Optimal patch residence time of a sit-and-wait forager

This paper addresses optimal giving-up time of a sit-and-waitforager by a rate maximization model. It was assumed that aforager takes at most only one prey item in a patch in one trial,that is, the forager leaves a patch with a prey item (if itattacks it) or without prey (if it gives up). Some kinds ofsit-and-wait foragers, like owls, hunt in this manner. The followingassumptions were made: (1) A forager recognizes the habitattype of patches (e.g., forest type or grassland type). (2) Spatialor temporal heterogeneity generates the uncertainty of the environmentin each habitat type. It was assumed that in a patch (in habitattype i), prey encounter rate (X) is fixed during the trial andencounter with prey depends on a Poisson process. However, preyencounter rate varies across trials within each habitat typeaccording to _i-(). Thus the forager does not know the prey encounterrate that is assigned to each patch in the type, but it knowsthe probability density function, _i-(). (3) The forager encounterseach habitat type randomly in the environment. The patch residencetime for each habitat type was considered as the only decisionparameter. Considering stochastic change of prey encounter ratein patches of a habitat type, information limitation for theforaging animal can be treated. Patch residence time was influencedby the pattern of the stochasticity. When the forager knowsperfectly the encounter rate of prey in each patch (i.e., nostochasticity), the optimal giving-up time is infinite or zero(reject the patch). With the limited information (stochasticenvironment), the condition for a finite, nonzero optimal giving-uptime in patches of a habitat depends on how far the worst caseis below the average among patches of the habitat and how badthe worst case is compared to the average of the whole environment.In a negatively skewed habitat, these conditions tend to holdeasily. The optimal forager should perform pessimistically ordoubt whether the patch contains prey, that is, set a finitegiving-up time. In a positively skewed habitat, the optimalforager should perform optimistically, that is, set an infinitegiving-up time. The expected gain is higher in the positivelyskewed habitat than in the negatively skewed habitat. When theforager must choose between the two habitats, it should choosethe positively skewed habitat. [Behav Ecol 1991;2:283–294]     

Evolutionary responses of dispersal distance to landscape structure and habitat loss

It is generally well understood that some ecological factors select for increased and others for decreased dispersal. However, it has remained difficult to assess how the evolutionary dynamics are influenced by the spatio-temporal structure of the environment. We address this question with an individual-based model that enables habitat structure to be controlled through variables such as patch size, patch turnover rate, and patch quality. Increasing patch size at the expense of patch density can select for more or less dispersal, depending on the initial configuration. In landscapes consisting of high-quality and long-lived habitat patches, patch degradation selects for increased dispersal, yet patch loss may select for reduced dispersal. These trends do not depend on the component of life-history that is affected by habitat quality or the component of life-history through which density-dependence operates. Our results are based on a mathematical method that enables derivation of both the evolutionary stable strategy and the stationary genotype distribution that evolves in a polymorphic population. The two approaches generally lead to similar predictions. However, the evolutionary stable strategy assumes that the ecological and evolutionary time scales can be separated, and we find that violation of this assumption can critically alter the evolutionary outcome.     

Homogenization techniques for population dynamics in strongly heterogeneous landscapes

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

The conflict between optimisation and orderliness in building behaviour of the caddis fly,Chaetopteryx villosa Fabr.(Limnephilidae: Trichoptera), larvae

The Optimal Foraging Theory predict that an animal should restrict its searching activity to those patches of environment, where the ratio of gain to time and energy spent is maximal. Experimenters usually verify the prediction against the null hypothesis of random activity distribution between patches. As animals always prefer profitable patches to some degree, experimental results can always be interpreted as confirmation of the theory. In opposite to this approach, we put forward the "regularity hypothesis". According to this hypothesis, the finding of a profitable item in some patch makes an animal to stay and test more items within the patch. The readiness to test decreases if the profitability of these items is low, and the animal eventually leaves the patch. It also searches in other patches less carefully. As a result, positive and negative responses to items are repeated by ordered series. In general, this regularity of responses helps animals to choose profitable patches. However, animals may also ignore some profitable patches because of the regularity, so that the behavioural optimazation fails. The regularity hypothesis have been tested in experiment with the search of building material and patch choice by caddisfly larvae. The first of two experimental patches contained egg shell fragments (profitable building material) mixed with a sand (unprofitable). The second patch contained sand only. Larva stayed within the first patch after a shell had been found, so that the probability to find more shells increased. However, larvae started walking after they had found several sand particles. Once starting to walk, they found new shell fragments and tested them, but tended to reject them and eventually leave the patch. Moreover, upon returning to the first patch, larvae also might reject fragments and leave the patch again. Rejections are accounted for by the fact that the duration of testing was too short to identify fragments correctly. As a result, negative responses were repeated to a certain degree independently of the profitability of building material, and the patch choice was not optimal. These results are agreed with the regularity hypothesis. It is argued that the hypothesis can be used as an alternative to the Optimal Foraging Theory.     

