Central-place foraging in honey bees: the effect of travel time and nectar flow on crop filling

Summary Crop-filling by honeybees foraging at sources of variable nectar flow at a fixed distance from the hive has been shown to maximize energetic efficiency, defined as ratio of energy gained to energy spent. Predictions based on maximisation of rate of energy gain, defined as net energy gained per unit time foraging, are significantly different from observed behaviour (Schmid-Hempel et al. 1985). In this paper we consider the effect of varying travel times in addition to flow rate. The predictions of an extended version of our theoretical model are confronted with experimental results obtained by Núñez (1982). Núñez found that bees filled their crops more fully for higher flows and longer travel times. We show that when the cost of carrying a load is considered, this trend can be predicted by maximising either energetic efficiency or net rate of gain. Figure 1 shows, however, that maximisation of net rate of gain can only produce an acceptable quantitative fit if unreasonably high costs are assumed to result from carrying the load. Energetic efficiency instead generates a good quantitative fit for acceptable assumptions about this cost (Fig. 2).     

Energetic and time costs of foraging in harvester ants,Pogonomyrmex occidentalis

Summary Western harvester ants, Pogonomyrmex occidentalis, preferentially utilize low vegetational cover pathways. Energetic costs for foraging ants were less than 0.1% of caloric rewards of harvested seeds, suggesting that reduction of energetic cost is not a major benefit of this preference. Walking speed was significantly faster on lower cover routes, increasing net return rates from equidistant artificial food sources. Undisturbed foragers on low cover routes traveled farther, increasing their total foraging area without increasing foraging time. These results suggest that in animals with low costs of locomotion relative to energetic rewards, time costs are more important than direct energetic costs in influencing foraging decisions. In baited experiments with equidistant food sources, preferential use of low cover routes resulted in a large increase in net energetic gain rate, but only a slight increase in energetic efficiency. Under natural conditions, net energetic gain rates were constant for foragers using low and high vegetational cover routes, but foragers using low cover paths had lower efficiencies. This suggests that net energetic gain rate is a more important currency than energetic efficiency for foraging harvester ants.     

Self-organization in collective honeybee foraging: emergence of symmetry breaking,cross inhibition and equal harvest-rate distribution

De Vries and Biesmeijer described in 1998 an individual-oriented model that simulates the collective foraging behaviour of a colony of honeybees. Here we report how this model has been expanded and show how, through self-organization, three colony-level phenomena can emerge: symmetry breaking, cross inhibition and the equal harvest-rate distribution. Symmetry breaking is the phenomenon that the numbers of foragers visiting two equally profitable food sources will diverge after some time. Cross inhibition is the phenomenon that, by increasing the profitability of one of two equal food sources, the number of foragers visiting the other source will decrease. In some circumstances, the bees foraging on two sources of different profitabilities will be distributed between these sources such that the two average energy harvest rates are equal. We will refer to this phenomenon as the equal harvest-rate distribution. For each of these three phenomena, we show what the necessary behavioural rules to be followed by the individual forager bees are, and what the necessary circumstances are (that is, what values the model parameters should take) in order for these phenomena to arise. It seems that patch size and forager group size largely determine when each of these phenomena will arise. Experimenting with two types of currency, net gain rate and net gain efficiency, revealed that only gain rate may result in an equal harvest-rate distribution of foragers visiting different food sources.     

What currency do scatter-hoarding gray jays maximize?

Gray jays (Perisoreus canadensis) cache thousands of food items during each summer for use during the subsequent winter. Previous work on the economics of gray jay scatter-hoarding behavior was based on the assumption that the jays maximize the rate at which they store food energy; alternative currencies were not considered. Here we develop and test models based on two currencies, net rate (net recoverable energy stored per unit time) and efficiency (recoverable energy stored per unit energy expended). Our experiment involved providing gray jays with two options. After collecting a single food item upon arrival at a feeding apparatus, a jay could wait for two additional food items to become (simultaneously) available and then transport all three items for storage in scattered arboreal sites. Alternatively, the jay could immediately transport the single item to a storage site and return to the source repeatedly for additional single-item loads. By incrementally increasing the amount of time jays were required to wait for multipleitem loads, we were able to determine how long jays would wait before switching from multiple- to single-item caching trips. In contrast with the finding in a variety of species that efficiency-maximization models provide a better account of foraging behavior, the net rate-maximization model was a better predictor of the jays' switching point than was the efficiency-maximization model (Figs. 2 and 3). We discuss these conflicting results in the context of recent theory that describes the conditions favoring rate- versus efficiency-maximizing behavior (Ydenberg et al. 1994). Offprint requests to: T.A. Waite     

