Optimal Foraging and Predator–Prey Dynamics

A system consisting of a population of predators and two types of prey is considered. The dynamics of the system is described by differential equations with controls. The controls model how predators forage on each of the two types of prey. The choice of these controls is based on the standard assumption in the theory of optimal foraging which requires that each predator maximizes the net rate of energy intake during foraging. Since this choice depends on the densities of populations involved, this allows us to link the optimal behavior of an individual with the dynamics of the whole system. Simple qualitative analysis and some simulations show the qualitative behavior of such a system. The effect of the optimal diet choice on the stability of the system is discussed.     

Simple order of prey preference technique for modelling the predator functional response

The predator functional response to several prey types and densities may be conceptualized as a multi-dimensional version of the one-dimensional Holling functional-response curves; however, this empirical approach requires inordinate amounts of data to develop and test. A simulation method of modelling this functional response is to consider the behavior of a predator faced with the choice of several prey types. In this model, when all prey are available the predator’s selection will depend on the absolute abundance of the most-preferred prey type, irrespective of the abundances of the less-preferred prey types. Consequently, the predator will consume only the most-preferred prey types while that type is available in sufficient numbers. When abundance of the most-preferred type declines below a certain level, the predator will begin to include in its diet the second-most-preferred prey type along with the most-preferred prey type. This order-of-preference technique holds up well when the model is compared to population data fromOligonychus pratensis (Acarina: Tetranychidae)/Neoseiulus fallacis (Acarina: Phytoseiidae), and is consistent with optimal foraging theory. Implementation is simple, and the data requirements are reduced to determining the predator’s order of preference and normalizing the nutritional values of the prey types to a single type.     

The influence of predation risk on diet selectivity: A theoretical analysis

Studies that have examined the effect of experimental increases in predation risk on diet selectivity have shown both decreased and increased diet selectivity. A possible explanation for these disparate results emerges from an examination of the prey sets used in these studies, which differed in the relationship between the values of risk components associated with the capture of different prey types (‘danger’) and their profitabilities. When less profitable prey were more dangerous, selectivity increased with predation risk. When prey were equally dangerous, selectivity did not change. Finally, when the more profitable prey were also more dangerous, selectivity decreased with risk. Here, we examine theoretically the influence of a forager's estimate of the probability that a predator is present (φ) on the selection of diets from prey sets with varying danger–profitability relationships. A dynamic programming model is used to determine the maximum attack time (or distance) for each of two types of prey, differing in their energetic content, for a range of forager energy state and φ levels. The diets which would result if foragers attacked prey according to the rules provided by the dynamic model are then determined. The model results indicate that the prey danger–profitability relationship determines the diet selectivity response to φ, confirming that variation in this relationship could be responsible for the range of experimental results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal diet selection,frequency dependence and prey renewal

This paper extends existing models of frequency-dependent diet selection by considering the optimal diet selection of a predator feeding upon prey populations which can be depleted but are also capable of renewal (e.g. immigration, growth, or reproduction). This model and existing models which include prey depletion, predict partial-preference and a generic diet preference for the commonest prey types (apostatic selection). Unlike previous diet selection models, it is found that the optimal diet selection of an individual predator can be to favour the rarest prey type (anti-apostatic selection) when encounter rates are high, even if the individual prey do not differ in their nutritional value. Studies have demonstrated that predators generally show apostatic selection, even when all prey have the same nutritional value. Anti-apostatic selection has also been observed when prey are crowded, and therefore at high density, consistent with the idea of high encounter rates. This anti-apostatic diet selection has previously been proposed as evidence for the use of prey search images by a predator, or variation in individual prey preference. In this paper it is suggested that prey renewal is a further factor, often confounded in experiments, which could favour anti-apostatic selection.     

Feeding rate and attack specialization: the roles of predator experience and energetic tradeoffs

Synopsis Individual mosquitofish, Gambusia affinis, can adopt a broad range of attack selectivities. In part, this variation can be explained by the past experiences of a fish. Individuals selected the more profitable Ceriodaphnia dubia (Cladocera) over less profitable cyclopoid copepods to a greater degree after being exposed to both prey types than did individuals experienced with only one of the prey types. Feeding rate (biomass ingested per unit time) declined with increased attack specialization on the profitable prey (Ceriodaphnia) when such prey were scarce, a result in agreement with assumptions of optimal diet theory. When profitable prey were abundant feeding rate was a bimodal function of the intensity of specialization on profitable prey; fish that specialized on cyclopoid copepods (the less profitable prey type) fed at higher rates than did generalists. This may be the result of antagonistic learning that precluded feeding efficiently on more than one type of prey at a time. The data are consistent with the hypothesis that rejection of unsuitable prey involves a time cost. The two preceeding aspects of foraging behavior, which are absent from most optimal diet models, could lead to failure in predicting the attack specialization of some predators, An additional aspect of the results was the generally weak relationship between feeding efficiency and specialization behavior. This suggests that feeding rate may not have been as tightly linked to the specialization behavior a predator adopts as is assumed by current foraging theory.     