Patch use behaviour in benthic fish depends on their long-term growth prospects

Animals foraging in a heterogeneous environment may combine prior information on patch qualities and patch sample information to maximize intake rate. Prior information dictates the long-term expectations, whereas prior information in combination with patch sample information determines when to leave an individual food patch. We examined patch use behaviour of benthic feeding fish in their natural environment at different spatial scales to test if they could determine patch quality and if patch use behaviour was correlated with environmental quality. In seven lakes along a gradient of environmental quality (measured as maximum benthivore size), we made repeated measurements of giving-up density (GUD) in artificial food patches of different qualities. At the largest spatial scale, between lakes, we tested if giving-up densities revealed the long-term growth expectation of benthic fish. At the local scale of patches and micro patches we tested for the ability of benthic fish to assess patch quality, and how this ability depended on the patch exploitation levels between the different lakes. We found that GUD was positively related to maximum size of bream, suggesting that short-term behavioural decisions reflected long-term growth expectations. Benthic fish discriminated between nearby rich and poor patches, but not between rich and poor micropatches within a food patch. This suggests that the foraging scale of benthic fish lies between the patch and micro patch scale in our experiments. We conclude that patch use behaviour of benthic fish can provide a powerful measure of habitat quality that reveals how benthic fish perceive their environment.     

A game theoretical model of kleptoparasitism with incomplete information

Kleptoparasitism, the stealing of food from one animal by another, is a common natural phenomenon that has been modelled mathematically in a number of ways. The handling process of food items can take some time and the value of such items can vary depending upon how much handling an item has received. Furthermore this information may be known to the handler but not the potential challenger, so there is an asymmetry between the information possessed by the two competitors. We use game-theoretic methods to investigate the consequences of this asymmetry for continuously consumed food items, depending upon various natural parameters. A variety of solutions are found, and there are complex situations where three possible solutions can occur for the same set of parameters. It is also possible to have situations which involve members of the population exhibiting different behaviours from each other. We find that the asymmetry of information often appears to favour the challenger, despite the fact that it possesses less information than the challenged individual. The research was supported by EPSRC grant EP/E043402/1 and NSF 0634182.     

Patch edges and insect populations

Responses of insect populations may be related to patch size and patch edge responses, but it is not clear how to identify these rapidly. We used a random-walk model to identify three qualitative responses to edges: no edge effect (the null model), reflecting edges and absorbing edges. Interestingly, no edge effect meant that abundance was lower at edges than in the center of patches, and reflecting edges have similar abundance at edges and centers. We then characterized several insect species’ response within maize plots to patch edges and patch size, using a simple, quick, qualitative experiment. Coleomegilla maculata and Trichogramma spp. were the only organisms that responded to patch size and edges as patch theory and the null edge model would predict. Ostrinia nubilalis larvae and possibly Rhopalosiphum maidis and eggs of Chrysopa spp. responded to patch size and edges as predicted by an attracting edge model. Estimation of predation rates suggested that the spatial distribution of these species might be determined by predators. Edge effects or the lack thereof relative to patch size may be rapidly determined for arthropod species, which could lead to understanding the mechanism(s) underlying these effects. This information may be useful in reaction diffusion models through a scaling-up approach to predict population structure of species among patches in a landscape. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Prior knowledge about spatial pattern affects patch assessment rather than movement between patches in tactile-feeding mallard

