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.     

Communal burrowing in the hystricognath rodent, Octodon degus: a benefit of sociality?

We examined the hypothesis that a main benefit of group-living in the semifossorial rodent, Octodon degus (Rodentia: Octodontidae), is to decrease individual cost of burrow construction. We contrasted the digging behavior of groups of three same-sex, adult-sized individuals with that of solitary degus. The behavior of singles and trios was recorded inside a large terrarium partially filled with natural soil and under controlled conditions of food, light, and temperature. The observation that degus in groups do not decrease their burrowing time or frequency of digging compared with solitary diggers does not support the hypothesis that communal burrowing is a primary cause of degu sociality. On the other hand, the observation that degus in groups removed significantly more soil per capita than solitary digging degus, and that grouped individuals coordinated their digging – group members burrowed mostly in the same sites and formed digging chains –, suggests that social burrowing may potentially reduce the cost of burrow construction in the long term. We suggest that such long-term benefits will be a consequence rather than a cause of degu group-living. Received: 9 December 1999 / Received in revised form: 2 January 2000 / Accepted: 8 February 2000     

Behavioral games involving a clever prey avoiding a clever predator: An individual-based model of dusky dolphins and killer whales

Faced with an intermittent but potent threat, animals exhibit behavior that allows them to balance foraging needs and avoid predators and over time, these behaviors can become hard-wired adaptations with both species trying to maximize their own fitness. In systems where both predator and prey share similar sensory modalities and cognitive abilities, such as with marine mammals, the dynamic nature of predator-prey interactions is poorly understood. The costs and benefits of these anti-predator adaptations need to be evaluated and quantified based on the dynamic engagement of predator and prey. Many theoretic models have addressed the complexity of predator-prey relationships, but few have translated into testable mechanistic models. In this study, we developed a spatially-explicit, geo-referenced, individual-based model of a prototypical adult dusky dolphin off Kaikoura, New Zealand facing a more powerful, yet infrequent predator, the killer whale. We were interested in two primary objectives, (1) to capture the varying behavioral game between a clever prey and clever predator based on our current understanding of the Kaikoura system, (2) to compare evolutionary costs vs. benefits (foraging time and number of predator encounters) for an adult non-maternal dusky dolphin at various levels of killer whale-avoidance behaviors and no avoidance rules. We conducted Monte Carlo simulations to address model performance and parametric uncertainty. Mantel tests revealed an 88% correlation (426 × 426 distance matrix, km²) between observed field sightings of dusky dolphins with model generated sightings for non-maternal adult dusky dolphin groups. Simulation results indicated that dusky dolphins incur a 2.7% loss in feeding time by evolving the anti-predator behavior of moving to and from the feeding grounds. Further, each evolutionary strategy we explored resulted in dolphins incurring an additional loss of foraging time. At low killer whale densities (appearing less than once every 3 days), each evolutionary strategy simulated converged towards the evolutionary cost of foraging, that is, the loss in foraging time approached the 2.7% loss experienced by evolving near shore-offshore movement behavior. However, the highest level of killer whale presence resulted in 38% decreases in foraging time. The biological significance of these losses potentially incurred by a dusky dolphin is dependent on various factors from dolphin group foraging behavior and individual energy needs to dolphin prey availability and behavior.     

Searching behavior and use of sampling information by free-ranging bison (Bos bison)

I examined the searching behavior of free-ranging plains bison (Bos bison bison) in their natural habitat, and determined whether their assessment of food patch quality was influenced by the short-term sampling information acquired during search. Bison used area-concentrated search during their winter foraging activity. Their movements between areas of suitable food patches were influenced by local environmental conditions, being sometimes less sinuous, and at other times more sinuous, than expected from a correlated random walk model. Bison also systematically avoided digging in areas where plants of low profitability lay under the snow. Where they dug, there was evidence that a bison's perception of food quality varied during a foraging bout, and was therefore influenced by short-term sampling information. After controlling for forage quality, I found that small feeding craters were more likely to be preceded by samples of high quality food patches. My observations suggest that bison take advantage of the structural characteristics of their environment during searching activity, and base foraging decisions on local rather than global availability.     