You can run--or you can hide: optimal strategies for cryptic prey against pursuit predators

We consider the optimal behavior of a cryptic prey individualas it is approached by a predator searching for prey. Althoughthe predator has not yet discovered the prey, it has an increasinglikelihood of doing so as it gets closer to the prey. Further,the closer the predator is to the prey when it discovers it,the more likely the predator will be to capture the prey. Thesearguments suggest that the prey should flee before the predatordiscovers it. However, the act of fleeing will alert the predatorto the presence of the prey and trigger an attack that mightnot have occurred otherwise. We capture these conflicting outcomesin a mathematical model, which we then use to predict the optimalbehavior of the prey and predator. We argue that the optimalstrategy for the prey is either to run as soon as they detecta predator approaching or to only flee in response to havingbeen detected by the predator. Running as soon as the predatoris detected is associated with low predator search speeds, alow nonpredation cost to running, a large advantage to the preyin initiating chases rather than reacting, limited ability tospot the predator at distance, a high ability to spot prey bythe predator, and a high probability that chases will be successful.The optimal strategy for the predator depends on whether itscurrent trajectory is taking it closer to or further from theprey. In the latter case, the predator should attack immediatelyon discovering the prey; in the former case, it should delayits attack until it reaches the point on its current trajectorywhere distance to the prey is minimized.     

Optimal foraging and predator-prey dynamics, II.

In this paper we consider one-predator-two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that the region of parameter space leading to permanence for optimal foraging behavior is smaller than that for specialized behavior, but larger than that for generalized behavior. This suggests that optimal foraging behavior of predators may promote coexistence in predator-prey systems. We also study the effects of the above three feeding behaviors on apparent competition between the two prey types.     

On optimal diet in a patchy environment

Optimal foraging theory has dealt with the following questions independently: (1) On what prey types should an individual predator feed (optimal diet)? (2) How long should a predator stay in each patch if prey is patchily distributed (optimal allocation of time to patches) ? This paper explores optimal foraging in patches containing several different kinds of prey. Results obtained by simulation show that deviations from recent predictions are to be expected, particularly for long interpatch travel times and rapid depletion of profitable prey types. In these situations the tactics of feeding as either specialist or as a generalist can be inferior to a tactic which starts as a specialist and then expands the diet after some time in the patch. Furthermore, predators should not necessarily stay longer in a patch if interpatch travel time increases. Some experimental tests of these new predictions are proposed.     

Optimal foraging and intraspecific diet differences in the lizard Cnemidophorus sexlineatus

Summary Previous studies have shown that adult and juvenile six-lined racerunners, Cnemidophorus sexlineatus, consume different sizes and taxa of arthropod prey. the purpose of this study was to determine if these differences could be explained in terms of energy cost and benefit parameters as related by the optimal diet model. Handling times and encounter rates with each of five categories of prey were determined by direct observation of lizard foraging behavior in the field. Energetic cost of search and energy content of prey were estimated from data in the literature. Mean values of all these parameters were used in the classic optimal diet model to determine which prey types yield the greatest rate of net energy gain for adult and juvenile racerunners. Grasshopper-like insects were the most valuable prey for adults, whereas plant and ground arthropods were the most valuable prey for juveniles. These findings correspond to the age-class specific diet differences.Each age-class adopts foraging tactics that increase the chance of finding the most valuable prey. Adult racerunners move hastily over a large area to find the relatively rare, but large and mobile grasshopper prey. Juveniles move much more slowly, and carefully investigate twigs and leaves to find smaller, cryptic plant and ground arthropods. However these foraging tactics do not preclude the taking of less valuable prey items, should they be encountered. This is because it is energetically better on average to eat the prey item rather than skipping it to search for better prey, except for the case of juvenile racerunners eating grasshoppers. That juvenile racerunners will attempt to capture and consume even very large grasshoppers is contrary to the expectations derived from the optimal diet model. This behavior may be the result of the foraging rule of thumb racerunners use to find their prey.     

