal Pre‐emptive Distribution habitat selection model. 2. Specifically we found that: (i) adult mottled sculpin established territories within patches characterised by significantly higher prey densities and prey renewal rates than patches occupied by juveniles or randomly selected patches; (ii) patches abandoned by adult sculpin possessed significantly lower prey densities than newly occupied patches, although this was not true for juveniles; (iii) the observed giving‐up density (GUD) for adult sculpin (i.e. average prey density in patches recently abandoned) increased linearly with increasing fish size up to the average prey density measured in randomly selected patches (i.e. 350 prey items per 0.1 m²) and decreased with increasing sculpin density and (iv) juveniles rapidly shifted their distribution towards the highest quality patches following removal of competitively dominant adult sculpin. 3. These results provide the first evidence of the applicability of GUD theory to a stream‐dwelling organism, and they elucidate the underlying factors influencing juvenile and adult sculpin habitat selection and movement behaviours. Furthermore, optimal patch use, ideal pre‐emptive habitat selection and juvenile ‘floating’ provide behavioural mechanisms linking environmental heterogeneity in the stream benthos to density‐dependent regulation of mottled sculpin populations in this system.     

Optimal patch use in a stochastic environment

This paper considers an animal foraging on prey which are distributed in well-defined patches. It is assumed that the environment may be stochastic and that the animal can gain information on patch type as it forages. The foraging policy which maximises mean reward rate for the environment is characterised in terms of a function of state called the potential function. This policy is shown to be given by the rule: continue foraging on the present patch while the potential is positive, when the potential falls to zero move on to the next patch. Let r denote the current reward rate on a patch and let γ denote the maximum mean reward rate for the environment. It is shown that r ? γ if it is optimal to leave. Conditions which ensure r < γ are also given. For a large class of environments the optimal policy is stated in terms of a revised reward rate r?, and is given by the rule: continue on the present patch while $\text{r}\text{?}\text{> γ}$, when r? falls to γ move on to the next patch. Finally, it is shown that the stay time on a patch is a decreasing function of γ.     

Adaptation of prey and predators between patches

Mathematical models are proposed to simulate migrations of prey and predators between patches. In the absence of predators, it is shown that the adaptation of prey leads to an ideal spatial distribution in the sense that the maximal capacity of each patch is achieved. With the introduction of co-adaptation of predators, it is proved that both prey and predators achieve ideal spatial distributions when the adaptations are weak. Further, it is shown that the adaptation of prey and predators increases the survival probability of predators from the extinction in both patches to the persistence in one patch. It is also demonstrated that there exists a pattern that prey and predators cooperate well through adaptations such that predators are permanent in every patch in the case that predators become extinct in each patch in the absence of adaptations. For strong adaptations, it is proved that the model admits periodic cycles and multiple stability transitions.     

Prior knowledge about spatial pattern affects patch assessment rather than movement between patches in tactile-feeding mallard

1. Heterogeneity in food abundance allows a forager to concentrate foraging effort in patches that are rich in food. This might be problematic when food is cryptic, as the content of patches is unknown prior to foraging. In such case knowledge about the spatial pattern in the distribution of food might be beneficial as this enables a forager to estimate the content of surrounding patches. A forager can benefit from this pre-harvest information about the food distribution by regulating time in patches and/or movement between patches. 2. We conducted an experiment with mallard Anas platyrhynchos foraging in environments with random, regular, and clumped spatial configurations of full and empty patches. An assessment model was used to predict the time in patches for different spatial distributions, in which a mallard is predicted to remain in a patch until its potential intake rate drops to the average intake rate that can be achieved in the environment. A movement model was used to predict lengths of interpatch movements for different spatial distributions, in which a mallard is predicted to travel to the patch where it expects the highest intake rate. 3. Consistent with predictions, in the clumped distribution mallard spent less time in an empty patch when the previously visited neighbouring patch had been empty than when it had been full. This effect was not observed for the random distribution. This shows that mallard use pre-harvest information on spatial pattern to improve patch assessment. Patch assessment could not be evaluated for the regular distribution. 4. Movements that started in an empty patch were longer than movements that started in a full patch. Contrary to model predictions this effect was observed for all spatial distributions, rather than for the clumped distribution only. In this experiment mallard did not regulate movement in relation to pattern. 5. An explanation for the result that pre-harvest information on spatial pattern affected patch assessment rather than movement is that mallard move to the nearest patch where the expected intake rate is higher than the critical value, rather than to the patch where the highest intake rate is expected.     

