Remarks on the number of persistent states to a fragmented predator–prey model system

We consider a predator–prey model system for spatially distributed species over patches. Each predator species has a unique preferred patch (shelter and reproduction site) and travel for chasing prey. Its individuals are split into resident from the preferred patch and travelers. Further there is at most one resident predator species per patch. Depending on the availability of local anthropized resources not related to local prey on the preferred patch, one distinguishes between well-fed and starving predators. We assume prey species do not disperse at the predator scale.In this study we are interested in the number of persistent stationary states for the resulting ordinary differential equations model system. There exists at most one persistent predator–prey stationary state when there is exactly one starving resident predators per patch provided all functional responses to predation are Lotka–Volterra like or when a single starving resident predators is available. Else multiple persistent predator–prey stationary state are likely to exist. A specific emphasis is put on toy-model systems with 2 or 3 patches. Slow–fast dynamical methodology is also used for locally asymptotically stable purposes.Numerical experiments suggest that several scalings may govern the dynamics at stabilization.     

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Evolution of handling time can destroy the coexistence of cycling predators

Several consumers (predators) with Holling type II functional response may robustly coexist even if they utilize the same resource (prey), provided that the population exhibits nonequilibrium dynamics and the handling time of predators is sufficiently different. We investigate the evolution of handling time and, in particular, its effect on coexistence. Longer handling time is costly in terms of lost foraging time, but allows more nutrients to be extracted from a captured prey individual. Assuming a hyperbolically saturating relationship between handling time and the number of new predators produced per prey consumed, we obtain three results: (i) There is a globally evolutionarily stable handling time; (ii) At most two predator strategies can coexist in this model; (iii) When two predators coexist, a mutant with intermediate handling time can always invade. This implies that there is no evolutionarily stable coexistence, and the evolution of handling time eventually leads to a single evolutionarily stable predator. These results are proven analytically and are valid for arbitrary (not only small) mutations; they however depend on the relationship between handling time and offspring production and on the assumption that predators differ only in their prey handling strategy.     

Evolutionary dynamics of prey exploitation in a metapopulation of predators

In well-mixed populations of predators and prey, natural selection favors predators with high rates of prey consumption and population growth. When spatial structure prevents the populations from being well mixed, such predators may have a selective disadvantage because they do not make full use of the prey's growth capacity and hence produce fewer propagules. The best strategy then depends on the degree to which predators can monopolize the exploitation of local prey populations, which in turn depends on the spatial structure, the number of migrants, and, in particular, the stochastic nature of the colonization process. To analyze the evolutionary dynamics of predators in a spatially structured predator-prey system, we performed simulations with a metapopulation model that has explicit local dynamics of nonpersistent populations, keeps track of the number of emigrants entering the migration pool, assumes individuals within local populations as well as within the migration pool to be well mixed, and takes stochastic colonization into account. We investigated which of the predator's exploitation strategies are evolutionarily stable and whether these strategies minimize the overall density of prey, as is the case in Lotka-Volterra-type models of competitive exclusion. This was analyzed by pairwise invasibility plots based on short-term simulations and tested by long-term simulation experiments of competition between resident and mutant predator-types that differed in one of the following parameters: the prey-to-predator conversion efficiency, the per capita prey consumption rate, or the per capita emigration rate from local populations. In addition, we asked which of these three strategies are most likely to evolve. Our simulations showed that under selection for conversion efficiency the predator-prey system always goes globally extinct yet persists under selection for consumption or emigration rates and that the evolutionarily stable (ES) exploitation strategies do not maximize local population growth rates. The most successful exploitation strategy minimizes the overall density of prey but does not make it settle exactly at the minimum. The system did not settle at the point where the mean time to co-invasion (i.e., immigration of a second predator in a local prey population) equals the mean local interaction time (an idea borne out from studies on host exploitation strategies in host-pathogen systems) but rather where the mean time to co-invasion was larger. The ES exploitation strategies represent more prudent strategies than the ones that minimize prey density. Finally, we show that-compared to consumption-emigration is a more likely target for selection to achieve prudent exploitation and that prudent exploitation strategies can evolve only provided the prey-to-predator conversion efficiency is subject to constraints.     

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.     

Foraging strategy of a non-omniscient predator in a changing environment (I) model with a data window and absolute criterion

1. Almost all the models so far presented assume that predators are omniscient in the sense that they always have complete information about the spatial distribution of prey abundance and its change over time. But this type of model cannot cover the situation where the prey abundance in each patch changes over time due to factors other than predation. The model with a data window and absolute criterion (SAC) here enables us to treat such situations.
2. The strategy of non-omniscient predators can be generally devided into four procedures; collection of information, its memorization, decision of tactics and its execution. SAC involves only two tactics; to stay another time period in the patch the predator is staying presently or to move to another patch chosen at random. The choice of either one of the two tactics is made by comparing the profitability of the current patch estimated by the data window with a pre-determined absolute criterion.
3. Three changing patterns of prey abundance are considered. In the most general pattern good patches have a higher mean profitability than poor patches, but the profitability changes cyclically in each of patches.
4. There are only two possibilities for an optimal strategy; the “patch choice strategy” in which once the predator has taken a good patch, it tries to stay there even when the state becomes poor, and the ‘state choice strategy” in which the predator seeks for only good states in good patches. The condition for which either of the two foraging strategies is superior to the other is specified analytically.

