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.     

Time and energy constraints and the relationships between currencies in foraging theory

Measured foraging strategies often cluster around values thatmaximize the ratio of energy gained over energy spent whileforaging (efficiency), rather than values that would maximizethe long-term net rate of energy gain (rate). The reasons forthis are not understood. This paper focuses on time and energyconstraints while foraging to illustrate the relationship betweenefficiency and rate-maximizing strategies and develops modelsthat provide a simple framework to analyze foraging strategiesin two distinct foraging contexts. We assume that while capturingand ingesting food for their own use (which we term feeding),foragers behave so as to maximize the total net daily energeticgain. When gathering food for others or for storage (which weterm provisioning), we assume that foragers behave so as tomaximize the total daily delivery, subject to meeting theirown energetic requirements. In feeding contexts, the behaviormaximizing total net daily gain also maximizes efficiency whendaily intake is limited by the assimilation capacity. In contrast,when time available to forage sets the limit to gross intake,the behavior maximizing total net daily gain also maximizesrate. In provisioning contexts, when daily delivery is constrainedby the energy needed to power self-feeding, maximizing efficiencyensures the highest total daily delivery. When time needed torecoup energetic expenditure limits total delivery, a low self-feedingrate relative to the rate of energy expenditure favors efficientstrategies. However, as the rate of self-feeding increases,foraging behavior deviates from efficiency maximization in thedirection predicted by rate maximization. Experimental manipulationsof the rate of self-feeding in provisioning contexts could bea powerful tool to explore the relationship between rate andefficiency-maximizing behavior.     

A guide to central place effects in foraging

We develop a general patch-use model of central place foraging, which subsumes and extends several previous models. The model produces a catalog of central place effects predicting how distance from a central place influences the costs and benefits of foraging, load-size, quitting harvest rates, and giving-up densities. In the model, we separate between costs that are load-size dependent, i.e. a direct effect of the size of the load, and load-size independent effects, such as correlations between distance and patch qualities. We also distinguish between predictions of between- and within-environment comparisons. Foraging costs, giving-up densities and quitting harvest rates should almost always increase with distance with these effects amplified by increases in metabolic costs, predation risk and load-costs. With respect to load-size: when comparing foraging in patches within an environment, we should often expect smaller loads to be taken from distant patches (negative distance–load correlation). However, when comparing between environments, there should be a positive correlation between average distance and load-size.     

What do foraging hummingbirds maximize?

Summary Hainsworth and Wolf (1976) reported that under certain conditions hummingbirds made food choices which did not maximize their net rate of energy intake while foraging. They concluded that the birds were not foraging optimally. We show here that their birds probably maximized a different utility function, the net energy per unit volume consumed (NEVC), which appears to be an optimal choice on a time scale longer than that of a foraging bout. Our own experiments with Archilochus colubris support the conclusion that hummingbirds make foraging decisions that maximize NEVC. A simulation model shows that, in nature, NEVC maximization would require fewer foraging trips and visits to fewer flowers per day to balance daily energy budgets. For territorial birds this can lead to smaller territory sizes and reduced costs of territorial defense. Plants that evolutionarily increase corolla length to enhance pollinator specificity need only increase nectar concentration slightly to maintain the same net energy per unit volume consumed (NEVC) by a given hummingbird pollinator.     

Development of net energy intake models for drift-feeding juvenile coho salmon and steelhead

We developed models to predict the effect of water velocity on prey capture rates and on optimal foraging velocities of two sympatric juvenile salmonids, coho salmon and steelhead. Mean fish size was ~80 mm, the size of age I+ coho and steelhead during their second summer in Southeast Alaska streams, when size overlap suggests that competition might be strongest. We used experimentally determined prey capture probabilities to estimate the effect of water velocity on gross energy intake rates, and we modeled prey capture costs using experimental data for search and handling times and published models of swimming costs. We used the difference between gross energy intake and prey capture costs to predict velocities at which each species maximized net energy intake rate. Predicted prey capture rates for both species declined from ~75 to 30–40 prey/h with a velocity increase from 0.30 to 0.60 m·s⁻¹. We found little difference between coho and steelhead in predicted optimum foraging velocities (0.29 m·s⁻¹ for coho and 0.30 m·s⁻¹ for steelhead). Although prey capture ability appears to be more important than are prey capture costs in determining optimum foraging velocities, capture costs may be important for models that predict fish growth. Because coho are assumed to pay a greater swimming cost due to a less hydrodynamic body form, we also modeled 10 and 25% increases in hydrodynamic drag to assess the effect of increased prey capture costs. This reduced optimum velocity by 0 and 0.01 m∙s⁻¹, respectively. Habitat segregation among equal-sized coho and steelhead does not appear to be related to the effects of water velocity on their respective foraging abilities.     

