The survival-rate-maximizing policy for Bayesian foragers: wait for good news

We present a model of the survival-maximizing foraging behaviorof an animal searching in patches for hidden prey with a clumpeddistribution. We assume the forager to be Bayesian: it updatesits statistical estimate of prey number in the current patchwhile foraging. When it arrives at the parch, it has an expectationof the patch's quality, which equals the average patch qualityin the environment While foraging, the forager uses its informationabout the time spent searching in the patch and how many preyhas been caught during this time. It can estimate both the instantaneousintake rate and the potential intake rate during the rest ofthe parch visit. When prey distribution is clumped, potentialintake rate may increase with time spent in the parch if preyis caught in the near future. Being optimal, a Bayesian foragershould therefore base its patch-leaving decision on the estimatedpotential patch value, not on the instantaneous parch value.When patch value is measured in survival rate and mortalitymay occur either as starvation or predation, the patch shouldbe abandoned when the forager estimates that its potential survivalrate dining the rest of the patch visit equals the long termsurvival rate in the environment This means that the instantaneousintake rate, when the patch is left, is nor constant but isan increasing function of searching time in the patch. Therefore,the giving-up densities of prey in the patches will also behigher the longer the search times. The giving-up densitiesare therefore expected to be an increasing, but humped, functionof initial prey densities. These are properties of Bayesianforaging behavior not included in previous empirical studiesand model tests.     

Bayesian foraging with only two patch types

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

Smart,smarter, smartest: foraging information states and coexistence

Animals possess different abilities to gain and use information about the foraging patches they exploit. When ignorant of the qualities of encountered patches, a smart forager should leave all patches after the same amount of fixed search time. A smarter forager can be Bayesian by using information on cumulative harvest and time spent searching a patch to better inform its patch‐departure decision. The smartest forager has immediate and continuous knowledge about patch quality, and can make a perfect decision about when to leave each patch. Here we let each of these three strategies harvest resources from a slowly regenerating environment. Eventually a steady‐state distribution of prey among patches arises where the environment‐wide resource renewal just balances the environment‐wide harvest of the foragers. The fixed time forager creates a distribution with the highest mean and highest variance of patch qualities, followed by the Bayesian and the prescient in that order. The less informed strategies promote distributions with both more resources and more exploitable information than the more informed strategies. While it is true that a better‐informed strategy will always out‐perform a less well‐informed, its increase in performance may not compensate it for any costs associated with being better informed. We imagine that the fixed time strategy may be least expensive and the prescient strategy most expensive in terms of sensory organs and associated assess and respond capabilities. To consider competition between such strategies with varying costs, we introduced a single individual of each of the strategies into the environments created by populations of the other strategies. There are threshold costs associated with the better‐informed strategy such that it can or cannot outcompete a less‐informed strategy. However, over a relatively narrow range of foraging costs, less‐informed and better‐informed strategies will coexist. Furthermore, for the prescient and the Bayesian strategies, some combinations of foraging costs produce alternate stable states – whichever strategy establishes first remains safe from invasion by the other.     

A guide to central place effects in foraging

We develop a general patch-use model of central place foraging, which subsumes and extends several previous models. The model produces a catalog of central place effects predicting how distance from a central place influences the costs and benefits of foraging, load-size, quitting harvest rates, and giving-up densities. In the model, we separate between costs that are load-size dependent, i.e. a direct effect of the size of the load, and load-size independent effects, such as correlations between distance and patch qualities. We also distinguish between predictions of between- and within-environment comparisons. Foraging costs, giving-up densities and quitting harvest rates should almost always increase with distance with these effects amplified by increases in metabolic costs, predation risk and load-costs. With respect to load-size: when comparing foraging in patches within an environment, we should often expect smaller loads to be taken from distant patches (negative distance–load correlation). However, when comparing between environments, there should be a positive correlation between average distance and load-size.     