Pattern-oriented modeling of bird foraging and pest control in coffee farms

We develop a model of how land use and habitat diversity affect migratory bird populations and their ability to suppress an insect pest on Jamaican coffee farms. Bird foraging—choosing which habitat patch and prey to use as prey abundance changes over space and time—is the key process driving this system. Following the “pattern-oriented” modeling strategy, we identified nine observed patterns that characterize the real system's dynamics. The model was designed so that these patterns could potentially emerge from it. The resulting model is individual-based, has fine spatial and temporal resolutions, represents very simply the supply of the pest insect and other arthropod food in six habitat types, and includes foraging habitat selection as the only adaptive behavior of birds. Although there is an extensive heritage of bird foraging theory in ecology, most of it addresses only the individual level and is too simple for our context. We used pattern-oriented modeling to develop and test foraging theory for this across-scale problem: rules for individual bird foraging that cause the model to reproduce a variety of patterns observed at the system level. Four alternative foraging theories were contrasted by how well they caused the model to reproduce the nine characteristic patterns. Four of these patterns were clearly reproduced with the “null” theory that birds select habitat randomly. A version of classical theory in which birds stay in a patch until food is depleted to some threshold caused the model to reproduce five patterns; this theory caused lower, not higher, use of habitat experiencing an outbreak of prey insects. Assuming that birds select the nearby patch providing highest intake rate caused the model to reproduce all but one pattern, whereas assuming birds select the highest-intake patch over a large radius produced an unrealistic distribution of movement distances. The pattern reproduced under none of the theories, a negative relation between bird density and distance to trees, appears to result from a process not in the model: birds return to trees at night to roost. We conclude that a foraging model for small insectivorous birds in diverse habitat should assume birds can sense higher food supply but over short, not long, distances.     

Biparental investment and reproductive success in a subsocial desert beetle: the role of maternal effort

Parastizopus armaticeps is a nocturnal subsocial detritivorous desert tenebrionid that produces very few offspring per brood. The two environmental factors that constrain reproduction, rapid sand desiccation rate and food scarcity, are countered by biparental effort. Males dig and extend breeding burrows, maintaining their moisture level; females forage on the surface at night for high-quality detritus, the larval food. This was shown to be a scarce and unpredictable resource for which there is high competition. When food was supplemented in a field experiment, offspring number and survivorship doubled and burrow failure due to desiccation dropped from approximately half, the typical failure rate for unsupplemented burrows, to zero. Food supplementation did not, however, increase larval foodstore size and there was no difference in the size of the offspring produced. Supplemented females reallocated their time, foraging less and digging more with the male. This change in maternal behaviour patterns resulted in deeper burrows which remained moist longer, thus extending the larval production period. Female foraging efficiency, particularly food retrieval speed, determined how much time females could allocate to digging, consequently increasing the reproductive success of the pair. Burrow depth and sand moisture level at the burrow base were the major correlates of reproductive success, but the scarcity and unpredictability of high-quality food on the surface and the competition for this resource influenced the number of offspring indirectly through their effect on female behaviour. Received: 29 November 1996 / Accepted after revision: 7 December 1997     

A patch use model to separate effects of foraging costs on giving-up densities: an experiment with white-tailed deer (<Emphasis Type="Italic">Odocoileus virginianus</Emphasis>)

The giving-up density of food (GUD), the amount of food remaining in a patch when a forager ceases foraging there, can be used to compare the costs of foraging in different food patches. But, to draw inferences from GUDs, specific effects of foraging costs (predation risk, metabolic and missed opportunities costs) on GUDs have to be identified. As high predation risk, high metabolic costs and abundant food all should produce high GUDs, this does not allow us to infer directly the quality of a habitat. In order to separate the effect of each foraging cost, we developed an optimal foraging model based on food supplementation. We illustrate the use of our model in a study where we assessed the impact of a power line right-of-way in a white-tailed deer (Odocoileus virginianus) winter yard by determining whether the negative effects of cover loss outweigh the positive effects of browse regeneration.     

The top-down mechanism for body-mass-abundance scaling

Scaling relationships between mean body masses and abundances of species in multitrophic communities continue to be a subject of intense research and debate. The top-down mechanism explored in this paper explains the frequently observed inverse linear relationship between body mass and abundance (i.e., constant biomass) in terms of a balancing of resource biomasses by behaviorally and evolutionarily adapting foragers, and the evolutionary response of resources to this foraging pressure. The mechanism is tested using an allometric, multitrophic community model with a complex food web structure. It is a statistical model describing the evolutionary and population dynamics of tens to hundreds of species in a uniform way. Particularities of the model are the detailed representation of the evolution and interaction of trophic traits to reproduce topological food web patterns, prey switching behavior modeled after experimental observations, and the evolutionary adaptation of attack rates. Model structure and design are discussed. For model states comparable to natural communities, we find that (1) the body-mass abundance scaling does not depend on the allometric scaling exponent of physiological rates in the form expected from the energetic equivalence rule or other bottom-up theories; (2) the scaling exponent of abundance as a function of body mass is approximately -1, independent of the allometric exponent for physiological rates assumed; (3) removal of top-down control destroys this pattern, and energetic equivalence is recovered. We conclude that the top-down mechanism is active in the model, and that it is a viable alternative to bottom-up mechanisms for controlling body-mass-abundance relations in natural communities.     

