Prey processing in central place foragers

The importance of prey processing as an integral part of foraging behaviour has long been acknowledged, but little theoretical consideration has been given to the optimization of the processing behaviour itself. Processing renders food down to ingestible, palatable portions, and also removes non-essential mass thus reducing transport costs. Here, several models of processing are developed for a central place forager. When the forager has to make a simple choice between processing the prey and not, a critical distance from the central place can be calculated, beyond which it is optimal to process prey. If the forager also decides on how much of the prey to remove, the optimal amount to be removed can also be calculated. Imposing a ceiling on overall metabolic expenditure is shown to reduce the distances at which processing becomes the optimal strategy. The models are tested using parameters derived for a provisioning merlin, Falco columbarius, and alternative explanations as to why observed behaviours should differ from the optimal behaviour predicted are discussed.     

Interruptions to foraging and learning in a changing environment

Many resources are both stochastic and variable in their average profitability. Animals have to sample them to track their current states, but whether it is economic to attempt this depends on many factors. Furthermore, there are many interruptions and distractions from foraging (e.g. escape from predators, bad weather, displacement by competitors) which interfere with the acquisition of information. We present a dynamic model of foraging in a stochastic and varying environment, under the constant threat of interruption, to investigate this very general problem. A forager faces two foraging options, one of which provides a known and constant reward, the other providing a reward that is not only stochastic, but whose mean payoff varies in time. The forager has to learn which option has the highest current payoff by sampling. However, interruptions to foraging can occur at any time, the timing and duration of which are beyond the animal's control. When there is a small probability of foraging being interrupted, the forager should forage extensively on the unknown option, but as the probability of interruptions is increased, there is a sudden transition to foraging only on the known option. This occurs because interruptions affect both the level of information required to make exploitation of the unknown option profitable, and the ability to acquire and maintain that information. At what probability of being interrupted this threshold emerges is affected by the value of learning about the unknown option and the duration of interruptions. We discuss the generality of our results with reference to the pervasive problem of updating information in the face of different types of interruption. Copyright 1999 The Association for the Study of Animal Behaviour.     

Smart,smarter, smartest: foraging information states and coexistence

Animals possess different abilities to gain and use information about the foraging patches they exploit. When ignorant of the qualities of encountered patches, a smart forager should leave all patches after the same amount of fixed search time. A smarter forager can be Bayesian by using information on cumulative harvest and time spent searching a patch to better inform its patch‐departure decision. The smartest forager has immediate and continuous knowledge about patch quality, and can make a perfect decision about when to leave each patch. Here we let each of these three strategies harvest resources from a slowly regenerating environment. Eventually a steady‐state distribution of prey among patches arises where the environment‐wide resource renewal just balances the environment‐wide harvest of the foragers. The fixed time forager creates a distribution with the highest mean and highest variance of patch qualities, followed by the Bayesian and the prescient in that order. The less informed strategies promote distributions with both more resources and more exploitable information than the more informed strategies. While it is true that a better‐informed strategy will always out‐perform a less well‐informed, its increase in performance may not compensate it for any costs associated with being better informed. We imagine that the fixed time strategy may be least expensive and the prescient strategy most expensive in terms of sensory organs and associated assess and respond capabilities. To consider competition between such strategies with varying costs, we introduced a single individual of each of the strategies into the environments created by populations of the other strategies. There are threshold costs associated with the better‐informed strategy such that it can or cannot outcompete a less‐informed strategy. However, over a relatively narrow range of foraging costs, less‐informed and better‐informed strategies will coexist. Furthermore, for the prescient and the Bayesian strategies, some combinations of foraging costs produce alternate stable states – whichever strategy establishes first remains safe from invasion by the other.     

