Optimal patch time allocation for time-limited foragers

The Charnov Marginal Value Theorem (MVT) predicts the optimal foraging duration of animals exploiting patches of resources. The predictions of this model have been verified for various animal species. However, the model is based on several assumptions that are likely too simplistic. One of these assumptions is that animals are living forever (i.e., infinite horizon). Using a simple dynamic programming model, we tested the importance of this assumption by analysing the optimal strategy for time-limited foragers. We found that, for time-limited foragers, optimal patch residence times should be greater than those predicted from the classic, static MVT, and the deviation should increase when foragers are approaching the end of their life. These predictions were verified for females of the parasitoid Anaphes victus (Hymenoptera: Mymaridae) exploiting egg patches of its host, the carrot weevil Listronotus oregonensis (Coleoptera: Curculionidae). As predicted by the model, females indeed remained for a longer time on host patches when they approached the end of their life. Experimental results were finally analysed with a Cox regression model to identify the patch-leaving decision rules females used to behave according to the model’s predictions.     

Time allocation strategies in insect parasitoids: from ultimate predictions to proximate behavioral mechanisms

As most parasitoids are time limited, they usually die before they have laid all their eggs. In such cases, optimal foraging theory predicts that female parasitoids will adopt behavioral reproductive strategies enabling them to maximize progeny production per unit of time. One key situation in which parasitoid females must optimize their time budget is related to the fact that most of their hosts are distributed in discrete patches in the environment. In this review, I first present the results of basic theoretical models predicting female wasp search duration on a patch of hosts. I then compile and analyze all studies investigating the effect of different factors on parasitoid patch time allocation and patch-leaving decision rules. Different patch-leaving mechanisms that were proposed to explain the results obtained are discussed, along with statistical methods that should be used to estimate them from experimental data. Finally, ideas for future research are presented.     

Optimal movement strategies for social foragers in unpredictable environments

Spatial movement models often base movement decision rules on traditional optimal foraging theories, including ideal free distribution (IFD) theory, more recently generalized as density-dependent habitat selection (DDHS) theory, and the marginal value theorem (MVT). Thus optimal patch departure times are predicted on the basis of the density-dependent resource level in the patch. Recently, alternatives to density as a habitat selection criterion, such as individual knowledge of the resource distribution, conspecific attraction, and site fidelity, have been recognized as important influences on movement behavior in environments with an uncertain resource distribution. For foraging processes incorporating these influences, it is not clear whether simple optimal foraging theories provide a reasonable approximation to animal behavior or whether they may be misleading. This study compares patch departure strategies predicted by DDHS theory and the MVT with evolutionarily optimal patch departure strategies for a wide range of foraging scenarios. The level of accuracy with which individuals can navigate toward local food sources is varied, and individual tendency for conspecific attraction or repulsion is optimized over a continuous spectrum. We find that DDHS theory and the MVT accurately predict the evolutionarily optimal patch departure strategy for foragers with high navigational accuracy for a wide range of resource distributions. As navigational accuracy is reduced, the patch departure strategy cannot be accurately predicted by these theories for environments with a heterogeneous resource distribution. In these situations, social forces improve foraging success and have a strong influence on optimal patch departure strategies, causing individuals to stay longer in patches than the optimal foraging theories predict.     

Patch departure rules in Bumblebees: evidence of a decremental motivational mechanism