Feeding behavior of the sea star Astropecten articulatus (Echinodermata: Asteroidea): an evaluation of energy-efficient foraging in a soft-bottom predator

The energy efficiency of the foraging behavior of Astropecten articulatus (Say) was evaluated in the laboratory. Individuals utilized in the study were collected in the northern Gulf of Mexico from 1990 to 1992. Sea stars presented with equal numbers and weights of low-quality and high-quality prey consistently selected prey of the higher quality. Choice of prey appeared to be mediated by contact chemoreception. Individuals presented with equal weights or equal numbers of different-sized prey models demonstrated a significant preference for smaller prey. Size-selective feeding may be attributable to the ease of manipulation and ingestion of smaller prey, which mazimizes food intake per unit time. In the absence of prey, A. articulatus exhibited a directional pattern of movement. However, as prey were encountered, both the frequency and magnitude of angular deviations in the foraging path increased, resulting in increased foraging in areas of higher prey density. This response to prey availability may increase foraging efficiency by maximizing the rate of prey encounter. Like four other species of the genus Astropecten, A. articulatus exhibited two peaks of activity corresponding with dawn and dusk. Diurnal activities with periods of increased prey availability or periods during which predators are diminished or absent. The sea star A. articulatus exhibits foraging behaviors consistent with the maximization of net energy intake per unit foraging time.     

Avian flocking reduces starvation risk: an experimental demonstration

Summary Theory suggests that variance in individual food intake is lower during group foraging. Consequently, group foraging can at times reduce starvation risk. In aviary experiments using green-finches we demonstrate how intake variability decreases during group foraging because individuals use feeding by flock mates as a cue to locate food (local enhancement). Flocking preferences of greenfinches responded to variance in energy gain as predicted by theoretical models for foragers attempting to reduce starvation risk. While energy budget was positive the greenfinches were risk averse and foraged socially. Their preference shifted towards more risk prone solitary foraging when kept on a negative energy budget. We conclude that time or energy net gains are not necessary for foraging groups to form, but reductions in starvation risk may be sufficient.     

The choice of two prey types that minimises the probability of starvation

Summary In this paper we investigate the optimal diet of a forager faced with two prey types. Classical optimal foraging theory, based on the maximization of the mean net rate of energetic gain , predicts that the optimal policy is either to take only the more profitable prey type or to take both prey types. The decision between these policies does not depend on the forager's energy reserves or the time available for foraging. We develop two alternative models, based on the minimization of the probability of starvation. In the first model, foraging occurs continuously, and it is optimal to take a prey type if and only if it increases the forager's energy reserves. In the second model foraging stops at dusk, and the forager dies during the night if its reserves at dusk are too low. The optimal policy, which has to be found numerically by dynamic programming, depends on the forager's reserves and the time left till dusk. In general the optimal policy is either to take both types or to take only the more profitable type. Taking both types is optimal when reserves are low, and there is some evidence that this occurs. The models show that factors that have been ignored in classical models may be of importance.     

