An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees

1. A model is described that evaluates the maximum economic foraging range in central place foragers by using optimality criteria to discriminate between foraging sites at different distances from the forager's central place. 2. The basic model can be varied to suit foragers that optimise either their rate of net energy uptake or their foraging efficiency. 3. The model requires specification of the time and energy budgets of travel and foraging, and of the rewards obtainable at potential foraging sites. 4. The specific case of bumblebees, whose foraging ranges are poorly known, is considered. 5. Numerical solutions of the model for parameter values that represent bumblebees and their forage predict economic foraging ranges exceeding several kilometres. The model demonstrates that economics alone can explain extensive flight ranges in bees.     

Effects of group size and group density on trade-offs in resource selection by a group-territorial central-place foraging woodpecker

Trade-offs in resource selection by central-place foragers are driven by the need to balance the benefits of selecting resources against the costs of travel from the central place. For group-territorial central-place foraging birds, trade-offs in resource selection are likely to be complicated by a competitive advantage for larger groups at high group density that may limit accessibility of high-quality distant resources to small groups. We used the group-territorial, central-place foraging Red-cockaded Woodpecker Leuconotopicus borealis (RCW) as a case study to test predictions that increases in group density lead to differences in foraging distances and resource selection for groups of different sizes. We used GPS tracking and LiDAR-derived habitat data to model effects of group size on foraging distances and selection for high-quality pines (≥ 35.6 cm diameter at breast height (dbh)) and lower quality pines (25.4–35.6 cm dbh) by RCW groups across low (n = 14), moderate (n = 10) and high group density (n = 10) conditions. At low and moderate group density, all RCW groups selected distant high-quality pines in addition to those near the central place because competition for resources was low. In contrast, at high group density, larger groups travelled further to select high-quality pines, whereas smaller groups selected high-quality pines only when they were close to the central place and, conversely, were more likely to select lower quality pines at greater distances from the central place. Selection for high-quality pines only when close to the cavity tree cluster at high group density is important to long-term fitness of small RCW groups because it allows them to maximize benefits from both territorial defence and selecting high-quality resources while minimizing costs of competition. These relationships suggest that intraspecific competition at high group density entails substantive costs to smaller groups of territorial central-place foragers by limiting accessibility of distant high-quality foraging resources.     

Resource characteristics and competition affect colony and individual foraging strategies of the wood ant Formica integroides

Abstract.  1. Resource characteristics and competitive pressure can affect an ant colony's foraging strategy. This study examined the ability of the wood ant Formica integroides to respond, at both the colony and individual levels, to changes in competitive pressure for access to terrestrial and arboreal resources.
2. Because foraging behaviours depend on resource characteristics, foraging for different resource types (e.g. terrestrial and arboreal habitats) produces different spatial or territorial arrangements. In this study, terrestrial contests for resources followed an interference-exploitation tradeoff, while arboreal foragers defended entire trees as absolute territories.
3. Competitive pressure for access to arboreal resources was shown to increase with distance from F. integroides nests.
4. In this study, the ability of F. integroides to defend a resource varied with body size. Large foragers were better defenders than small foragers. For groups of foragers, the ability to defend a resource increased with the ratio of large to small foragers.
5. In response to competitive pressure, F. integroides colonies altered the size distribution of arboreal, but not terrestrial, foragers. An increase in competitive pressure was matched by an increase in the number of large foragers allocated to trees. This response to competition affected the relationship between body size and distance from the nest for arboreal foragers.
6. Foraging behaviours for individual arboreal foragers also varied with competitive pressure. As competition increased, large arboreal foragers spent more time in direct contact with the resource rather than standing between resource patches.     

Central place foraging in the Eastern chipmunk, Tamias striatus

Orians & Pearson (1979) considered the optimal foraging strategies of ‘central place foragers’, animals that repeatedly return with their food to a fixed location. We tested some of their predictions on eastern chipmunks, Tamias striatus. The rate of cheek pouch loading declines as the pouches fill; thus the optimal load size may vary, depending on the time required to travel between the feeding site and burrow. This ‘travel time’ may also affect the choice of feeding site. A method was developed to test this, and preliminary results confirm the hypothesis. Methodological and theoretical implications of these empirical results are discussed.     

Does group foraging promote efficient exploitation of resources?