The patch living rules of a pollinator, the bumblebee Bombus terrestris L., are studied here in the framework of motivational models widely used for parasitoids: The rewarding events found during the foraging process are supposed to increase or decrease suddenly the tendency of the insect to stay in the current patch and therefore to adjust the patch residence time to the patch profitability. The foraging behaviour of these pollinators was observed in two environment types to determine their patch-leaving decisions. The rich environment was composed of male-fertile flowers, offering pollen and nectar, and the poor one of male-sterile flowers, offering little nectar and no pollen. The experimental design consisted of a patch system in which inflorescences were evenly arranged in two rows (1 m distance). Residence times of foragers inside inflorescences and rows were analysed by a Cox proportional hazards model, taking into account recent and past experience acquired during the foraging bout. Most of the results showed a decremental motivational mechanism, that is, a reduction in the residence time on the inflorescence or in the row related to exploitation of flowers within inflorescences and inflorescences within rows These results indicate that bumblebees tend to leave the patch using departure rules similar to those found in parasitoids. The results also provide information on the memory, learning and evaluating capabilities of bumblebees especially when rich and poor environments were compared. The patch-leaving mechanism suggested by this study is consistent with the central place foraging theory.     

Past experiences and future expectations generate context-dependent costs of foraging

Because environments can vary over space and time in non-predictable ways, foragers must rely on estimates of resource availability and distribution to make decisions. Optimal foraging theory assumes that foraging behavior has evolved to maximize fitness and provides a conceptual framework in which environmental quality is often assumed to be fixed. Another more mechanistic conceptual framework comes from the successive contrast effects (SCE) approach in which the conditions that an individual has experienced in the recent past alter its response to current conditions. By regarding foragers’ estimation of resource patches as subjective future value assessments, SCE may be integrated into an optimal foraging framework to generate novel predictions. We released Allenby’s gerbils (Gerbillus andersoni allenbyi) into an enclosure containing rich patches with equal amounts of food and manipulated the quality of the environment over time by reducing the amount of food in most (but not all) food patches and then increasing it again. We found that, as predicted by optimal foraging models, gerbils increased their foraging activity in the rich patch when the environment became poor. However, when the environment became rich again, the gerbils significantly altered their behavior compared to the first identical rich period. Specifically, in the second rich period, the gerbils spent more time foraging and harvested more food from the patches. Thus, seemingly identical environments can be treated as strikingly different by foragers as a function of their past experiences and future expectations.     

Patch leaving decision rules in parasitoids: do they use sequential decisional sampling?

Within the framework of optimal foraging theory, models assume that parasitoid insects are able to evaluate the quality of the patch in which they are currently searching for hosts and the travel time between patches. They can adjust their residence time in consequence. Simple and more realistic decision mechanisms that induce behavior compatible with the predictions of these models have been proposed for a number of species. Most of these decision mechanisms only take into account the presence of unparasitized hosts. Here, we studied the consequences for leaving patches containing different proportions of unparasitized and parasitized hosts. We support the hypothesis that parasitoids sample their environment and we propose a binomial sequential model, based on the type of host encountered (unparasitized or parasitized) instead of on the time spent in a patch, to explain the giving-up behavior of a parasitoid in a patch. A motivational incremental/decremental stochastic process is proposed to explain a possible mechanism of the apparent sampling scheme followed by the insect. The empirical data support the hypothesis of a sequential, decisional, binomial sampling scheme performed with a limited memory. This memory is, in fact, more an effect of habituation than the "true memory" of the parasitoid. The theoretical model was applied to real data obtained with an encyrtid parasitoid. These data were also compared to realizations of the incremental/decremental process.     

Imperfectly optimal animals

Summary We consider models of behavior that apply to two different problems: when a predator should leave a foraging site and how a female should choose the best available male. In each case we derive rules for an optimal solution to the problem. We also derive models based on very simple, plausible rules of behavior that we suspect animals may actually use. Although the expected payoffs from optimality models always exceed the expected payoffs from our simpler behavioral models, under certain conditions the difference is not large. When good foraging sites last but a short time and when females' mobility in their habitat is limited, the results of simple models and optimal models are very close indeed.Because of the difficulty of distinguishing between the results of each type of model and because natural selection will presumably provide a best mix of solutions to a range of problems rather than a best solution to any one problem, we suggest that behavioral ecologists expend more effort on simple, plausible models of animal behavior. Such models provide ready-made testable hypotheses about the animal's approximation to optimality and about the actual mechanisms of behavior.     