Dynamic versus instantaneous models of diet choice

We investigate the dynamics of a series of two-prey-one-predator models in which the predator exhibits adaptive diet choice based on the different energy contents and/or handling times of the two prey species. The predator is efficient at exploiting its prey and has a saturating functional response; these two features combine to produce sustained population cycles over a wide range of parameter values. Two types of models of behavioral change are compared. In one class of models ("instantaneous choice"), the probability of acceptance of the poorer prey by the predator instantaneously approximates the optimal choice, given current prey densities. In the second class of models ("dynamic choice"), the probability of acceptance of the poorer prey is a dynamic variable, which begins to change in an adaptive direction when prey densities change but which requires a finite amount of time to approach the new optimal behavior. The two types of models frequently predict qualitatively different population dynamics of the three-species system, with chaotic dynamics and complex cycles being a common outcome only in the dynamic choice models. In dynamic choice models, factors that reduce the rate of behavioral change when the probability of accepting the poorer prey approaches extreme values often produce complex population dynamics. Instantaneous and dynamic models often predict different average population densities and different indirect interactions between prey species. Alternative dynamic models of behavior are analyzed and suggest, first, that instantaneous choice models may be good approximations in some circumstances and, second, that different types of dynamic choice models often lead to significantly different population dynamics. The results suggest possible behavioral mechanisms leading to complex population dynamics and highlight the need for more empirical study of the dynamics of behavioral change.     

Mixed encounters, limited perception and optimal foraging

This article demonstrates how perceptual constraints of predators and the possibility that predators encounter prey both sequentially (one prey type at a time) and simultaneously (two or more prey types at a time) may influence the predator attack decisions, diet composition and functional response of a behavioural predator-prey system. Individuals of a predator species are assumed to forage optimally on two prey types and to have exact knowledge of prey population numbers (or densities) only in a neighbourhood of their actual spatial location. The system characteristics are inspected by means of a discrete-time, discrete-space, individual-based model of the one-predator-two-prey interaction. Model predictions are compared with ones that have been obtained by assuming only sequential encounters of predators with prey and/or omniscient predators aware of prey population densities in the whole environment. It is shown that the zero-one prey choice rule, optimal for sequential encounters and omniscient predators, shifts to abruptly changing partial preferences for both prey types in the case of omniscient predators faced with both types of prey encounters. The latter, in turn, become gradually changing partial preferences when predator omniscience is considered only local.     

Cooperative foraging in neotropical pseudoscorpions: effects of prey changes on behavioral adjustments of colonies

The pseudoscorpion Paratemnoides nidificator is a generalist predator that captures large arthropods that live on tree trunks. Few pseudoscorpions species show some degree of sociality. We investigated how colonies of the pseudoscorpion P. nidificator adjust their cooperative capture behavior under a situation of changing prey types as a simulation of variation in prey availability. We hypothesized that colonies would be more efficient at prey capture under repeated exposure to the same prey, and that the change in the availability of prey would be followed by new behavioral adjustments to adequately exploit the new prey. Eight experimental colonies housed in the laboratory received repetitions of three different ant species as prey. The number of pseudoscorpions attacking the prey, the number of behavioral acts, and the time expended subduing prey were evaluated as measures of prey capture performance, in relation to repetitive exposure to the same prey and also in relation to prey type changes. However, only individuals’ recruitment significantly responded to prey type exposure. Prey capture behavior was heterogeneous among colonies, resulting in highly variable behavioral responses. Colonies showed a tendency toward increasing capture success through repeated prey type exposure. However, 50% of the colonies were unable to capture the new prey type and died of starvation. Although it is a generalist predator, prey capture behavior could depend on different coordination components for subduing and handling large prey. Therefore, changes in prey availability could cause the attenuation of a cooperative relationship in some colonies, making them more prone to failure during capture.     

A stochastic foraging model with predator training effects: I. Functional response,switching, and run lengths

Training effects are changes in a predator's behavior while it is searching for the next prey to eat which are caused by the predator's experience with the last prey encountered. A stochastic foraging model is formulated incorporating several specific types of training effects, and their impact on the functional response shape, switching, and mean prey run lengths is evaluated. The main result is that training effects such as search image formation can cause sigmoid functional responses and switching, and can result in runs of prey captures longer than expected in the absence of training.     

When is general wariness favored in avoiding multiple predator types?