Determinants of seed removal distance by scatter-hoarding rodents in deciduous forests

Scatter-hoarding rodents should space food caches to maximize cache recovery rate (to minimize loss to pilferers) relative to the energetic cost of carrying food items greater distances. Optimization models of cache spacing make two predictions. First, spacing of caches should be greater for food items with greater energy content. Second, the mean distance between caches should increase with food abundance. However, the latter prediction fails to account for the effect of food abundance on the behavior of potential pilferers or on the ability of caching individuals to acquire food by means other than recovering their own caches. When considering these factors, shorter cache distances may be predicted in conditions of higher food abundance. We predicted that seed caching distances would be greater for food items of higher energy content and during lower ambient food abundance and that the effect of seed type on cache distance variation would be lower during higher food abundance. We recorded distances moved for 8636 seeds of five seed types at 15 locations in three forested sites in Pennsylvania, USA, and 29 forest fragments in Indiana, U.S.A., across five different years. Seed production was poor in three years and high in two years. Consistent with previous studies, seeds with greater energy content were moved farther than less profitable food items. Seeds were dispersed less far in seed-rich years than in seed-poor years, contrary to predictions of conventional models. Interactions were important, with seed type effects more evident in seed-poor years. These results suggest that, when food is superabundant, optimal cache distances are more strongly determined by minimizing energy cost of caching than by minimizing pilfering rates and that cache loss rates may be more strongly density-dependent in times of low seed abundance.     

Energy use and animal abundance in litter and soil communities

Tools from metabolic scaling and food web theory were used to construct a general model of carbon flux by litter and soil invertebrates. The flux model was used to explore the energetic basis of invertebrate abundance and predicted that abundance should (1) scale linearly with net primary production; (2) be related to the body mass of animals as a power function, with an exponent between -0.65 and -0.85; (3) be related to the average body temperature of animals according to the Boltzmann factor, with an activation energy between 0.27 and 0.79 eV; and (4) decrease by a factor of 0.05 to 0.15 across trophic levels due to gross production efficiency of prey. Model predictions were generally supported by a global data set on invertebrate abundance that was amassed during the International Biological Programme, indicating that fundamental energetic principles explain a large degree of variation in invertebrate abundance across the globe.     

Net energy versus efficiency maximizing by foraging ring-billed gulls

Summary Ring-billed gulls (Larus delawarensis) breeding at Dog Lake, Manitoba often feed by following tractors pulling cultivating implements around fields. Tractor-following gulls always land immediately behind the cultivating implement, where they feed on earthworms or grain. Afeer a feeding bout on the ground (patch residence time), gulls fly up, pursue the tractor and repeat the cycle. We use net energy maximizing (energy gained per unit time) and efficiency maximizing (energy gained per unit energy expended) models to make quantitative predictions of patch residence time, and compare these predictions to observations. If we assume flight speed to be constrained at the observed mean, the observations fall between the predictions of the two models, and the models explain approximately equal and highly significant proportions of the overall variation in patch residence time. If both flight speed and patch residence time are allowed to vary in the models, the efficiency maximizing model more closely predicts observed patch residence times, and the net energy maximizing model more closely predicts observed flight speeds. We discuss whether breeding ringbilled gulls may be truly intermediate between net energy and efficiency maximizing, and how measurements of flight speed may be useful in further investigations.     

On the integration of individual foraging strategies with colony ergonomics in social insects: nectar-collection in honeybees

Summary We experimentally tested whether foraging strategies of nectar-collecting workers of the honeybee (Apis mellifera) vary with colony state. In particular, we tested the prediction that bees from small, fast growing colonies should adopt higher workloads than those from large, mature colonies. Queenright small colonies were set up by assembling 10 000 worker bees with approximately 4100 brood cells. Queenright large colonies contained 35 000 bees and some 14 500 brood cells. Thus, treatments differed in colony size but not in worker/brood ratios. Differences in workload were tested in the context of single foraging cycles. Individuals could forage on a patch of artificial flowers offering given quantities and qualities of nectar rewards. Workers of small colonies took significantly less nectar in an average foraging excursion (small: 40.1 ± 1.1 SE flowers; large: 44.8 ± 1.1), but spent significantly more time handling a flower (small: 7.3 ± 0.4 s ; large: 5.8 ± 0.4 s). When the energy budgets for an average foraging trip were calculated, individuals from all colonies showed a behavior close to maximization of net energetic efficiency (i.e., the ratio of net energetic gains to energetic costs). However, bees from small colonies, while incurring only marginally smaller costs, gained less net energy per foraging trip than those from large colonies, primarily as a result of prolonged handling times. The differences between treatments were largest during the initial phases of the experimental period when also colony development was maximally different. Our results are at variance with simple models that assume natural selection to have shaped behavior in a single foraging trip only so as to maximize colony growth. Offprint requests to: P. Schmid-Hempel     