1. Heterogeneity in food abundance allows a forager to concentrate foraging effort in patches that are rich in food. This might be problematic when food is cryptic, as the content of patches is unknown prior to foraging. In such case knowledge about the spatial pattern in the distribution of food might be beneficial as this enables a forager to estimate the content of surrounding patches. A forager can benefit from this pre-harvest information about the food distribution by regulating time in patches and/or movement between patches. 2. We conducted an experiment with mallard Anas platyrhynchos foraging in environments with random, regular, and clumped spatial configurations of full and empty patches. An assessment model was used to predict the time in patches for different spatial distributions, in which a mallard is predicted to remain in a patch until its potential intake rate drops to the average intake rate that can be achieved in the environment. A movement model was used to predict lengths of interpatch movements for different spatial distributions, in which a mallard is predicted to travel to the patch where it expects the highest intake rate. 3. Consistent with predictions, in the clumped distribution mallard spent less time in an empty patch when the previously visited neighbouring patch had been empty than when it had been full. This effect was not observed for the random distribution. This shows that mallard use pre-harvest information on spatial pattern to improve patch assessment. Patch assessment could not be evaluated for the regular distribution. 4. Movements that started in an empty patch were longer than movements that started in a full patch. Contrary to model predictions this effect was observed for all spatial distributions, rather than for the clumped distribution only. In this experiment mallard did not regulate movement in relation to pattern. 5. An explanation for the result that pre-harvest information on spatial pattern affected patch assessment rather than movement is that mallard move to the nearest patch where the expected intake rate is higher than the critical value, rather than to the patch where the highest intake rate is expected.     

Similarity from Multi-Dimensional Scaling: Solving the Accuracy and Diversity Dilemma in Information Filtering

Recommender systems are designed to assist individual users to navigate through the rapidly growing amount of information. One of the most successful recommendation techniques is the collaborative filtering, which has been extensively investigated and has already found wide applications in e-commerce. One of challenges in this algorithm is how to accurately quantify the similarities of user pairs and item pairs. In this paper, we employ the multidimensional scaling (MDS) method to measure the similarities between nodes in user-item bipartite networks. The MDS method can extract the essential similarity information from the networks by smoothing out noise, which provides a graphical display of the structure of the networks. With the similarity measured from MDS, we find that the item-based collaborative filtering algorithm can outperform the diffusion-based recommendation algorithms. Moreover, we show that this method tends to recommend unpopular items and increase the global diversification of the networks in long term.     

A model of food stealing with asymmetric information

Many animals acquire food by stealing it from others. There are species of specialist thieves, but more commonly animals will search for both food items and items already found by others, often conspecifics, that can be stolen. This type of behaviour has previously been modelled using a range of approaches. One of these is the Finder–Joiner model, where one animal, the “Finder”, discovers a food patch that takes some time to be consumed. Before consumption of the patch can be completed, another individual, the “Joiner”, discovers the Finder and its food patch, and has the opportunity to attempt to steal it. Depending upon how large the patch was, and how long the Finder has been alone on the patch, there may be much or little food remaining. In this paper, building on previous work, we consider a version of this game where the Finder knows the value of the remaining food patch, but the Joiner does not. We see that depending upon the model parameters, the extra information possessed by the Finder can be beneficial or detrimental in comparison to the case where both individuals have full information.     

Fast coding of orientation in primary visual cortex

Understanding how populations of neurons encode sensory information is a major goal of systems neuroscience. Attempts to answer this question have focused on responses measured over several hundred milliseconds, a duration much longer than that frequently used by animals to make decisions about the environment. How reliably sensory information is encoded on briefer time scales, and how best to extract this information, is unknown. Although it has been proposed that neuronal response latency provides a major cue for fast decisions in the visual system, this hypothesis has not been tested systematically and in a quantitative manner. Here we use a simple 'race to threshold' readout mechanism to quantify the information content of spike time latency of primary visual (V1) cortical cells to stimulus orientation. We find that many V1 cells show pronounced tuning of their spike latency to stimulus orientation and that almost as much information can be extracted from spike latencies as from firing rates measured over much longer durations. To extract this information, stimulus onset must be estimated accurately. We show that the responses of cells with weak tuning of spike latency can provide a reliable onset detector. We find that spike latency information can be pooled from a large neuronal population, provided that the decision threshold is scaled linearly with the population size, yielding a processing time of the order of a few tens of milliseconds. Our results provide a novel mechanism for extracting information from neuronal populations over the very brief time scales in which behavioral judgments must sometimes be made.     