To scan or not to scan? Occurrence of the group‐size effect in a seasonally nongregarious forager

Group‐living requires a compromise between safety and direct/indirect costs for individuals. The larger is the group, the greater is the collective vigilance, leading to a greater net food intake per forager because of the time saved individually from scanning behaviour. In turn, individual alertness usually decreases with increasing group size (“group‐size effect”). Information on the occurrence of group‐size effect is still unclear. Previous studies have shown that it may fail to occur or even reverse, for example when costs of interference between conspecifics are high. In turn, assessing whether the group‐size effect would occur in weakly or seasonally gregarious species may help to understand its drivers. We evaluated the occurrence and the extent of group‐size effect in a seasonally nongregarious herbivore, the roe deer Capreolus capreolus. We examined the roles of sex/age class and season as drivers of vigilance behaviour. In roe deer, the group‐size effect did not depend on sex/age class: time spent foraging increased with increasing group size; in turn, vigilance increased with decreasing group size, in all sex/age classes. Females with fawns were the most vigilant sex/age class, thus revealing the cost of offspring protection. Accordingly, the higher spring vigilance levels of does could be related to reproductive costs (e.g., defence of newborn fawns). Conversely, the greater summer vigilance of bucks could result from patrolling/defence of territories. Both adult males and females also showed the higher vigilance in winter, likely because of an increase in the perception of predation risk and/or, possibly, hormones linked to an increase in intolerance of conspecifics, in males. However, the group‐size effect occurred in all the seasons, for adult males and females. Our findings suggest that foraging benefits provided by the group‐size effect may have overcome costs of group‐living, even in a weakly gregarious forager.     

Benefits and costs of increased levels of corticosterone in seabird chicks

Seabird chicks respond to food shortages by increasing corticosterone (cort) secretion, which is probably associated with fitness benefits and costs. To examine this, we experimentally increased levels of circulating cort in captive black-legged kittiwake chicks fed ad libitum. We found that cort-implanted chicks begged more frequently and were more aggressive compared to controls. These behavioral modifications must be beneficial to chicks as they facilitate acquisition of food from the parents and might trigger brood reduction and reduced competition for food. Cort-implanted chicks also increased food intake; however, their growth rates were similar to controls. To examine the costs of chronically increased circulating levels of cort, we removed cort implants and, after a 10-day recovery period, tested cognitive abilities of young kittiwakes. We found that the ability of kittiwakes to associate a visual cue with the presence of food in a choice situation was compromised by the experimental elevation of cort during development. To examine the long-term costs of increased levels of cort, 8 months later we tested the performance of the same individuals in a spatial task requiring them to make a detour around a barrier in order to escape from an enclosure. Individuals treated with cort during development took significantly more time to solve this task compared to controls. The results of this study suggest that the adrenocortical response of a developing bird to environmental stressors is associated with both benefits (increased food intake, foraging behavior, and aggression) and costs (low growth efficiency and compromised cognitive abilities later in life). This provides an evolutionary framework for relating juvenile physiological traits to fitness of birds in subsequent life-history stages.     

A quantitative model of honey bee colony population dynamics

Since 2006 the rate of honey bee colony failure has increased significantly. As an aid to testing hypotheses for the causes of colony failure we have developed a compartment model of honey bee colony population dynamics to explore the impact of different death rates of forager bees on colony growth and development. The model predicts a critical threshold forager death rate beneath which colonies regulate a stable population size. If death rates are sustained higher than this threshold rapid population decline is predicted and colony failure is inevitable. The model also predicts that high forager death rates draw hive bees into the foraging population at much younger ages than normal, which acts to accelerate colony failure. The model suggests that colony failure can be understood in terms of observed principles of honey bee population dynamics, and provides a theoretical framework for experimental investigation of the problem.     

The effect of costly information in diet choice

Summary We distinguish three cases which consider the effect of information on animal behaviour: static information, obligate information and facultative information. Static information deals with the case in which the animal does not acquire additional information; it starts with enough information to discriminate options. Obligate information deals with the case in which the animal acquires information at no additional cost. Facultative information is when the animal may choose to pay a cost in order to acquire information. We illustrate the differences among these three situations by analysing the optimal diet problem subject to the different information regimes. Compared to the case with static information, obligate recognition time narrows the range of prey densities over which an optimal forager feeds selectively, and facultative recognition time reduces it further still. The three models yield qualitatively different predictions regarding how the optimal diet varies with relative abundances of alternative resources. In the space of resource densities, the line separating the optimal behaviours of selectivity and opportunism is straight for both the perfect and obligate information cases. In the case of facultative recognition time this line or isoleg is part of a quadratic curve. This non-linearity yields two completely new predictions: a less profitable resource may be lost from the diet after becoming more abundant and the poor resource may be included in the diet as a result of the rich resource becoming more common.     