Foraging time allocation in relation to sex by the gulf coast fiddler crab (Uca panacea)

Summary Schoener (1971) proposed that the reproductive demands of animals should be important in shaping their foraging behavior because fitness is affected. He defined two forager types: energy maximizers (reproductive success depends on energetic intake) and time minimizers (reproductive success depends on time spent in activities other than foraging), and suggested that females most often illustrate the former and males the latter. We tested whether mating activities influence the foraging behavior of Uca panacea, and the predictions that females would be energy maximizers because of their reproductive strategy and that males would also be energy maximizers because of their courtship activity. Time allocated to foraging by 800 male and female fiddler crabs (at two sites) was quantified; no significant difference in foraging time was found between the sexes. Both male and female crabs allotted a large portion of their time to foraging because both sexes depend on stored energy during their reproductive bouts. Our results show that the particular forager type can be predicted based on reproductive demands, but a forager type can not always be assigned to a particular sex without consideration of all important ecological and physiological factors determining reproductive success.     

Interference competition,payoff asymmetries,and the social relationships of central place foragers

We present a central place foraging model that shows how payoff asymmetries originate in contests for access to resources. The essence of the model is that interference competition at resource points lowers the rate at which foragers can load prey, thereby depressing the rate of food delivery to the central place. We show that interference leads to asymmetric payoffs when contests involve foragers with (i) unequal travel distances between the central place and the contested resource points; (ii) inequalities in the rate of food delivery available from alternative foraging sites; (iii) differences in loading efficiency; or (iv) different abilities to interfere. We use the asymmetries to predict dominance rankings, and the patch exploitation tactics of individual foragers. We also consider the implications of the model for changes in the travel distance (= area) over which foragers can exclude competitors (= territoriality) as food density changes. Finally, incorporation of interference permits our model to predict the transition between scramble and contest competition.     

Short-term foraging costs and long-term fueling rates in central-place foraging swans revealed by giving-up exploitation times

Foragers tend to exploit patches to a lesser extent farther away from their central place. This has been interpreted as a response to increased risk of predation or increased metabolic costs of prey delivery. Here we show that migratory Bewick's swans (Cygnus columbianus bewickii), though not incurring greater predation risks farther out or delivering food to a central place, also feed for shorter periods at patches farther away from their roost. Predictions from an energy budget model suggest that increasing metabolic travel costs per se are responsible. Establishing the relation between intake rate and exploitation time enabled us to express giving-up exploitation times as quitting harvest rates (QHRs). This revealed that net QHRs were not different from observed long-term net intake rates, a sign that the birds were maximizing their long-term net intake rate. This study is unique because giving-up decisions were measured at the individual level, metabolic and predation costs were assessed simultaneously, the relation with harvest rate was made explicit, and finally, short-term giving-up decisions were related to long-term net intake rates. We discuss and conceptualize the implications of metabolic traveling costs for carrying-capacity predictions by bridging the gap between optimal-foraging theory and optimal-migration theory.     

Foraging behavior and morphology: seed selection in the harvester ant genus, Pogonomyrmex

Optimally foraging animals can be behaviorally or morphologically adapted to reduce the energetic and time costs of foraging. We studied the foraging behavior and morphology of three seed harvester ant species, Pogonomyrmex barbatus, P. desertorum, and P. occidentalis, to determine the importance of behavioral strategies and morphological features associated with load carriage in reducing the costs of foraging. We found that none of five morphological features we measured had a significant impact on seed selection. Also, body size did not influence running speed, an important variable in time costs of foraging. Temperature had the largest effect on running speed in these species. Our results show that these species have foraging strategies which minimize the time costs of traveling with seeds. We also describe a pattern where the running speed in individual-foraging species is less affected by increasing seed size than in trunk-trail foragers, when temperature and body mass are held constant. These results support previous work which showed that time costs are most important in seed selection for Pogonomyrmex, and suggest that central place foraging theory may need to accommodate variation in foraging strategy to more accurately predict optimal seed size selection in harvester ants. Received: 16 June 1997 / Accepted: 15 December 1997     

Distinguishing Energy Maximizers from Time Minimizers: A Comparative Study of Two Hummingbird Species