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

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

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

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

The effects of habitat manipulation on population distribution and foraging behavior in meadow voles

Individuals, free to choose between different habitat patches, should settle among them such that fitness is equalized. Alternatives to this ideal free distribution result into fitness differences among the patches. The concordance between fitnesses and foraging costs among inhabitants of different quality patches, demonstrated in recent studies, suggests that the mode of habitat selection and the resulting fitness patterns may have important implications to the resource use of a forager and to the survival of its prey. We studied how coarse scale selection between habitat patches of different quality and quitting harvest rate in these patches are related to each other and to fine scale patch use in meadow voles (Microtus pennsylvanicus). To demonstrate these relationships, we manipulated habitat patches within large field enclosures by mowing vegetative cover and adding supplemental food according to a 2×2 factorial design. We tracked vole population densities, collected giving‐up densities (GUDs, a measure of patch quitting harvest rate), and monitored the removal of seeds from lattice grids with 1.5 m intervals (an index of fine‐scale space use) in the manipulated habitat patches. Changes in habitat quality induced changes in habitat use at different spatial scales. In preferred habitats with intact cover, voles were despotic and GUDs were low, but increased with the addition of food. In contrast, voles in less‐preferred mowed habitats settled into an ideal free distribution, GUDs were high and uninfluenced by the addition of food. Seed removal was enhanced by the presence of cover but inhibited by supplemental food. Across all treatments, vole densities and GUDs were strongly correlated making it impossible to separate their effects on seed removal rates. However, this relationship broke down in unmowed habitats, where GUDs rather than vole density primarily influenced seed removal by voles. GUDs and seed removal correlated with predation on tree seedlings formerly planted into the enclosures, demonstrating the mechanisms between coarse‐scale habitat manipulations and community level consequences on a forager's prey.     

Foraging and community consequences of seed size for coexisting Negev Desert granivores

We examined the effects of seed size on patch use and diet selection for three co-existing Negev Desert granivores: Allenby's gerbil ( Gerbillus allenbyi ), greater Egyptian sand gerbil ( Gerbillus pyramidum ), and crested lark ( Galerida cristata ). We manipulated size and spatial distribution of seeds in experimental food patches and quantified foraging behavior by measuring giving-up densities (GUDs: the amount of food remaining in a resource patch following exploitation by a forager). In one experiment, we presented small (<1.4 mm in diameter cracked wheat), medium (2.0–3.3 mm), and large (>3.4 mm) seeds in separate trays; in a second, we presented small and medium seeds separately and mixed together. Gerbils had a higher handling time efficiency on smaller seeds, but a much higher encounter probability on larger seeds (20 times higher on large than medium seeds, and 2–5 times higher on medium than small seeds). This led gerbils to have significantly lower GUDs on larger seeds than smaller seeds and to harvest a higher proportion of the larger seeds. When presented with rich and poor patches, G. allenbyi tended to equalize GUDs in both patches, indicating a quitting harvest rate rule for patch exploitation. In contrast, larks appeared to use a fixed time rule for patch exploitation. For larks, seed size did not influence encounter probabilities, and they showed no seed-size selectivity. Still, larks had higher handling efficiencies on smaller than larger seeds, and consequently had a significantly lower GUD on small than medium seeds. Despite large differences between the gerbils and larks in their foraging, our results do not support species coexistence via seed-size partitioning: the larks had much higher GUDs than the gerbils on all seed sizes. Nonetheless, seed size, seed abundance, seed distribution and the animal's patch use behavior all played major roles in determining gerbils' and larks' diet selectivities and GUDs.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