An Extra Dimension to Decision-Making in Animals: The Three-way Trade-off between Speed,Effort per-Unit-Time and Accuracy

The standard view in biology is that all animals, from bumblebees to human beings, face a trade-off between speed and accuracy as they search for resources and mates, and attempt to avoid predators. For example, the more time a forager spends out of cover gathering information about potential food sources the more likely it is to make accurate decisions about which sources are most rewarding. However, when the cost of time spent out of cover rises (e.g. in the presence of a predator) the optimal strategy is for the forager to spend less time gathering information and to accept a corresponding decline in the accuracy of its decisions. We suggest that this familiar picture is missing a crucial dimension: the amount of effort an animal expends on gathering information in each unit of time. This is important because an animal that can respond to changing time costs by modulating its level of effort per-unit-time does not have to accept the same decrease in accuracy that an animal limited to a simple speed-accuracy trade-off must bear in the same situation. Instead, it can direct additional effort towards (i) reducing the frequency of perceptual errors in the samples it gathers or (ii) increasing the number of samples it gathers per-unit-time. Both of these have the effect of allowing it to gather more accurate information within a given period of time. We use a modified version of a canonical model of decision-making (the sequential probability ratio test) to show that this ability to substitute effort for time confers a fitness advantage in the face of changing time costs. We predict that the ability to modulate effort levels will therefore be widespread in nature, and we lay out testable predictions that could be used to detect adaptive modulation of effort levels in laboratory and field studies. Our understanding of decision-making in all species, including our own, will be improved by this more ecologically-complete picture of the three-way tradeoff between time, effort per-unit-time and accuracy.     

The Effects of 24-hour Sleep Deprivation on the Exploration-Exploitation Trade-off

Sleep deprivation has a complex set of neurological effects that go beyond a mere slowing of mental processes. While cognitive and perceptual impairments in sleep deprived individuals are widespread, some abilities remain intact. In an effort to characterize these effects, some have suggested an impairment of complex decision making ability despite intact ability to follow simple rules. To examine this trade-off, 24-hour total sleep deprived individuals performed two versions of a resource acquisition foraging task, one in which exploration is optimal (to succeed, abandon low value, high saliency options) and another in which exploitation is optimal (to succeed, refrain from switching between options). Sleep deprived subjects exhibited decreased performance on the exploitation task compared to non-sleep deprived controls, yet both groups exhibited increased performance on the exploratory task. These results speak to previous neuropsychological work on cognitive control.     

Theory of oviposition strategy of parasitoids. I. Effect of mortality and limited egg number

The optimal oviposition strategies of parasitoids, the host range, and the number of eggs laid per host which result in the maximum lifetime performance of reproduction, are investigated. To study the effects of parasitoid mortality and of limiting total number of eggs laid by a parasitoid, a standard criterion used in previous theories of optimal diet and optimal patch use, the maximization of the foraging rate, is no longer suitable. The model is solved analytically by using dynamic programming. The results are as follows: The host preference of solitary parasitoids depends on the mortality during handling times; i.e., the forager tends to avoid hosts with high risk of foraging mortality. If the total number of eggs produced by a parasitoid is limited, and if the mortality during handling is negligible, the host range is wider when a larger number of eggs remains in the parasitoid's body. In general, however, the mortality-cost of forager and the egg-cost interplay, because the loss of future reproduction by mortality increases with the number of available eggs. In an example with two host types, host range is widest with an intermediate number of eggs available in the body. The optimal number of eggs per host laid by a gregarious parasitoid is also affected by the differential mortality of the forager, and by the number of available eggs.     