Effects of within- and among-patch experiences on the patch-leaving decision rules in an insect parasitoid

The present study aimed to address how an insect parasitoid makes patch-departure decisions from various types of host patches and how previous patch experiences in the environment modify this decision-making process. Experiments were done with the parasitic wasp Aphidius rhopalosiphi attacking the grain aphid Sitobion avenae. In the experiments, wasps were observed in a laboratory environment containing several patches of various host densities, and behavioural records were analysed using a Coxs proportional hazards model. Consideration of the effect of the within-patch experience gave a classic pattern of patch-leaving decision rules in parasitoids: A. rhopalosiphi used local information on host quality (i.e. numbers of ovipositions or rejections) and availability (i.e. patch density) to determine departure decision. However, consideration of previous patch experiences provided evidence that these departure rules are fundamentally dynamic, responding to the physiological state of the animal and the information it has about its environment. Results showed that A. rhopalosiphi decreased its tendency to leave the visited patch after an oviposition. However, when a female has already laid several other eggs in the environment, such an incremental mechanism gradually switched to a decremental one. Hence, A. rhopalosiphi responded to egg-load depletion by leaving the visited patches sooner and by depositing a smaller number of eggs in those patches, which probably led to a decreased level of superparasitism. Results also indicated that previous experiences enabled wasps to estimate spatial host distribution and then to adjust their behavioural decisions accordingly. Thus, A. rhopalosiphi was shown to adjust its patch residence time according to the quality and the number of the patches previously visited. These proximate mechanistic rules adopted by A. rhopalosiphi females are discussed in the context of general predictions from optimality models.Communicated by D. Gwynne     

Differential use of conspecific-derived information by sexual and asexual parasitic wasps exploiting partially depleted host patches

When foraging partially depleted patches (i.e., a fraction of hosts are already parasitized), female parasitoids must decide: 1—whether to superparasitize, and 2—whether to stay in their current patch (thus missing the opportunity of finding a better patch elsewhere). To make these decisions, parasitoids may rely on different cues, produced both by the environment and by conspecifics. Animals thriving in different environments may differ in cues they use. In the solitary parasitoid Venturia canescens, thelytokous (asexual) and arrhenotokous (sexual) individuals are found in two contrasting environments. Thelytokous females, from anthropogenic conditions, are known to cope with superparasitism in an adaptive way. On the other hand, little is known about superparasitism by arrhenotokous females. We compared the host exploitation strategies of thelytokous and arrhenotokous females in partially depleted patches. Hosts parasitized by thelytokous females were more frequently avoided than those parasitized by arrhenotokous females, suggesting a stronger chemical marking of the former. Only thelytokous females used information from conspecifics for patch-leaving decisions. The conformity of the differences in the behavior of thelytokous and arrhenotokous females with the environmental conditions they experience in their habitat is discussed.     

Sampling behavior of starlings foraging in simple patchy environments

Summary Starlings were allowed to forage in patchy laboratory environments where patches contained either zero or a fixed number of prey. The condition of a given patch (prey or no prey) could only be determined from information gained while exploiting the patch. A starling's task was to determine to what extent to sample an apparently prey-less patch before giving it up as such, in a way which maximizes long-term energy intake rate. The simple model presented to predict the optimal sampling solutions was qualitatively but not quantitatively supported by the data. The main discrepancy was in the fact that an apparently prey-less patch should have been sampled to a fixed extent before leaving, whereas a distribution of sampling behavior was actually observed. The qualitative agreement was very good, however, as the modes of the observed sampling distributions often corresponded to the predicted optimal sampling solutions. Starlings seem to possess a patch-sampling ability which, at least for those simple situations analyzed, can lead to an efficient foraging strategy.     