Incorporating behaviour into simple models of dispersal using the biological control agent Dicyphus hesperus

We explored the utility of incorporating easily measured, biologically realistic movement rules into simple models of dispersal. We depart from traditional random walk models by designing an individual-based simulation model where we decompose animal movement into three separate processes: emigration, between-patch movement, and immigration behaviour. These processes were quantified using experiments on the omnivorous insect Dicyphus hesperus moving through a tomato greenhouse. We compare the predictions of the individual-based model, along with a series of biased random walk models, against an independent experimental release of D. hesperus. We find that in this system, the short-term dispersal of these insects is described well by our individual-based model, but can also be described by a 2D grid-based biased random walk model when mortality is accounted for.     

Movement of foraging Tundra Swans explained by spatial pattern in cryptic food densities

We tested whether Tundra Swans use information on the spatial distribution of cryptic food items (below ground Sago pondweed tubers) to shape their movement paths. In a continuous environment, swans create their own food patches by digging craters, which they exploit in several feeding bouts. Series of short (<1 m) intra-patch movements alternate with longer inter-patch movements (>1 m). Tuber biomass densities showed a positive spatial auto-correlation at a short distance (<3 m), but not at a larger distance (3-8 m). Based on the spatial pattern of the food distribution (which is assumed to be pre-harvest information for the swan) and the energy costs and benefits for different food densities at various distances, we calculated the optimal length of an inter-patch movement. A swan that moves to the patch with the highest gain rate was predicted to move to the adjacent patch (at 1 m) if the food density in the current patch had been high (>25 g/m2) and to a more distant patch (at 7-8 m) if the food density in the current patch had been low (<25 g/m2). This prediction was tested by measuring the response of swans to manipulated tuber densities. In accordance with our predictions, swans moved a long distance (>3 m) from a low-density patch and a short distance (<3 m) from a high-density patch. The quantitative agreement between prediction and observation was greater for swans feeding in pairs than for solitary swans. The result of this movement strategy is that swans visit high-density patches at a higher frequency than on offer and, consequently, achieve a 38% higher long-term gain rate. Swans also take advantage of spatial variance in food abundance by regulating the time in patches, staying longer and consuming more food from rich than from poor patches. We can conclude that the shape of the foraging path is a reflection of the spatial pattern in the distribution of tuber densities and can be understood from an optimal foraging perspective.     

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.     

Social foraging and dominance relationships: the effects of socially mediated interference

In socially foraging animals, it is widely acknowledged that the position of an individual within the dominance hierarchy of the group has a large effect upon its foraging behaviour and energetic intake, where the intake of subordinates can be reduced through socially mediated interference. In this paper, we explore the effects of interference upon group dynamics and individual behaviour, using a spatially explicit individual-based model. Each individual follows a simple behavioural rule based upon its energetic reserves and the actions of its neighbours (where the rule is derived from game theory models). We show that dominant individuals should have larger energetic reserves than their subordinates, and the size of this difference increases when either food is scarce, the intensity of interference suffered by the subordinates increases, or the distance over which dominant individuals affect subordinates increases. Unlike previous models, the results presented in this paper about differences in reserves are not based upon prior assumptions of the effects of social hierarchy and energetic reserves upon predation risk, and emerge through nothing more than a reduction in energetic intake by the subordinates when dominants are present. Furthermore, we show that increasing interference intensity, food availability or the distance over which dominants have an effect also causes the difference in movement between ranks to increase (where subordinates move more than dominants), and the distance over which dominants have an effect changes the size of the groups that the different ranks are found in. These results are discussed in relation to previous studies of intra- and interspecific dominance hierarchies.     