Increased avoidance of food patches previously exploited by other companions has been proposed as one adaptive benefit of group foraging. However, does group foraging really represent the most efficient way to exploit non- or slowly-renewing resources? Here, I used simulations to explore the costs and benefits of exploiting non-renewing resources by foragers searching for food patches independently or in groups in habitats with different types of resource distribution. Group foragers exploited resources in a patch more quickly and therefore spent proportionately more time locating new patches. Reduced avoidance of areas already exploited by others failed to overcome the increased time cost of searching for new food patches and group foragers thus obtained food at a lower rate than solitary foragers. Group foraging provided one advantage in terms of a reduction in the variance of food intake rate. On its own, reduced avoidance of exploitation competition through group foraging appears unlikely to increase mean food intake rate when exploiting non-renewing patches but may provide a way to reduce the risk of an energy shortfall.     

Temperature and forager body size affect carbohydrate collection in German yellowjackets, Vespula germanica (Hymenoptera, Vespidae)

The classic formulation of optimal foraging theory predicts that a central-place forager will gather more food if it is required to travel farther from the nest to find that food. We examined the foraging behavior of German yellowjackets (Vespula germanica) to determine whether carbohydrate foragers follow this pattern. We trained foragers to collect 2 M fructose solution at 5 or 50 m from the nest and measured the time spent feeding, load size, and the rate of delivery. We show that as a forager’s crop fills during a foraging bout, the amount of solution ingested per second decreased. However, load size did not change as wasps collected food up to 50 m from the nest. Instead, temperature and body size were better predictors of the volume of fructose a forager carried. Finally, the rate of fructose delivered to the nest was higher at warmer temperatures. Due to the fact that wasps gather more food but feed for shorter periods of time at warmer temperatures, we found an overall negative relationship between feeding time and load size. We conclude that the strong effects temperature had on the behavior of V. germanica foragers imply that feeding time may not always be an accurate predictor of the size of the load an individual carries back to the nest. Results from this study suggest that in yellowjacket colonies, foragers can collect and bring disproportionately more food back to the nest during the warmest days of the summer, a time of year when this pest species reaches peak population size during its annual colony cycle.     

Some effects of energy costs on foraging strategies

We consider the effect of including energy costs on the optimal strategy for animals exploiting a depleting food resource. In the context of central place foraging this leads to the problem of what load size should be brought back to the central place. Two strategies are discussed: (i) maximize gross rate of energy delivery and (ii) maximize net rate of energy delivery. The optimal load size (or optimal patch time) for net maximizers is not always larger than for gross maximizers, as has been claimed. Instead, the difference in optimal load size has the same sign as the difference between metabolic rates of travelling and foraging. We point out that the influence of costs has not always been correctly incorporated in experimental tests of the theory.     

Patch Use in Free‐Ranging Goats: Does a Large Mammalian Herbivore Forage like Other Central Place Foragers?

Classic central place foraging theory does not focus on the foraging of central place herbivores. This is especially true with regard to large mammalian herbivores. To understand the foraging dynamics of these neglected foragers, we measured giving‐up densities (GUDs) in artificial food patches. We did this at different distances away from the central point (i.e. corral) for a herd of free‐ranging domestic goats. To determine temporal changes, we conducted the study over a 3‐mo period during an extended dry season. Throughout our study, goats foraged across a gradient of food availability where forage was more available farther away from the central point. In contrast to the prediction that predation risk and/or increased travel costs were the main drivers of foraging decisions, we found that the goats increased their feeding effort (i.e. achieved lower GUDs) the farther away they moved from the central point. This suggests that either metabolic or missed opportunity costs were the main factors that influenced foraging decisions. In addition, we suggest that social foraging may have also played a role. With increases in foraging opportunities away from the central point, a herd will likely move slowly while foraging. As a result, individuals can feed intensively from patches but remain part of the group. Ironically, owing to the sustained close proximity of other group members, individuals may perceive patches farther from the central point as being safer. Temporally, the goats increased their feeding effort throughout the dry season. This suggests there was a decline in food quality and/or availability across the environment as the study progressed. Despite this increase in feeding effort, the negative relationship with distance did not change. Ultimately, our results provide key insight into how metabolic, missed opportunity and perceived predation costs influence the feeding decisions of large central place herbivores.     