Foraging tactics of two guilds of web-spinning spiders

Summary The foraging behavior of orbweaving and sheetweb weaving guilds of spiders was investigated. Orbweavers move among web-sites frequently, but sheetweb weavers do not. A simple model that examines the adaptive advantages of active foraging and sit-and-wait strategies leads to three predictions: 1) Orbweavers should have a simple decision rule for leaving web-sites, 2) Orbweavers' web-sites should have more variable payoffs than do the web-sites of sheetweb weavers, and 3) Orbweavers should have a lower cost of moving than do sheetweb weavers. Field and experimental data bear out each prediction. In addition, analysis of the residence times of spiders at web-sites that are used more than once reveals that members of the two guilds do not compete with each other for web-sites.The distinction between active foragers and sit-and-wait predators stems from the relative frequency of the decision to leave a foraging site. Thus active foragers are those predators that move often from patch to patch, and sit-and-wait predators are those that leave patches infrequently. In this sense, orbweaving spiders are active foragers and sheetweb weavers are sit-and-wait predators.     

Look before you leap: is risk of injury a foraging cost?

Theory states that an optimal forager should exploit a patch so long as its harvest rate of resources from the patch exceeds its energetic, predation, and missed opportunity costs for foraging. However, for many foragers, predation is not the only source of danger they face while foraging. Foragers also face the risk of injuring themselves. To test whether risk of injury gives rise to a foraging cost, we offered red foxes pairs of depletable resource patches in which they experienced diminishing returns. The resource patches were identical in all respects, save for the risk of injury. In response, the foxes exploited the safe patches more intensively. They foraged for a longer time and also removed more food (i.e., had lower giving up densities) in the safe patches compared to the risky patches. Although they never sustained injury, video footage revealed that the foxes used greater care while foraging from the risky patches and removed food at a slower rate. Furthermore, an increase in their hunger state led foxes to allocate more time to foraging from the risky patches, thereby exposing themselves to higher risks. Our results suggest that foxes treat risk of injury as a foraging cost and use time allocation and daring—the willingness to risk injury—as tools for managing their risk of injury while foraging. This is the first study, to our knowledge, which explicitly tests and shows that risk of injury is indeed a foraging cost. While nearly all foragers may face an injury cost of foraging, we suggest that this cost will be largest and most important for predators.     

A field investigation of scrounging in semipalmated sandpipers

Animals that forage in groups can produce their own food patches or scrounge the food discoveries of their companions. Mean tactic payoffs are expected to be the same at equilibrium for phenotypically equal foragers. Scrounging is also typically viewed as a risk-averse foraging strategy that provides a more even food intake rate over time. The occurrence of scrounging and the payoffs from different foraging modes have rarely been investigated in the field. Over two field seasons, I examined patch sharing in semipalmated sandpipers (Calidris pusilla) foraging on minute food items at the surface of the substrate. Birds could find patches on their own, a producing event, or join the food patches discovered by others, a scrounging event. I found that the average search time per patch did not differ between producing and scrounging but that the average time spent exploiting a patch was reduced nearly by half when scrounging. As a result, the proportion of time spent exploiting a patch, a measure of foraging payoffs, was significantly lower when scrounging. The variance in payoffs was similar for producing and scrounging. When producing their own patches, individuals that scrounged spent the same proportion of time exploiting a patch as those that only produced. However, within the same individuals, the search time for a scrounged patch was longer than the search time for a produced patch. The results show unequal payoffs for producing and scrounging in this system and suggest that low success in finding patches elicited scrounging.     