Socially stable territories: the negotiation of space by interacting foragers

This article presents a theory of territoriality that integrates optimal foraging and conflict resolution through negotiation. Using a spatially explicit model of a sit-and-wait forager, we show that when resources are scarce, there is a conflict between foragers: there is not enough space for all individuals to have optimal home ranges. We propose that a division of space that solves this conflict over resources is the outcome of a negotiation between foragers. We name this outcome the socially stable territories (SST). Using game theory we show that in a homogenous patch occupied by two interacting foragers, both individuals receive identical energy yields at the socially stable territories; that is, there is economic equity. Economic inequity can arise in a heterogeneous patch or from asymmetries in fighting abilities between the foragers. Opportunity costs play a role in reducing economic inequity. When the asymmetry in fighting abilities is very large, a negotiated division of space is not possible and the forager with lowest fighting ability may be evicted from the habitat patch. A comparison between territories and overlapping home ranges shows that energy yields from territories are generally higher. We discuss why there are instances in which individuals nevertheless overlap home ranges.     

Reduced dietary conservatism in a wild bird in the presence of intraspecific competition

The presence of intraspecific competitors can increase foraging costs through exploitation of resources. Optimal foraging theory suggests that when the cost of pursuing one food type increases, alternative resources should be accepted. Accepting novel foods readily might put a competitor at an advantage over its more conservative rivals in the race for sufficient sustenance, but also opens it to the danger of poisoning by chemically protected food. Dietary conservatism is a foraging behaviour characterised by a prolonged avoidance of novel foods, long after neophobia (initial fear of novel objects) has been overcome, and so might be seen as a disadvantage to foragers in a competitive situation. There are two stable foraging strategies found within forager populations: 1) adventurous consumers (AC) which rapidly accept novel foods and 2) foragers showing dietary conservatism (DC). The expression of these two strategies may also vary with environmental conditions. The aim of this study was to investigate the effect of intraspecific competition on the levels of dietary conservatism displayed among wild caught blue tits Cyanistes caeruleus. Blue tits were offered items of both novel and familiar foods under two conditions: with a competitor and without. Our results showed that individuals who experienced competition incorporated the novel items into their diet faster than those who did not experience competition. This study demonstrates, for the first time, the degree of plasticity in the expression of the DC trait using wild birds in laboratory conditions. This plasticity represents a significant adaptation to reduce the costs of foraging conservatively when novel alternative resources should be accepted.     

Foraging for intermittently refuged prey: theory and field observations of a parasitoid

Many insect herbivores feed in concealed locations but become accessible intermittently, creating windows of greater vulnerability to attack, and generating a proportion of the prey population that is readily accessible to foraging natural enemies. We incorporated accessible prey into an extant optimal foraging model, and found that this addition allowed opportunistic exploitation of prey that have already emerged from refugia (the leaving strategy) as a viable strategy, in addition to waiting at refugia for prey to emerge (the waiting strategy). We parameterized the model empirically for the parasitoid Macrocentrus grandii and its host, Ostrinia nubilalis, under field conditions. The model predicted that M. grandii should adopt a leaving strategy when host patch density is high (travel time between patches is short), but a waiting strategy when host patch density is low (travel time between patches is long). Field observations of M. grandii patch tenure were consistent with model predictions, indicating that M. grandii exhibited flexible behaviour based on experience within a foraging bout, and that these behavioural shifts improved foraging efficiency. Behaviour of M. grandii was responsive to heterogeneity in host emergence rates, and appeared to be driven by the relatively small proportion of the host population that became accessible at a fast rate. Therefore understanding forager responses to intermittently refuged prey may require characterization of the behaviour of a subset of the prey population, rather than the average prey individual. The model can potentially be used as a framework for comparative studies across forager taxa, to understand when foragers on intermittently accessible prey should adopt fixed waiting or leaving strategies vs. a flexible strategy that is responsive to the current environment.     

Task Partitioning in Insect Societies. I. Effect of Colony Size on Queueing Delay and Colony Ergonomic Efficiency

The collection and handling of colony resources such as food, water, and nest construction material is often divided into subtasks in which the material is passed from one worker to another. This is known as task partitioning. When material is transferred directly from one individual to another, queueing delays frequently occur because individuals must sometimes wait for a transfer partner. A stochastic simulation model was written to study the effect of colony size on these delays. Queueing delay decreases roughly exponentially with colony size because stochastic fluctuations in the arrival of individuals are lower in larger colonies. These results support empirical studies of Polybia occidentalis and other theoretical studies of honeybees. The effect of the relative number of individuals in the two subtask groups was also studied. There is a unique optimal ratio of the number of workers associated with each of the subtasks that simultaneously minimizes mean queueing delay and maximizes colony nectar-processing rate. Deviations from this optimal ratio, for example, as a result of forager mortality or changes in nectar productivity that affect foraging trip duration, increase mean queueing delays greatly, especially in smaller colonies.     