The Regulation of Ant Colony Foraging Activity without Spatial Information

Many dynamical networks, such as the ones that produce the collective behavior of social insects, operate without any central control, instead arising from local interactions among individuals. A well-studied example is the formation of recruitment trails in ant colonies, but many ant species do not use pheromone trails. We present a model of the regulation of foraging by harvester ant (Pogonomyrmex barbatus) colonies. This species forages for scattered seeds that one ant can retrieve on its own, so there is no need for spatial information such as pheromone trails that lead ants to specific locations. Previous work shows that colony foraging activity, the rate at which ants go out to search individually for seeds, is regulated in response to current food availability throughout the colony's foraging area. Ants use the rate of brief antennal contacts inside the nest between foragers returning with food and outgoing foragers available to leave the nest on the next foraging trip. Here we present a feedback-based algorithm that captures the main features of data from field experiments in which the rate of returning foragers was manipulated. The algorithm draws on our finding that the distribution of intervals between successive ants returning to the nest is a Poisson process. We fitted the parameter that estimates the effect of each returning forager on the rate at which outgoing foragers leave the nest. We found that correlations between observed rates of returning foragers and simulated rates of outgoing foragers, using our model, were similar to those in the data. Our simple stochastic model shows how the regulation of ant colony foraging can operate without spatial information, describing a process at the level of individual ants that predicts the overall foraging activity of the colony.     

Interactions with Combined Chemical Cues Inform Harvester Ant Foragers' Decisions to Leave the Nest in Search of Food

Social insect colonies operate without central control or any global assessment of what needs to be done by workers. Colony organization arises from the responses of individuals to local cues. Red harvester ants (Pogonomyrmex barbatus) regulate foraging using interactions between returning and outgoing foragers. The rate at which foragers return with seeds, a measure of food availability, sets the rate at which outgoing foragers leave the nest on foraging trips. We used mimics to test whether outgoing foragers inside the nest respond to the odor of food, oleic acid, the odor of the forager itself, cuticular hydrocarbons, or a combination of both with increased foraging activity. We compared foraging activity, the rate at which foragers passed a line on a trail, before and after the addition of mimics. The combination of both odors, those of food and of foragers, is required to stimulate foraging. The addition of blank mimics, mimics coated with food odor alone, or mimics coated with forager odor alone did not increase foraging activity. We compared the rates at which foragers inside the nest interacted with other ants, blank mimics, and mimics coated with a combination of food and forager odor. Foragers inside the nest interacted more with mimics coated with combined forager/seed odors than with blank mimics, and these interactions had the same effect as those with other foragers. Outgoing foragers inside the nest entrance are stimulated to leave the nest in search of food by interacting with foragers returning with seeds. By using the combined odors of forager cuticular hydrocarbons and of seeds, the colony captures precise information, on the timescale of seconds, about the current availability of food.     

Habitat and patch use by hyraxes: there’s no place like home?

Models of central place foraging predict that animals should forage more thoroughly in resource patches located closer to the central place. Travel time, cost of transporting food back to the central place, and exposure to predators should all act to increase foraging costs with increasing distance from the refuge. We examined habitat and patch use in rock hyraxes ( Procavia capensis ) inhabiting a group of kopjes in a semiarid savanna, Augrabies Falls National Park, South Africa. We tested the prediction of more intense patch use closer to the central place by measuring giving-up densities (GUDs) in experimental resource patches set at four different distances from the kopje and in two microhabitats differing in cover. Surprisingly, hyraxes had their lowest GUDs at intermediate distances from the kopje. These unexpected results suggest that the sentinel behaviour of hyraxes alters the probability of detection of predators for animals foraging away from the kopje.     

A model for habitat selection and species distribution derived from central place foraging theory

We have developed a habitat selection model based on central place foraging theory. An individual’s decision to include a patch in its habitat depends on the marginal fitness contribution of that patch, which is characterized by its quality and distance to the central place. The essence of the model we have developed is a fitness isocline which is a function of patch quality and travel time to the patch. It has two parameters: the maximum travel distance to a patch of infinite quality and a coefficient that appropriately scales quality by travel time. Patches falling below the isocline will have positive marginal fitness values and should be included in the habitat. The maximum travel distance depends on the availability and quality of patches, as well as on the forager’s life history, whereas the scaling parameter mostly depends on life history properties. Using the model, we derived a landscape quality metric (which can be thought of as a connectivity measure) that sums the values of available habitat in the landscape around a central place. We then fitted the two parameters to foraging data on breeding white storks (Ciconia ciconia) and estimated landscape quality, which correlated strongly with reproductive success. Landscape quality was then calculated for a larger region where re-introduction of the species is currently going on in order to demonstrate how this model can also be regarded as a species distribution model. In conclusion, we have built a general habitat selection model for central place foragers and a novel way of estimating landscape quality based on a behaviorally scaled connectivity metric.     

