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.     

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.     

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

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

Foraging behavior of an estuarine predator, the blue crab Callinectes sapidus in a patchy environment

To define general principles of predator‐prey dynamics in an estuarine subtidal environment, we manipulated predator density (the blue crab, Callinectes sapidus) and prey (the clam, Macoma balthica) patch distribution in large field enclosures in the Rhode River subestuary of the central Chesapeake Bay. The primary objectives were to determine whether predators forage in a way that maximizes prey consumption and to assess how their foraging success is affected by density of conspecifics. We developed a novel ultrasonic telemetry system to observe behavior of individual predators with unprecedented detail. Behavior of predators was more indicative of optimal than of opportunistic foraging. Predators appeared responsive to the overall quality of prey in their habitat. Rather than remaining on a prey patch until depletion, predators appeared to vary their patch use with quality of the surrounding environment. When multiple (two) prey patches were available, residence time of predators on a prey patch was shorter than when only a single prey patch was available. Predators seemed to move among the prey patches fairly regularly, dividing their foraging time between the patches and consuming prey from each of them at a similar rate. That predators more than doubled their consumption of prey when we doubled the number of prey (by adding the second patch) is consistent with optimizing behaviors ‐ rather than with an opportunistic increase in prey consumption brought about simply by the addition of more prey. Predators at high density, however, appeared to interfere with each other's foraging success, reflected by their lower rates of prey consumption. Blue crabs appear to forage more successfully (and their prey to experience higher mortality) in prey patches located within 15–20 meters of neighboring patch, than in isolated patches. Our results are likely to apply, at least qualitatively, to other crustacean‐bivalve interactions, including those of commercial interest; their quantitative applicability will depend on the mobility of other predators and the scale of patchiness they perceive.     

Sex differences in foraging behaviour and oviposition site preference in an insect predator, Orius sauteri

The effects of patch quality on the foraging behaviour of an anthocorid predator Orius sauteri (Poppius) were compared between sexes. Prior experience in patches was also studied to determine whether this was a factor affecting oviposition decisions. Patch quality affected patch residence time differently for the two sexes; females stayed much longer in a patch with prey (60 Thrips palmi larvae) than a patch without prey, while males did not remain in any patch for extended periods. Most of the females remained in or moved to patches with prey, whereas males dispersed, irrespective of patch quality. Both females released in patches with prey and females released in patches without prey deposited more eggs per hour in patches with prey than in patches without prey. Females released in patches without prey laid eggs in patches with prey at higher rates than did females released in patches with prey. Causes for the sex difference in patch residence time and allocation are discussed in relation to optimal foraging theory. The significance of selective oviposition and the role of experience in oviposition decisions within heterogeneous environments are also discussed.     

Animal response to nested self-similar patches: a test with woolly bears

To gain insight into how animals respond to resource patchiness at different spatial scales, we envision their responses in environments comprised of nested, self-similar patches. In these environments, all resources reside within the smallest patches, and resource density declines as a constant exponent of patch size. Accordingly, we use simple mathematical formulations to describe a self-similar environment and a null model of how animals should respond to this environment if they do not perceive resource distribution. We then argue that animals that can perceive resource distribution should partition space by reducing the relative time searching between patches as patch size increases. On an experimental landscape, we found that woolly bear caterpillars Grammia geneura could partition space in this manner, but the range of patch sizes over which they did so tended to increase with resource aggregation. Nevertheless, scaling efficiency (i.e. the scaling of search time versus the scaling or resource density) was similar in all distributions when averaged over all patch sizes. These disparate patterns with similar outcomes resulted from differences in caterpillars' abilities to discriminate spatially among patches of different sizes via their movement pathways, and differences in their use of speed to detect resource items. Our work is relevant to the characterization of resource availability from an animal's perspective, and to the linking of optimal foraging theory to the modeling of search behavior.     

