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.     

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.     

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.     

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.     

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.     

Intake rate at differently scaled heterogeneous food distributions explained by the ability of tactile-foraging mallard to concentrate foraging effort within profitable areas

The ability to respond to spatial heterogeneity in food abundance depends on the scale of the food distribution and the foraging scale of the forager. The aim of this study is to illustrate that a foraging scale exists, and that at larger scaled food distributions foragers benefit from the ability to subdivide a continuous (non-discrete) heterogeneous environment into profitable and non-profitable areas. We recorded search patterns of mallards Anas plathyrhynchos foraging in shallow water on cryptic prey items (millet seeds), distributed at different scales. A small magnet attached to the lower mandible allowed us to record in great detail the position and movements of the bill tip within a feeding tray underlain by magnet sensors. Instantaneous intake rate was determined in a subsequent experiment. We successfully determined the foraging scale (about 2×2 cm), defined as the scale above which foragers do respond (coarse scaled distribution) and below which foragers do not respond (fine scaled distribution) to spatial heterogeneity, by concentrating foraging effort within areas of high food density. A response resulted in a significantly higher intake rate, compared to a homogeneous distribution with an equal overall density. Unlike systematic search cell revisitation was common in trials, and at coarse scaled food distributions even slightly (but significantly) more frequently observed than predicted for random search. Mallards respond to food capture by restricting displacement (area restricted search) at food distributions that are considered to be clumped for the forager (large scaled coarse distributions). We argue that partitioning the environment at the foraging scale in itself could be a mechanism to concentrate foraging efforts within profitable areas, because mallard were able to respond to heterogeneity at coarse scaled food distributions even when non-clumped (i.e. without conducting area restricted search).     

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.     

Energy benefits and emergent space use patterns of an empirically parameterized model of memory‐based patch selection

Many species frequently return to previously visited foraging sites. This bias towards familiar areas suggests that remembering information from past experience is beneficial. Such a memory‐based foraging strategy has also been hypothesized to give rise to restricted space use (i.e. a home range). Nonetheless, the benefits of empirically derived memory‐based foraging tactics and the extent to which they give rise to restricted space use patterns are still relatively unknown. Using a combination of stochastic agent‐based simulations and deterministic integro‐difference equations, we developed an adaptive link (based on energy gains as a foraging currency) between memory‐based patch selection and its resulting spatial distribution. We used a memory‐based foraging model developed and parameterized with patch selection data of free‐ranging bison Bison bison in Prince Albert National Park, Canada. Relative to random use of food patches, simulated foragers using both spatial and attribute memory are more efficient, particularly in landscapes with clumped resources. However, a certain amount of random patch use is necessary to avoid frequent returns to relatively poor‐quality patches, or avoid being caught in a relatively poor quality area of the landscape. Notably, in landscapes with clumped resources, simulated foragers that kept a reference point of the quality of recently visited patches, and returned to previously visited patches when local patch quality was poorer than the reference point, experienced higher energy gains compared to random patch use. Furthermore, the model of memory‐based foraging resulted in restricted space use in simulated landscapes and replicated the restricted space use observed in free‐ranging bison reasonably well. Our work demonstrates the adaptive value of spatial and attribute memory in heterogeneous landscapes, and how home ranges can be a byproduct of non‐omniscient foragers using past experience to minimize temporal variation in energy gains.     

The foraging benefits of information and the penalty of ignorance

Patch use theory and the marginal value theorem predict that a foraging patch should be abandoned when the costs and benefits of foraging in the patch are equal. This has generally been interpreted as all patches being abandoned when their instantaneous intake rate equals the foraging costs. Bayesian foraging – patch departure is based on a prior estimate of patch qualities and sampling information from the current patch – predicts that instantaneous quitting harvest rates sometimes are not constant across patches but increase with search time in the patch. That is, correct Bayesian foraging theory has appeared incompatible with the widely accepted cost–benefit theories of foraging. In this paper we reconcile Bayesian foraging with cost–benefit theories. The general solution is that a patch should be left not when instantaneous quitting harvest rate reaches a constant level, but when potential quitting harvest rate does. That is, the forager should base its decision on the value now and in the future until the patch is left. We define the difference between potential and instantaneous quitting harvest rates as the foraging benefit of information, FBI. For clumped prey the FBI is positive, and by including this additional benefit of patch harvest the forager is able to reduce its penalty of ignorance.     