Using habitat selection theories to predict the spatiotemporal distribution of migratory birds during stopover – a case study of pink‐footed geese Anser brachyrhynchus

Understanding how animals select for habitat and foraging resources therein is a crucial component of basic and applied ecology. The selection process is typically influenced by a variety of environmental conditions including the spatial and temporal variation in the quantity and quality of food resources, predation or disturbance risks, and inter‐ and intraspecific competition. Indeed, some of the most commonly employed ecological theories used to describe how animals choose foraging sites are: nutrient intake maximisation, density‐dependent habitat selection, central‐place foraging, and predation risk effects. Even though these theories are not mutually exclusive, rarely are multiple theoretical models considered concomitantly to assess which theory, or combination thereof, best predicts observed changes in habitat selection over space and time. Here, we tested which of the above theories best‐predicted habitat selection of Svalbard‐breeding pink‐footed geese at their main spring migration stopover site in mid‐Norway by computing a series of resource selection functions (RSFs) and their predictive ability (k‐fold cross validation scores). At this stopover site geese fuel intensively as a preparation for breeding and further migration. We found that the predation risk model and a combination of the density‐dependent and central‐place foraging models best‐predicted habitat selection during stopover as geese selected for larger fields where predation risk is typically lower and selection for foraging sites changed as a function of both distance to the roost site (i.e. central‐place) and changes in local density. In contrast to many other studies, the nutritional value of the available food resources did not appear to be a major limiting factor as geese used different food resources proportional to their availability. Our study shows that in an agricultural landscape where nutritional value of food resources is homogeneously high and resource availability changes rapidly; foraging behaviour of geese is largely a tradeoff between fast refuelling and disturbance/predator avoidance.     

Intra- and interspecific dominance hierarchies and variation in foraging tactics of two species of stream-dwelling chars

Aggressive interactions, foraging behavior, habitat use and diet were studied in sympatric populations of white-sported char,Salvelinus leucomaenis, and Dolly Varden,Salvelinus malma, in a Japanese mountain stream. Underwater observations on individuals of both species revealed two distinct behavioral regimes: aggressive drift foragers and non-aggressive benthos foragers. Aggressive drift foragers defended partial territories around focal points from which they made forays to capture invertebrates drifting in the water column. Non-aggressive benthos foragers cruised around and beneath cobble in large foraging ranges that overlapped each other. Intra- and interspecific, size-dependent dominance hierarchies were recognized among aggressive drift foragers, whereas non-aggressive benthos foragers showed no such relationships. Terrestrial invertebrates were the most abundant prey in the diets of drift foragers, whereas a very small proportion of the diet of benthos foragers was made up of these taxa. Benthos foragers showed more complex diet composition than drift foragers. These results suggest that non-aggressive benthos foragers may avoid not only interference but also exploitative competition by using alternative foraging tactics. The proportion of drift foragers to benthos foragers among white-spotted char was more than 35 times that among Dolly Varden. The significant difference in the proportion of each species using the two types of foraging strategy results in interspecific food segregation in sympatric populations.     

Density‐Dependent Foraging and Interference Competition by Common Gartersnakes are Temperature Dependent

The ideal free distribution (IFD) predicts that optimal foragers will select foraging patches to maximize food rewards and that groups of foragers should thus be distributed between food patches in proportion to the availability of food in those patches. Because many of the underlying mechanisms of foraging are temperature dependent in ectotherms, the distribution of ectothermic foragers between food patches may similarly depend on temperature because the difference in fitness rewards between these patches may change with temperature. We tested the hypothesis that the distribution of Common Gartersnakes (Thamnophis sirtalis) between food patches can be explained by an IFD, but that conformance to an IFD weakens as temperature departs from the optimal temperature because fitness rewards, interference competition and the number of individuals foraging are highest at the optimal temperature. First, we determined the optimal temperature for foraging. Second, we examined group foraging at three temperatures and three density treatments. Search time was optimized at 27°C, handling time at 29°C and digestion time at 32°C. Gartersnakes did not match an IFD at any temperature, but their distribution did change with temperature: snakes at 20°C and at 30°C selected both food patches equally, while snakes at 25°C selected the low food patch more at low density and the high food patch more at high density. Food consumption and competition increased with temperature, and handling time decreased with temperature. Temperature therefore had a strong impact on foraging, but did not affect the IFD. Future work should examine temperature‐dependent foraging in ectotherms that are known to match an IFD.     