Utilization of different prey type patches in the Ural owl(Strix uralensis): a sit-and-wait predator

To quantify the pattern of allocation of foraging activity ofa sit-and-wait forager among feeding sites of different profitability,I conducted an experimental study of patch utilization behaviorof Ural owls (Strix uralensis) in an experimental flight cage.The owls were allowed to search among four patches containingequal numbers of mice, two with the large Japanese field mouse(Apodemus speciosus) and two with the small Japanese field mouse(A. argenteus). Patches with A. speciosus were more profitablethan those with A. argenteus, and owls visited more profitablepatches more frequently. Visiting frequency to richer patchesdid not increase with experience; however, owls changed searchtime according to experience. Search time in a patch becamelonger in later visits than in earlier visits during a givennight according to an owl’s sampling experience amongpatches. Furthermore, owls stayed longer in richer patches thanin poor ones if they had caught mice in both types of patches.Search time had great variance. Mean search time that endedwith attack was longer than that ended without attack (giveup). In effect, Ural owls improved their resource utilizationpattern as they accumulated experience in the environment. [BehavEcol 1991;2:99–105J]     

Presampling sensory information and prey density assessment by wolf spiders (Araneae, Lycosidae)

Decisions regarding foraging patch residence time and the assessmentof patch quality may be mediated by various sources of information.This study examined the use of sensory cues by hunting spidersto assess prey density in the absence of prey capture. Adultfemale wolf spiders [Schizocosa ocreata (Hentz); Lycosidae]had food withheld for 4 days and then were exposed to artificialforaging patches containing four densities of crickets (0, 3,10, 20) with different sensory stimuli (visual and vibratoryinformation, visual only, and vibratory only). The spiders werenot allowed to feed during trials, and patch residence timewas recorded. The spiders varied patch residence time basedon sensory cues alone and spent more time in patches with higherprey density. With visual information only, spiders could apparentlydistinguish among prey densities almost as well as with visualand vibratory cues combined, but residence time did not differamong prey densities when only vibratory information was presented.Measurements of vibration levels produced by cricket activityunder experimental sensory treatments conform to test results,suggesting that visual detection of crickets is important inpatch assessment used in determining patch residence time.     

Search mechanism of a stream grazer in patchy environments: the role of food abundance

Summary The search behavior of the grazing stream insect Baetis tricaudatus (Ephemeroptera: Baetidae) was examined in field and laboratory experiments. Regardless of food abundance in experimental habitats, nymphs spent significantly more time in food patches than predicted if they had moved randomly with respect to patches. A significant reduction in movement rate within patches relative to movement rate between patches largely accounted for these results. The movement pattern within patches was highly systematic and in agreement with predictions of optimal foraging theory since food was uniformly distributed within patches. Between-patch search movements were affected by food abundance in the most recently grazed patch. Search intensity after departure from a patch was positively related to food abundance in the patch while movement rate after patch departure was inversely related to patch food level. These effects produced between-patch movement patterns that were suboptimal in the experimental habitats because they resulted in revisitation of previously depleted patches. However, differences between experimental and natural habitats in the spatial occurrence of patch types suggest that Baetis between-patch search behavior may be adaptive in natural habitats.     

Foraging strategies in solitary parasitoids: The trade-off between female and offspring mortality risks

Summary It is often assumed that oviposition rate is the currency that parasitoids should maximize in order to maximize reproductive success. Female parasitoids foraging in a patchy environment face a variety of mortality risks that influence the survival of both themselves and their offspring. Maximizing oviposition rate ignores these risks. A model is developed to analyse the influence of female and offspring mortality risks on optimal patch residence time in time-limited solitary parasitoids. The optimal compromize between minimizing a female's own mortality risks and the mortality risks of her offspring in characterized. The optimal patch residence time is shown to be dependent on the relative magnitude of these mortality risks, as well as the rate with which reproductive success accumulates while on a patch. If travel time between patches is not fixed but a random variable, the optimal patch residence time decreases. However, variability in travel time increases expectations of total reproductive success. The model is illustrated with a case study in two aphid parasitoids.     

Effects of resource distribution, patch spacing, and preharvest information on foraging decisions of northern bobwhites

We investigated patch assessment by northern bobwhites (Collinusvirginianus) in an experimental arena where the distributionof resources in patches, preharvest information about thesepatches, and spacing of patches varied. We found that preharvestinformation about patch quality and a bimodal distribution ofpatch rewards allowed birds to selectively exploit patches highin resources. In contrast, uniform distribution of patch qualitiesand lack of preharvest information caused birds to forage nonselectivelyamong patches. Birds distinguished among patches of differentquality when these patches were spaced 13 m apart, but failedto react to patch quality differences when patches were 0 or3 m apart We also found a strong effect of the level of patchdepletion on foraging decisions: as resources in die arena becamescarce, birds increasingly foraged selectively in die most profitablepatches. Foraging decisions of bobwhites are biased by die waythey experience and memorize a spatially and temporally variableenvironment. The relative cost of this cognitive bias (i.e.,lost opportunity) is nonlinearty related to die mean resourcedensity in die environment and to die difference between thismean density and die resource density in die exploited patch.Cognitive bias should be considered when evaluating patch assessmentcapabilities of foragers in complex environments.     