Comparisons of forager distributions from matched honey bee colonies in suburban environments

We conducted experiments designed to examine the distribution of foraging honey bees (Apis mellifera) in suburban environments with rich floras and to compare spatial patterns of foraging sites used by colonies located in the same environment. The patterns we observed in resource visitation suggest a reduced role of the recruitment system as part of the overall colony foraging strategy in habitats with abundant, small patches of flowers. We simultaneously sampled recruitment dances of bees inside observation hives in two colonies over 4 days in Miami, Florida (1989) and from two other colonies over five days in Riverside, California (1991). Information encoded in the dance was used to determine the distance and direction that bees flew from the hive for pollen and nectar and to construct foraging maps for each colony. The foraging maps showed that bees from the two colonies in each location usually foraged at different sites, but occasionally they visited the same patches of flowers. Each colony shifted foraging effort among sites on different days. In both locations, the mean flight distances differed between colonies and among days within colonies. The flight distances observed in our study are generally shorter than those reported in a similar study conducted in a temperate deciduous forest where resources were less dense and floral patches were smaller.     

Dynamic response to danger in a parasitoid wasp

Despite the multitude of work on patch time allocation and the huge number of studies on patch choice in the face of danger, the patch leaving response of foragers perceiving cues of danger has received relatively little attention. We investigated the response of parasitoid insects to cues of danger both theoretically and experimentally. Using stochastic dynamic theory, we demonstrate that patch-leaving responses in response to the detection of danger should be seen as a dynamic decision that depends upon reproductive options on the current host patch and on alternative patches that might be found after leaving the current patch. Our theory predicts a sigmoidal response curve of parasitoids, where they should accept the danger and stay on the patch when patch quality is high and should increasingly avoid the risk and emigrate from the patch with decreasing patch quality and decreasing costs of traveling to an alternative host patch. Experiments with females of the drosophilid parasitoid Asobara tabida that were exposed to a puff of formic acid (a danger cue) at different times through their patch exploitation confirmed the theoretical predictions (i.e., a sigmoid response curve); however, the predicted curve was significantly steeper than observed. We discuss the impact of dynamic patch-exit decisions of individual foragers on population and community dynamics.     

Nonlinear effects of food aggregation on interference competition in mallards

Previous studies of interference competition have shown an asymmetric effect on intake rate of foragers on clumped resources, with only subordinate individuals suffering. However, the food distributions in these studies were uniform or highly clumped, whereas in many field situations, food aggregation is intermediate. Here we investigated whether food distribution (i.e., uniform, slightly clumped, and highly clumped) affects the behavioral response of mallards foraging alone or competing with another. Although the amount of food was the same in all distributions, the mallards reached higher intake rates, visited fewer patches, and showed longer average feeding times in the highly clumped distribution. Competing mallards had lower intake rates on the slightly clumped than on the uniform or highly clumped food distributions. Subordinates generally visited more patches and had shorter feeding times per patch, but their intake rates were not significantly lower than those of dominants. Therefore, we propose that subordinates do not necessarily suffer from interference competition in terms of intake rate, but do suffer higher search costs. In addition, although dominants had significantly higher average feeding times on the best quality patches of the highly clumped food distribution, such an effect was not found in the slightly clumped distribution. These findings indicate that in environments where food is aggregated to a lesser extent, monopolization is not the best strategy for dominants. Our results suggest that interference experiments should use food distributions that resemble the natural situation animals are faced with in the field.     

Behavioral response races, predator-prey shell games, ecology of fear, and patch use of pumas and their ungulate prey

The predator-prey shell game predicts random movement of prey across the landscape, whereas the behavioral response race and landscape of fear models predict that there should be a negative relationship between the spatial distribution of a predator and its behaviorally active prey. Additionally, prey have imperfect information on the whereabouts of their predator, which the predator should incorporate in its patch use strategy. I used a one-predator-one-prey system, puma (Puma concolor)-mule deer (Odocoileus hemionus) to test the following predictions regarding predator-prey distribution and patch use by the predator. (1) Pumas will spend more time in high prey risk/low prey use habitat types, while deer will spend their time in low-risk habitats. Pumas should (2) select large forage patches more often, (3) remain in large patches longer, and (4) revisit individual large patches more often than individual smaller ones. I tested these predictions with an extensive telemetry data set collected over 16 years in a study area of patchy forested habitat. When active, pumas spent significantly less time in open areas of low intrinsic predation risk than did deer. Pumas used large patches more than expected, revisited individual large patches significantly more often than smaller ones, and stayed significantly longer in larger patches than in smaller ones. The results supported the prediction of a negative relationship in the spatial distribution of a predator and its prey and indicated that the predator is incorporating the prey's imperfect information about its presence. These results indicate a behavioral complexity on the landscape scale that can have far-reaching impacts on predator-prey interactions.     

