Stochastic patch exploitation model

A solitary animal is foraging in a patch consisting of discrete prey items. We develop a stochastic model for the accumulation of gain as a function of elapsed time in the patch. The model is based on the waiting times between subsequent encounters with the prey items. The novelty of the model is in that it renders possible–via parameterization of the waiting time distributions: the incorporation of different foraging situations and patch structures into the gain process. The flexibility of the model is demonstrated with different foraging scenarios. Dependence of gain expectation and variance of the parameters of the waiting times is studied under these conditions. The model allows us to comment upon some of the basic concepts in contemporary foraging theory.     

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.     

Foraging for intermittently refuged prey: theory and field observations of a parasitoid

Many insect herbivores feed in concealed locations but become accessible intermittently, creating windows of greater vulnerability to attack, and generating a proportion of the prey population that is readily accessible to foraging natural enemies. We incorporated accessible prey into an extant optimal foraging model, and found that this addition allowed opportunistic exploitation of prey that have already emerged from refugia (the leaving strategy) as a viable strategy, in addition to waiting at refugia for prey to emerge (the waiting strategy). We parameterized the model empirically for the parasitoid Macrocentrus grandii and its host, Ostrinia nubilalis, under field conditions. The model predicted that M. grandii should adopt a leaving strategy when host patch density is high (travel time between patches is short), but a waiting strategy when host patch density is low (travel time between patches is long). Field observations of M. grandii patch tenure were consistent with model predictions, indicating that M. grandii exhibited flexible behaviour based on experience within a foraging bout, and that these behavioural shifts improved foraging efficiency. Behaviour of M. grandii was responsive to heterogeneity in host emergence rates, and appeared to be driven by the relatively small proportion of the host population that became accessible at a fast rate. Therefore understanding forager responses to intermittently refuged prey may require characterization of the behaviour of a subset of the prey population, rather than the average prey individual. The model can potentially be used as a framework for comparative studies across forager taxa, to understand when foragers on intermittently accessible prey should adopt fixed waiting or leaving strategies vs. a flexible strategy that is responsive to the current environment.     

Patch exploitation, group foraging, and unequal competitors

Charnov's (1976) marginal value theorem, MVT, addresses howlong a forager should stay in a patch of prey to maximize itsgain. Information-sharing models of group foraging suggest thatindividuals should join groups to improve their patch-findingrate. This is achievable if group members share informationabout the location of food patches. The determinants of theMVT are searching time and cumulative gain against time in apatch, those of the group foraging models are searching time,group size, and individual differences in ability to monopolizethe prey found. After combining the MVT and information-sharingmodels we explore the consequences of unequal competitors (good,G, and poor, P) foraging in groups. Under this domain G andP differ in their accumulated harvest against time in a patch.When the gain function of P is obtained by mere scaling of thatof G, optimal patch residence times for individuals of the twophenotypes do not differ. However, if the gain functions ofG and P cannot be derived from each other by a constant scalingmultiplier, the optimal patch times for G and P are not necessarilythe same. Under these conditions the model suggests that foraginggroups should become assorted by foraging ability.     

Does group foraging promote efficient exploitation of resources?

Increased avoidance of food patches previously exploited by other companions has been proposed as one adaptive benefit of group foraging. However, does group foraging really represent the most efficient way to exploit non- or slowly-renewing resources? Here, I used simulations to explore the costs and benefits of exploiting non-renewing resources by foragers searching for food patches independently or in groups in habitats with different types of resource distribution. Group foragers exploited resources in a patch more quickly and therefore spent proportionately more time locating new patches. Reduced avoidance of areas already exploited by others failed to overcome the increased time cost of searching for new food patches and group foragers thus obtained food at a lower rate than solitary foragers. Group foraging provided one advantage in terms of a reduction in the variance of food intake rate. On its own, reduced avoidance of exploitation competition through group foraging appears unlikely to increase mean food intake rate when exploiting non-renewing patches but may provide a way to reduce the risk of an energy shortfall.     

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.     