A search theory model of patch-to-patch forager movement with application to pollinator-mediated gene flow

We present a spatially implicit analytical model of forager movement, designed to address a simple scenario common in nature. We assume minimal depression of patch resources, and discrete foraging bouts, during which foragers fill to capacity. The model is particularly suitable for foragers that search systematically, foragers that deplete resources in a patch only incrementally, and for sit-and-wait foragers, where harvesting does not affect the rate of arrival of forage. Drawing on the theory of job search from microeconomics, we estimate the expected number of patches visited as a function of just two variables: the coefficient of variation of the rate of energy gain among patches, and the ratio of the expected time exploiting a randomly chosen patch and the expected time travelling between patches. We then consider the forager as a pollinator and apply our model to estimate gene flow. Under model assumptions, an upper bound for animal-mediated gene flow between natural plant populations is approximately proportional to the probability that the animal rejects a plant population. In addition, an upper bound for animal-mediated gene flow in any animal-pollinated agricultural crop from a genetically modified (GM) to a non-GM field is approximately proportional to the proportion of fields that are GM and the probability that the animal rejects a field.     

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.     

An evolutionarily stable joining policy for group foragers

For foragers that exploit patchily distributed resources thatare challenging to locate, detecting discoveries made by otherswith a view to joining them and sharing the patch may oftenbe an attractive tactic, and such behavior has been observedacross many taxa. If, as will commonly be true, the time takento join another individual on a patch increases with the distanceto that patch, then we would expect foragers to be selectivein accepting joining opportunities: preferentially joining nearbydiscoveries. If competition occurs on patches, then the profitabilityof joining (and of not joining) will be influenced by the strategiesadopted by others. Here we present a series of models designedto illuminate the evolutionarily stable joining strategy. Weconfirm rigorously the previous suggestion that there shouldbe a critical joining distance, with all joining opportunitieswithin that distance being accepted and all others being declined.Further, we predict that this distance should be unaffectedby the total availability of food in the environment, but shouldincrease with decreasing density of other foragers, increasingspeed of movement towards joining opportunities, increased difficultyin finding undiscovered food patches, and decreasing speed withwhich discovered patches can be harvested. We are further ableto make predictions as to how fully discovered patches shouldbe exploited before being abandoned as unprofitable, with discoveredpatches being more heavily exploited when patches are hard tofind: patches can be searched for remaining food more quickly,forager density is low, and foragers are relatively slow intraveling to discovered patches.     

Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness

Optimal foraging theory concerns animal behavior in landscapes where food is concentrated in patches. The efficiency of foraging is an effect of both the animal behavior and the geometry of the landscape; furthermore, the landscape is itself affected by the foraging of animals. We investigated the effect of landscape heterogeneity on the efficiency of an optimal forager. The particular aspect of heterogeneity we considered was "clumpiness"– the degree to which food resource patches are clustered together. The starting point for our study was the framework of the Mean Value Theorem (MVT) by Charnov. Since MVT is not spatially explicit, and thus not apt to investigate effects of clumpiness, we built an agent-based (or individual-based) model for animal movement in discrete landscapes extending the MVT. We also constructed a model for generating landscapes where the clumpiness of patches can be easily controlled, or "tuned", by an input parameter. We evaluated the agent based model by comparing the results with what the MTV would give, i.e. if the spatial effects were removed. The MVT matched the simulations best on landscapes with random patch configuration and high food recovery rates. As for our main question about the effects of clumpiness, we found that, when landscapes were highly productive (rapid food replenishment), foraging efficiency was greatest in clumped landscapes. In less productive landscapes, however, foraging efficiency was lowest in landscapes with a clumped patch distribution.     

Quantifying the effect of colony size and food distribution on harvester ant foraging

Desert seed-harvester ants, genus Pogonomyrmex, are central place foragers that search for resources collectively. We quantify how seed harvesters exploit the spatial distribution of seeds to improve their rate of seed collection. We find that foraging rates are significantly influenced by the clumpiness of experimental seed baits. Colonies collected seeds from larger piles faster than randomly distributed seeds. We developed a method to compare foraging rates on clumped versus random seeds across three Pogonomyrmex species that differ substantially in forager population size. The increase in foraging rate when food was clumped in larger piles was indistinguishable across the three species, suggesting that species with larger colonies are no better than species with smaller colonies at collecting clumped seeds. These findings contradict the theoretical expectation that larger groups are more efficient at exploiting clumped resources, thus contributing to our understanding of the importance of the spatial distribution of food sources and colony size for communication and organization in social insects.     