Nectar provisioning close to host patches increases parasitoid recruitment,retention and host parasitism

In the adult stage, many parasitoids require hosts for their offspring growth and plant-derived food for their survival and metabolic needs. In agricultural fields, nectar provisioning can enhance biological control by increasing the longevity and fecundity of many species of parasitoids. Provided in a host patch, nectar can also increase patch quality for parasitoids and affect their foraging decisions, patch time residence, patch preference or offspring allocation. The aim of this study was to investigate the impact of extrafloral nectar (EFN) provisioning close to hosts on parasitoid aggregation in patches. The aphid parasitoid Diaeretiella rapae (M’Intosh) was released inside or outside patches containing Brassica napus L. infested by Brevicoryne brassicae L. aphids and Vicia faba L. with or without EFN. When parasitoids were released outside patches, more parasitoids were observed in patches with EFN than in patches deprived of EFN. This higher recruitment could be linked to a higher attraction of a combination of host and food stimuli or a learning process. A release–recapture experiment of labeled parasitoids released within patches showed the higher retention of parasitoids in patches providing EFN and hosts, suggesting that food close to the host patch affects patch residence time. Both attractiveness and patch retention could be involved in the higher number of parasitoids foraging in host patches surrounded by nectar and for the higher parasitism recorded. Nectar provisioning in host patches also affected female offspring allocation inside the patch.     

Habitat assessment by parasitoids: mechanisms for patch use behavior

Animals foraging for patchily distributed resources may optimizetheir foraging decisions concerning the patches they encounter,provided that they base these decisions on reliable informationabout the profitability of the habitat as a whole. Females ofthe parasitoid Lysiphlebus testaceipes exploit aphid hosts,which typically aggregate in discrete colonies. We show herehow between-colony travel time and the number of aphids in previouslyvisited colonies affect parasitoid foraging behavior. We firstassumed that parasitoids use travel time and previous colonysize to estimate a mean rate of fitness gain in the habitatand derived quantitative predictions concerning the effect ofthese two variables on patch residence time and patch-leavingrate of attack. We then tested these theoretical predictionsin laboratory experiments in which female parasitoids were allowedto visit two successive colonies. As predicted, the observedresidence time in the second colony increased with increasingtravel time and decreasing size of the first colony. Patch-leavingrate of attack decreased with increasing travel time but wasnot affected by previous colony size. These results suggestthat parasitoids use these two variables to assess habitat quality.However, discrepancies between the data obtained and quantitativepredictions show that the effect of travel time on patch usemay be more complex than assumed in our model.     

Depletion of seed patches by Merriam’s kangaroo rats: are GUD assumptions met?

Depletion of experimental seed patches by granivorous animals often is used as a qualitative assay of foraging activity. An optimal foraging model suggests that seed amounts remaining when foragers leave patches ("giving-up-density", GUD) also provide quantitative measures of foraging economics, diet strategies and foraging abilities. Such quantitative uses of GUDs rest on several largely untested assumptions. We tested two of these with Merriam's kangaroo rats: that gain curves are smoothly decelerating, and that foragers leave patches at a constant harvest rate. Harvest rates indeed declined with patch residence time, but in the piecewise linear fashion expected of systematic search. Animals also revisited areas within patches less frequently than expected with random search. In the field, they depleted patches in multiple visits and did not use a constant-rate leaving rule. These deviations from model assumptions cast doubt on inferences about foraging ecology that have been based on quantitative GUD theory.     

