Using spatially explicit models to characterize foraging performance in heterogeneous landscapes

ABSTRACT The success of most foragers is constrained by limits to their sensory perception, memory, and locomotion. However, a general and quantitative understanding of how these constraints affect foraging benefits, and the trade-offs they imply for foraging strategies, is difficult to achieve. This article develops foraging performance statistics to assess constraints and define trade-offs for foragers using biased random walk behaviors, a widespread class of foraging strategies that includes area-restricted searches, kineses, and taxes. The statistics are expected payoff and expected travel time and assess two components of foraging performance: how effectively foragers distinguish between resource-poor and resourcerich parts of their environments and how quickly foragers in poor parts of the environment locate resource concentrations. These statistics provide a link between mechanistic models of individuals' movement and functional responses, population-level models of forager distributions in space and time, and foraging theory predictions of optimal forager distributions and criteria for abandoning resource patches. Application of the analysis to area-restricted search in coccinellid beetles suggests that the most essential aspect of these predators's foraging strategy is the "turning threshold," the prey density at which ladybirds switch from slow to rapid turning. This threshold effectively determines whether a forager exploits or abandons a resource concentration. Foraging is most effective when the threshold is tuned to match physiological or energetic requirements. These performance statistics also help anticipate and interpret the dynamics of complex spatially and temporally varying forager-resource systems.     

State‐dependent Bayesian foraging on spatially autocorrelated food distributions

When prey are cryptic and are distributed in discrete clumps (patches), Bayesian foragers revise their prior expectation about a patch's prey density by using their foraging success in the patch as a source of information. Prey densities are often spatially autocorrelated, meaning that rich patches are often surrounded by other rich patches, while poor patches are often in the midst of other poor patches. In that case, foraging success is informative about prey densities in the current patch and in the surrounding patches. In a spatially explicit environment where prey are cryptic and their densities autocorrelated, I modelled two types of Bayesian foragers that aim to maximize their survival rate: (1) the spatially ignorant forager which does not take account of the spatial structure in its food supply and (2) the spatially informed forager which does take this into account. Not surprisingly, the spatially informed forager has a higher survivorship than the spatially ignorant forager, simply because it is able to obtain more reliable prey density estimates than the spatially ignorant forager. Surprisingly though, the emerging policy used by the spatially informed forager is to leave patches at a lower (expected) giving‐up density (GUD) the further away from its latest prey capture. This is because this forager is willing to wait for good news: a prey capture far from the latest prey capture drastically changes the forager's expectations about prey densities in the patches that it will exploit in the near future, whereas a prey capture near its latest prey capture hardly affects these expectations. Thus, by sacrificing current intake rate for information gain, the spatially informed forager ultimately maximizes its long‐term pay‐off. Finally, as the value of food is less the more energy is stored, both types make state‐dependent giving‐up decisions: the higher their energy store levels, the higher their GUDs.     

On the role of patch density and patch variability in central-place foraging

Existing models of the foraging behavior of single-prey loaders in patchy environments differ on whether the optimal forager is predicted to stay in a patch until a prey is found, or to leave a patch for a next one if a prey is not found by a certain “deadline.” This article examines conditions on the probability distribution of prey density across patches that are necessary or sufficient for the existence of a finite, optimal deadline. It is shown that, for environments in which prey density is variable but never falls below some strictly positive level, a finite, optimal deadline exists when and only when the spatial density of patches is “high.” Also, a characterization is given of a large class of distributions (including the gamma distribution) for which a finite, optimal deadline exists for all levels of spatial density of patches.     

The effects of spatially heterogeneous prey distributions on detection patterns in foraging seabirds

Many attempts to relate animal foraging patterns to landscape heterogeneity are focused on the analysis of foragers movements. Resource detection patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior. By exploring simple foraging models in unpredictable environments we show that the distribution of intervals between detected prey (detection statistics) is mostly determined by the spatial structure of the prey field and essentially distinct from predator displacement statistics. Detections are expected to be Poissonian in uniform random environments for markedly different foraging movements (e.g. Lévy and ballistic). This prediction is supported by data on the time intervals between diving events on short-range foraging seabirds such as the thick-billed murre (Uria lomvia). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross (Diomedea exulans) due to the fractal nature of the prey field, covering a wide range of spatial scales. For this scenario, models of fractal prey fields induce non-Poissonian patterns of detection in good agreement with two albatross data sets. We find that the specific shape of the distribution of time intervals between prey detection is mainly driven by meso and submeso-scale landscape structures and depends little on the forager strategy or behavioral responses.     