Information Retrieval during Free Listing Is Biased by Memory: Evidence from Medicinal Plants

Free listing is a methodological tool that is widely used in various scientific disciplines. A typical assumption of this approach is that individual lists reflect a subset of total knowledge and that the first items listed are the most culturally important. However, little is known about how cognitive processes influence free lists. In this study, we assess how recent memory of use, autonoetic and anoetic memory, and long-term associative memory can affect the composition and order of items in free lists and evaluate whether free lists indicate the most important items. Based on a model of local knowledge about medicinal plants and their therapeutic targets, which was collected via individual semi-structured interviews, we classify each item recorded in free lists according to the last time that the item was used by the informant (recently or long ago), the type of relevant memory (autonoetic or anoetic memory) and the existing associations between therapeutic targets (similar or random). We find that individuals have a tendency to recall information about medicinal plants used during the preceding year and that the recalled plants were also the most important plants during this period. However, we find no trend in the recall of plants from long-term associative memory, although this phenomenon is well established in studies on cognitive psychology. We suggest that such evidence should be considered in studies that use lists of medicinal plants because this temporal cognitive limit on the retrieval of knowledge affects data interpretation.     

The survival-rate-maximizing policy for Bayesian foragers: wait for good news

We present a model of the survival-maximizing foraging behaviorof an animal searching in patches for hidden prey with a clumpeddistribution. We assume the forager to be Bayesian: it updatesits statistical estimate of prey number in the current patchwhile foraging. When it arrives at the parch, it has an expectationof the patch's quality, which equals the average patch qualityin the environment While foraging, the forager uses its informationabout the time spent searching in the patch and how many preyhas been caught during this time. It can estimate both the instantaneousintake rate and the potential intake rate during the rest ofthe parch visit. When prey distribution is clumped, potentialintake rate may increase with time spent in the parch if preyis caught in the near future. Being optimal, a Bayesian foragershould therefore base its patch-leaving decision on the estimatedpotential patch value, not on the instantaneous parch value.When patch value is measured in survival rate and mortalitymay occur either as starvation or predation, the patch shouldbe abandoned when the forager estimates that its potential survivalrate dining the rest of the patch visit equals the long termsurvival rate in the environment This means that the instantaneousintake rate, when the patch is left, is nor constant but isan increasing function of searching time in the patch. Therefore,the giving-up densities of prey in the patches will also behigher the longer the search times. The giving-up densitiesare therefore expected to be an increasing, but humped, functionof initial prey densities. These are properties of Bayesianforaging behavior not included in previous empirical studiesand model tests.     

Using GIS to model tree population parameters in the Rocky Mountain National Park forest–tundra ecotone

Climatic change may alter vegetation composition and structure, but the response to climatic change can be expected to be spatially heterogeneous. Tree populations in the alpine forest–tundra ecotone, for example, may find only certain locations to be favourable for regeneration and growth. If monitoring and detection of vegetation responses to climatic change is to be most successful, the monitoring system must be tuned to the locations where a response is most likely. We used the grass geographical information system ( gis ) to map population parameters indicating potential change throughout the forest–tundra ecotone (FTE) of Rocky Mountain National Park (RMNP). Seedling density in patch forest and krummholz openings, as well as annual krummholz height growth, were measured in the field. These parameters were then modelled over the heterogeneity of the FTE environment, using principle components regression analysis. The grass gis was used to extrapolate the resulting predictive equations to the entire RMNP FTE. Potential FTE responses to climate change were evaluated in the context of species-specific differences in how tree seedling density and krummholz height growth are associated with the present environment. For example, climate change leading towards moister conditions, causing currently xeric environments to become more mesic, might increase the spatial extent of existing tree invasion into patch forest openings. This would increase the potential for widespread conversion of patch forest to closed forest. Present population parameters extrapolated spatially may provide a useful guide to where future change is likely.     

