Competition in a group of equal foragers

Abstract Using techniques from renewal process theory, we build a stochastic model for gain accumulation in a group of equal competitors foraging in a patchy environment. The model for gain of the individuals is based on the waiting times between subsequent prey encounters by the group. These waiting times depend on the number of foragers in the group. A single parameter of this dependency encompasses a variety of foraging scenarios, from co-operation to scramble. With constant patch size, correlations between gains of any pair of foragers are negative. This dependency is most intense in small groups. Increased variation in patch size makes correlations in gains between group members positive irrespective of the group size. For a solitary forager, variance in gain approaches zero with increasing time in the patch. For an individual member in a group, variance grows monotonically. Thus, depending on the patch departure rule controlling the time to be spent in the patch, solitary foragers may have a smaller variance in gain than members in a group. As solitary foragers also potentially harvest all prey in the patch, it is hard to believe that grouping behavior would evolve solely on the basis of foraging.     

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.     

Maximizing feeding efficiency and minimizing time exposed to predators: a trade-off in the black-capped chickadee

Summary Animals often must feed away from protective cover, sometimes at a considerable risk of being preyed upon. Feeding at the maximum rate while away from cover may simultaneously minimize the time spent exposed to predators, but this is not always the case. Under some circumstances, carrying prey items to protective cover before they are consumed will minimize the time spent exposed to predators, whereas feeding at maximum efficiency (staying to eat prey where they are found) will actually increase the time spent exposed to predators. Whether or not there is a conflict between maximizing foraging efficiency and minimizing exposure time, depends upon the travel time to cover relative to the handling time of a prey item; short handling times and/or long travel times are associated with the no-conflict situation, whereas the conflict situation is associated with long handling times and/or short travel times to cover. Free-ranging chickadees foraging at an artificial patch at various distances from cover can distinguish between these two foraging situations. When there is no conflict, they stay and eat at the patch. Their behavior in the conflict situation indicates that they are tradingoff foraging considerations against the risk of predation. When the cost of carrying is low and the benefit gained is high, the chickadees elect to carry items to cover; they tend to stay and eat at the patch when the relative magnitudes of costs and benefits are reversed.     

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.     

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.     

Foraging in yellow dung flies: testing for a small-male time budget advantage

1. Mating and foraging are generally mutually exclusive activities. Individuals are thus faced with a continuous trade-off between time and energy expended in foraging and mating, but different phenotypes should respond to this trade-off in different ways. 2. Sexual selection theory predicts that females should maximize their time and energy spent gathering resources, whereas males should maximize their time and energy spent obtaining mates, thus minimizing their time spent foraging, subject to the constraint that they need to forage minimally to sustain their activity. 3. Smaller individuals require less food to maintain their activity. Small males in particular could therefore increase mating effort at the expense of foraging effort and, all else being equal, may thus enjoy a time budget advantage relative to large males. On the other hand, larger individuals may compensate by being more efficient at finding prey and/or extracting nutrients. 4. The effects of sex, body size, and prey density on foraging time budgets of male and female yellow dung flies, Scathophaga stercoraria, were investigated in the laboratory. 5. Higher prey density (Drosophila melanogaster) resulted in reduced feeding (= handling) and hunting (= waiting or search) times for both sexes, as predicted by the marginal value theorem applied to foraging theory. Females fed longer on a prey item than did males, and also caught the next prey item more quickly. Large individuals extracted nutrients more quickly, but were not faster at catching prey. Small individuals satiated more quickly than larger individuals and also ate fewer prey items. 6. These results are largely consistent with the predictions and suggest a small-male time budget advantage in the yellow dung fly. Integrating the various predictions to test directly for a small-male time budget advantage is difficult in the laboratory, however, because hunting times are unlikely to reflect the natural situation. To what extent these results lead to increased probabilities for small males of obtaining matings in the field remains to be demonstrated.     

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.     

Optimal foraging: food patch depletion by ruddy ducks

Summary I studied the foraging behavior of ruddy ducks (Oxyura jamaicensis) feeding on patchily distributed prey in a large (5-m long, 2-m wide, and up to 2-m deep) aquarium. The substrate consisted of a 4x4 array of wooden trays (1.0-m long, 0.5-m wide, and 0.1-m deep) which contained 6 cm of sand. Any tray could be removed from the aquarium and loaded with a known number of prey. One bird foraged in the aquarium at a time; thus, by removing a food tray after a trial ended and counting the remaining prey, I calculated the number of prey consumed by the bird. I designed several experiments to determine if ruddy ducks abandoned a food patch in a manner consistent with the predictions of a simple, deterministic, patch depletion model. This model is based on the premise that a predator should maximize its rate of net energy intake while foraging. To accomplish this, a predator should only remain in a food patch as long as its rate of energy intake from that patch exceeds the average rate of intake from the environment. In the majority of comparisons, the number of food items consumed by the ruddy ducks in these experiments was consistent with the predictions of the foraging model. When the birds did not forage as predicted by the model, they stayed in the patch longer and consumed more prey than predicted by the model. An examination of the relation between rate of net energy intake and time spent foraging in the food patch indicated that by staying in a patch longer than predicted, the ruddy ducks experienced only a small deviation from maximum rate of net energy intake. These results provided quantitative support for the prediction that ruddy ducks maximize their rate of net energy intake while foraging.     