The Relative Importance of Habitat Structure and of Prey Characteristics for the Foraging Success of Water Pipits (Anthus spinoletta)*

While many studies on foraging have related energy gain to the density and the size of prey, only few have investigated whether and how habitat structure modifies the gain through affecting foraging success. In this study, the influences of habitat structure and prey characteristics on the foraging success of water pipits, Anthus spinoletta, were investigated experimentally. The birds take longer to find prey in tall than in short vegetation. The effects of vegetation on searching times differ between prey types. These differences are probably caused by variation in prey behaviour and in cryptic colouration, but not by prey size. Searching times increase with decreasing density for mealworms and tipulids, but not for caterpillars. Handling large prey items requires more time than handling smaller prey. Tipulids and caterpillars, which were offered alive, are handled for a longer time than dead mealworms of corresponding size. The success of attacks on flying insects is probably influenced by the prey's flight speed: fast houseflies are missed more often than slow tipulids. Overall, the results show that the time costs of foraging water pipits are influenced to a comparable degree by vegetation structure, by prey density and by other specific prey characteristics such as camouflage, hiding behaviour or agility. The amount of food gathered per unit time is determined primarily by factors that affect searching times, and less by handling and travelling times. Insertion of our data into an optimal diet model leads to the prediction that water pipits should be generalist foragers, which agrees with the observed behaviour.     

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.     

Foraging rate versus sociality in the starling Sturnus vulgaris

It is well established that social conditions often modify foraging behaviour, but the theoretical interpretation of the changes produced is not straightforward. Changes may be due to alterations of the foraging currency (the mathematical expression that behaviour maximizes) and/or of the available resources. An example of the latter is when both solitary and social foragers maximize rates of gain over time, but competition alters the behaviour required to achieve this, as assumed by ideal free distribution models. Here we examine this problem using captive starlings Sturnus vulgaris. Subjects had access to two depleting patches that replenished whenever the alternative patch was visited. The theoretical rate-maximizing policy was the same across all treatments, and consisted of alternating between patches following a pattern that could be predicted using the marginal value theorem (MVT). There were three treatments that differed in the contents of an aviary adjacent to one of the two patches (called the 'social' patch). In the control treatment, the aviary was empty, in the social condition it contained a group of starlings, and in a non-specific stimulus control it contained a group of zebra finches. In the control condition both patches were used equally and behaviour was well predicted by the MVT. In the social condition, starlings foraged more slowly in the social than in the solitary patch. Further, foraging in the solitary patch was faster and in the social patch slower in the social condition than in the control condition. Although these changes are incompatible with overall rate maximization (gain rate decreased by about 24% by self-imposed changes), if the self-generated gain functions were used the MVT was a good predictor of patch exploitation under all conditions. We discuss the complexities of nesting optimal foraging models in more comprehensive theoretical accounts of behaviour integrating functional and mechanistic perspectives.     

Maintaining social cohesion is a more important determinant of patch residence time than maximizing food intake rate in a group-living primate,Japanese macaque (Macaca fuscata)

Animals have been assumed to employ an optimal foraging strategy (e.g., rate-maximizing strategy). In patchy food environments, intake rate within patches is positively correlated with patch quality, and declines as patches are depleted through consumption. This causes patch-leaving and determines patch residence time. In group-foraging situations, patch residence times are also affected by patch sharing. Optimal patch models for groups predict that patch residence times decrease as the number of co-feeding animals increases because of accelerated patch depletion. However, group members often depart patches without patch depletion, and their patch residence time deviates from patch models. It has been pointed out that patch residence time is also influenced by maintaining social proximity with others among group-living animals. In this study, the effects of maintaining social cohesion and that of rate-maximizing strategy on patch residence time were examined in Japanese macaques (Macaca fuscata). I hypothesized that foragers give up patches to remain in the proximity of their troop members. On the other hand, foragers may stay for a relatively long period when they do not have to abandon patches to follow the troop. In this study, intake rate and foraging effort (i.e., movement) did not change during patch residency. Macaques maintained their intake rate with only a little foraging effort. Therefore, the patches were assumed to be undepleted during patch residency. Further, patch residence time was affected by patch-leaving to maintain social proximity, but not by the intake rate. Macaques tended to stay in patches for short periods when they needed to give up patches for social proximity, and remained for long periods when they did not need to leave to keep social proximity. Patch-leaving and patch residence time that prioritize the maintenance of social cohesion may be a behavioral pattern in group-living primates.     