Intake rate at differently scaled heterogeneous food distributions explained by the ability of tactile-foraging mallard to concentrate foraging effort within profitable areas

The ability to respond to spatial heterogeneity in food abundance depends on the scale of the food distribution and the foraging scale of the forager. The aim of this study is to illustrate that a foraging scale exists, and that at larger scaled food distributions foragers benefit from the ability to subdivide a continuous (non-discrete) heterogeneous environment into profitable and non-profitable areas. We recorded search patterns of mallards Anas plathyrhynchos foraging in shallow water on cryptic prey items (millet seeds), distributed at different scales. A small magnet attached to the lower mandible allowed us to record in great detail the position and movements of the bill tip within a feeding tray underlain by magnet sensors. Instantaneous intake rate was determined in a subsequent experiment. We successfully determined the foraging scale (about 2×2 cm), defined as the scale above which foragers do respond (coarse scaled distribution) and below which foragers do not respond (fine scaled distribution) to spatial heterogeneity, by concentrating foraging effort within areas of high food density. A response resulted in a significantly higher intake rate, compared to a homogeneous distribution with an equal overall density. Unlike systematic search cell revisitation was common in trials, and at coarse scaled food distributions even slightly (but significantly) more frequently observed than predicted for random search. Mallards respond to food capture by restricting displacement (area restricted search) at food distributions that are considered to be clumped for the forager (large scaled coarse distributions). We argue that partitioning the environment at the foraging scale in itself could be a mechanism to concentrate foraging efforts within profitable areas, because mallard were able to respond to heterogeneity at coarse scaled food distributions even when non-clumped (i.e. without conducting area restricted search).     

Foraging behaviour of predators in heterogeneous landscapes: the role of perceptual ability and diet breadth

Oligophagous and polyphagous predators are confronted with spatially and temporally varying distributions of prey. Their species-specific foraging strategies should be able to cope with this variability. Using an individual based model, we explore how diet breath and the spatial scale at which predators respond to prey affects their capture efficiency in four heterogeneous prey landscapes, and combinations thereof. We interpret the spatial scale of the predator's response as perceptual range, and propose giving-up density as a proxy for diet breadth. Foraging behaviour is evaluated for a total of 121 perceptual range/giving-up density combinations, with four of them reflecting the strategies adopted by real ladybeetle species. Foraging rules of oligophagous ladybeetles were generally not very effective in terms of attained predation rate when foraging in a single prey landscape, but appear to be more effective when foraging in multiple prey landscapes. This finding is compatible with the notion that oligophagous predators do not adopt a foraging strategy that is especially adapted to a specific prey landscape, but to multiple prey landscapes. Simulations further indicated that there was not a 'best' foraging rule that resulted in the highest predation rates for a range of spatial prey distributions and prey densities. The findings thus suggest that strategies of four ladybeetle species are effective in generating sufficient prey capture under a broad range of spatial distributions, rather than maximum capture under a narrower set of distributions.     

Spatial and reversal learning in congeneric lizards with different foraging strategies

Environmental demands that require intensive search for mates, food and nest sites are correlated with efficient spatial memory in many mammalian and avian species. This convergence of evidence has led to the view that spatial memory, and the neurological structures associated with it, have been selected in niches that require memory for the location of goal objects. Whether such evolutionary demands are also correlated with nonspatial abilities that require flexible use of associations similar to those required for spatial memory has not been well studied. In addition, correlations between niche types and the use of spatial or nonspatial memory have not been investigated in nonmammalian, nonavian taxa. In this study, we investigated the relationship between foraging strategies and performance on two tasks, one spatial and the other nonspatial, in congeneric lizard species: Acanthodactylus boskianus, an active forager that collects clumped sedentary prey, Acanthodactylus scutellatus, a sit-and-wait predator that collects distributed mobile prey. The two species did not differ in their performance of a spatial memory task, but A. boskianus, the active forager, performed better on the reversal of a visual discrimination, a nonspatial task. These findings question the generality of the spatial adaptation model for vertebrates. We present the pliancy hypothesis, which we developed to account for these results. Copyright 1999 The Association for the Study of Animal Behaviour.     

