The spatial distribution of flocking foragers: disentangling the effects of food availability,interference and conspecific attraction by means of spatial autoregressive modeling

Patch choice of foraging animals is typically assumed to depend positively on food availability and negatively on interference while benefits of the co‐occurrence of conspecifics tend to be ignored. In this paper we integrate a classical functional response model based on resource availability and interference with a conspecific attraction model and use it to simulate spatial distributions of animals in their continuous resource landscapes. We consider both equilibrium and non‐equilibrium distributions. We show that the integrated model produces distributions of foraging animals that closely match the distributions observed in nature. The simulations also show that under information uncertainty the locations of flocks are highly variable when conspecific attraction is strong. We furthermore explain how we can estimate the impacts of conspecific attraction and interference on the distribution of foraging animals by spatial autoregression. On the basis of simulated data we show that the separate impacts of interference and conspecific attraction can be disentangled when prior information on either is available, in addition to information on resource density and predator density, and that the total food effect is given by the spatial multiplier.     

Knowing your habitat: linking patch-encounter rate and patch exploitation in parasitoids

According to optimal foraging theory, animals should decidewhether or not to leave a resource patch by comparing the currentprofitability of the patch with the expected profitability ofsearching elsewhere in the habitat. Although there is abundantevidence in the literature that foragers in general are wellable to estimate the value of a single resource patch, theirdecision making has rarely been investigated with respect tohabitat quality. This is especially true for invertebrates.We have conducted experiments to test whether parasitic waspsadjust patch residence time and exploitation in relation tothe abundance of patches within the environment. We used thebraconid Asobara tabida, a parasitoid of Drosophila larvae,as our model species. Our experiments show that these waspsreduce both the residence time and the degree of patch exploitationwhen patches become abundant in their environment, as predictedby optimal foraging models. Based upon a detailed analysis ofwasp foraging behavior, we discuss proximate mechanisms thatmight lead to the observed response. We suggest that parasitoidsuse a mechanism of sensitization and desensitization to chemicalsassociated with hosts and patches, in order to respond adaptivelyto the abundance of patches within their environment.     

Tolerance of understory plants subject to herbivory by roe deer

Classical foraging theory states that animals feeding in a patchy environment can maximise their long term prey capture rates by quitting food patches when they have depleted prey to a certain threshold level. Theory suggests that social foragers may be better able to do this if all individuals in a group have access to the prey capture information of all other group members. This will allow all foragers to make a more accurate estimation of the patch quality over time and hence enable them to quit patches closer to the optimal prey threshold level. We develop a model to examine the foraging efficiency of three strategies that could be used by a cohesive foraging group to initiate quitting a patch, where foragers do not use such information, and compare these with a fourth strategy in which foragers use public information of all prey capture events made by the group. We carried out simulations in six different prey environments, in which we varied the mean number of prey per patch and the variance of prey number between patches. Groups sharing public information were able to consistently quit patches close to the optimal prey threshold level, and obtained constant prey capture rates, in groups of all sizes. In contrast all groups not sharing public information quit patches progressively earlier than the optimal prey threshold value, and experienced decreasing prey capture rates, as group size increased. This is more apparent as the variance in prey number between patches increases. Thus in a patchy environment, where uncertainty is high, although public information use does not increase the foraging efficiency of groups over that of a lone forager, it certainly offers benefits over groups which do not, and particularly where group size is large.     

Emergence of adaptive global movement from a subjective inference about local resource distribution

In animal foraging, the optimal search strategy in an unknown environment varies depending on the context, such as the resource density and season. When food is distributed sparsely and uniformly, superdiffusive walks outperform normal-diffusive walks. However, superdiffusive walks are no longer advantageous when random walkers forage in resource-rich environments. It is not currently clear whether a relationship exists between an agent's use of local information to make subjective inferences about global food distribution and the optimal random walk strategy. Therefore, I investigated how flexible exploration is achieved if an agent alters its directional rule based on the local resource distribution. In the proposed model, the agent, a Brownian-like walker, estimates whether an abundant or sparse area is nearby using local resource patterns and then makes a decision by altering its movement rules. I show that the agent can behave like a non-Brownian walker if it interacts with a prey distribution. The agent can adaptively switch between diffusive properties depending on the resource density. This leads to a more effective resource-searching performance than a simple random-walk model. These results demonstrate that optimal searching is a context-dependent process.     