Prey size affects the costs and benefits of group predation in nymphs of the predatory stink bug Andrallus spinidens (Heteroptera: Pentatomidae)

Group predation promotes foraging efficiency because it increases the size of prey that can be killed and improves hunting success compared to solitary predation. However, group predation may increase competition among group members during feeding. Earlier studies have focused on the advantages of group predation, but little is known about the costs and benefits of group predation for individual members of the group. Here, we show that the costs and benefits of group predation for individuals of the predatory stink bug Andrallus spinidens vary with prey size in laboratory experiments. We found that when A. spinidens fed on small prey, group predation did not significantly increase foraging efficiency but did increase competition for food among group members. In contrast, when prey was large, group predation promoted foraging efficiency, and competition over food was not detected. Our results suggest that group predation by A. spinidens nymphs is advantageous for individual members because it enables each member to hunt larger prey that could not be hunted alone. However, when group size was large or prey size was small, group predation increased competition among group members.     

Patch selection by juvenile black surfperch (Embiotocidae) under variable risk: Interactive influence of food quality and structural complexity

The influence of risk on the selection of foraging patches by young-of-year black surfperch, Embiotoca jacksoni Agassiz, was investigated by laboratory and field experiments. These foragers harvest crustacean prey from a variety of benthic algal substrata. In field environments, patch types vary in two ways. First, substrata differ in structural complexity and probably afford different degrees of protection from predators. Second, substratum types vary in prey richness. There was no correlation between structural complexity and prey richness, and either or both factors could be a component of foraging patch value. Each patch is small and individual foragers are simultaneously confronted with arrays of patches encompassing the full range of variation in structure and prey richness. Furthermore, a major predator of young-of-year black surfperch, the kelp bass, Paralabrax clathratus (Girard), is patchily distributed in space and time. Thus similar arrays of patch types can be characterized by different levels of overall risk. Risk to foragers is dependent on light level as well as the presence and density of predators.The interplay between food quality and shelter potential in influencing patch choice was examined under different regimes of risk. Both laboratory and field experiments indicated patch preference was based primarily on food quality. However, the physical structure of a patch did become a component of patch choice as risk increased. The relative value of physical structure under high risk was dependent on the prey richness of a patch; food-poor substrata with high shelter potential remained unfavored even in situations of high risk.     

Exponential Versus Hyperbolic Discounting of Delayed Outcomes: Risk and Waiting Time

Frequently, animals must choose between more immediate, smallerrewards and more delayed, but larger rewards. For example, theyoften must decide between accepting a smaller prey item versuscontinuing to search for a larger one, or between entering aleaner patch versus travelling to a richer patch that is furtheraway. In both situations, choice of the more immediate, butsmaller reward may be interpreted as implying that the valueof the later reward is discounted; that is, the value of thelater reward decreases as the delay to its receipt increases.This decrease in value may occur because of the increased riskinvolved in waiting for rewards, or because of the decreasedrate of reward associated with increased waiting time. The presentresearch attempts to determine the form of the relation betweenvalue and delay, and examines implications of this relationfor mechanisms underlying risk-sensitive foraging. Two accounts of the relation between value and delay have beenproposed to describe the decrease in value resulting from increasesin delay: an exponential model and a hyperbolic model. Our researchdemonstrates that, of the two, a hyperbola-like discountingmodel consistently explains more of the variance in temporaldiscounting data at the group level and, importantly, at theindividual level as well. We show mathematically that the hyperbolicmodel shares fundamental features with models of prey and patchchoice. In addition, the present review highlights the implicationsof a psychological perspective for the behavioral biology ofrisksensitive foraging, as well as the implications of an ecologicalperspective for the behavioral psychology of risk-sensitivechoice and decision-making.     