SYNOPSIS. The potential reproductive success of a food energymaximizer increases with foraging time, while that of a foragingtime minimizer increases with time spent in nonforaging activitiesgiven a set energy requirement has been met. How can these foraging"goals" be distinguished for nonbreeding animals in the field?If individuals of two species occupying the same habitat consumethe same foods, face similar foraging constraints, and havesimilar meal sizes (food intake per foraging bout), then relativeto a time minimizer, an energy maximizer should: (1) spend moretime foraging, with greater foragingbout frequency, but no differencein foraging-bout duration; (2) spend less time sitting, withlower sitting-bout duration yet greater sitting-bout frequency;(3) gain mass more rapidly, if net energy intake results inmass accumulation; and (4) exhibit no other differences in timebudgeting. These assumptions and predictions were verified bypopulation- and individual-level comparisons of immature malesof two species of nectar-feeding hummingbirds studied over threefield seasons. The results suggest that, relative to each other,migrant Rufous Hummingbirds are energy maximizers and nonmigrantCosta Hummingbirds are time minimizers. Despite significantdifferences in time budgeting, by far the most striking differencebetween the species was that the Rufous gained mass four toeight times as rapidly as the Costa. This was due to the Rufousentering torpor at night, resulting in relatively little overnightloss in body mass. These patterns underscore the importanceof measuring net energy intake as directly as possible (in thiscase by fat accumulation) in testing foraging theory. Indirectmeasures (such as time budgets) may not always provide the resolutionnecessary to detect important energetic differences betweendifferent foragers.     

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.     

Central place foraging by swallows (Hirundinidae): The question of load size

Some predictions of Orians & Pearson's (1979) models for central place foragers (CPF) were tested with three species of swellows (Hirundinidae). House martins (Delichon urbica) and sand martins (Riparia riparia) brought larger food loads to the nest mainly when foraging distances were great, whereas swallows (Hirundo rustica) gathered large loads when food was plentiful. For all three species the outcome conformed qualitatively with the predictions of the CPF models. Overall, house martins were the most sensitive to travel time effects, but in a quantitative test the predicted load size was 20–40% less than the observed size for a range of realistic travel times. Additional models are presented which emphasize the significance of foraging techniques and foraging costs for optimal load size in multiple prey loaders.     

经济学思想和方法在行为生态学中的应用

从经济学观点看,动物的任何一种行为都是一种投资,同时又能获得一定的收益。进化和自然选择将趋于使动物行为的净收益增至最大,这种思想也是组建行为生态学最适模型的基础。如果为海滨蟹提供各种大小不同的贻贝任其选食的话,那么它所选食的贻贝大小往往能使它得到最大的能量净收益。为了精确地计算捕食者应当吃多少不同大小的食物,就需要建立一个最适模型。当动物领域行为的收益大于投资时,自然选择就会促进这种行为的产生和发展,而最佳领域大小则可借助于建立经济模型进行预测。将饥饿风险降至最小的原则可应用于动物的觅食决策。绒斑啄木鸟在觅食时可利用它们所收集的信息使其食物摄取率达到最大。     

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.     

Time Budgets and Territory Size: Some Simultaneous Optimization Models for Energy Maximizers

A set of optimization models in two variables of choice, territorysize and time spent patrolling for intruders, is presented forenergy maximizers. Models vary in the curvilinearity of therelationship between territory circumference and both intrusionrate and cost of expelling a single intruder. Models are analyzedboth with and without constraints; constraints are on processingrate and on the time spent patrolling, feeding and activelydefending. The models all include the concept of "intruder equilibrium,"an equilibrial density of intruders in a territory resultingfrom a balance between intrusion rate and expulsion by the defender.This equilibrial density can be considered a measure of territorialexclusiveness. The two-variable models predict effects on territory size andpatrol time of variation in food density, intrusion rate, costsof expelling a single intruder in energy and time, food-consumptionrate of an intruder, area of detection while patrolling, totaltime available for territorial and feeding activities, timeto eat a unit of food energy, energy cost of patrol per time,and processing-rate capacity. With increasing intruder rate,optimal territory size usually decreases, whereas optimal patroltime behaves much more irregularly. With increasing food density,optimal patrol time usually decreases, whereas optimal territorysize behaves irregularly. In particular, when intrusion rateand expulsion costs accelerate sufficiently with increasingterritory size and no constraints exist, the higher the fooddensity the smaller the optimal territory size. When food densityis large enough for a constraint to be effective, the oppositerelation can hold and will always hold for a processing constraint. When a particular parameter changes, optimal territory sizeand optimal patrol time may covary or one may increase whilethe other decreases, depending on the parameter and model. A new set of one-variable models is suggested by the two-variablemodels; models optimizing patrol time while holding territorysize constant could correspond to a tightly packed system ofterritories initially determined by settlement patterns. A unifiedonevariable analysis suggests that how food density affectsterritory size when patrol time is constant depends upon whethera constraint is operating: Provided that invasion rate doesnot vary with density of intruders on the territory, time minimizersand constrained energy maximizers decrease territory size withincreasing food density; unconstrained energy maximizers dothe opposite. The addition of a second optimization variable to a one-variablemodel can change qualitative predictions about variation inparticular parameters (e.g., food density) and can increasethe number of parameters predicted to affect optimal territorysize and patrol time.     