Foraging responses ofFormica truncorum (Hymenoptera; Formicidae); exploiting stable vs spatially and temporally variable resources

Summary Social organization allows a division of labor between reproduction and foraging, as well as a task allocation among foraging individuals. Therefore, a colony simultaneously exploiting various resources can use different ways of getting them. This work analyzes wood ant foraging tactics both at the collective and the individual level. The main issues are: (1) How does a wood ant colony respond to stable vs temporally and spatially variable resources in terms of worker force allocation? (2) How is retrieval of ephemeral but rich resources effected at the individual level? The results show a correspondence between resource stability and behavior. Ants visited stable resources continually and recruited to ephemeral ones. They also visited empty food sites at a low frequency suggesting territoriality and constant scanning. The results suggest that recruitment may involve defence of the resource, since only a small fraction of all the workers available carry the food home. Additional ants arriving at the resource are recruited from inside the nest, not by reallocating outdoor workers. The foragers also form two separate groups, one site-persistent and another site-flexible. These two forager groups may reflect specialization on two different kinds of diet: honeydew or insect prey (spatially and temporally stable vs unstable resources, respectively).Formica truncorum is thus an example of how sociality allows the use of two different foraging strategies simultaneously: one that is based on recruitment to ephemeral resources and another that is based on search persistance and memory.     

Smart,smarter, smartest: foraging information states and coexistence

Animals possess different abilities to gain and use information about the foraging patches they exploit. When ignorant of the qualities of encountered patches, a smart forager should leave all patches after the same amount of fixed search time. A smarter forager can be Bayesian by using information on cumulative harvest and time spent searching a patch to better inform its patch‐departure decision. The smartest forager has immediate and continuous knowledge about patch quality, and can make a perfect decision about when to leave each patch. Here we let each of these three strategies harvest resources from a slowly regenerating environment. Eventually a steady‐state distribution of prey among patches arises where the environment‐wide resource renewal just balances the environment‐wide harvest of the foragers. The fixed time forager creates a distribution with the highest mean and highest variance of patch qualities, followed by the Bayesian and the prescient in that order. The less informed strategies promote distributions with both more resources and more exploitable information than the more informed strategies. While it is true that a better‐informed strategy will always out‐perform a less well‐informed, its increase in performance may not compensate it for any costs associated with being better informed. We imagine that the fixed time strategy may be least expensive and the prescient strategy most expensive in terms of sensory organs and associated assess and respond capabilities. To consider competition between such strategies with varying costs, we introduced a single individual of each of the strategies into the environments created by populations of the other strategies. There are threshold costs associated with the better‐informed strategy such that it can or cannot outcompete a less‐informed strategy. However, over a relatively narrow range of foraging costs, less‐informed and better‐informed strategies will coexist. Furthermore, for the prescient and the Bayesian strategies, some combinations of foraging costs produce alternate stable states – whichever strategy establishes first remains safe from invasion by the other.     