Benefits of Group Foraging Depend on Prey Type in a Small Marine Predator,the Little Penguin

Group foraging provides predators with advantages in over-powering prey larger than themselves or in aggregating small prey for efficient exploitation. For group-living predatory species, cooperative hunting strategies provide inclusive fitness benefits. However, for colonial-breeding predators, the benefit pay-offs of group foraging are less clear due to the potential for intra-specific competition. We used animal-borne cameras to determine the prey types, hunting strategies, and success of little penguins (Eudyptula minor), a small, colonial breeding air-breathing marine predator that has recently been shown to display extensive at-sea foraging associations with conspecifics. Regardless of prey type, little penguins had a higher probability of associating with conspecifics when hunting prey that were aggregated than when prey were solitary. In addition, success was greater when individuals hunted schooling rather than solitary prey. Surprisingly, however, success on schooling prey was similar or greater when individuals hunted on their own than when with conspecifics. These findings suggest individuals may be trading-off the energetic gains of solitary hunting for an increased probability of detecting prey within a spatially and temporally variable prey field by associating with conspecifics.     

The use and misuse of public information by foraging red crossbills

Group foragers may assess patch quality more efficiently bypaying attention to the sampling behavior of group members foragingin the same patch (i.e., using "public information"). To determinewhether red crossbills (Loxia curvirostra) use public informationto aid their patch departure decisions, we conducted experimentsthat compared the sampling behavior of crossbills foraging ona two-patch system (one patch was always empty, one patch containingseeds) when alone, in pairs, and in flocks of three. When foragingalone, crossbills departed from empty patches in a way thatwas qualitatively consistent with energy maximization. We foundevidence for the use of public information when crossbills werepaired with two flock mates, but not when paired with one flockmate. When foraging with two flock mates, crossbills sampledapproximately half the number of cones on the empty patch beforedeparting as compared to when solitary. Furthermore, as expected ifpublic information is used, the variance in both the numberof cones and time spent on the empty patch decreased when crossbillsforaged with two flock mates as compared to when alone. Althoughhigh frequencies of scrounging reduce the availability of publicinformation, scrounging is usually uncommon in crossbills, apparentlybecause they exploit divisible patches. Consequently, publicinformation is likely to be important to crossbills in the wild.We also show that feeding performance is greatly diminishedwhen the feeding performances of flock mates differ. This providesa mechanism that will favor assortative grouping by phenotypewhen phenotypes affect feeding performance, which may in turnpromote speciation in some groups of animals.     

Individuals in foraging groups may use vocal cues when assessing their need for anti-predator vigilance

Many studies of social species have reported variation in the anti-predator vigilance behaviour of foraging individuals depending on the presence and relative position of other group members. However, little attention has focused on how foragers assess these variables. It is commonly assumed that they do so visually, but many social species produce frequent calls while foraging, and these 'close' calls might provide valuable spatial information. Here, we show that foraging pied babblers (Turdoides bicolor) are less vigilant when in larger groups, in the centre of a group and in closer proximity to another group member. We then show that foragers are less vigilant during playbacks of close calling by more individuals and individuals on either side of them when compared with calls of fewer individuals and calls on one side of them. These results suggest that foragers can use vocal cues to gain information on group size and their spatial position within a group. Future studies of anti-predator vigilance should consider the relative importance of both visual and vocal monitoring of group members.     

Testing predictions of foraging theory for a sit-and-wait forager, Anolis gingivinus

Research in foraging theory has been dominated by studies ofactive foragers choosing among patches and among prey withina patch. Studies of central-place foraging have mainly focusedon loading decisions of an animal provisioning a central place.The problem faced by a sit-and-wait forager that encountersprey at a distance has received little attention. In this studywe tested foraging theory predictions for such foragers, Anolisgingivinus females in the West Indies island of Anguilla. Wepresented lizards with antlion larvae at various distances.Experiment 1 showed that an individual's probability of pursuingprey decreases with the prey's distance and is best describedby a sigmoidal function (which may be as steep as a step function).This function's inflection point defines a cutoff distance.Experiment 3 tested how cutoff distance changes as a functionof prey size. Cutoff distances were greater for larger prey,as predicted for an energy-maximizing forager. Experiments 2and 4 tested how cutoff distance changes as a function of preyabundance. As predicted, cutoff distance were greater at a sitewhere prey abundance was lower. Furthermore, cutoff distancesdecreased immediately following prey augmentation and returnedto previous values within one day of ending augmentation. Thus,moles' foraging behavior is a dynamic process, consistent withthe qualitative predictions of foraging theory. We attributethe success of this study in supporting fundamental foragingtheory predictions to the lizards exhibiting natural behaviorunder field conditions and to particular advantages of studyingsit-and-wait foragers.     

