Simple models of feeding with time and enery contstraints

We analyze how the foraging currencies "rate" (net energy gainper unit time) and "efficiency" (net energy gain per unit energyexpenditure) relate to the workload adopted by a forager. Weconsider feeding (gathering food for immediate consumption)as opposed to provisioning and investigate the influence oftime and energy constraints. In our model the forager may varythe level of energy expenditure while foraging; increased expenditureincreases the rate of gain, but with diminishing returns. Weshow that rate maximizing requires a higher rate of energy expenditurethan efficiency-maximizing, and we compare the performance ofrate- and efficiency-maximizing tactics when the feeding strategyis (1) to maximize the total net gain while foraging; (2) tomaximize the total net daily gain; or (3) to meet a requirement.Generally, the rate-maximizing tactic only performs best whentime is limiting; otherwise, a lighter workload and slower feedingrate perform better. Under the restricted conditions analyzedhere, no general statement can be made about the best tacticwhen the strategy is to meet a requirement. These results mayhelp explain several instances of "submaximal" foraging describedin the literature.     

Parental provisioning in a variable environment: Evaluation of three foraging currencies and a state variable model

We estimated the reproductive success of black terns (Chlidonias niger) based on three optimal foraging currencies (maximizing the net rate of energy intake, daily delivery rate, and efficiency, respectively) and a state variable model. There was a broad range of capture intervals (the time required for the parent to capture a single prey) when the flight speeds predicted by the three currencies were so high that they resulted in daily provisioning costs which parents could not fully recover through self-feeding. Whenever the efficiency currency produced higher estimates of reproductive success, parents lost comparatively less weight than when they foraged as rate-maximizers. If parents did not experience any weight loss, the net rate and efficiency currencies made equivalent fitness projections. However, both of these currencies provided lower fitness returns than daily delivery rate at longer capture intervals. There were a number of capture intervals when estimates of reproductive success from the state variable model and at least one of the foraging currencies were equal. Provisioning behaviour under the state variable model was much more flexible and parents were therefore able to reduce their self-feeding rate on days when food was particularly scarce, thereby increasing the total delivery to the nest. This resulted in higher fitness returns than was possible under the foraging currencies. Our results suggest that efficiency-maximizing is more likely to provide fitness returns that are equivalent to the state variable model in comparison with the rate-maximizing alternatives. Furthermore, only the efficiency currency and the state variable model made predictions of flight speed that were similar to speeds measured in black tern parents provisioning young at natural nests.     

Energetic constraints and foraging efficiency

Previous research considers foraging options that differ interms of their gross rate of gain b and rate of energy expenditurec. This research argues that maximizing efficiency b/c willmaximize net energetic gain when there is an upper limit onthe amount of energy that can be assimilated. This analysisdoes not include the expenditure during the time for which theanimal is unable to forage because of this constraint. Whenthis expenditure is included, maximizing efficiency is no longeroptimal. Instead the best feeding option is the one with thehighest value of b/(c – c₁), where c, is the metabolicrate when the animal is not foraging.     

What Currency Do Bumble Bees Maximize?

In modelling bumble bee foraging, net rate of energetic intake has been suggested as the appropriate currency. The foraging behaviour of honey bees is better predicted by using efficiency, the ratio of energetic gain to expenditure, as the currency. We re-analyse several studies of bumble bee foraging and show that efficiency is as good a currency as net rate in terms of predicting behaviour. We suggest that future studies of the foraging of bumble bees should be designed to distinguish between net rate and efficiency maximizing behaviour in an attempt to discover which is the more appropriate currency.     

Pushed for time or saving on fuel: fine-scale energy budgets shed light on currencies in a diving bird

Animals may forage using different currencies depending on whether time minimization or energy maximization is more pertinent at the time. Assessment of net energy acquisition requires detailed information on instantaneous activity-specific power use, which varies according to animal performance, being influenced, for example, by speed and prey loading, and which has not been measured before in wild animals. We used a new proxy for instantaneous energy expenditure (overall dynamic body acceleration), to quantify foraging effort in a model species, the imperial shag Phalacrocorax atriceps, during diving. Power costs varied nonlinearly with depth exploited owing to depth-related buoyancy. Consequently, solutions for maximizing the gross rate of gain and energetic efficiency differed for dives to any given depth. Dive effort in free-ranging imperial shags measured during the breeding season was consistent with a strategy to maximize the gross rate of energy gain. We suggest that the divergence of time and energy costs with dive depth has implications for the measurement of dive efficiency across diverse diving taxa.     