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.     

Influence of density‐dependent competition on foraging and migratory behavior of a subtropical colonial seabird

Density‐dependent competition for food resources influences both foraging ecology and reproduction in a variety of animals. The relationship between colony size, local prey depletion, and reproductive output in colonial central‐place foragers has been extensively studied in seabirds; however, most studies have focused on effects of intraspecific competition during the breeding season, while little is known about whether density‐dependent resource depletion influences individual migratory behavior outside the breeding season. Using breeding colony size as a surrogate for intraspecific resource competition, we tested for effects of colony size on breeding home range, nestling health, and migratory patterns of a nearshore colonial seabird, the brown pelican (Pelecanus occidentalis), originating from seven breeding colonies of varying sizes in the subtropical northern Gulf of Mexico. We found evidence for density‐dependent effects on foraging behavior during the breeding season, as individual foraging areas increased linearly with the number of breeding pairs per colony. Contrary to our predictions, however, nestlings from more numerous colonies with larger foraging ranges did not experience either decreased condition or increased stress. During nonbreeding, individuals from larger colonies were more likely to migrate, and traveled longer distances, than individuals from smaller colonies, indicating that the influence of density‐dependent effects on distribution persists into the nonbreeding period. We also found significant effects of individual physical condition, particularly body size, on migratory behavior, which in combination with colony size suggesting that dominant individuals remain closer to breeding sites during winter. We conclude that density‐dependent competition may be an important driver of both the extent of foraging ranges and the degree of migration exhibited by brown pelicans. However, the effects of density‐dependent competition on breeding success and population regulation remain uncertain in this system.     

The marginal value theorem: A quantitative test using load size variation in a central place forager,the Eastern chipmunk, Tamias striatus

Chipmunks filling their cheek pouches with sunflower seeds decrease their rate of loading as their cheek pouches fill. Under these conditions, Charnov's (1976) marginal value theorem, as adapted for load size in ‘central place foragers’ by Orians & Pearson (1979), predicts an increase in load size with increased travel time between the foraging site and burrow. This prediction was verified. However, the quantitative predictive value of the theory is questioned because it failed to predict accurately either the actual loads or the trend in load size with distance.     

Self-organized asymmetries in ant foraging: a functional response to food type and colony needs

The dominant paradigm to explain asymmetries in the spatialdistribution of foraging animals is that they track the spatialheterogeneity of their environment. However, in social insects,endogenous spatial asymmetries can emerge within a uniformenvironment as an outcome from the self-organizing processof trail recruitment. We studied how self-organized asymmetries contribute to the exploitation of different food sources (carbohydrateor proteins) in colonies of the aphid-tending ant Lasius nigervarying in their nutritional needs (presence or absence ofbrood). Colonies with brood fed on sucrose sources exhibita higher mobilization of foragers than the other experimentalgroups. Foraging patterns differ greatly according to food type: colonies strongly focus their activity on only one dropletof sucrose, whereas they show a rather homogeneous distributionof foragers between proteinaceous sources. In addition, thepresence of brood in the colony enhances the asymmetry of collectiveforaging for both types of food. These spatial differencesin self-organized foraging patterns allow efficient exploitationof natural resources and play a role in the competitive strategy of this widespread palearctic ant.     

An experimental design and a statistical analysis separating interference from exploitation competition

Previous experimental studies of competition among foragers rarely distinguished between exploitation and interference competition. In many systems this separation is experimentally impossible without interfering with the natural behavior of the animals. Consequently, these studies can only demonstrate the combined effect of interference and exploitation on the forager’s feeding rate, namely, it usually decreases in a decelerating rate as a function of density. We suggest here a simple experimental and statistical procedure that facilitates the separation of the effects of interference from those of exploitation. This procedure includes manipulation of both predator density and the foraging experiment duration. The statistical analysis is based on multiple linear regression. The working assumption is that exploitation can be neglected at the beginning of the foraging experiment because, initially, predators do not experience diminishing returns in prey capture rates. Using both the results of an individual-based simulation and a field experiment dataset of gerbils foraging for seeds in an artificial food patch located in the field, we demonstrate that our procedure can successfully detect and separate the effect of interference from the combined overall effect of competition (i.e., interference plus exploitation). Inon Scharf and Ido Filin contributed equally to this paper.