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

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

The value of fat reserves and the tradeoff between starvation and predation

It is shown that in a range of models, the probability that a forager dies from starvation is, to a good approximation, an exponential function of energy reserves. Using a time and energy budget for a 19g passerine, we explore the consequences, in terms of starvation and predation, of various levels of energy reserves. It is shown that there exists an optimal level L of reserves at which total mortality (starvation plus predation) is minimized. L increases when the environment deteriorates as a result of a decrease in either temperature or mean gross gain or an increase in the mean search time. The effect of combined deteriorations is greater than the sum of their individual effects. At L, the probability of predation is much higher than the probability of starvation. A simple analytic model suggests that this result will be fairly general, but also indicates conditions under which the result might not hold.     

Constrained Optimization of Average Arrival Time via a Probabilistic Approach to Transport Reliability

To achieve greater transit-time reduction and improvement in reliability of transport services, there is an increasing need to assist transport planners in understanding the value of punctuality; i.e. the potential improvements, not only to service quality and the consumer but also to the actual profitability of the service. In order for this to be achieved, it is important to understand the network-specific aspects that affect both the ability to decrease transit-time, and the associated cost-benefit of doing so. In this paper, we outline a framework for evaluating the effectiveness of proposed changes to average transit-time, so as to determine the optimal choice of average arrival time subject to desired punctuality levels whilst simultaneously minimizing operational costs. We model the service transit-time variability using a truncated probability density function, and simultaneously compare the trade-off between potential gains and increased service costs, for several commonly employed cost-benefit functions of general form. We formulate this problem as a constrained optimization problem to determine the optimal choice of average transit time, so as to increase the level of service punctuality, whilst simultaneously ensuring a minimum level of cost-benefit to the service operator.     

The foraging benefits of information and the penalty of ignorance

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

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

Patch use, apprehension, and vigilance behavior of Nubian Ibex under perceived risk of predation

Foraging theory predicts that animals will sacrifice feedingeffort in order to reduce predation risk. Once a forager choosesa habitat, it must decide how to allocate its foraging effort.Nubian Ibex are diurnal, social, cliff-dwelling herbivores.Many of their characteristics seem to have evolved as responsesto predation risk. In order to assess the effects that perceivedrisk of predation might have on foraging behavior of free-rangingNubian Ibex in the Negev Desert, Israel, we measured giving-updensities (GUDs) in artificial food patches and used them togauge apprehension level. (Apprehension can be defined as areduction in attention devoted to performing an activity asa consequence of reallocating attention to detecting or respondingto predation risk. A forager can also be vigilant. Vigilanceis often defined as time spent scanning the surroundings withthe head up.) We also quantified time budgeting using focalobservation of individual Nubian Ibex. Habitat preferences andpatch selectivity as a measure of apprehension were considered.In particular, we tested the effect of distance from refugeon GUDs, the effect of micropatch structure on selectivity,and the effect of distance from the refuge and group size onNubian Ibex vigilance level and apprehension. Nubian Ibex allocatetheir foraging effort more toward patches closer to the escapeterrain. At the same time, Nubian Ibex are more apprehensiveat intermediate distances from the cliff edge than nearer thecliff, and their use of vigilance increases with distance fromthe cliff edge. These results suggest that Nubian Ibex may switchfrom apprehension to a more extreme behavior of vigilance atgreater distances from the refuge. This study demonstrated theuse of antipredatory behaviors, apprehension, and vigilanceby a forager. Estimating apprehension and vigilance levels ofa forager simultaneously gives a more complete and accuratepicture of how the habitat is perceived by them and combinedwith measurements of GUD allow a more accurate assessment ofhabitat quality.