Patch assessment in foraging flocks of European starlings: evidence for the use of public information

A field experiment was carried out to determine whether group-foragingstarlings (Sturnus vulgaris) use public information to helpthem estimate the quality of an artificial resource patch anddepart accordingly. Three kinds of information are potentiallyavailable in a group: patch-sample information, pre-harvestinformation, and public information. These three types of informationcan be combined into four patch assessment strategies: (1) patch-samplealone; (2) patch-sample and pre-harvest; (3) patch-sample andpublic; and (4) patch-sample, pre-harvest, and public. Dependingon the foraging environment we presented to the starlings, eachassessment strategy made a unique set of predictions concerningthe patch departure decisions of pairs of birds based on differencesin their foraging success. The environment was manipulated intwo ways: by altering the variability in patch quality and bychanging compatibility, the ease with which individual birdscould simultaneously acquire both patch-sample and public information.Our observations on patch persistence and departure order demonstratethat the starlings used a combination of patch-sample and publicinformation, but not pre-harvest information, to estimate thequality of the experimental patch. Moreover, our results suggestthat starlings use public information only when it is easilyavailable and ignore it under incompatible conditions. Thisstudy provides the first evidence of public information usein a patch assessment problem.     

Spatial pattern of distribution of marine invertebrates within a subtidal community: do communities vary more among patches or plots?

Making links between ecological processes and the scales at which they operate is an enduring challenge of community ecology. Our understanding of ecological communities cannot advance if we do not distinguish larger scale processes from smaller ones. Variability at small spatial scales can be important because it carries information about biological interactions, which cannot be explained by environmental heterogeneity alone. Marine fouling communities are shaped by both the supply of larvae and competition for resources among colonizers—these two processes operate on distinctly different scales. Here, we demonstrate how fouling community structure varies with spatial scale in a temperate Australian environment, and we identify the spatial scale that captures the most variability. Community structure was quantified with both univariate (species richness and diversity) and multivariate (similarity in species composition) indices. Variation in community structure was unevenly distributed between the spatial scales that we examined. While variation in community structure within patch was usually greater than among patch, variation among patch was always significant. Opportunistic taxa that rely heavily on rapid colonization of free space spread more evenly among patches during early succession. In contrast, taxa that are strong adult competitors but slow colonizers spread more evenly among patches only during late succession. Our findings show significant patchiness can develop in a habitat showing no systematic environmental spatial variation, and this patchiness can be mediated through different biological factors at different spatial scales.     

Bayes' theorem and its applications in animal behaviour

Bayesian decision theory can be used to model animal behaviour. In this paper we give an overview of the theoretical concepts in such models. We also review the biological contexts in which Bayesian models have been applied, and outline some directions where future studies would be useful. Bayesian decision theory, when applied to animal behaviour, is based on the assumption that the individual has some sort of "prior opinion" of the possible states of the world. This may, for example, be a previously experienced distribution of qualities of food patches, or qualities of potential mates. The animal is then assumed to be able use sampling information to arrive at a "posterior opinion", concerning e.g. the quality of a given food patch, or the average qualities of mates in a year. A correctly formulated Bayesian model predicts how animals may combine previous experience with sampling information to make optimal decisions. We argue that the assumption that animals may have "prior opinions" is reasonable. Their priors may come from one or both of two sources: either from their own individual experience, gained while sampling the environment, or from an adaptation to the environment experienced by previous generations. This means that we should often expect to see "Bayesian-like" decision-making in nature.     

Optimal patch use in a stochastic environment

This paper considers an animal foraging on prey which are distributed in well-defined patches. It is assumed that the environment may be stochastic and that the animal can gain information on patch type as it forages. The foraging policy which maximises mean reward rate for the environment is characterised in terms of a function of state called the potential function. This policy is shown to be given by the rule: continue foraging on the present patch while the potential is positive, when the potential falls to zero move on to the next patch. Let r denote the current reward rate on a patch and let γ denote the maximum mean reward rate for the environment. It is shown that r ? γ if it is optimal to leave. Conditions which ensure r < γ are also given. For a large class of environments the optimal policy is stated in terms of a revised reward rate r?, and is given by the rule: continue on the present patch while $\text{r}\text{?}\text{> γ}$, when r? falls to γ move on to the next patch. Finally, it is shown that the stay time on a patch is a decreasing function of γ.