Currencies for foraging based on energetic gain

We carry out a theoretical investigation of the behavior of a foraging animal that maximizes either the net amount of energy obtained (self-feeding) or the amount of energy delivered to another animal such as its young or to a store (provisioning). Using an novel graphical approach, we derive general results concerning the effects of constraints on the amount of energy the animal can spend or acquire. In the context of an animal that is provisioning, that is, both feeding itself and delivering energy to a given location, we establish a general relationship between the best foraging option when feeding itself and the best option to use when delivering energy. Our results extend and unify previous results in this area.     

The cost of disturbance: a waste of time and energy?

Quantifying the effect of disturbance is a central issue in conservation. Using time and energy budgets, we obtain a range of ways to assess the importance of disturbance. One measure is the time that must be spent foraging in order to balance the energy budget. From this we derive critical levels of wastage (rate of disturbance multiplied by duration of disturbance) at which the animal runs out of time or reaches a limit on energy expenditure. In the case of the time constraint, the critical wastage is the net rate of energetic gain while foraging divided by the rate of energetic expenditure during a disturbance. The associated critical rate of disturbance is the net rate of energetic gain while foraging divided by the energy spent during a disturbance. The model is illustrated using data from the African wild dog, which suffers disturbance from lions and kleptoparasitism from hyenas. Findings suggest that disturbance imposes significant costs on wild dog time and energy budgets. We show how alternative environments can be evaluated in terms of their effective rate of gain, which is the net rate of gain from foraging minus the rate of energy expenditure as a result of disturbance.     

An energetic correlate between colony size and foraging effort in seabirds, an example of the Adélie penguin Pygoscelis adeliae

Central-place foraging seabirds alter the availability of their prey around colonies, forming a "halo" of reduced prey access that ultimately constrains population size. This has been indicated indirectly by an inverse correlation between colony size and reproductive success, numbers of conspecifics at other colonies within foraging range, foraging effort (i.e. trip duration), diet quality and colony growth rate. Although ultimately mediated by density dependence relative to food through intraspecific exploitative or interference competition, the proximate mechanism involved has yet to be elucidated. Herein, we show that Adélie penguin Pygoscelis adeliae colony size positively correlates to foraging trip duration and metabolic rate, that the metabolic rate while foraging may be approaching an energetic ceiling for birds at the largest colonies, and that total energy expended increases with trip duration although uncompensated by increased mass gain. We propose that a competition-induced reduction in prey availability results in higher energy expenditure for birds foraging in the halo around large colonies, and that to escape the halo a bird must increase its foraging distance. Ultimately, the total energetic cost of a trip determines the maximum successful trip distance, as on longer trips food acquired is used more for self maintenance than for chick provisioning. When the net cost of foraging trips becomes too high, with chicks receiving insufficient food, chick survival suffers and subsequent colony growth is limited. Though the existence of energetic studies of the same species at multiple colonies is rare, because foraging metabolic rate increases with colony size in at least two other seabird species, we suggest that an energetic constraint to colony size may generally apply to other seabirds.     

To minimize foraging time,use high‐efficiency,energy‐expensive search and capture methods when food is abundant but low‐efficiency,low‐cost methods during food shortages