Adaptive responses to predation are generally studied assuming only one predator type exists, but most prey species are depredated by multiple types. When multiple types occur, the optimal antipredator response level may be determined solely by the probability of attack by the relevant predator: "specific responsiveness." Conversely, an increase in the probability of attack by one predator type might increase responsiveness to an alternative predator type: "general wariness." We formulate a mathematical model in which a prey animal perceives a cue providing information on the probability of two predator types being present. It can perform one of two evasive behaviors that vary in their suitability as a response to the "wrong" predator type. We show that general wariness is optimal when incorrect behavioral decisions have differential fitness costs. Counterintuitively, difficulty in discriminating between predator types does not favor general wariness. We predict that where responses to predator types are mutually exclusive (e.g., referential alarm-calling), specific responsiveness will occur; we suggest that prey generalize their defensive responses based on cue similarity due to an assumption of response utility; and we predict, with relevance to conservation, that habituation to human disturbance should generalize only to predators that elicit the same antipredator response as humans.     

Trait‐mediated indirect interactions in a marine intertidal system as quantified by functional responses

Studies of trait‐mediated indirect interactions (TMIIs) typically focus on effects higher predators have on per capita consumption by intermediate consumers of a third, basal prey resource. TMIIs are usually evidenced by changes in feeding rates of intermediate consumers and/or differences in densities of this third species. However, understanding and predicting effects of TMIIs on population stability of such basal species requires examination of the type and magnitude of the functional responses exhibited towards them. Here, in a marine intertidal system consisting of a higher‐order fish predator, the shanny Lipophrys pholis, an intermediate predator, the amphipod Echinogammarus marinus, and a basal prey resource, the isopod Jaera nordmanni, we detected TMIIs, demonstrating the importance of habitat complexity in such interactions, by deriving functional responses and exploring consequences for prey population stability. Echinogammarus marinus reacted to fish predator diet cues by reducing activity, a typical anti‐predator response, but did not alter habitat use. Basal prey, Jaera nordmanni, did not respond to fish diet cues with respect to activity, distribution or aggregation behaviour. Echinogammarus marinus exhibited type II functional responses towards J. nordmanni in simple habitat, but type III functional responses in complex habitat. However, while predator cue decreased the magnitude of the type II functional response in simple habitat, it increased the magnitude of the type III functional response in complex habitat. These findings indicate that, in simple habitats, TMIIs may drive down consumption rates within type II responses, however, this interaction may remain de‐stabilising for prey populations. Conversely, in complex habitats, TMIIs may strengthen regulatory influences of intermediate consumers on prey populations, whilst potentially maintaining prey population stability. We thus highlight that TMIIs can have unexpected and complex ramifications throughout communities, but can be unravelled by considering effects on intermediate predator functional response types and magnitudes. Synthesis Higher‐order predators and habitat complexity can influence behaviour of intermediate species, affecting their consumption of prey through trait‐mediated indirect interactions (TMIIs). However, it is not clear how these factors interact to determine prey population stability. Using functional responses (FRs), relating predator consumption to prey density, we detected TMIIs in a marine system. In simple habitats, TMIIs reduced consumption rates, but FRs remained de‐stabilising for prey populations. In complex habitats, TMIIs strengthened prey regulation with population stabilizing FRs. We thus demonstrate that FRs can assess interactions of environmental and biological cues that result in complex and unexpected outcomes for prey populations.     

A specialized araneophagic predator's short‐term nutrient utilization depends on the macronutrient content of prey rather than on prey taxonomic affiliation

A specialist predator that has a specialized diet, prey‐specific prey‐capture behaviour and a preference for a particular type of prey may or may not be specialized metabolically. Previous studies have shown that jumping spiders of the genus Portia prey on other spiders using prey‐specific prey‐capture behaviour, prefer spiders as prey to insects and gain long‐term benefits in terms of higher survival and growth rates on spider diets than on insect diets. However, it is unclear whether there are substances uniquely present in spiders on which Portia depends, or, alternatively, spiders and insects all contain more or less the same nutrients but the relative amounts of these substances are such that Portia perform better on a spider diet. These questions are addressed by testing the hypothesis that prey specialization includes metabolic adaptations that allow Portia an enhanced nutrient extraction or nutrient utilization efficiency when feeding on spider prey compared with insect prey. Three groups of Portia quei Zabka are fed either their preferred spider prey or one of two types of flies (Drosophila melanogaster Meigen) that differ in nitrogen and lipid content. Portia quei shows a higher feeding rate of high‐protein flies than of high‐lipid flies and spiders but, after 5 days of feeding, there is no significant difference in growth between treatments, and the diets lead to significant changes in the macronutrient composition of P. quei as a result of variable extraction and utilization of the prey. The short‐term utilization of spider prey is similar to that of high‐lipid flies and both differ in several respects from the utilization of high‐protein flies. Thus, the short‐term nutrient utilization is better explained by prey macronutrient content than by whether the prey is a spider or not. The results suggest that spider prey may have a more optimal macronutrient composition for P. quei and that P. quei does not depend on spider‐specific substances.     