     

The influence of sediment type on the aggregative response of oystercatchers, Haematopus ostralegus, searching for cockles, Cerastoderma edule

Models that describe the dispersion patterns of predators between a series of patches that vary in prey density frequently assume that predators, in the absence of interference, will aggregate in patches with the highest prey density, at any point in time. This assumption has important implications for patterns of prey mortality, and the extent to which prey mortality is density dependent. In natural predator-prey systems, it is likely that environmental factors interact with spatial variation in prey density to influence the aggregative response of predators. We show data consistent with this idea on a population of overwintering oystercatchers foraging on cockles. There was no evidence that birds aggregated in patches with the highest biomass density of cockles. The biomass density of cockles was highest in muddy patches at the start of winter, and birds aggregated in patches that switched from being muddy at the start of winter to being sandy at some point during the winter. We argue that sediment type influences foraging costs experienced by the birds, so birds avoid feeding in muddy patches unless the fine sediment is removed from a patch, as happens during winter storms. When this happens a high biomass density of cockles suddenly becomes available and the birds aggregate in such patches. The rate of biomass loss was greatest in patches used intensively by birds for feeding, suggesting that the birds' aggregative response influences cockle mortality. We discuss the implications of our results for ideal free models.     

Foraging speed in staging flocks of semipalmated sandpipers: evidence for scramble competition

Foraging speed is a key determinant of fitness affecting both foraging success and predator attack survival. In a scramble for food, for instance, evolutionary stable strategy models predict that speed should increase with competitor density and decrease when the risk of attack by predators increases. Foraging speed should also decrease in richer food patches where the level of competition is reduced. I tested these predictions in fall staging flocks of semipalmated sandpipers (Calidris pusilla) foraging for an evasive prey. Capture rate of these prey decreased with sandpiper density as the presence of competitors reduced the availability of resources for those behind. Foraging speed was evaluated indirectly by measuring the time needed to cross fixed boundaries on mudflats over 6 years. As predicted, foraging speed increased with sandpiper density and decreased with food density, but, unexpectedly, increased closer to obstructive cover where predation risk was deemed higher. When foraging closer to cover, from where predators launch surprise attacks, the increase in foraging speed may compensate for an increase in false alarms that interrupted foraging. While foraging in denser flocks decreases foraging success, joining such flocks may also increase safety against predators. In semipalmated sandpipers that occupy an intermediate position in the food chain, foraging behavior is influenced simultaneously by the evasive responses of their prey and by the risk of attack from their own predators.     

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.     

Predator hunting modes and predator–prey space games

Predators and prey are often engaged in a game where their expected fitnesses are affected by their relative spatial distributions. Game models generally predict that when predators and prey move at similar temporal and spatial scales that predators should distribute themselves to match the distribution of the prey's resources and that prey should be relatively uniformly distributed. These predictions should better apply to sit-and-pursue and sit-and-wait predators, who must anticipate the spatial distributions of their prey, than active predators that search for their prey. We test this with an experiment observing the spatial distributions and estimating the causes of movements between patches for Pacific tree frog tadpoles (Pseudacris regilla), a sit-and-pursue dragonfly larvae predator (Rhionaeschna multicolor), and an active salamander larval predator (Ambystoma tigrinum mavortium) when a single species was in the arena and when the prey was with one of the predators. We find that the sit-and-pursue predator favors patches with more of the prey's algae resources when the prey is not in the experimental arena and that the prey, when in the arena with this predator, do not favor patches with more resources. We also find that the active predator does not favor patches with more algae and that prey, when with an active predator, continue to favor these higher resource patches. These results suggest that the hunting modes of predators impact their spatial distributions and the spatial distributions of their prey, which has potential to have cascading effects on lower trophic levels.     