Optimal foraging area: Size and allocation of search effort

A model is derived for the optimal spatial allocation of foraging effort for an animal returning with food to a central place in a uniform habitat. The forager is assumed to maximize its yield of food during a given period. Foraging effort is expended on search for food, and on transportation to the central place. It is shown that the allocation of search has been optimal if and only if the “marginal cost” of additional food is equal throughout the foraging area when the period has elapsed. The model is used to predict the optimal area radius and allocation of search time. With realistic parameter values, the optimal time per unit area roughly decreases linearly with the distance from the central place. The influence of food density and forager characteristics is examined.     

Population dynamics and the ecological stability of obligate pollination mutualisms

Mutualistic interactions almost always produce both costs and benefits for each of the interacting species. It is the difference between gross benefits and costs that determines the net benefit and the per-capita effect on each of the interacting populations. For example, the net benefit of obligate pollinators, such as yucca and senita moths, to plants is determined by the difference between the number of ovules fertilized from moth pollination and the number of ovules eaten by the pollinator's larvae. It is clear that if pollinator populations are large, then, because many eggs are laid, costs to plants are large, whereas, if pollinator populations are small, gross benefits are low due to lack of pollination. Even though the size and dynamics of the pollinator population are likely to be crucial, their importance has been neglected in the investigation of mechanisms, such as selective fruit abortion, that can limit costs and increase net benefits. Here, we suggest that both the population size and dynamics of pollinators are important in determining the net benefits to plants, and that fruit abortion can significantly affect these. We develop a model of mutualism between populations of plants and their pollinating seed-predators to explore the ecological consequences of fruit abortion on pollinator population dynamics and the net effect on plants. We demonstrate that the benefit to a plant population is unimodal as a function of pollinator abundance, relative to the abundance of flowers. Both selective abortion of fruit with eggs and random abortion of fruit, without reference to whether they have eggs or not, can limit pollinator population size. This can increase the net benefits to the plant population by limiting the number of eggs laid, if the pollination rate remains high. However, fruit abortion can possibly destabilize the pollinator population, with negative consequences for the plant population.     

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.     

Why do some nectar foragers perch and others hover while probing flowers?

Diurnal hawkmoths, Hemaris fuciformis, and bumblebees, Bombus pasquorum, were observed foraging for nectar in flowers of Viscaria vulgaris. The hawkmoths hovered in front of the flowers, while the bees perched on them. The hawkmoths had a faster probing rate than the bees, and consequently also had higher gross and net rates of energy gain. A model is presented that shows that hovering only yields a higher net rate of energy gain (NREG) than perching when nectar volumes are high due to low competition for the resource. The difference in NREG of perchers and hoverers decreases with an increase of competition, and eventually perching yields the highest NREG. This is an effect of the higher cost of hovering. The results suggest that hovering can only evolve as a pure evolutionarily stable strategy (ESS) if competition is reduced, for example by co-evolutionary specializations with plants. The possibility that it has evolved as a mixed ESS (i.e. individuals can both hover and perch depending on the resource level) is discussed. The evolution of optimal foraging strategies is discussed, and it is pointed out that the rate of gain of an animal is independent of the strategy used when all competing foragers use the same strategy, but competitively superior strategies will nevertheless evolve because they are ESSs. Competition between strategies with different energy costs are special, because resource availability determines which strategy is competitively superior. A high-cost strategy can only evolve as a pure ESS at high resource levels, or as a mixed ESS at intermediate levels.     

Snowshoe hare optimal foraging and its implications for population dynamics

The results of an optimal foraging model using linear programming with constraints for feeding time, digestive capacity, sodium requirements, and energy requirements indicate that snowshoe hare (Lepus americanus) may forage as energy maximizers. The solution provides the quantities of major food classes (leaves, herbs, fungus, twigs) included in the diet. The species composition of each diet class also is determined using a simultaneous search model based upon the probability of encounter, the probability of sufficient item size, and the probability of sufficient quality. The results also indicate that hare life history parameters (weaning size, size at first reproduction, average adult size) and potential demographic changes in hare populations may be controlled by foraging considerations.