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.     

Foraging tactics of an aquatic insect: Partial consumption of prey

Optimal patch foraging theory has recently been used to model partial consumption of prey by predators (Cook & Cockrell 1978; Sih 1980). I tested several predictions of this model with larvae of the predaceous diving beetle Dytiscus verticalis, which are predators of anuran tapdoles. The results of the study supported the qualitative predictions of the model. The prediction of decreasing search time with increasing prey density was confirmed. Handling time and the amount ingested per prey item also decreased with decreasing search time. A quantitative test of the optimal foraging model revealed that it accurately predicted handling times when prey densities were high but failed to do so at low prey densities. Two hypotheses based on mean extraction rates are proposed in an attempt to explain these results.     

On optimal diet in a patchy environment

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

The waiting game: a "battle of waits" between predator and prey

Many prey respond to the presence of a predator by retreatinginto a shell or burrow, or by taking refuge in some other waythat guarantees their safety but restricts further informationfrom being obtained about the predator's continued presence.When this occurs, the individual predator and prey involvedbecome opponents in a "waiting game." The prey must decide howlong to wait for the predator to depart before re-emerging andpotentially exposing itself to attack. The predator must decidehow long to wait for the prey to re-emerge before departingin search of other foraging opportunities. I use a numericalapproach to determine the evolutionarily stable waiting strategyof both players and examine the effects of various parameterson the ESS. The model predicts that each player's waiting distribution—thedistribution of waiting times one would expect to observe forindividuals in that role—will have a characteristic shape:the predator's distribution should resemble a negative exponentialfunction, whereas the waiting time of the prey is predictedto be more variable and follow a positively skewed distribution.The model also predicts that very little overlap will occurbetween the players' waiting distributions, and that the predatorwill rarely outwait the prey. Empirical studies relating tothe model and comparisons between the waiting game and the asymmetricwar of attrition are discussed.     

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.     

斑块质量对大斑啄木鸟冬季觅食行为的影响

为了解大斑啄木鸟(Dendrocopos major)冬季对食物斑块的利用对策,2011年1月和2012年2～3月,在内蒙古乌拉特前旗的农田防护林中,采用目标动物取样法和全事件记录法,观察了大斑啄木鸟在食物斑块的觅食行为,利用主成分分析方法对斑块质量进行评价,通过比较不同质量斑块中大斑啄木鸟的觅食频次、停留时间、觅食成功频次及觅食成功率等指标,分析斑块质量对其觅食行为的影响。结果显示,在不同质量斑块中大斑啄木鸟的觅食频次、停留时间、觅食成功频次差异都极显著,但觅食成功率差异不显著;除停留时间外,不同性别间觅食差异不显著。大斑啄木鸟的觅食频次、停留时间、觅食成功频次与斑块质量呈显著正相关,觅食成功率与斑块质量相关性不显著。大斑啄木鸟倾向于在质量水平高的斑块觅食,表现为在这些斑块停留时间更长、往返次数更频繁;但觅食成功率不受斑块质量影响,这可能是大斑啄木鸟适应不同觅食环境的一种生存本能。     

Patch time allocation and patch sampling by foraging great and blue tits

The rate at which parents deliver energy to their brood is an important factor in avian reproduction because poor condition caused by malnutrition may reduce the offspring's survival to breeding. Models of central place foraging predict that nesting parents should optimize their prey delivery rate by minimizing travelling distances and by selecting patches where the gain per unit cost is high. I investigated the allocation of searching time amongst food patches in the home ranges of breeding great tits, Parus major, and blue tits P. caeruleus, by radiotracking. The density of locations in individual trees was positively correlated with prey biomass within trees and negatively with the distance of the trees from the nest. These two factors explained 52% of the variance in the allocation of the birds' search time. In rich patches, food was reduced considerably within 20 m of the nests, and the birds' travelling distances increased significantly during the nestling period. In parallel to foraging selectively in rich resources near the nest, the birds continually sampled the trees in their territory. The average surplus search time due to resource exploration was 1.52 times (range 1.25-1.99) the expected search time if the birds had exclusively used the most profitable patch. Despite considerable effort in patch sampling, the overall search time per unit prey was 30% better than expected by an equal use of trees. The results suggest that foraging tit parents come close to the maximum rate of prey delivery possible in a given patch distribution. Copyright 2000 The Association for the Study of Animal 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.     