Nonconsumptive effects in a multiple predator system reduce the foraging efficiency of a keystone predator

Many studies have demonstrated that the nonconsumptive effect (NCE) of predators on prey traits can alter prey demographics in ways that are just as strong as the consumptive effect (CE) of predators. Less well studied, however, is how the CE and NCE of multiple predator species can interact to influence the combined effect of multiple predators on prey mortality. We examined the extent to which the NCE of one predator altered the CE of another predator on a shared prey and evaluated whether we can better predict the combined impact of multiple predators on prey when accounting for this influence. We conducted a set of experiments with larval dragonflies, adult newts (a known keystone predator), and their tadpole prey. We quantified the CE and NCE of each predator, the extent to which NCEs from one predator alters the CE of the second predator, and the combined effect of both predators on prey mortality. We then compared the combined effect of both predators on prey mortality to four predictive models. Dragonflies caused more tadpoles to hide under leaf litter (a NCE), where newts spend less time foraging, which reduced the foraging success (CE) of newts. Newts altered tadpole behavior but not in a way that altered the foraging success of dragonflies. Our study suggests that we can better predict the combined effect of multiple predators on prey when we incorporate the influence of interactions between the CE and NCE of multiple predators into a predictive model. In our case, the threat of predation to prey by one predator reduced the foraging efficiency of a keystone predator. Consequently, the ability of a predator to fill a keystone role could be compromised by the presence of other predators.     

Tolerance of understory plants subject to herbivory by roe deer

Classical foraging theory states that animals feeding in a patchy environment can maximise their long term prey capture rates by quitting food patches when they have depleted prey to a certain threshold level. Theory suggests that social foragers may be better able to do this if all individuals in a group have access to the prey capture information of all other group members. This will allow all foragers to make a more accurate estimation of the patch quality over time and hence enable them to quit patches closer to the optimal prey threshold level. We develop a model to examine the foraging efficiency of three strategies that could be used by a cohesive foraging group to initiate quitting a patch, where foragers do not use such information, and compare these with a fourth strategy in which foragers use public information of all prey capture events made by the group. We carried out simulations in six different prey environments, in which we varied the mean number of prey per patch and the variance of prey number between patches. Groups sharing public information were able to consistently quit patches close to the optimal prey threshold level, and obtained constant prey capture rates, in groups of all sizes. In contrast all groups not sharing public information quit patches progressively earlier than the optimal prey threshold value, and experienced decreasing prey capture rates, as group size increased. This is more apparent as the variance in prey number between patches increases. Thus in a patchy environment, where uncertainty is high, although public information use does not increase the foraging efficiency of groups over that of a lone forager, it certainly offers benefits over groups which do not, and particularly where group size is large.     

Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.     

Prey‐driven behavioral habitat use in a low‐energy ambush predator

Food acquisition is an important modulator of animal behavior and habitat selection that can affect fitness. Optimal foraging theory predicts that predators should select habitat patches to maximize their foraging success and net energy gain, likely achieved by targeting areas with high prey availability. However, it is debated whether prey availability drives fine‐scale habitat selection for predators. We assessed whether an ambush predator, the timber rattlesnake (Crotalus horridus), exhibits optimal foraging site selection based on the spatial distribution and availability of prey. We used passive infrared camera trap detections of potential small mammal prey (Peromyscus spp., Tamias striatus, and Sciurus spp.) to generate variables of prey availability across the study area and used whether a snake was observed in a foraging location or not to model optimal foraging in timber rattlesnakes. Our models of small mammal spatial distributions broadly predicted that prey availability was greatest in mature deciduous forests, but T. striatus and Sciurus spp. exhibited greater spatial heterogeneity compared with Peromyscus spp. We found the spatial distribution of cumulative small mammal encounters (i.e., overall prey availability), rather than the distribution of any one species, to be highly predictive of snake foraging. Timber rattlesnakes appear to forage where the probability of encountering prey is greatest. Our study provides evidence for fine‐scale optimal foraging in a low‐energy, ambush predator and offers new insights into drivers of snake foraging and habitat selection.     

Aggregative response in bats: prey abundance versus habitat

In habitats where prey is either rare or difficult to predict spatiotemporally, such as open habitats, predators must be adapted to react effectively to variations in prey abundance. Open-habitat foraging bats have a wing morphology adapted for covering long distances, possibly use information transfer to locate patches of high prey abundance, and would therefore be expected to show an aggregative response at these patches. Here, we examined the effects of prey abundance on foraging activities of open-habitat foragers in comparison to that of edge-habitat foragers and closed-habitat foragers. Bat activity was estimated by counting foraging calls recorded with bat call recorders (38,371 calls). Prey abundance was estimated concurrently at each site using light and pitfall traps. The habitat was characterized by terrestrial laser scanning. Prey abundance increased with vegetation density. As expected, recordings of open-habitat foragers clearly decreased with increasing vegetation density. The foraging activity of edge- and closed-habitat foragers was not significantly affected by the vegetation density, i.e., these guilds were able to forage from open habitats to habitats with dense vegetation. Only open-habitat foragers displayed a significant and proportional aggregative response to increasing prey abundance. Our results suggest that adaptations for effective and low-cost foraging constrains habitat use and excludes the guild of open-habitat foragers from foraging in habitats with high prey abundance, such as dense forest stands.     