Based on a mathematical model, I show that the amount of food in the habitat determines which among alternative methods for search of prey, respectively, for pursuit‐and‐capture give the shortest daily foraging time. The higher the locomotor activity, the higher the rate of energy expenditure and the larger the habitat space a predator can search for prey per time unit. Therefore, I assume that the more efficient a foraging method is, the higher its rate of energy expenditure. Survival selection favors individuals that use foraging methods that cover their energy needs in the shortest possible time. Therefore, I take the optimization criterion to be minimization of the daily foraging time or, equivalently, maximization of the rate of net energy gain. When time is limiting and food is in short supply, as during food bottleneck periods, low‐efficiency, low‐cost foraging methods give shorter daily foraging times than high‐efficiency, energy‐expensive foraging methods. When time is limiting, food is abundant and energy needs are large, as during reproduction, high‐efficiency high‐cost foraging methods give shorter daily foraging times than low‐efficiency low‐cost foraging methods. When time is not limiting, food is abundant, and energy needs are small, the choice of foraging method is not critical. Small animals have lower rates of energy expenditure for locomotion than large animals. At a given food density and with similar diet, small animals are therefore more likely than large ones to minimize foraging time by using high‐efficiency energy‐expansive foraging methods and to exploit patches and sites that require energy‐demanding locomotion modes. Survival selection takes place at food shortages, while low‐efficiency low‐cost foraging methods are used, whereas reproduction selection occurs when food is abundant and high‐efficiency energy‐expensive foraging methods do better. In seasonal environments, selection therefore acts on different foraging methods at different times. Morphological adaptation to one method may oppose adaptation to another. Such conflicts select against foraging and morphological specialization and tend to give species‐poor communities of year‐round resident generalists. But a stable year‐round food supply favors specialization, niche narrowing, and dense species packing.     

Optimal foraging and beyond: how starlings cope with changes in food availability

Foraging adaptations include behavioral and physiological responses, but most optimal foraging models deal exclusively with behavioral decision variables, taking other dimensions as constraints. To overcome this limitation, we measured behavioral and physiological responses of European starlings Sturnus vulgaris to changes in food availability in a laboratory environment. The birds lived in a closed economy with a choice of two foraging modes (flying and walking) and were observed under two treatments (hard and easy) that differed in the work required to obtain food. Comparing the hard with the easy treatment, we found the following differences. In the hard treatment, daily amount of work was higher, but daily intake was lower. Even though work was greater, total daily expenditure was smaller, partly because overnight metabolism was lower. Body mass was lower, but daily oscillation in body mass did not differ. Feces' caloric density was lower, indicating greater food utilization. Energy expenditure rate expressed as multiples of basal metabolic rate (BMR) increased during the working period from 3.5 x BMR (easy) to 5.2 x BMR (hard), but over the 24-h period, it was close to 2.4 x BMR in both treatments. We also found that rate of expenditure during flight was very high in both treatments (52.3 W in easy and 45.5 W in hard), as expected for short (as opposed to cruising) flights. The relative preferences between walking and flying were incompatible with maximizing the ratio of energy gains per unit of expenditure (efficiency) but compatible with maximizing net gain per unit of time during the foraging cycle (net rate). Neither currency explained the results when nonforaging time was included. Time was not a direct constraint: the birds rested more than 90% of the time in both treatments. Understanding this complex picture requires reasoning with ecological, physiological, and cognitive arguments. We defend the role of optimality as an appropriate tool to guide this integrative perspective.     

Neandertal energetics and foraging efficiency

Mechanical interpretations of Neandertal skeletal robusticity suggest extremely high activity levels compared to modern humans. Such activity patterns imply high energy requirements; yet it has been argued that Neandertals were also inefficient foragers. The present study addresses this apparent conflict by estimating energy needs in Neandertals and then evaluating those estimates in the context of energetic and foraging data compiled for contemporary human foragers and nonhuman primates. Energy demands for Neandertals were determined by first predicting basal metabolic rates (BMR) from body weight estimates using human standards developed by the World Health Organization [FAO/WHO/UNU (1985) Energy and Protein Requirements. Report of the Joint FAO/WHO/UNU Export Committee, Geneva: WHO]. Total daily energy expenditure (kcal/day) was then estimated assuming high levels of physical activity (i.e., 2--3 x BMR), comparable to those observed among subsistence-level populations today. These estimates of energy requirements (ranging from 3000--5500 kcal/day) were then used to determine Neandertal foraging efficiency assuming (1) minimal survival-level foraging returns, and (2) daily foraging times longer than those observed among any contemporary foraging group and comparable to a nonhuman primate. Even with these extremely conservative parameters, estimates of Neandertal foraging efficiency (approximately 800--1150 kcal/h foraged) were comparable to those observed among living hunter-gatherers. These results indicate that if Neandertals did have heavy activity levels, as implied by their skeletal robusticity, they would have required foraging efficiencies within the range observed among modern groups. Thus, Neandertals could have been either highly active or poor foragers, but they could not have been both.     