From random walks to informed movement

The analysis of animal movement is a large and continuously growing field of research. Detailed knowledge about movement strategies is of crucial importance for understanding eco‐evolutionary dynamics at all scales – from individuals to (meta‐)populations. This and the availability of detailed movement and dispersal data motivated Nathan and colleagues to published their much appreciated call to base movement ecology on a more thorough mechanistic basis. So far, most movement models are based on random walks. However, even if a random walk might describe real movement patterns acceptably well, there is no reason to assume that animals move randomly. Therefore, mechanistic models of foraging strategies should be based on information use and memory in order to increase our understanding of the processes that lead to animal movement decisions. We present a mechanistic movement model of an animal with a limited perceptual range and basic information storage capacities. This ‘spatially informed forager’ constructs an internal map of its environment by using perception, memory and learned or evolutionarily acquired assumptions about landscape attributes. We analyse resulting movement patterns and search efficiencies and compare them to area restricted search strategies (ARS) and biased correlated random walks (BCRW) of omniscient individuals. We show that, in spite of their limited perceptual range, spatially informed individuals boost their foraging success and may perform much better than the best ARS. The construction of an internal map and the use of spatial information results in the emergence of a highly correlated walk between patches and a rather systematic search within resource clusters. Furthermore, the resulting movement patterns may include foray search behaviour. Our work highlights the strength of mechanistic modelling approaches and sets the stage for the development of more sophisticated models of memory use for movement decisions and dispersal.     

Environmental heterogeneity amplifies behavioural response to a temporal cycle

Resource acquisition is integral to maximise fitness, however in many ecosystems this requires adaptation to resource abundance and distributions that seldom stay constant. For predators, prey availability can vary at fine spatial and temporal scales as a result of changes in the physical environment, and therefore selection should favour individuals that can adapt their foraging behaviour accordingly. The tidal cycle is a short, yet predictable, temporal cycle, which can influence prey availability at temporal scales relevant to movement decisions. Here, we ask whether black‐legged kittiwakes Rissa tridactyla can adjust their foraging habitat selection according to the tidal cycle using GPS tracking studies at three sites of differing environmental heterogeneity. We used a hidden Markov model to classify kittiwake behaviour, and analysed habitat selection during foraging. As expected for a central‐place forager, we found that kittiwakes preferred to forage nearer to the breeding colony. However, we also show that habitat selection changed over the 12.4‐h tidal cycle, most likely because of changes in resource availability. Furthermore, we observed that environmental heterogeneity was associated with amplified changes in kittiwake habitat selection over the tidal cycle, potentially because environmental heterogeneity drives greater resource variation. Both predictable cycles and environmental heterogeneity are ubiquitous. Our results therefore suggest that, together, predictable cycles and environmental heterogeneity may shape predator behaviour across ecosystems.     

Effects of spatial scale and foraging efficiency on the predictions made by spatially-explicit models of fish growth rate potential

Synopsis Spatially-explicit modeling of fish growth rate potential is a relatively new approach that uses physical and biological properties of aquatic habitats to map spatial patterns of fish growth rate potential. Recent applications of spatially-explicit models have used an arbitrary spatial scale and have assumed a fixed foraging efficiency. We evaluated the effects of spatial scale, predator foraging efficiency (combined probabilities of prey recognition, attack, capture, and ingestion), and predator spatial distribution on estimates of mean growth rate potential of chinook salmon,Oncorhynchus tshawytscha. We used actual data on prey densities and water temperatures taken from Lake Ontario during the summer, as well as, simulated data assuming binomial distribution of prey. Results show that a predator can compensate for low foraging efficiency by inhabiting the most profitable environments (regions of high growth rate potential). Differences exist in predictions of growth rate potential across spatial scales of observation and a single scale may not be adequate for interpreting model results across seasons. Continued refinements of this modeling approach must focus on the assumptions of stationary distributions of predator and prey populations and predator foraging tactics.     

The Effect of Food Size and Dispersion Pattern on Retrieval Rate by the Argentine Ant, Linepithema humile (Hymenoptera: Formicidae)