Predicting national sustainability: The convergence of energetic,economic and environmental realities

The “constraint space” dictated by energetic, economic and environmental realities on scenarios for future organization of humanity and nature is explored from the perspective of the energy and resources driving economies. Net energy of energy sources is presented as an index (Emergy Yield Ratio; EYR) that must be evaluated for energy sources to better understand their potential contributions to society, but more important, as an indicator of the changes needed in the future if lower net yielding sources are to be relied upon. An aggregate EYR was calculated for the USA economy and shown to have decreased by 38% since 1950, from 11/1 to 6.8/1. Several measures of efficiency at the scale of national economies are explored and the data suggest that the most efficient economies are also the most energetically intense (as measured by empower intensity). An index of environmental loading is suggested as a measure to evaluate environmental efficacy. An obvious outcome is that the smallest most energetically intense countries have the highest environmental loads, and those with large land area and/or continental shelves have the lowest ratios. An Emergy Sustainability Index (EmSI) is defined, computed for countries, and proposed as a multi-dimensional measure of long-term sustainability. The most sustainable economies are those with the highest EYR and lowest environmental loads.     

Ideal free distributions under predation risk

 We examine the trade-off between gathering food and avoiding predation in the context of patch use by a group of animals. Often a forager will have to choose between feeding sites that differ in both energetic gain rate and predation risk. The ideal site will have a high gain rate and low risk of predation. However, intake rate will often decrease when the patch is shared with other foragers and it may be optimal for some individuals to feed elsewhere. Within the framework of ideal free theory, we investigate the distribution of foragers that will equalise individual fitness gains. We focus on a two-patch environment with continuous inputs of food. With reference to existing experimental studies, we examine the effects of risk dilution, food input rates and an animal’s expectations of the future. We identify the effect of total animal numbers when one patch is subject to predation risk and the other is safe. Conditions under which the difference in intake rate in the two patches is constant are identified, as are conditions in which the ratio of animals in the two patches is constant. If current conditions do not alter future expectations an increase in input rates to the patches promotes increased use of the risky patch. Yet, if conditions are assumed to persist indefinitely the opposite effect is seen. When both patches are subject to predation risk, dilution of risk favours more extreme distributions, and may lead to more than one stable distribution. The results of these models are used to critically analyse previous work on the energetic equivalence of risk. This paper is intended to help guide the development of new experimental studies into the energy-risk trade-off. Received: 10 February 1995/Accepted after revision: 1 October 1995     

Social foraging by honeybees: how colonies allocate foragers among patches of flowers

Summary To understand how a colony of honeybees keeps its forager force focussed on rich sources of food, and analysis was made of how the individual foragers within a colony decide to abandon or continue working (and perhaps even recruit to) patches of flowers. A nectar forager grades her behavior toward a patch in response to both the nectar intake rate of her colony and the quality of her patch. This results in the threshold in patch quality for acceptance of a patch being higher when the colonial intake rate of nectar is high than when it is low. Thus colonies can adjust their patch selectivity so that they focus on rich sources when forage is abundant, but spread their workers among a wider range of sources when forage is scarce. Foragers assess their colony's rate of nectar intake while in the nest, unloading nectar to receiver bees. The ease of unloading varies inversely with the colonial intake rate of nectar. Foragers assess patch quality while in the field, collecting nectar. By grading their behavior steeply in relation to such patch variables as distance from the nest and nectar sweetness, foragers give their colony high sensitivity to differences in profitability among patches. When a patch's quality declines, its foragers reduce their rate of visits to the patch. This diminishes the flow of nectar from the poor patch which in turn stimulates recruitment to rich patches. Thus a colony can swiftly redistribute its forager force following changes in the spatial distribution of rich food sources. The fundamental currency of nectar patch quality is not net rate of energy intake, (Gain-Cost)/Time, but may be net energy efficiency, (Gain-Cost)/Cost.     