Scale-dependent foraging and patch choice in fractal environments

Many spatially complex environments are fractal, and consumers in these environments face scale-dependent trade-offs between encountering high densities of small resource patches versus low densities of large resource patches. I address the effects of these trade-offs on foraging by incorporating scale-dependent encounter of resources in fractal landscapes into classical optimal foraging theory. This model is then used to predict optimal scales of perception (foraging scale) and patch choice in response to spatial features of landscapes. The model predicts that, for a given density of resources, landscapes with greater extent and fractal dimension and that contain patchy (low fractal dimension) resources favour large foraging scales and specialization on a small proportion of resource patches. Fragmented (low fractal dimension) landscapes of small extent with dispersed (high fractal dimension) resources favour smaller foraging scales and generalists that use a large proportion of available resource patches. These predictions synthesize the results of other spatially explicit consumer–resource models into a simple framework and agree reasonably well with results of several empirical studies. This study thus places optimal foraging theory in a spatial context and suggests evolutionary mechanisms of consumers' responses to important spatial phenomena (e.g. habitat fragmentation, resource aggregation). This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of the spatio-temporal distribution and niche overlap in neotropical earthworm assemblages

The spatial distribution of soil invertebrates is aggregated with high-density patches alternating with low-density zones. A high degree of spatio-temporal organization generally exists with identified patches of specific species assemblages, in which species coexist according to assembly rules related to competitive mechanisms for spatial and trophic resources occur. However, these issues have seldom been addressed. The spatio-temporal structure of a native earthworm community in a natural savanna and a grass–legume pasture in the Colombian “Llanos” was studied during a 2-year-period. A spatially explicit sampling design (regular grid) was used to discern the distribution pattern of species assemblages in both systems. Earthworms were collected from small soil pits at three different sampling dates. Data collected from 1 m² soil monoliths were also used in the present study. Data were analyzed with the partial triadic analysis (PTA) and correlograms, while niche overlap was computed with the Pianka index. The PTA and correlogram analysis revealed that earthworm communities displayed a similar stable spatial structure in both systems during the 2-year study period. An alternation of population patches where different species' assemblages dominated was common to all sampling dates. The medium-sized Andiodrilus sp. and Glossodrilus sp. exhibited a clear spatial opposition in natural savanna and the grass–legume pasture for the duration of the study. The Pianka index showed a high degree of niche overlapping in several dimensions (vertical distribution, seasonality of population density) between both species. The inclusion of space-time data analysis tools as the PTA and the use of classical ecological indices (Pianka) in soil ecology studies may improve our knowledge of earthworm assemblages' dynamics.     

Sex‐related spatial patterns of Poa ligularis in relation to shrub patch occurrence in northern Patagonia

Abstract. Poa ligularis is a dioecious species and a valuable forage plant which is widespread in the arid steppe of northern Patagonia (Argentina). The vegetation in these areas consists of a system of perennial plant patches alternating with bare soil areas defining contrasting micro‐environments. We hypothesized that (1) male and female individuals of P. ligularis are spatially segregated in different micro‐environments, (2) the intensity of spatial segregation of sexes depends on plant structure and (3) spatial segregation of sexes is enhanced by competitive interactions between the sexes within the vegetation patches. We analysed the spatial distribution of female and male individuals in relation to the spatial pattern of vegetation in two areas differing in their vegetation structure. The location of P. ligularis within patches where either male, female or both sexes occurred was also analysed. The results indicate that different patterns of spatial distribution of sexes of P. ligularis may be found at the community level depending on the dominant life forms and geometric structure of plant patches. Where patches are of a lower height, with a high internal patch cover, individuals of both sexes are concentrated within patch canopies. In sites characterized by large, tall patches and less internal patch cover suitable microsites for female and male P. ligularis occur both within and outside the patch with males located at further distances from the patch edge. Where the patch is large and tall enough to allow the establishment of males and females at relatively high numbers, males occupy the patch periphery or even colonize the interpatch bare soil. These spatial patterns are consistent with selective traits in which females better tolerate intraspecific competition than males, while males tolerate wider fluctuations in the physical environment (soil moisture, nitrogen availability, wind intensity, etc.).     

Influence of prey availability and conspecifics on patch quality for a cannibalistic forager: laboratory experiments with the wolf spider Schizocosa