Taking the rough with the smooth: foraging for particulate food in continuous time

This paper describes the development of the general dynamical model of foraging developed by Ollason (1980, Theoret. Popul. Biol. 18, 44-65) to predict foraging for particulate food in three different types of environment. In an environment containing particles of different types of food, the model predicts the selection of an approximately optimal diet; in an environment in which the particles occur in patches, the model predicts a time budget of patch occupancy that approximates to the optimal time budget; and in an environment containing patches of particles that regenerate by the addition of particles of food at constant rates, the model predicts that animals will dispose themselves among the patches approximately as predicted by the ideal free distribution. Where the predictions of the model depart from the predictions of optimal foraging theory, they are qualitatively similar to the observed departures of the behaviour of real animals from the predictions of optimal foraging theory. The model provides a general representation of the foraging decisions of animals whether they feed strictly continuously or discontinuously on particles of food, and does so without explicit reference to optimization processes.     

Evolutionary models of metabolism, behaviour and personality

I explore the relationship between metabolism and personality by establishing how selection acts on metabolic rate and risk-taking in the context of a trade-off between energy and predation. Using a simple time budget model, I show that a high resting metabolic rate is not necessarily associated with a high daily energy expenditure. The metabolic rate that minimizes the time spent foraging does not maximize the net gain rate while foraging, and it is not always advantageous for animals to have a higher metabolic rate when food availability is high. A model based on minimizing the ratio of mortality rate to net gain rate is used to determine how a willingness to take risks should be correlated with metabolic rate. My results establish that it is not always advantageous for animals to take greater risks when metabolic rate is high. When foraging intensity and metabolic rate coevolve, I show that in a particular case different combinations of foraging intensity and metabolic rate can have equal fitness.     

Mass regulation in response to predation risk can indicate population declines

In theory, survival rates and consequent population status might be predictable from instantaneous behavioural measures of how animals prioritize foraging vs. avoiding predation. We show, for the 30 most common small bird species ringed in the UK, that one quarter respond to higher predation risk as if it is mass-dependent and lose mass. Half respond to predation risk as if it only interrupts their foraging and gain mass thus avoiding consequent increased starvation risk from reduced foraging time. These mass responses to higher predation risk are correlated with population and conservation status both within and between species (and independently of foraging habitat, foraging guild, sociality index and size) over the last 30 years in Britain, with mass loss being associated with declining populations and mass gain with increasing populations. If individuals show an interrupted foraging response to higher predation risk, they are likely to be experiencing a high quality foraging environment that should lead to higher survival. Whereas individuals that show a mass-dependent foraging response are likely to be in lower quality foraging environments, leading to relatively lower survival.     

Exploration or exploitation: life expectancy changes the value of learning in foraging strategies

The acquisition of information is a fundamental part of individual foraging behaviour in heterogeneous and changing environments. We examine how foragers may benefit from utilizing a simple learning rule to update estimates of temporal changes in resource levels. In the model, initial expectation of resource conditions and rate of replacing past information by new experiences are genetically inherited traits. Patch-time allocation differs between learners and foragers that use a fixed patch-leaving threshold throughout the foraging season. It also deviates from foragers that obtain information about the environment at no cost. At the start of a foraging season, learners sample the environment by frequent movements between patches, sacrificing current resource intake for information acquisition. This is done to obtain more precise and accurate estimates of resource levels, resulting in increased intake rates later in season. Risk of mortality may alter the trade-off between exploration and exploitation and thus change patch sampling effort. As lifetime expectancy decreases, learners invest less in information acquisition and show lower foraging performance when resource level changes through time.     

How simple grazing rules can lead to persistent boundaries in vegetation communities

Natural landscape boundaries between vegetation communities are dynamically influenced by the selective grazing of herbivores. Here we show how this may be an emergent property of very simple animal decisions, without the need for any sophisticated choice rules etc., using a model based on biased diffusion. Animal grazing intensity is coupled with plant competition, resulting in reaction-diffusion dynamics, from which stable boundaries spontaneously emerge. In the model, animals affect their resources by both consumption and trampling. It is assumed that forage consists of two heterogeneously distributed competing resource species, one that is preferred (grass) over the other (heather) by the animals. The solutions to the resulting system of differential equations for three cases a) optimal foraging, b) random walk foraging and c) taxis-diffusion are presented. Optimal and random foraging gave unrealistic results, but taxis-diffusion accorded well with field observations. Persistent boundaries between patches of near-monoculture vegetation were predicted, with these boundaries drifting in response to overall grazing pressure (grass advancing with increased grazing and vice versa). The reaction-taxis-diffusion model provides the first mathematical explanation for such vegetation mosaic dynamics and the parameters of the model are open to experimental testing.     

Learning to forage in a regenerating patchy environment: Can it fail to be optimal?