Incompletely informed shorebirds that face a digestive constraint maximize net energy gain when exploiting patches

Foragers that feed on hidden prey are uncertain about the intake rate they can achieve as they enter a patch. However, foraging success can inform them, especially if they have prior knowledge about the patch quality distribution in their environment. We experimentally tested whether and how red knots (Calidris canutus) use such information and whether their patch-leaving decisions maximized their long-term net energy intake rate. The results suggest that the birds combined patch sample information with prior knowledge by making use of the potential value assessment rule. We reject five alternative leaving rules. The potential encounter rate that the birds choose as their critical departure threshold maximized their foraging gain ratio (a modified form of efficiency) while foraging. The high experimental intake rates were constrained by rate of digestion. Under such conditions, maximization of the foraging gain ratio during foraging maximizes net intake rate during total time (foraging time plus digestive breaks). We conclude that molluscivore red knots, in the face of a digestive constraint, are able to combine prior environmental knowledge about patch quality with patch sample information to obtain the highest possible net intake over total time.     

Hunger effects on foraging responses to perceptual cues in immature and adult wolf spiders (Lycosidae)

The wolf spider, Schizocosa ocreata (Hentz), varies foraging patch residence time in the presence of different sensory cues from prey, even without food rewards. This study examines the influence and interaction of hunger state, age and sex on the use of different types of sensory information to determine foraging patch sampling duration. In a series of two-chambered artificial foraging patches, I tested 26 S. ocreata once as immatures, and again as adults, under two hunger states (satiated and 7 days without food). Patches varied in the type of sensory information provided by live prey (crickets) as follows: visual cues alone; vibratory cues alone; combined visual/vibratory cues; and control (no prey). Without feeding in patches, the type of sensory stimuli available from prey strongly affected patch residence time, with spiders using primarily visual rather than vibratory cues. Hunger level as a main effect had no influence on residence time, but hunger state did mediate the importance of visual or vibratory information. Significant age- and sex-related differences in patch residence time in the presence of different sensory cues were found.These data suggest that ontogenetic and sex-specific foraging strategies are influenced by use of prefeeding perceptual cues rather than hunger state in wolf spiders. Copyright 1999 The Association for the Study of Animal Behaviour.     

Failure of simple optimal foraging models to predict residence time when patch quality is uncertain

Blue jays (Cyanocitta cristata) were presented with a foragingsituation in which half of the patches they encountered containedno prey and half contained a single prey item. Experimentallydetermined probability distributions controlled prey arrivaltimes in those patches that contained prey. Patch residencein empty patches was studied during four experiments. In thefirst, prey arrival was exponentially distributed. Residencetimes increased with travel time as predicted by a rate-maximizationmodel, but the bird stayed in empty patches much longer thanpredicted. During the second experiment, prey arrival was uniformlydistributed. The jays again stayed longer than optimal, andpatch residence times increased as travel time increased, althoughthe residence time that maximized rate of intake was independentof travel time under these conditions. In the third experiment,exponential and uniform patches were randomly intermixed. Thejays showed larger travel-time effects in the exponential thanin the uniform patch. However, the travel-time effect in theuniform patch was contrary to rate-maximization predictions,and the birds again overstayed in both patch types. In the fourthexperiment, prefeeding at the start of each foraging bout slightlyincreased overstaying rather than decreasing overstaying, aswould be expected if overstaying were due to underestimatingenvironmental quality. Consistent and dramatic overstaying anda travel-time effect under conditions where travel time hasno effect on optimal residence times suggest that the rate-maximizationapproach does not apply to foraging problems involving patchuncertainty.     

Effects of Foraging Experiences on Residence Time of the Predatory Mite <Emphasis Type="BoldItalic">Neoseiulus womersleyi</Emphasis> in a Prey Patch

We investigated the effects of foraging experiences on the residence time of Neoseiulus womersleyi in a currently inhabited prey (Tetranychus urticae) patch. Satiated predators that had experienced starvation stayed longer in a current patch than those that had not experienced starvation. Satiated predators that had experienced a prey-rich patch showed approximately the same residence time in the current patch irrespective of the number of prey therein. By contrast, satiated predators that had experienced a prey-poor patch stayed longer in a current patch of high prey density than in one of low prey density. N. womersleyi appears to determine residence time in the current patch based on foraging experiences together with the quantity of prey in the current patch.