 Because cannibals are potentially both predator and prey, the presence of conspecifics and alternative prey may act together to influence the rate at which cannibals prey upon each other or emigrate from a habitat patch. Wolf spiders (Lycosidae) are cannibalistic-generalist predators that hunt for prey with a sit-and-wait strategy characterized by changes in foraging site. Little information is available on how both prey abundance and the presence of conspecifics influence patch quality for these cursorial, non-web-building spiders. To address this question, laboratory experiments were conducted with spiderlings and older juveniles of the lycosid genus Schizocosa. The presence of insect prey consistently reduced rates of spider emigration when spiders were housed either alone or in groups. Solitary juvenile Schizocosa that had been recently collected from the field exhibited a median giving-up time (GUT) of 10 h in the absence of prey (Collembola); providing Collembola increased the median GUT to 64 h. For solitary spiders, the absence of prey increased by about fourfold the rate of emigration during the first 24 h. In contrast, for spiders in patches with a high density of conspecifics, the absence of prey increased the 24-h emigration rate by only 1.6-fold. For successful cannibals in the no-prey patches, the presence of conspecifics improved patch quality by providing a source of food. Mortality by cannibalism was affected by both prey availability and openness of the patch to net emigration. In patches with no net emigration, the presence of prey reduced rates of cannibalism from 79% to 57%. Spiders in patches open to emigration but not immigration experienced a rate of cannibalism (16%) that was independent of prey availability. The results of these experiments indicate that for a cannibalistic forager such as the wolf spider Schizocosa, (1) the presence of conspecifics can improve average patch quality when prey are absent, and (2) cannibalism has the potential to be a significant mortality factor under natural field conditions because cannibalism persisted in prey patches that were open to emigration. Received: 12 April 1996 / Accepted: 14 August 1996     

Flexible use of patch marks in an insect predator: effect of sex, hunger state, and patch quality

Abstract 1. Patch marks that allow the subsequent avoidance of marked areas may be used by small animals to increase foraging efficiency. This study is the first to demonstrate the presence of a patch-marking system in insect predators. Furthermore, the marking system is found only in females, and factors such as hunger state and patch quality play a key role in determining whether a female will re-investigate a self-marked patch.
2. Females of the insect predator Orius sauteri avoided areas where the female itself had searched previously but did not avoid areas searched by conspecific females when deprived of prey for 24 h . There was no evidence that males use such a patch-marking system, indicating the presence of a sex difference in patch-mark use.
3. Females did not discriminate between patches visited previously and patches not visited when they were either well fed or when patches contained abundant prey.
4. The patch mark used by females was effective for ≤ 1 h and may be a reliable indicator of a recently visited area in which prey have been depleted.
5. These results suggest that O. sauteri females have the flexibility to adjust their behavioural responses to a previously searched area depending on their hunger state and the availability of prey in their foraging environment.     

The effects of prey depletion on the patch choice of foraging blue jays (Cyanocitta cristata)

Blue jays (Cyanocitta cristata) were trained to hunt for non-cryptic moths, presented in projected images. On each trial, the jays chose one of two patches to hunt in: (1) a uniform, ‘non-depleting’ patch with constant prey density of 0·25; or (2) a ‘depleting’ patch in which prey density changed during the foraging bout. In the depleting patch, the initial prey density was 0·50, declining to zero in a single step part-way through each foraging bout (session). The patch choices of the jays were greatly affected by these conditions. The jays chose the depleting patch early in the session, and then switched to the uniform patch. They obtained nearly all of the prey available. Analysis of the events preceding switches between patches suggested that the jays used different rules to switch out of each of the two patches.     

Foraging behavior of an estuarine predator, the blue crab Callinectes sapidus in a patchy environment

To define general principles of predator‐prey dynamics in an estuarine subtidal environment, we manipulated predator density (the blue crab, Callinectes sapidus) and prey (the clam, Macoma balthica) patch distribution in large field enclosures in the Rhode River subestuary of the central Chesapeake Bay. The primary objectives were to determine whether predators forage in a way that maximizes prey consumption and to assess how their foraging success is affected by density of conspecifics. We developed a novel ultrasonic telemetry system to observe behavior of individual predators with unprecedented detail. Behavior of predators was more indicative of optimal than of opportunistic foraging. Predators appeared responsive to the overall quality of prey in their habitat. Rather than remaining on a prey patch until depletion, predators appeared to vary their patch use with quality of the surrounding environment. When multiple (two) prey patches were available, residence time of predators on a prey patch was shorter than when only a single prey patch was available. Predators seemed to move among the prey patches fairly regularly, dividing their foraging time between the patches and consuming prey from each of them at a similar rate. That predators more than doubled their consumption of prey when we doubled the number of prey (by adding the second patch) is consistent with optimizing behaviors ‐ rather than with an opportunistic increase in prey consumption brought about simply by the addition of more prey. Predators at high density, however, appeared to interfere with each other's foraging success, reflected by their lower rates of prey consumption. Blue crabs appear to forage more successfully (and their prey to experience higher mortality) in prey patches located within 15–20 meters of neighboring patch, than in isolated patches. Our results are likely to apply, at least qualitatively, to other crustacean‐bivalve interactions, including those of commercial interest; their quantitative applicability will depend on the mobility of other predators and the scale of patchiness they perceive.