Foraging across a variable landscape: behavioral decisions made by woodland caribou at multiple spatial scales

We examined the foraging behavior of woodland caribou (Rangifer tarandus caribou) relative to the spatial and temporal heterogeneity of their environment. We assessed (1) whether caribou altered their behavior over time while making trade-offs between forage abundance and accessibility; and (2) whether foraging decisions were consistent across spatial scales (i.e., as scale increased, similar decision criteria were used at each scale). We discuss whether caribou adjusted their behavior to take advantage of changing forage availability through time and space. At the scale of the feeding site (as revealed by discriminant function analyses), caribou in both forested and alpine (above tree-line) environments selected sites where the biomass of particular lichen species was greatest and snow the least deep. Caribou did not select those species with the highest nutritional value (i.e., digestible protein and energy) in either area. Where snow depth, density, and hardness limited access to terrestrial lichens in the forest, caribou foraged instead at those trees with the greatest amount of arboreal lichen. Selection of lichen species and the influence of snow differed across time, indicating that in this system the abundance or accessibility of forage temporally influenced foraging behavior. A path analysis of forest data and multiple regression analysis of alpine data were used to test the hypothesis that variables important at the scale of the feeding site explained foraging effort at the scale of the patch. For forest patches, our hypothesized model reliably explained foraging effort, but not all variables that were statistically important at the scale of the feeding site were significant predictors at the scale of the patch. For alpine patches, our hypothesized model did not explain a statistically significant portion of the variation in the number of feeding sites within the patch, and none of the individual variables from the feeding site remained statistically significant at the patch scale. The incongruity between those variables important at the scale of the feeding site and those important at the patch showed that spatial scale affects the foraging decisions of woodland caribou. At the scale of the landscape, there was a trade-off between forage abundance and accessibility. Relative to the alpine environment, caribou in the forest foraged at feeding sites and patches with greater amounts of less variably distributed lichen, but deeper less variable snow depths. Considering the behavioral plasticity of woodland caribou, there may be no distinct advantage to foraging in one landscape over the other.     

Patch exploitation strategies of parasitoids under indirect intra‐ and inter‐specific competition

1. Insect parasitoids are expected to evolve behavioural strategies to exploit resources in competitive environments optimally. Indirect competition between parasitoids is particularly common because exploited host patches remain available in the environment for other foraging individuals. 2. The effects of indirect competition on the behaviour of two closely related generalist egg parasitoids were investigated: Trichogramma pintoi Voegelé and Trichogramma minutum Riley (Hymenoptera: Trichogrammatidae). Patch residence time, a patch‐leaving mechanism, and progeny sex allocation of females foraging were analysed: (i) alone, (ii) in patches partially parasitised by conspecifics, and (iii) in patches partially parasitised by heterospecifics. 3. Each species responded differently to indirect competition. Trichogramma pintoi females shortened their patch residence times, but they did not adjust their progeny sex ratios. In contrast, T. minutum females did not modify their patch residence times, but they did increase their progeny sex ratios in response to competition. Both Trichogramma species used host rejection, either by antenna rejection or by ovipositor rejection, as a patch‐leaving mechanism. 4. In agreement with a companion study of direct competition using the same model species, the present results indicate that even amongst closely related species, responses to competition can vary considerably.     

Seasonal dynamic shifts in patch exploitation by parasitic wasps

We developed and tested predictions of a dynamic life historymodel that is concerned with how temperate-zone parasitic waspsadjust patch residence time and tendency to superparasitizewhen expectation of life and habitat quality varies. The theorypredicts that wasps with short life expectancy should continueto search longer and superparasitize more frequently than similarwasps with long life expectancy. Similarly, wasps with longlife expectancy that forage in habitats where patches are alreadyheavily exploited should continue to search longer and superparasitizemore frequently than similar wasps foraging in habitats wherepatches are relatively unexploited. In contrast, the theorypredicts that wasps with short life expectancy will be insensitiveto habitat quality. We tested the predictions on Drosophilaparasitoids (Lep-topilina heterotoma) by (1) rearing wasps underfall and summer photoperiod (i.e., short versus long life expectancy)and (2) giving wasps foraging experience on different qualitypatches (i.e., exploited versus unexploited habitats). Resultsof the experiments corroborated our predictions. We discusshow parasitic wasp behavior can be shaped by globally predictableand locally unpredictable events.     