Feeding and metabolic compensations in response to different foraging costs

How energetic cost of locomotion affects foraging decisions, and its metabolic consequences are poorly understood. In several groups of animals, including hermit crabs, exploratory walking enhances the efficiency of foraging by increasing the probability of finding more and better food items; however, the net gain of energy will only be enhanced if the costs of walking are lower than the benefits of enhanced food acquisition. In hermit crabs, the cost of walking increases with the mass of the shell type occupied. Thus, we expected that hermit crabs should adjust their foraging strategy to the cost of movement in different shells. We assessed the foraging, the quantity and quality of food intake, and the energetic cost of maintenance of hermit crabs paying different costs of foraging in the wild. The exploratory walking negatively correlated with shell mass, showing that hermit crabs use different foraging strategies in response to the expenditure required to move. Hermit crabs deal with high energetic costs of foraging in heavy shells by reduces their exploratory walking and overall metabolic rate, as a strategy to maximize the net energy intake. This study integrates behavioral and metabolic compensations as a response to foraging at different costs in natural conditions.     

Feeding: Models of Costs and Benefits in Energy Regulation

Models to predict feeding behavior at the level of consumptionand use of energy involve either details of internal (physiological)controls or economic principles of regulation based on optimal(evolutionary) foraging theory. These two approaches will ultimatelybe related, but the former requires more information for specificpredictions. The latter can provide predictions based on selectedcriteria for regulation. Meal sizes and feeding frequencies of hummingbirds are examinedrelative to two regulatory, criteria: maximizing rate of netenergy gain and maximizing efficiency (intakes/expenditures)through a "crop emptying" model that incorporates energy intakefrom food and energy expenditures for short-term (meal to meal)maintenance and longer-term (overnight) energy storage. Experimentalresults suggest that the feeding behavior of hummingbirds isdifferentially sensitive to short-term and daily uses of energy.Changes in overnight energy storage requirements result primarilyin changes in meal size, while changes in meal to meal maintenancerequirements result primarily in feeding frequency changes.The economic models predict these responses. The feeding behaviorof hummingbirds also appears to be sensitive to food quality,time spent flying to and from a food source, and costs associatedwith the weight of ingested food.     

The relationship between foraging behaviour and energy expenditure in Antarctic fur seals

By using time-depth recorders to measure diving activity and the doubly-labelled water method to determine energy expenditure, the relationship between foraging behaviour and energy expenditure was investigated in nine Antarctic fur seal females rearing pups. At-sea metabolic rate (MR) (mean of 6.34 ± 0.4 W. kg^-1; 4.6 times predicted BMR) was positively correlated to foraging trip duration (mean of 4.21 ± 0.54 days; r²= 0.5, P < 0.04). There were no relationships between MR and the total number of dives, the total time spent diving or the total vertical distance travelled during the foraging trip. There was, however, a close negative sigmoidal relationship (r²= 0.93) between at-sea MR and the proportion of time at sea spent diving. This measure of diving behaviour may provide a useful, inexpensive means of estimating foraging energy expenditure in this species and possibly in other otariids. The rate of diving (m.h^-1) was also negatively related to at-sea MR (r²= 0.69, P < 0.005). Body mass gain during a foraging trip had a positive relationship to the time spent at sea (r²= 0.58, P < 0.02) and the total amount of energy expended while at sea (r²= 0.72, P < 0.004) such that, while females undertaking long trips have higher metabolic rates, the energetic efficiency with which females gain mass is independent of the time spent at sea. Therefore, within the range of conditions observed, there is no apparent energetic advantage for females in undertaking foraging trips of any particular duration.     