The behaviour of animals foraging along closed traplines of regenerating patches of food has been simulated using a learning rule that determines when an animal should leave the patch at which it is currently feeding to search for another one. The rule causes the animal to stay at the patch as long as it is feeding faster than it remembers doing. The foraging behaviour of one animal, and of two or more animals together, feeding in traplines containing patches of the same and of differing types has been simulated, and in all cases the foraging behaviour generated by the rule allowed the animals to exploit the food very efficiently. The learning model is also responsible for indirect social interactions among animals sharing the same trapline because the feeding of each animal reduces the availability of food for the others. This causes a population of animals to disperse themselves, on average, among patches of food according to the ideal free distribution. The relationship between the learning model and conventional optimal foraging models is examined and it is shown that it is pointless to try to account for learned behaviour in the context of optimal foraging theory.     

Patch assessment in foraging flocks of European starlings: evidence for the use of public information

A field experiment was carried out to determine whether group-foragingstarlings (Sturnus vulgaris) use public information to helpthem estimate the quality of an artificial resource patch anddepart accordingly. Three kinds of information are potentiallyavailable in a group: patch-sample information, pre-harvestinformation, and public information. These three types of informationcan be combined into four patch assessment strategies: (1) patch-samplealone; (2) patch-sample and pre-harvest; (3) patch-sample andpublic; and (4) patch-sample, pre-harvest, and public. Dependingon the foraging environment we presented to the starlings, eachassessment strategy made a unique set of predictions concerningthe patch departure decisions of pairs of birds based on differencesin their foraging success. The environment was manipulated intwo ways: by altering the variability in patch quality and bychanging compatibility, the ease with which individual birdscould simultaneously acquire both patch-sample and public information.Our observations on patch persistence and departure order demonstratethat the starlings used a combination of patch-sample and publicinformation, but not pre-harvest information, to estimate thequality of the experimental patch. Moreover, our results suggestthat starlings use public information only when it is easilyavailable and ignore it under incompatible conditions. Thisstudy provides the first evidence of public information usein a patch assessment problem.     

The effect of energy reserves and food availability on optimal immune defence

In order to avoid both starvation and disease, animals must allocate resources between energy reserves and immune defence. We investigate the optimal allocation. We find that animals with low reserves choose to allocate less to defence than animals with higher reserves because when reserves are low it is more important to increase reserves to reduce the risk of starvation in the future. In general, investment in immune defence increases monotonically with energy reserves. An exception is when the animal can reduce its probability of death from disease by reducing its foraging rate. In this case, allocation to immune defence can peak at intermediate reserves. When food changes over time, the optimal response depends on the frequency of changes. If the environment is relatively stable, animals forage most intensively when the food is scarce and invest more in immune defence when the food is abundant than when it is scarce. If the environment changes quickly, animals forage at low intensity when the food is scarce, but at high intensity when the food is abundant. As the rate of environmental change increases, immune defence becomes less dependent on food availability. We show that the strength of selection on reserve-dependent immune defence depends on how foraging intensity and immune defence determine the probability of death from disease.     

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.     

Momentary maximizing and optimal foraging theories of performance on concurrent VR schedules

Optimal foraging theory proposes that animals obtain the highest rate of reinforcers for the least effort and momentary maximizing theory proposes that animals make the response that at that instant is most likely to be reinforced. While each theory may account for matching on concurrent schedules, the data supporting each theory are weak. Two experiments assessed these theories by considering concurrent choice as consisting of two pairs of stay and switch schedules. Symmetrical arrangements, which are equivalent to standard concurrent schedules, maintained behavior described by the generalized matching law. Weighted arrangements, in which the programmed rate of earning reinforcers was always greater at one alternative, maintained behavior that was biased towards the weighted alternative, yet the bias was less than that predicted by optimal foraging theory. Asymmetrical arrangements, in which the stay and switch schedules operating at an alternative are the same, maintained behavior that favored one alternative, even though momentary maximizing predicted indifference. The generalized matching law poorly described each rat's pooled data from all conditions but these data were described by an equation based on the stay and switch reinforcers earned per-visit and included elements of optimal foraging and momentary maximizing theories of choice.     

Ant Navigation: Fractional Use of the Home Vector

Home is a special location for many animals, offering shelter from the elements, protection from predation, and a common place for gathering of the same species. Not surprisingly, many species have evolved efficient, robust homing strategies, which are used as part of each and every foraging journey. A basic strategy used by most animals is to take the shortest possible route home by accruing the net distances and directions travelled during foraging, a strategy well known as path integration. This strategy is part of the navigation toolbox of ants occupying different landscapes. However, when there is a visual discrepancy between test and training conditions, the distance travelled by animals relying on the path integrator varies dramatically between species: from 90% of the home vector to an absolute distance of only 50 cm. We here ask what the theoretically optimal balance between PI-driven and landmark-driven navigation should be. In combination with well-established results from optimal search theory, we show analytically that this fractional use of the home vector is an optimal homing strategy under a variety of circumstances. Assuming there is a familiar route that an ant recognizes, theoretically optimal search should always begin at some fraction of the home vector, depending on the region of familiarity. These results are shown to be largely independent of the search algorithm used. Ant species from different habitats appear to have optimized their navigation strategy based on the availability and nature of navigational information content in their environment.     