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

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

State‐dependent Bayesian foraging on spatially autocorrelated food distributions

When prey are cryptic and are distributed in discrete clumps (patches), Bayesian foragers revise their prior expectation about a patch's prey density by using their foraging success in the patch as a source of information. Prey densities are often spatially autocorrelated, meaning that rich patches are often surrounded by other rich patches, while poor patches are often in the midst of other poor patches. In that case, foraging success is informative about prey densities in the current patch and in the surrounding patches. In a spatially explicit environment where prey are cryptic and their densities autocorrelated, I modelled two types of Bayesian foragers that aim to maximize their survival rate: (1) the spatially ignorant forager which does not take account of the spatial structure in its food supply and (2) the spatially informed forager which does take this into account. Not surprisingly, the spatially informed forager has a higher survivorship than the spatially ignorant forager, simply because it is able to obtain more reliable prey density estimates than the spatially ignorant forager. Surprisingly though, the emerging policy used by the spatially informed forager is to leave patches at a lower (expected) giving‐up density (GUD) the further away from its latest prey capture. This is because this forager is willing to wait for good news: a prey capture far from the latest prey capture drastically changes the forager's expectations about prey densities in the patches that it will exploit in the near future, whereas a prey capture near its latest prey capture hardly affects these expectations. Thus, by sacrificing current intake rate for information gain, the spatially informed forager ultimately maximizes its long‐term pay‐off. Finally, as the value of food is less the more energy is stored, both types make state‐dependent giving‐up decisions: the higher their energy store levels, the higher their GUDs.     

Driven to distraction: detecting the hidden costs of flea parasitism through foraging behaviour in gerbils

Gerbilline rodents such as Allenby's gerbils (Gerbillus andersoni allenbyi), when parasitized by fleas such as Synosternus cleopatrae pyramidis, devote long hours of grooming to remove the ectoparasites. Yet no detrimental energetic or immunological effects of the ectoparasites have been found in adult Allenby's gerbil. Why should gerbils go to such trouble? We tested for the various ways that fleas can negatively affect gerbils by manipulating flea infestation on gerbils and the presence of a fox. We demonstrate that gerbils responded to fleas by leaving resource patches at higher giving-up densities. Furthermore, they stayed in those resource patches less time and left them at higher quitting harvest rates so long as a fox was also present. When flea-ridden, gerbils also abandoned using vigilance to manage risk and relied mainly on time allocation. Thus, having fleas imposed a foraging cost similar in nature to that arising from the risk of predation from foxes and may be even larger in magnitude. More than that, the presence of fleas acted as a magnifier of foraging costs, especially those arising from the risk of predation. The fleas reduced the gerbils' foraging aptitude and altered how they went about managing risk of predation. We hypothesize that fleas reduce the attention that gerbils otherwise have for foraging and predator detection. We suggest that this is the major cost of ectoparasitism.     

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.     

Honeybee (Apis mellifera ligustica) Response to Differences in Handling Time, Rewards and Flower Colours

Free flying honeybees were tested outdoors on blue–white and blue–yellow dimorphic artificial flower patches to examine the influence of reward difference, flower handling‐time difference and flower colour choice on foraging decisions. We employed different flower‐well depths to vary handling times (costs), and differences in sucrose molarity to vary reward quality. Tests were performed with 2 and 6 μl rewards to vary quantity. We show that when handling time is correlated with flower‐colour morphs on a pedicellate artificial flower patch, a honeybee's foraging behaviour is dependent on the flower colours used in the choice tests. This supports a honeybee foraging model where constraints are a significant factor in decision making. Bees visiting blue–yellow flower patches exhibited flower constancy to colour, where they restricted most visits to a single flower colour, some bees to blue and others to yellow, irrespective of handing time differences. When offered a choice of equally rewarding blue or white flowers, bees were not constrained by flower colour and chose to visit flowers with a lower handling time. When reward molarity varied with well depth between blue and white flowers, foragers chose shallow‐well flowers (short‐handling time) with a smaller net harvest rate over deep‐well flowers (long‐handling time) with a greater net harvest rate. Results using the blue–white dimorphic flower patch suggest that when foraging options simultaneously involve reward and handling‐time choices, honeybee forager behaviour is inconsistent with an absolute method of evaluating profit.     