The effect of group size on vigilance in Ruddy Turnstones Arenaria interpres varies with foraging habitat

Foraging birds can manage time spent vigilant for predators by forming groups of various sizes. However, group size alone will not always reliably determine the optimal level of vigilance. For example, variation in predation risk or food quality between patches may also be influential. In a field setting, we assessed how simultaneous variation in predation risk and intake rate affects the relationship between vigilance and group size in foraging Ruddy Turnstones Arenaria interpres. We compared vigilance, measured as the number of ‘head‐ups’ per unit time, in habitat types that differed greatly in prey energy content and proximity to cover from which predators could launch surprise attacks. Habitats closer to predator cover provided foragers with much higher potential net energy intake rates than habitats further from cover. Foragers formed larger and denser flocks on habitats closer to cover. Individual vigilance of foragers in all habitats declined with increasing flock size and increased with flock density. However, vigilance by foragers on habitats closer to cover was always higher for a given flock size than vigilance by foragers on habitats further from cover, and habitat remained an important predictor of vigilance in models including a range of potential confounding variables. Our results suggest that foraging Ruddy Turnstones can simultaneously assess information on group size and the general likelihood of predator attack when determining their vigilance contribution.     

Behavioral and energetic costs of group membership in a coral reef fish

Animals in social aggregations often spend more time foraging than solitary conspecifics. This may be a product of the relative safety afforded by aggregations: group members can devote more time to foraging and less time to antipredator behaviors than solitary animals (the “risk reduction” effect). All else being equal, risk reduction should result in higher food intake for grouped animals. However, intragroup competition may force group members to spend more time foraging in order to obtain the same food ration as solitary individuals (the “resource competition” effect). We compared these opposing explanations of foraging time allocation in a coral reef fish, bluehead wrasse (Thalassoma bifasciatum). Aggregations of juvenile bluehead wrasse experience safety-in-numbers, and preliminary observations suggested that juveniles in aggregations spent more time foraging for copepods in the water column than solitary juveniles. However, the risk reduction and resource competition hypotheses are indistinguishable on the basis of behavioral observations alone. Therefore, we collected behavioral, dietary, and growth data (using otolith growth rings) for bluehead wrasse at multiple reefs around a Caribbean island. Despite spending more time foraging in the water column, grouped fish did not capture more prey items and had slower growth rates than solitary fish. Thus, the increased foraging time of grouped fish appears to reflect resource competition, not risk reduction. This competition may limit the size and frequency of aggregations among juvenile bluehead wrasse, which have been shown to experience reduced mortality rates in larger groups. Bluehead wrasse recruits also spent less time foraging but grew faster at sites where planktonic copepod prey were more abundant. This suggests the possibility that large-scale spatiotemporal variability in the abundance of planktonic copepods over coral reefs may produce corresponding variability in the dynamics of reef fish populations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The hidden cost of information in collective foraging

Many animals nest or roost colonially. At the start of a potential foraging period, they may set out independently or await information from returning foragers. When should such individuals act independently and when should they wait for information? In a social insect colony, for example, information transfer may greatly increase a recruit's probability of finding food, and it is commonly assumed that this will always increase the colony's net energy gain. We test this assumption with a mathematical model. Energy gain by a colony is a function both of the probability of finding food sources and of the duration of their availability. A key factor is the ratio of pro-active foragers to re-active foragers. When leaving the nest, pro-active foragers search for food independently, whereas re-active foragers rely on information from successful foragers to find food. Under certain conditions, the optimum strategy is totally independent (pro-active) foraging because potentially valuable information that re-active foragers may gain from successful foragers is not worth waiting for. This counter-intuitive outcome is remarkably robust over a wide range of parameters. It occurs because food sources are only available for a limited period. Our study emphasizes the importance of time constraints and the analysis of dynamics, not just steady states, to understand social insect foraging.