An energy-based model of optimal feeding-territory size

An energy-based model of feeding territoriality is described. The model predicts an optimal territory size where the territory holder's net energy intake is maximized, on a daily or seasonal time scale. Simulated effects on optimal territory size of animal size, food availability, and competitor density are in general agreement with observed relationships in a wide variety of animals. When salmonid data are used to estimate the model parameter values, predicted territory sizes are similar to those actually observed. When emigration is allowed, the model predicts that territoriality, through individual selection alone, can regulate population size, but that this regulation breaks down when initial densities exceed some threshold value. Sensitivity analysis shows optimal territory size to be most affected by those parameters influencing food intake and energy expenditure. Some alternative criteria for optimization are also discussed. An animal maximizing net foraging efficiency has a smaller territory than one maximizing net energy, but the effects of animal size, food availability, and competitor density on territory size are the same in either case.     

Cost of reproduction and allocation of food between parent and young in the swift (Apus apus)

We manipulated brood sizes to promote different levels of parentaleffort in the common swift (Apus apus). This provided a powerfulmethod for testing hypotheses regarding parental investmentdecisions concerning optimal allocation strategies between parentsand young. Data were analyzed on a visit-by-visit basis regardingchanges in parental and chick body mass, the mass of prey delivered,and the estimated mass of parental self-feeding. Our resultswere consistent with current theory in that food delivery increasedwith brood size, whereas the food received per chick, and hencemean chick body mass, decreased with brood size. Parental bodymass decreased with brood size and increasing parental effortbut recovered quickly during lower levels of chick feeding immediatelybefore fledging, suggesting some short-term cost of reproduction.Parents feeding at the highest level experienced criticallylow body mass and responded by a temporary cessation of chickfeeding. On any one foraging trip, total mass of prey captureddid not differ between brood sizes, but load mass deliveredto the young was negatively related to the amount of estimatedparental self-feeding. Allocation decisions of parents feedingthemselves and their young matched differential allocation theories,but estimated provisioning efficiency of parents at differentbody masses did not suggest any adaptive advantage from parentalmass loss.     

Provisioning offspring and others: risk-energy trade-offs and gender differences in hunter-gatherer foraging strategies

Offspring provisioning is commonly referenced as the most important influence on men's and women's foraging decisions. However, the provisioning of other adults may be equally important in determining gender differences in resource choice, particularly when the goals of provisioning offspring versus others cannot be met with the acquisition of the same resources. Here, we examine how resources vary in their expected daily energetic returns and in the variance or risk around those returns. We predict that when available resources impose no trade-off between risk and energy, the targets of men's and women's foraging will converge on high-energy, low-risk resources that allow for the simultaneous provisioning of offspring and others. However, when minimizing risk and maximizing energy trade-off with one another, we expect men's foraging to focus on provisioning others through the unreliable acquisition of large harvests, while women focus on reliably acquiring smaller harvests to feed offspring. We test these predictions with foraging data from three populations (Aché, Martu and Meriam). The results uphold the predictions, suggesting that men's and women's foraging interests converge when high-energy resources can be reliably acquired, but diverge when higher-energy resources are associated with higher levels of risk. Social factors, particularly the availability of alloparental support, may also play a major role.     

Modelling social insect foraging

Foraging in the social insects can be viewed as a provisioning process, in which workers are powered by one resource (e.g. nectar) to deliver another (e.g. pollen) for the colony. The rate of delivery of a resource depends on the number of workers and how hard they work, which may depend on self-feeding rate. Whether individuals sacrifice their own foraging efficiency in favour of colony performance is unclear, as theory and experiment have not yet properly addressed these issues.     

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

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

Intraspecific variation in competitive ability and food intake in salmonids: consequences for energy budgets and growth rates

The interactions between dominance status, feeding rate and growth in rainbow trout, Salmo gairdneri Richardson, were analyzed using published data on experimental populations. There was a positive correlation between metabolic expenditure and food intake in both dominant and subordinate fish, but dominants obtained a greater intake for a given expenditure than did subordinates. Subordinates that adopted a high–return/high–cost foraging strategy actually expended more energy than they acquired, whereas those that minimized energy expenditure obtained a net energy gain. This led to the surprising finding that the growth rate of subordinates was negatively correlated with food intake.