Individual energetic state can prevail over social regulation of foraging in honeybees

The energetic state of an individual is a fundamental driver of its behavior. However, an individual in a eusocial group such as the honeybees is subject to the influence of both the individual and the colony energetic states. As these two states are normally coupled, it has led to the predominant view that behaviors, such as foraging, are dictated by the colony state acting through social regulatory mechanisms. Uncoupling the energetic state of an individual honeybee from its colony by feeding it with a non-nutritious sugar, we show that energetically stressed bees in a colony with full food stores do not consume this food to meet their energetic shortfall but instead compensate by first reducing their activity level and then by increasing their foraging rate. This suggests that foraging in eusocial groups is still partly under the regulatory control of the energetic state of the individual and supports the notion that regulatory mechanisms in solitary insects have been co-opted to drive altruistic behavior in eusocial insects. The observation that energetically stressed bees also experience higher mortality during foraging also suggests that energetic stress mediated by a variety of factors can be a common mechanism that underlies the recent observation of bees disappearing from their colonies. We also discuss how nutritional imbalance in a social insect individual can alter its behavior to influence colony life history.     

A simple individual model for simulating weight gain dynamics in response to intake rate and daily behavior

It is often necessary to estimate the weight that an individual may be capable of gaining depending on its degree of activity. A simple individual-based model was developed for studying the dynamics of weight in terms of daily behavior and ingestion rate. It was based on the balance between the individual's energy intake and the cost of its daily activities. Costs depend on the weight of the individual and the photoperiod, as well as on the time spent on each activity. Different combinations of ingestion rate, individual's weight, photoperiod length, and time assigned to different activities were used for simulating the weight dynamics, taking the species Rhea americana as a study case. Estimations of energetic costs of the activities were obtained from specialized literature. Using different photoperiods and individual behaviors, the model yields field metabolic rate (FMR) values in agreement with those obtained from direct measurements for other omnivorous bird species.     

Risk and cost of immobility in the presence of an immobile predator

Escape latency theory models the tradeoff between maintaining crypsis by remaining immobile near an immobile predator versus moving to flee or engage in fitness-enhancing activities. The model predicts that latency to flee increases as cost of fleeing increases and decreases as cost of remaining immobile increases. As predation risk increases, cost of fleeing, primarily due to abandoning crypsis due to immobility, decreases. Predictions have been tested for few risks and a single cost of immobility factor in only two species of active foragers. To gauge the breadth of applicability of the model, we tested effects of four risk factors and two cost of immobility factors in ambush-foraging phrynosomatid lizards, which we selected for testing because foraging mode strongly affects many aspects of ecology and behavior of lizards. Latency to flee decreased as standing distance (predator–prey distance before fleeing) decreased, predator approach speed increased, directness of approach increased, and predator persistence increased. Latency to move was shorter in the presence of food and shorter for males in the presence of females. Lizards often moved toward food or females instead of fleeing. Latency was affected as predicted by all risk and by cost of remaining immobile factors. Our findings agree with previous results for the same four risk factors and the foraging cost of immobility. That social cost of immobility affects latency as predicted is a novel finding. The model is robust, applying to ecologically diverse prey and to a wide range of factors affecting costs of fleeing and of immobility.     

Pattern formation and individual-based models: The importance of understanding individual-based movement

This paper demonstrates that while pattern formation can stabilize individual-based models of predator–prey systems, the same individual-based models also allow for stabilization by alternate mechanisms, particularly localized consumption or diffusion limitation. The movement rules of the simulation are the critical feature which determines which of these mechanisms stabilizes any particular predator–prey individual-based model. In particular, systems from well-connected subpopulations, in each of which a predator can attack any prey, generally exhibit stabilization by pattern formation. In contrast, when restricted movement within a (sub-)population limits the ability of predators to consume prey, localized consumption or diffusion limitation can stabilize the system. Thus while the conclusions from differential equations on the role of pattern formation for stability may apply to discrete and noisy systems, it will take a detailed understanding of movement and scales of interaction to examine the role of pattern formation in real systems. Additionally, it will be important to link an understanding of both foraging and inter-patch movement, since by analogy to the models, both would be critical for understanding how real systems are stabilized by being discrete and spatial.     

A geometrical model for the effect of interference on food intake

Interference competition is often due to kleptoparasitism (food stealing). In which case, the attack distance, the distance over which one animal attacks another in an attempt to steal food, determines to a large extent the competitor density range over which interference significantly affects the intake rate of foraging animals.We develop a simple model of kleptoparasitism containing three parameters: attack distance, the density of foraging animals and a single dimensionless parameter α which summarizes the non-geometrical aspects of the interference process. Dominant and subdominant animals are not considered separately. The model predicts that the average intake rate will decrease exponentially with animal density and that a measure of the strength of interference depends on attack distance squared.The simple model is compared with a much more detailed individual-based foraging model from the literature. Simulated average intake rates are indeed well approximated by an exponential decrease with competitor density. Also the measure of interference behaves in the way expected from the simple model. By explaining the shape of the relationship between intake rate and animal density, the simple model provides insight into the behaviour of the detailed behavioural model.Insight into the role of geometry is important in the interpretation of field results and in the further development of detailed foraging models.     