Food abundance affects energy intake and reproduction in frugivorous female Assamese macaques

In most mammals, female fertility and reproduction are strongly influenced by nutritional status and, therefore, by foraging conditions. Here, we investigate the relationship between food resources, feeding competition, energy intake and reproduction in a group of wild female Assamese macaques (Macaca assamensis) in northeastern Thailand. Over 2,100 h of data on feeding behaviour, energy intake and activity budgets were combined with data on resource characteristics, female reproduction and physical condition. We found that an increase in food availability had a positive effect on female energy intake and conception rates. In addition, it appeared that females incurred energetic costs during lactation and that females with a better physical condition during the mating season were more likely to conceive. The annual birth season occurred a few months before the annual peak in food availability, causing peak lactation to coincide with a period of high food availability. This suggests that females use the increased food abundance to compensate for the energetic costs of lactation. Neither energy intake rates nor activity budgets were influenced by female dominance rank, even during periods when the levels of contest competition were predicted to be high. In line with this, we found no evidence for rank-related differences in reproduction. The apparently limited influence of feeding competition in female Assamese macaques adds to the debate on the extent to which patterns in feeding competition and fitness can reliably be predicted based on ecological conditions. We suggest that this may partially be resolved by including potential competition-reducing mechanisms into the predictive framework.     

杉木观光木混交林群落的能量生态

对杉木观光木混交林群落能量的研究结果表明：混交林中观光木地上部分灰分含量以皮最高,而杉则以叶最高,两者GCV（干重热值）和AFCV（去灰分热值）均以叶为最高;观光木、杉木地下各部分的灰分含量均随径级的减小而增加,GCV均以粗根最高,细根最低;观光木的平均灰分含量高于杉木,但GCV和AFCV均低于杉木;从乔木层、灌木层到草本层,灰分含量依次增加,GCV和AFCV则依次降低,混交林群落的能量现存量公占群落的很小一部分,而其能量年净增量、归还量和净固定量却占有一定比重,混交林群落的太阳能转化率为1.57%,而纯林为1.44%,表明杉观混交林是一种能量生产力较高和维持地力能力较强的杉阔混交类型。同时,混交林的能量累积比大于纯林,能量流动速率则低于纯林;乔木层的能量累积比高于林下植被,能量流动速率则低于林下植被,从能量的角度看,构建合理的群落结构必须选择高能量累积比的乔木层树种,同时须促进能量流动速率快的林下植被的发育以维持和提高地力。     

Integrated modelling of foraging behaviour, energy budget and memory properties

A predator's foraging performance is related to its ability to acquire sufficient information on environmental profitability. This process can be affected by the patchy distribution and clustering of food resources and by the food intake process dynamics.We simulated body mass growth and behaviour in a forager acting in a patchy environment with patchy distribution of both prey abundance and body mass by an individual-based model. In our model, food intake was a discrete and stochastic process and leaving decision was based on the estimate of net energy gain and searching time during their foraging activities. The study aimed to investigate the effects of learning processes and food resource exploitation on body mass and survival of foragers under different scenarios of intra-patch resource distribution.The simulation output showed that different sources of resource variability between patches affected foraging efficiency differently. When prey abundance varied across patches, the predator stayed longer in poorest patches to obtain the information needed and its performance was affected by the cost of sampling and the resulting assessment of the environment proved unreliable. On the other hand, when prey body mass, but not abundance, varied among the patches the predator was quickly able to assess local profitability. Both body mass and survival of the predator were greatly affected by learning processes and patterns of food resource distribution.     