Downy woodpecker foraging behavior: foraging by expectation and energy intake rate

Summary I describe an artificial patch system that was used to study the foraging behavior of free-roaming downy woodpeckers (Picoides pubescens) in a woodlot in southeastern Michigan. The artificial patches used were thin logs into which were drilled small holes to hold food items (bits of sunflower seed kernels). Downy woodpeckers would systematically search the holes of a patch for food items and thus by manipulating the food distribution within the patches, the birds could be made to experience differing rates of energy intake while foraging.Simple deterministic theories of optimal foraging in patchy environments indicate that an optimal forager, who experiences a decreasing rate of energy intake while foraging in a patch, should leave a patch when its rate of energy intake falls below the average intake rate for the overall environment. In other words, an optimal forager is continually assessing the quality of a patch and makes decisions as to when to leave a patch via its energy intake rate. When the downy woodpeckers studied could encounter any one of several types of patches each with differing, decreasing rates of energy intake, they followed a patch quality assessment strategy similar to that suggested by theory. Upon encountering a single type of patch for a number of consecutive days, however, the birds appeared to forage according to prior expectations of patch quality and not according to a quality assessment strategy based on energy intake rates. The observed expectations were not related to the number of food items per patch but they appeared to be based on expectations of when or where to leave a patch.     

Patch use in time and space for a meso-predator in a risky world

Predator–prey studies often assume a three trophic level system where predators forage free from any risk of predation. Since meso-predators themselves are also prospective prey, they too need to trade-off between food and safety. We applied foraging theory to study patch use and habitat selection by a meso-predator, the red fox. We present evidence that foxes use a quitting harvest rate rule when deciding whether or not to abandon a foraging patch, and experience diminishing returns when foraging from a depletable food patch. Furthermore, our data suggest that patch use decisions of red foxes are influenced not just by the availability of food, but also by their perceived risk of predation. Fox behavior was affected by moonlight, with foxes depleting food resources more thoroughly (lower giving-up density) on darker nights compared to moonlit nights. Foxes reduced risk from hyenas by being more active where and when hyena activity was low. While hyenas were least active during moon, and most active during full moon nights, the reverse was true for foxes. Foxes showed twice as much activity during new moon compared to full moon nights, suggesting different costs of predation. Interestingly, resources in patches with cues of another predator (scat of wolf) were depleted to significantly lower levels compared to patches without. Our results emphasize the need for considering risk of predation for intermediate predators, and also shows how patch use theory and experimental food patches can be used for a predator. Taken together, these results may help us better understand trophic interactions.     

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.     

The Sunk-cost Effect as an Optimal Rate-maximizing Behavior

Optimal foraging theory has been criticized for underestimating patch exploitation time. However, proper modeling of costs not only answers these criticisms, but it also explains apparently irrational behaviors like the sunk-cost effect. When a forager is sure to experience high initial costs repeatedly, the forager should devote more time to exploitation than searching in order to minimize the accumulation of said costs. Thus, increased recognition or reconnaissance costs lead to increased exploitation times in order to reduce the frequency of future costs, and this result can be used to explain paradoxical human preference for higher costs. In fact, this result also provides an explanation for how continuing a very costly task indefinitely provides the optimal long-term rate of gain; the entry cost of each new task is so great that the forager avoids ever returning to search. In general, apparently irrational decisions may be optimal when considering the lifetime of a forager within a larger system.     

Spatial learning and discrimination of food patches in the European badger (Meles meles L.)

Theories of foraging often assume that concentrations of prey (‘patches’) can be discriminated by a forager, but there have been few studies of how this is achieved when patches are not recognizable by means of an obvious proximal cue. We observed the search trajectories of two badgers (Meles meles L.) foraging for peanuts in artificial patches to see how efficiently they could map a new patch in the first place, and whether they would remember the location and extent of a previously visited patch. The results suggest that when a patch is encountered for the first time, a strategy of area-restricted searching keeps the animal's trajectory largely within the patch boundary. After a single exposure to a novel patch, however, badgers show evidence of being able to remember its location and extent, apparently with reference to distal landmarks.