Neuroeconomics in parasitoids: computing accurately with a minute brain

In the so‐called ‘patch problem’, at any given moment, the forager must decide whether to leave the current patch or to remain there and continue foraging. Optimal foraging theory and subsequent theoretical works have identified theoretical optimal policies governing this decision. In a stochastic environment, the Bayesian framework has proved to be effective. A set of mechanistic proximal mechanisms explaining how parasitoid wasps may take decisions has been proposed. These mechanisms are based in on changes in the degree of motivation to continue foraging during a particular foraging episode. Using a simple, straightforward model, we show here that the psychological mechanism proposed mimics precisely the theoretical Bayesian solution, provided that motivation displays exponential decay, rather than the linear pattern of decay initially assumed. Changes in motivation thus function as a sort of analogue computer, and may be seen as more than purely heuristic rules of thumb. This link between psychological processes and ultimate optimisation places foraging theory in the domain of neuroeconomics.     

Patch choice and population size

The distribution of animals between feeding patches has been the subject of considerable theoretical and empirical investigation. When all animals are equal and fitness is well represented by intake rate, the ideal free distribution requires the animals to be distributed in such a way as to equalize intake rate in each feeding patch. We refer to this as the equal rates policy. This approach ignores the effect of stochasticity in the food supply on starvation. It also ignores predation. An alternative approach is based on the assumption that each animal tries to minimize its death rate. An optimal policy now involves making decisions about which patch to use on the basis of the current level of energy reserves. We investigate a simple model of population dynamics in which over-winter mortality is either derived from animals adopting the equal rates policy or the optimal state-dependent policy to decide between two feeding patches. We show that the state-dependent policy results in a larger equilibrium population size than the equal rates policy. This difference can be considerable when the foraging environment is very stochastic. Furthermore, the state-dependent policy may result in a viable equilibrium population when the equal rates policy does not. The equilibrium under the state-dependent policy may be less stable than that under the equal rates policy. We identify conditions under which the state-dependent policy results in approximately equal intake rates on the two feeding patches. Levels of mortality as a result of predation are investigated. We show that, under some circumstances, the proportion of mortality that is due to predation may decrease as the predation pressure increases.     

Time's crooked arrow: optimal foraging and rate-biased time perception

Time perception is critical to animal behaviours requiring anticipation of future events based on present information about the environment. Most models of animal foraging assume that animals are capable of measuring absolute time despite evidence that animals measure time with predictable biases in mean and variance. We incorporate the evidence for a rate-biased subjective time perception into a classic model of optimal foraging, the marginal value theorem. If acceleration of the clock rate is proportional to food intake rate and time is perceived similarly when in transit between patches as it is while waiting in a patch following eating, organisms are predicted to follow the predictions of the marginal value theorem exactly. However, a nonlinear relationship between clock rate and food intake rate, unequal wait and transit time perception, or any lag in the clock predicts characteristic suboptimal behaviour. We discuss how this mechanism for suboptimal behaviour compares with others in the literature and how it can be recognized in experiments. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Horseshoe bats make adaptive prey-selection decisions, informed by echo cues

Foragers base their prey-selection decisions on the information acquired by the sensory systems. In bats that use echolocation to find prey in darkness, it is not clear whether the specialized diet, as sometimes found by faecal analysis, is a result of active decision-making or rather of biased sensory information. Here, we tested whether greater horseshoe bats decide economically when to attack a particular prey item and when not. This species is known to recognize different insects based on their wing-beat pattern imprinted in the echoes. We built a simulation of the natural foraging process in the laboratory, where the bats scanned for prey from a perch and, upon reaching the decision to attack, intercepted the prey in flight. To fully control echo information available to the bats and assure its unambiguity, we implemented computer-controlled propellers that produced echoes resembling those from natural insects of differing profitability. The bats monitored prey arrivals to sample the supply of prey categories in the environment and to inform foraging decisions. The bats adjusted selectivity for the more profitable prey to its inter-arrival intervals as predicted by foraging theory (an economic strategy known to benefit fitness). Moreover, unlike in previously studied vertebrates, foraging performance of horseshoe bats was not limited by costly rejections of the profitable prey. This calls for further research into the evolutionary selection pressures that sharpened the species's decision-making capacity.     

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.