Predation risk and foraging behavior of the hoary marmot in Alaska

Summary I observed hoary marmots for three field seasons to determine how the distribution of food and the risk of predation influenced marmots' foraging behavior. I quantified the amount of time Marmota caligata foraged in different patches of alpine meadows and assessed the distribution and abundance of vegetation eaten by marmots in these meadows. Because marmots dig burrows and run to them when attacked by predators, marmot-toburrow distance provided an index of predation risk that could be specified for different meadow patches.Patch use correlated positively with food abundance and negatively with predation risk. However, these significant relationships disappeared when partial correlations were calculated because food abundance and risk were intercorrelated. Using multiple regression, 77.0% of the variance in patch use was explained by a combination of food abundance, refuge burrow density, and a patch's distance from the talus where sleeping burrows were located. Variations in vigilance behavior (look-ups to search for predators while feeding) according to marmots' ages, the presence of other conspecifics, and animals' proximity to their sleeping burrows all indicated that predation risk influenced foraging.In a forage-manipulation experiment, the use of forage-enhanced patches increased six-fold, verifying directly the role of food availability on patch used. Concomitant with increased feeding, however, was the intense construction of refuge burrows in experimental patches that presumably reduced the risk of feeding. Thus, I suggest that food and predation risk jointly influence patch use by hoary marmots and that both factors must be considered when modeling the foraging behavior of species that can be predator and prey simultaneously.     

Look before you leap: is risk of injury a foraging cost?

Theory states that an optimal forager should exploit a patch so long as its harvest rate of resources from the patch exceeds its energetic, predation, and missed opportunity costs for foraging. However, for many foragers, predation is not the only source of danger they face while foraging. Foragers also face the risk of injuring themselves. To test whether risk of injury gives rise to a foraging cost, we offered red foxes pairs of depletable resource patches in which they experienced diminishing returns. The resource patches were identical in all respects, save for the risk of injury. In response, the foxes exploited the safe patches more intensively. They foraged for a longer time and also removed more food (i.e., had lower giving up densities) in the safe patches compared to the risky patches. Although they never sustained injury, video footage revealed that the foxes used greater care while foraging from the risky patches and removed food at a slower rate. Furthermore, an increase in their hunger state led foxes to allocate more time to foraging from the risky patches, thereby exposing themselves to higher risks. Our results suggest that foxes treat risk of injury as a foraging cost and use time allocation and daring—the willingness to risk injury—as tools for managing their risk of injury while foraging. This is the first study, to our knowledge, which explicitly tests and shows that risk of injury is indeed a foraging cost. While nearly all foragers may face an injury cost of foraging, we suggest that this cost will be largest and most important for predators.     

Optimal movement strategies for social foragers in unpredictable environments

Spatial movement models often base movement decision rules on traditional optimal foraging theories, including ideal free distribution (IFD) theory, more recently generalized as density-dependent habitat selection (DDHS) theory, and the marginal value theorem (MVT). Thus optimal patch departure times are predicted on the basis of the density-dependent resource level in the patch. Recently, alternatives to density as a habitat selection criterion, such as individual knowledge of the resource distribution, conspecific attraction, and site fidelity, have been recognized as important influences on movement behavior in environments with an uncertain resource distribution. For foraging processes incorporating these influences, it is not clear whether simple optimal foraging theories provide a reasonable approximation to animal behavior or whether they may be misleading. This study compares patch departure strategies predicted by DDHS theory and the MVT with evolutionarily optimal patch departure strategies for a wide range of foraging scenarios. The level of accuracy with which individuals can navigate toward local food sources is varied, and individual tendency for conspecific attraction or repulsion is optimized over a continuous spectrum. We find that DDHS theory and the MVT accurately predict the evolutionarily optimal patch departure strategy for foragers with high navigational accuracy for a wide range of resource distributions. As navigational accuracy is reduced, the patch departure strategy cannot be accurately predicted by these theories for environments with a heterogeneous resource distribution. In these situations, social forces improve foraging success and have a strong influence on optimal patch departure strategies, causing individuals to stay longer in patches than the optimal foraging theories predict.