Food acquisition in central-place foraging animals demands efficient detection and retrieval of resources. Most ant species rely on a mass recruitment foraging strategy, which requires that some potential foragers remain at the nest where they can be recruited to food once resources are found. Because this strategy reduces the number of workers initially looking for food, it may reduce the food detection rate while increasing the postdiscovery food retrieval rate. In previous studies this tradeoff has been analyzed by computer simulation and mathematical models. Both kinds of models show that food acquisition rate is greatly influenced by food distribution and resource patch size: as food is condensed into fewer patches, the maximal acquisition rate is achieved by a shift to fewer initial searchers and more potential recruits. In general, these models show that a mass recruitment strategy is most effective when resources are clumped. We tested this prediction in two experiments by letting laboratory colonies of the Argentine ant (Linepithema humile) forage for resources placed in different distributions. When all prey were small, retrieval rate increased with increasing resource patch size, in support of foraging models. When prey were large, however, the mass of prey returned to the colony over time was much lower than when prey were small and widely distributed. As more ants reached a large prey item, the distance the prey item was transported decreased due to a greater emphasis on feeding rather than transport. Because Argentine ants can transport more biomass externally than they can ingest, food retrieval that depends only on ingestion can depress the biomass retrieval rate. Thus, our results generally support theoretical foraging models, but we show how prey size, through differential prey-handling behavior, can produce an outcome greatly different from that predicted only on the distribution of resources.     

Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness

Optimal foraging theory concerns animal behavior in landscapes where food is concentrated in patches. The efficiency of foraging is an effect of both the animal behavior and the geometry of the landscape; furthermore, the landscape is itself affected by the foraging of animals. We investigated the effect of landscape heterogeneity on the efficiency of an optimal forager. The particular aspect of heterogeneity we considered was "clumpiness"– the degree to which food resource patches are clustered together. The starting point for our study was the framework of the Mean Value Theorem (MVT) by Charnov. Since MVT is not spatially explicit, and thus not apt to investigate effects of clumpiness, we built an agent-based (or individual-based) model for animal movement in discrete landscapes extending the MVT. We also constructed a model for generating landscapes where the clumpiness of patches can be easily controlled, or "tuned", by an input parameter. We evaluated the agent based model by comparing the results with what the MTV would give, i.e. if the spatial effects were removed. The MVT matched the simulations best on landscapes with random patch configuration and high food recovery rates. As for our main question about the effects of clumpiness, we found that, when landscapes were highly productive (rapid food replenishment), foraging efficiency was greatest in clumped landscapes. In less productive landscapes, however, foraging efficiency was lowest in landscapes with a clumped patch distribution.     

Indirect risk effects reduce feeding efficiency of ducks during spring

Indirect risk effects of predators on prey behavior can have more of an impact on prey populations than direct consumptive effects. Predation risk can elicit more vigilance behavior in prey, reducing the amount of time available for other activities, such as foraging, which could potentially reduce foraging efficiency. Understanding the conditions associated with predation risk and the specific effects predation risk have on prey behavior is important because it has direct influences on the profitability of food items found under various conditions and states of the forager. The goals of this study were to assess how ducks perceived predation risk in various habitat types and how strongly perceived risk versus energetic demand affected foraging behavior. We manipulated food abundance in different wetland types in Illinois, USA to reduce confounding between food abundance and vegetation structure. We conducted focal‐animal behavioral samples on five duck species in treatment and control plots and used generalized linear mixed‐effects models to compare the effects of vegetation structure versus other factors on the intensity with which ducks fed and the duration of feeding stints. Mallards fed more intensively and, along with blue‐winged teal, used longer feeding stints in open habitats, consistent with the hypothesis that limited visibility was perceived to have a greater predation risk than unlimited visibility. The species temporally nearest to nesting, wood ducks, were willing to take more risks for a greater food reward, consistent with an increase in a marginal value of energy as they approached nesting. Our results indicate that some duck species value energy differently based on the surrounding vegetation structure and density. Furthermore, increases in the marginal value of energy can be more influential than perceived risk in shaping foraging behavior patterns. Based on these findings, we conclude that the value of various food items is not solely determined by energy contained in the item but by conditions in which it is found and the state of the forager.     