Patch area, substrate depth, and richness affect giving-up densities: a test with mourning doves and cottontail rabbits

We compared the foraging behavior of mourning doves Zenaida macroura and cottontail rabbits Sylvilagus floridanus in patches that varied in initial food abundance, surface area and substrate depth. We measured giving‐up densities (GUD), food harvest and proportion of food harvested to investigate their ability to respond to characteristics of resource patches. GUDs have been analyzed in three ways: grams of per patch, grams per unit surface area (GUD_AREA), and grams per unit volume of sand (GUD_VOL). Mourning doves and cottontails exhibited similar responses to resource density and sand depth. Both foragers detected and responded to variation in initial food abundance. The proportion of food harvested from a patch increased from 40.7, 43.8 to 48.3% (for the doves) and 34.9, 35.8 to 38.4% (for the rabbits) in patches of low, medium and high initial food abundance, respectively. Deeper substrates reduced the foragers’ encounter probability with food, decreased patch quality and resulted in higher GUDs (60% higher in the deepest relative to shallowest substrate) and lower harvests. A significant interaction between initial food abundance and substrate depth showed that both species were willing to dig deeper in patches with higher resource density. Patch size (surface area) had no effect on food harvest or the proportion of food harvested. Consequently, GUD_AREA and GUD_VOL increased in patches with a smaller surface area. Smaller patches appeared to hamper the dove's and cottontail's movement across the surface. Our results revealed that mourning doves and cottontails forage under imperfect information. Both species were able to respond to patch properties by biasing their feeding efforts toward rich and easy opportunities, however, mourning doves were more efficient at food harvesting. The interaction of patch area, volume and food abundance directly influenced food harvest. Such resource characters occur under natural situations where food varies in abundance, area of distribution, and accessibility.     

Testing assumptions of central place foraging theory: a study of Adélie penguins Pygoscelis adeliae in the Ross Sea

We investigated central place foraging (CPF) in the context of optimal foraging theory in Adélie penguins Pygoscelis adeliae of the southern Ross Sea by using satellite tracking and time‐depth recorders to explore foraging at two spatio‐temporal scales: within the day‐to‐day (sub‐mesoscale: single foraging trip, 10s of km²) and the entire breeding season (mesoscale: trips by multiple individuals across the collective foraging area, 100s of km²). Specifically, we examine whether three basic assumptions of the Orians–Pearson CPF model, shown to occur in other CPF species, are met: 1) within a patch, the rate of prey acquisition declines with time spent in that patch; 2) food is distributed in discrete patches and is not available between those patches; and 3) CPF species have knowledge of the potential (or average, at least) feeding rate within their universe of patches, and use this knowledge to determine their foraging strategy when planning or engaging in a foraging trip. We found that prey consumption rates did not decline with time spent in patches, and penguins foraged to some degree most of the time when at sea. Food availability, as measured by foraging dive rate, appeared to be predictable within the same day at the same location, but predictability broke down after 2 d at distances > 10 km away. We conclude that the assumptions of the Orians–Pearson CPF model are not a good fit to the circumstances of Ross Sea penguins, which clearly are central place foragers.     

Unpacking chimpanzee (Pan troglodytes) patch use: Do individuals respond to food patches as predicted by the marginal value theorem?

The marginal value theorem is an optimal foraging model that predicts how efficient foragers should respond to both their ecological and social environments when foraging in food patches, and it has strongly influenced hypotheses for primate behavior. Nevertheless, experimental tests of the marginal value theorem have been rare in primates and observational studies have provided conflicting support. As a step towards filling this gap, we test whether the foraging decisions of captive chimpanzees (Pan troglodytes) adhere to the assumptions and qualitative predictions of the marginal value theorem. We presented 12 adult chimpanzees with a two-patch foraging environment consisting of both low-quality (i.e., low-food density) and high-quality (i.e., high-food density) patches and examined the effect of patch quality on their search behavior, foraging duration, marginal capture rate, and its proxy measures: giving-up density and giving-up time. Chimpanzees foraged longer in high-quality patches, as predicted. In contrast to predictions, they did not depress high-quality patches as thoroughly as low-quality patches. Furthermore, since chimpanzees searched in a manner that fell between systematic and random, their intake rates did not decline at a steady rate over time, especially in high-quality patches, violating an assumption of the marginal value theorem. Our study provides evidence that chimpanzees are sensitive to their rate of energy intake and that their foraging durations correlate with patch quality, supporting many assumptions underlying primate foraging and social behavior. However, our results question whether the marginal value theorem is a constructive model of chimpanzee foraging behavior, and we suggest a Bayesian foraging framework (i.e., combining past foraging experiences with current patch sampling information) as a potential alternative. More work is needed to build an understanding of the proximate mechanisms underlying primate foraging decisions, especially in more complex socioecological environments.