Autotomy and its Effects on Wolf Spider Foraging Success

Few studies have attempted to determine how physical injury affects predators. One of the ways that physical injury can be expressed is by autotomy or the voluntary loss of a body part. Here, we examined whether the loss of specific legs affects the foraging success of the wolf spider Rabidosa santrita (predator) on another species, Pardosa valens (prey). We also wanted to identify whether the loss of legs in both the predator and prey would impact the outcome of a predation event. Both predator and prey were collected from a creek bed at Portal, AZ, in 2012. Predators were randomly assigned groups where all prey items were intact or all prey had one randomly chosen leg IV removed. Within these groups, predators were organized into a control, leg I autotomy, or leg IV autotomy treatment. All predators had their pre‐ and post‐foraging running speed determined. Predators were introduced into chambers with five prey items and allowed to forage for 1 h. The leg position autotomized or the comparison of pre‐ and post‐foraging trials had no effect on predator running speed. Additionally, there was no significant effect of either predator or prey leg treatment on the total proportion of prey items captured by the end of the foraging trials. Survival analyses indicated that intact prey items tended to have a higher survival rate when predators were missing a leg IV than when predators were intact. When both the predator and prey were missing legs, no significant difference in prey survival rates was detected. We suggest that for predators that inhabit complex, heterogeneous habitats and are classified as ambush predators, the loss of a limb may affect prey capture success, especially when the prey is intact, but that increased sample size is necessary to determine whether this trend is significant.     

Does prey size matter? Novel observations of feeding in the leatherback turtle (Dermochelys coriacea) allow a test of predator–prey size relationships

Optimal foraging models predict that large predators should concentrate on large prey in order to maximize their net gain of energy intake. Here, we show that the largest species of sea turtle, Dermochelys coriacea, does not strictly adhere to this general pattern. Field observations combined with a theoretical model suggest that a 300 kg leatherback turtle would meet its energetic requirements by feeding for 3-4 h a day on 4 g jellyfish, but only if prey were aggregated in high-density patches. Therefore, prey abundance rather than prey size may, in some cases, be the overriding parameter for foraging leatherbacks. This is a classic example where the presence of small prey in the diet of a large marine predator may reflect profitable foraging decisions if the relatively low energy intake per small individual prey is offset by high encounter rates and minimal capture and handling costs. This study provides, to our knowledge, the first quantitative estimates of intake rate for this species.     

Predation-Related Costs and Benefits of Conspecific Attraction in Songbirds—An Agent-Based Approach

Songbirds that follow a conspecific attraction strategy in the habitat selection process prefer to settle in habitat patches already occupied by other individuals. This largely affects the patterns of their spatio-temporal distribution and leads to clustered breeding. Although making informed settlement decisions is expected to be beneficial for individuals, such territory clusters may potentially provide additional fitness benefits (e.g., through the dilution effect) or costs (e.g., possibly facilitating nest localization if predators respond functionally to prey distribution). Thus, we hypothesized that the fitness consequences of following a conspecific attraction strategy may largely depend on the composition of the predator community. We developed an agent-based model in which we simulated the settling behavior of birds that use a conspecific attraction strategy and breed in a multi-predator landscape with predators that exhibited different foraging strategies. Moreover, we investigated whether Bayesian updating of prior settlement decisions according to the perceived predation risk may improve the fitness of birds that rely on conspecific cues. Our results provide evidence that the fitness consequences of conspecific attraction are predation-related. We found that in landscapes dominated by predators able to respond functionally to prey distribution, clustered breeding led to fitness costs. However, this cost could be reduced if birds performed Bayesian updating of prior settlement decisions and perceived nesting with too many neighbors as a threat. Our results did not support the hypothesis that in landscapes dominated by incidental predators, clustered breeding as a byproduct of conspecific attraction provides fitness benefits through the dilution effect. We suggest that this may be due to the spatial scale of songbirds’ aggregative behavior. In general, we provide evidence that when considering the fitness consequences of conspecific attraction for songbirds, one should expect a trade-off between the benefits of making informed decisions and the costs of clustering.     

Experimental determination of the spatial scale of a prey patch from the predator’s perspective

Foraging theory predicts that predators should prefer foraging in habitat patches with higher prey densities. However, density depends on the spatial scale at which a “patch” is defined by an observer. Ecologists strive to measure prey densities at the same scale that predators do, but many natural landscapes lack obvious, well-defined prey patches. Thus one must determine the scale at which predators define patches of prey. We estimated the scale at which guppies, Poecilia reticulata, selected patches of zooplankton prey using a behavioral assay. Guppies could choose between two prey arrays, each manipulated to have a density that depended on the spatial scale at which density was calculated. We estimated the scale of guppy foraging by comparing guppy preferences across a series of trials in which we systematically varied the scale associated with “high” prey density. This approach enables the application of foraging theory to non-discrete habitats and prey landscapes.