Effects of human‐induced prey depletion on large carnivores in protected areas: Lessons from modeling tiger populations in stylized spatial scenarios

Prey depletion is a major threat to the conservation of large carnivore species globally. However, at the policy‐relevant scale of protected areas, we know little about how the spatial distribution of prey depletion affects carnivore space use and population persistence. We developed a spatially explicit, agent‐based model to investigate the effects of different human‐induced prey depletion experiments on the globally endangered tiger (Panthera tigris) in isolated protected areas—a situation that prevails throughout the tiger's range. Specifically, we generated 120 experiments that varied the spatial extent and intensity of prey depletion across a stylized (circle) landscape (1,000 km²) and Nepal's Chitwan National Park (~1,239 km²). Experiments that created more spatially homogenous prey distributions (i.e., less prey removed per cell but over larger areas) resulted in larger tiger territories and smaller population sizes over time. Counterintuitively, we found that depleting prey along the edge of Chitwan National Park, while decreasing tiger numbers overall, also decreased female competition for those areas, leading to lower rates of female starvation. Overall our results suggest that subtle differences in the spatial distributions of prey densities created by various human activities, such as natural resource‐use patterns, urban growth and infrastructure development, or conservation spatial zoning might have unintended, detrimental effects on carnivore populations. Our model is a useful planning tool as it incorporates information on animal behavioral ecology, resource spatial distribution, and the drivers of change to those resources, such as human activities.     

Spatial and trophic niche differentiation in two sympatric lizards (Tropidurus torquatus and Cnemidophorus ocellifer) with different foraging tactics

Abstract In a ‘restinga’ habitat of southeastern Brazil, we studied the food habits and the microhabitat use of two lizards with distinct foraging modes: the tropidurid Tropidurus torquatus, a sit-and-wait predator, and the teiid Cnemidophorus ocellifer, a wide forager. The diet of the two species differed strongly, indicating a low level of similarity in their trophic niche. The sit-and-wait predator fed mainly on mobile prey, whereas the wide forager fed mainly on sedentary prey (larvae). The spatial niche breadth of T. torquatus was larger than that of C. ocellifer. Despite interspecific differences, the two species overlapped greatly in micro-habitat use. The data indicate that at Linhares the two lizard species differed more in food resources than in microhabitat, and that most of the food differences reflect the foraging patterns of the species.     

Assessment of food source profitability in honeybees (<Emphasis Type="Italic">Apis mellifera</Emphasis>): how does disturbance of foraging activity affect trophallactic behaviour?

When forager honeybees (Apis mellifera) return to the hive after a successful foraging trip, they unload the collected liquid to recipient hive mates through mouth-to-mouth contacts (trophallaxis). The speed at which the liquid is transferred (unloading rate) from donor to recipient is related to the profitability of the recently visited food source. Two main characteristics that define this profitability are the flow of solution delivered by the feeder and the time invested by the forager at the source (visit time). To investigate the effect of visit time on trophallactic behaviour, donor foragers were trained to a rate feeder that could deliver different flows of solution. We dissociated visit time and flow of solution by introducing pauses in the solution's deliverance at different moments of the foraging visit. We analysed whether timing of the non-deliverance period within the visit is important for the forager's assessment of resource profitability. During the subsequent trophallactic encounter with a hive mate, unloading rate was related to the total time invested by the forager at the food source only if the ingestion process had already been started. These results together with previous ones suggest that foragers integrate an overall flow rate of solution of the feeder throughout the entire foraging visit.     

Short‐term prey field lability constrains individual specialisation in resource selection and foraging site fidelity in a marine predator

Spatio‐temporally stable prey distributions coupled with individual foraging site fidelity are predicted to favour individual resource specialisation. Conversely, predators coping with dynamic prey distributions should diversify their individual diet and/or shift foraging areas to increase net intake. We studied individual specialisation in Scopoli's shearwaters (Calonectris diomedea) from the highly dynamic Western Mediterranean, using daily prey distributions together with resource selection, site fidelity and trophic‐level analyses. As hypothesised, we found dietary diversification, low foraging site fidelity and almost no individual specialisation in resource selection. Crucially, shearwaters switched daily foraging tactics, selecting areas with contrasting prey of varying trophic levels. Overall, information use and plastic resource selection of individuals with reduced short‐term foraging site fidelity allow predators to overcome prey field lability. Our study is an essential step towards a better understanding of individual responses to enhanced environmental stochasticity driven by global changes, and of pathways favouring population persistence.