Impacts of Biotic Resource Enrichment on a Predator–Prey Population

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator–prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator–prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system’s dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.     

Plankton predation rates in turbulence: a study of the limitations imposed on a predator with a non-spherical field of sensory perception

This paper presents an extension to previously published work which studied encounter rates of planktonic predators with restricted perception fields, to examine the related problems of prey capture and predation rates. Small-scale turbulence influences planktonic predation in two ways: the extra energy of the flow enhances the number of encounter events between individual predator and prey meso/micro-zooplankton, but it lowers the capture probability (because the time spent by the predator and prey in close proximity is reduced). Typically, an 'encounter' has usually been defined as an event when a potential prey swims (or is advected) to within a distance R of the predator in any direction. However, there is a considerable body of experimental evidence showing that predators perception fields are far from spherical; often they are wedge shaped (e.g. fish larvae), or strongly aligned with the directions of sensory antennae (e.g. copepods); and this is certain to influence optimal predation strategies. This paper presents a theoretical model which for the first time examines the combined problems of both encounter and capture for a predator with a restricted perception field swimming in a turbulent flow. If such a predator adopts a cruising strategy (continuous swimming, possibly with direction changes) the model predictions suggest that predation rates actually vary little with swimming speed, in contrast to predictions made for spherical perception fields. Consequently, cruising predators are predicted to swim at relatively low speeds whilst foraging. However, application of the model to examine the net energy gain of a typical pause-travel predator (the Atlantic cod larva), does predict the existence of an optimal ratio of the length of pauses to time spent swimming (specifically one pause phase to every two travel phases), in line with experimental observations. Kinematic simulations are presented which support these findings.     

Incidental predation, enemy-free space and the coexistence of incidental prey

Many communities consist of a generalist predator that consumes multiple prey species whose persistence is thereby threatened through the indirect effect of apparent competition. However, uncommon and/or ephemeral prey may be encountered only incidentally through the predator's effort expended to consume primary prey. In such instances, the functional response to incidental prey is driven entirely through the density of primary prey. Moreover, rarity and brevity in the predator's diet precludes a numerical response to incidental prey. Instead, the persistence of incidental prey may be critically linked to gaps in space unexploited by predators, i.e. enemy-free space. I use optimal foraging theory to derive a mechanism by which enemy-free space is created as a result of a predator's forging aptitude and patch-use behavior. In non-competitive environments enemy-free space provides a behavioral refuge for incidental prey that may prevent their extinction. In competitive environments, greater enemy-free space is associated with higher incidental prey densities and concomitantly greater competitive effects. As a result, incidental prey diversity declines with an increase in enemy-free space.     

Inferring Predator Behavior from Attack Rates on Prey-Replicas That Differ in Conspicuousness

Behavioral ecologists and evolutionary biologists have long studied how predators respond to prey items novel in color and pattern. Because a predatory response is influenced by both the predator’s ability to detect the prey and a post-detection behavioral response, variation among prey types in conspicuousness may confound inference about post-prey-detection predator behavior. That is, a relatively high attack rate on a given prey type may result primarily from enhanced conspicuousness and not predators’ direct preference for that prey. Few studies, however, account for such variation in conspicuousness. In a field experiment, we measured predation rates on clay replicas of two aposematic forms of the poison dart frog Dendrobates pumilio, one novel and one familiar, and two cryptic controls. To ask whether predators prefer or avoid a novel aposematic prey form independently of conspicuousness differences among replicas, we first modeled the visual system of a typical avian predator. Then, we used this model to estimate replica contrast against a leaf litter background to test whether variation in contrast alone could explain variation in predator attack rate. We found that absolute predation rates did not differ among color forms. Predation rates relative to conspicuousness did, however, deviate significantly from expectation, suggesting that predators do make post-detection decisions to avoid or attack a given prey type. The direction of this deviation from expectation, though, depended on assumptions we made about how avian predators discriminate objects from the visual background. Our results show that it is important to account for prey conspicuousness when investigating predator behavior and also that existing models of predator visual systems need to be refined.