Travel time affects optimal diets in depleting patches

Models of prey choice in depleting patches predict an expanding specialist strategy: Animals should start as specialists on the most profitable prey and then at some point during patch exploitation switch to a generalist foraging strategy. When patch residence time is long, the switch to a generalist diet is predicted to occur earlier than when patch residence time is short. We tested these predictions under laboratory conditions using female parasitoids (Aphidius colemani) exploiting patches of mixed instars aphid hosts (Myzus persicae, L1 and L4). The duration of patch exploitation was manipulated by changing travel time between patches. As predicted, patch residence times increase with travel time between patches. Our results provide empirical support for the expanding specialist prediction: Parasitoid females specialized initially on the more profitable hosts (L4), and as the patch depleted, they switched to a generalist diet by accepting more frequently the less profitable hosts (L1). The point at which they switched from specialist to generalist occurred later when travel times and hence patch residence times were short. By affecting the patch exploitation strategy, travel time also determines the composition of hosts left behind, the “giving up composition.” The change in the relative density of remaining host types alters aphid populations’ age structure.     

Collective foraging decision in a gregarious insect

Group foraging by eusocial insects implies sophisticated recruitment processes that often result in collective decisions to exploit the most profitable sources. These advanced levels of cooperation, however, remain limited to a small range of species, and we still know little about the mechanisms underlying group foraging behaviours in the great mass of animals exhibiting lower levels of social complexity. In this paper, we report, for the first time in a gregarious insect, the cockroach Blattella germanica (L.), a collective foraging decision whereby the selection of food sources is reached without requiring active recruitment. Groups of cockroaches given a binary choice between identical food sources exhibited exploitation asymmetries whose amplitude increases with group size. By coupling behavioural observations to computer simulations, we demonstrate that selection of food sources relies uniquely on a retention effect of feeding individuals on newcomers without comparison between available opportunities. This self-organised pattern presents similarities with the foraging dynamics of eusocial species, thus stressing the generic dimension of collective decision-making mechanisms based on social amplification rules despite fundamental differences in recruitment processes. We hypothesise that such parsimony could apply to a wide range of species and help understand the emergence of collective behaviours in simple social systems.     

Locating food in a spatially heterogeneous environment: Implications for fitness of the macrodecomposer Armadillidium vulgare (Isopoda: Oniscidea)

To assess the fitness consequences of foraging on patchy resources, consumption rates, growth rates and survivorship of Armadillidium vulgare were monitored while feeding in arenas in which the spatial distribution of patches of high quality food (powdered dicotyledonous leaf litter) was varied within a matrix of low quality food (powdered grass leaf litter). Predictions from behavioural experiments that these fitness correlates would be lower when high quality food is more heterogeneously distributed in space were tested but not supported either by laboratory or field experiments. To investigate whether A. vulgare can develop the ability to relocate high quality food patches, changes in foraging behaviour, over a comparable time period to that used in the fitness experiments, were monitored in arenas in which there was a high quality food patch in a low quality matrix. A. vulgare increased its ability to relocate the position of high quality food over time. It reduced time spent in low quality food matrices and increased time spent in high quality food patches with time after the start of the experiment. When the position of a high quality food patch was moved, the time spent in the low quality food matrix increased and less time was spent in high quality food patches, compared to arenas in which the food was not moved. The fitness benefits for saprophages of developing the ability to relocate high quality patches while foraging in spatially heterogeneous environments are discussed.