Proximate mechanisms of contest competition among female Bwindi mountain gorillas (Gorilla beringei beringei)

Socioecological models provide a framework for predicting how animals respond competitively to the abundance and distribution of food resources. Testing predictions of socioecological models requires analysis of relationships among food resource characteristics, competitive behaviors, and measures of rank-related skew in energy balance or reproductive success. A positive relationship between dominance rank and energy balance has been observed among female mountain gorillas in Bwindi Impenetrable National Park, Uganda. This study examines the proximate mechanisms underlying feeding competition among those females. To assess the contestability of food resources, we measured the time a female spent feeding at a food site (food site residence time). We also examined the relationship between dominance rank and the access to resources, as well as the rate, context, and direction of aggression, and the number of neighbors in close proximity. As predicted, females had longer food site residence times and higher aggression rates with fruit and decaying wood than with herbaceous vegetation, suggesting that those resources may be contestable. Aggression was predominantly directed down the dominance hierarchy, although against expectation, rank was not significantly correlated with aggression rates or the time spent feeding on contestable foods. Higher-ranking females had significantly fewer neighbors, suggesting that lower-ranking females avoid higher-ranking ones. This study provides additional support for the claim that there is variability in how primates respond to the quality and distribution of food resources and that avoidance as a strategy to cope with feeding competition may result in similar skew in energy balance as rank-related aggression.     

Courtship display by great frigatebirds, Fregata minor: an energetically costly handicap signal?

We used detailed time-budget observations, mark-resight data, and doubly labeled water estimates of energy expenditure to test whether energy spent on courtship display by male frigatebirds functions as a sexually selected handicap signal. During a 2-day period of time budget observations, males displayed on average 29.5% of the time (range 0–100% for 15 different males), and this value was correlated with an index of season-long display effort. Season-long display effort was strongly predictive of pairing success. Average field metabolic rate (FMR) during the 2-day time budget period was 676.5 kJ/day (range 464.8–1035.0), substantially lower than the mass-specific FMR predicted from studies of other seabirds during incubation or chick-rearing. Despite a low overall FMR, display effort could function as an energetic handicap, either if FMR correlates positively with the amount of courtship performed or if high-quality males display at a high rate because they pay a lower energy cost per unit of display than do low-quality males. We found no relationship between FMR and display rate, despite good power for doing so. We also did not find a significant difference in energy spent divided by courtship time for males that were or were not chosen by females (inferred to be high- and low-quality males, respectively), though the medians differed in the predicted direction (preferred males having lower relative costs than non-preferred males) and the confidence interval on the difference between groups was very wide. Thus, we found evidence that male courtship effort is predictive of pairing success, we rejected one mechanism by which energetic cost of display could function as a handicap, and our test of the alternate energetic handicap mechanism was equivocal.     

Giving-updensity and dietary shifts in the white-footed mouse, Peromyscus leucopus

Dietary shifts are commonly exhibited by omnivorous consumers when foraging from variable food resources. One advantage of dietary shifts for a consumer is the ability to gain complementary resources from different foods. In addition, dietary shifts often affect food-web dynamics. Despite the importance of dietary shifts to organismal, community, and ecosystem ecology, empirical studies of the ecological mechanisms that control dietary shifts are limited in scope. In this study, we tested the effects of complementary resources on dietary shifts of an omnivorous mammal, the white-footed mouse Peromyscus leucopus, in the context of depletable food patches in the natural environment. We used two complementary resources: seeds that provide a higher energy gain per unit handling time and mealworms that provide a higher protein gain per unit handling time. Stable isotopes of carbon and nitrogen (delta13C, delta15N) in mouse plasma were used to quantify dietary shifts, and we determined giving-up density (GUD), the food density at which a forager leaves a food patch (for an optimal forager, it should correspond to the quitting harvest rate that balances net fitness gain with various costs of foraging). The results showed that GUD increased most significantly when a mixture of seeds and mealworms was added, compared to when only seeds or mealworms were added. This suggests that, given a similar level of food availability, a patch with a mixture of complementary foods is of higher quality than a patch with only one type of food. Moreover, GUD measured with seeds (GUDs) correlated positively with seed availability, and GUD measured with mealworms (GUDmw) correlated positively with mealworm availability, indicating that the marginal value of seeds or mealworms decreases with their relatively availability in the environment. As GUDs increased, P. leucopus shifted their diets toward higher trophic levels, and as GUDmw increased, P. leucopus shifted their diets toward lower trophic levels, suggesting dietary shifts driven by food complementarity. This study demonstrated that the combination of giving-up density and stable-isotope analysis holds great potential for testing ecological mechanisms underlying dietary shifts.