Food Recruitment Information can Spatially Redirect Employed Stingless Bee Foragers

Within a rewarding floral patch, eusocial bee foragers frequently switch sites, going from one flower to another. However, site switching between patches tends to occur with low frequency while a given patch is still rewarding, thus reducing pollen dispersal and gene flow between patches. In principle, forager switching and gene flow between patches could be higher when close patches offer similar rewards. We investigated site switching during food recruitment in the stingless bee Scaptotrigona mexicana . Thus, we trained three groups of foragers to three feeders in different locations, one group per location. These groups did not interact each other during the training phase. Next, interaction among trained foragers was allowed. We found that roughly half of the foragers switched sites, the other half remaining faithful to its training feeder. Switching is influenced by the presence of recruitment information. In the absence of recruitment information (bees visiting and recruiting for feeders), employed foragers were site specific. Foragers only switched among feeders that were being visited and recruited to. Switching was not caused by learned aversion to experimental handling. Switching in response to recruitment could provide a fitness benefit to the colony by facilitating rapid switching among exploited patches and provide a benefit of increasing plant gene flow between patches.     

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.     

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

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

Effects of spatial distribution on plant associational defense against herbivory

Several studies have shown that consumption of a focal plant by herbivores depends not only on its own defense traits but also on the characteristics of the neighboring plants. A number of studies have reported on plant associational defense in relation to neighboring plant palatability but the effect of the spatial distribution of the focal plant within patches of different neighboring plants has received less attention. We conducted a manipulative experiment to determine whether and how spatial distribution of focal plants affects the associational defense between plant species. In our experimental setup sheep encountered two patches varying in spatial distribution of the focal plant within patches (dispersed or clumped) and patch quality, good patch and bad patch, where the focal plant, Lathyrus quinquenervius, was neighbored to high- (Chloris virgata) or low-palatable (Kalimeris integrifolia) species, respectively. Results showed that, when focal plants were dispersed within both patches, the risk of attack was significantly lower for focal plants in the patches with low- than high-palatable neighbors, indicating associational defense. Alternatively, when focal plants were clumped within both patches, they were consumed in bad-patch as much as in good-patch plots, which indicates the absence of associational defense. However, if the focal plants have different spatial distributions in the two patches (dispersed in good-patch and clumped in bad-patch or vice versa), sheep foraging success for focal plants was greatly reduced in dispersed spatial pattern irrespective of the palatability of neighboring plants. Therefore, we concluded that spatial distribution is as important as traits of neighboring plants in predicting vulnerability of the focal plant to grazing by generalist herbivores. The outcome of plant associational defense for different types of neighborhood strongly depends on the magnitude of herbivore foraging selectivity between and within patches, which further depended on the contrasts between plant species or between patches.     

Bumble bee olfactory information flow and contact-based foraging activation

Nestmate foraging activation and interspecific variation in foraging activation is poorly understood in bumble bees, as compared to honey bees and stingless bees. We therefore investigated olfactory information flow and foraging activation in the New World bumble bee species, Bombus impatiens. We (1) tested the ability of foragers to associate forager-deposited odor marks with rewarding food, (2) determined whether potential foragers will seek out the food odor brought back by a successful forager, and (3) examined the role of intranidal tactile contacts in foraging activation. Bees learned to associate forager-deposited odor marks with rewarding food. They were significantly more attracted to an empty previously rewarding feeder presented at a random position within an array of eight previously non-rewarding feeders. However, foragers did not exhibit overall odor specificity for short-term, daily floral shifts. For two out of three tested scents, activated foragers did not significantly prefer the feeder providing the same scent as that brought back by a successful forager. Finally, bees contacted by the successful forager inside the nest were significantly more likely to leave the nest to forage (38.6% increase in attempts to feed from empty feeders) than were non-contacted bees. This is the first demonstration that tactile contact, a hypothesized evolutionary basal communication mechanism in the social corbiculate bees, is involved in bumble bee foraging activation. Received 4 September 2007; revised 30 May 2008; accepted 15 July 2008.