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.     

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.     

Optimal strategies of spatial distribution: the Olli effect

The selection of strategies of spatial distribution of individuals has been studied. In case of non-monotonous dependence of reproduction coefficient on the mean population density, a cluster formation is possible. At low mean densities, parity strategies of spatial distribution are realized, and at high densities, non-parity ones. A generalized notion of parity strategy of spatial distribution has been proposed. It includes such expenditures as expenditure for the movement of an individual, defense of the territory etc. A problem of evolutionary stability of different strategies of spatial distribution has been discussed.     

How insects sense olfactory patches – the spatial scaling of olfactory information

When searching for resources in heterogeneous environments, animals must rely on their abilities to detect the resources via their sensory systems. However, variation in the strength of the sensory cue may be mediated by the physical size of the resource patch. Patch detection of insects are often predicted by the scaling of sensory cues to patch size, where visual cues has been proposed to scale proportional to the diameter of the patch. The scaling properties of olfactory cues are, however, virtually unknown. Here, we investigated scaling rules for olfactory information in a gradient of numbers of odour sources, relevant to odour‐mediated attraction under field conditions. We recorded moth antennal responses to sex pheromones downwind from pheromone patches and estimated the slope in the scaling relationship between the effective length of the odour plumes and the number of odour sources. These measurements showed that the effective plume length increased proportional to the square root of the number of odour sources. The scaling relationship, as estimated in the field experiment, was then evaluated against field data of the slope in the relationship between trap catch and release rate of chemical attractants for a wide range of insects. This meta‐analysis revealed an average slope largely consistent with the estimated scaling relationship between the effective plume length and the number of odour sources. This study is the first to estimate the scaling properties of olfactory cues empirically and has implications for understanding and predicting the spatial distributions of insects searching by means of olfactory cues in heterogeneous environments.     

Movement between patches, unequal competitors and the ideal free distribution

Researchers have often commented on the ability of the original ideal free distribution (IFD) model to approximate observed animal distributions even though the critical assumption that competitors are of equal ability is usually violated. We provide an explanation by recognizing that animals will occasionally move between patches for reasons other than to simply maximize their resource payoffs, given perfect (i.e. ideal) information about the current payoff in each patch, and that these movements will continue to occur even after an equilibrium is reached. When such movements are incorporated into an unequal competitors IFD model, a single, stable distribution of each competitor type is predicted. This equilibrium will usually be characterized by under-matching of total competitive units relative to the distribution of resources (i.e. too few competitive units in the good patch). More importantly, it will often resemble the original, equal competitors IFD, in that total competitor numbers will come close to matching the distribution of resources. We argue that researchers claiming to have observed an IFD of equal competitors have actually observed this equilibrium distribution of unequal competitors. Our model predicts that the deviation from input-matching will usually be an under-matching of total competitor numbers relative to resources (i.e. too few competitors in the good patch). Examination of published data reveals that post-equilibrium movement between patches occurs frequently and, although the reported distributions are similar to those predicted by input-matching, under-matching is usually observed.     

A computer‐activated food delivery system for dispensing natural prey items among complex arrays of patches

Experimental studies of the foraging ecology of drift‐feeding fishes have been limited in scope because of the lack of systems for dispensing suitable prey items to a number of patches with complex and controlled spatio‐temporal patterns of delivery rate. Here, tests are reported of a computer‐controlled feeding system that performs this requirement with considerable flexibility.     

A stochastic model of the distribution of unequal competitors between resource patches

We present a stochastic model of individuals' movements between two patches of resources. The population is made up of two types of individual with differing competitive abilities, and two types of movements occur, with individuals moving either to increase their intake rate or at random. Several previous models have used simulations to evaluate the likely distribution of individuals. We instead derive equations for the equilibrium distribution of the population, which can be solved numerically. This avoids the need to choose an initial distribution for the population, and enables us to obtain the probability with which rare events occur. This may not be possible when simulations are used, since a rare event may not occur at all. We find that when random movements are rare, an increase in the rate of random movements out of a patch can increase the number of individuals on that patch. We consider an approximation to the model with rare random movements, which provides an explanation for this phenomenon.     

The effect of dispersal between patches on the stability of large trophic food webs

Theoretical Ecology - Using computer simulations for the population dynamics of systems with many species, we investigate the stability of food webs distributed over several patches that are...     

Optimal foraging: movement patterns of bumblebees between inflorescences

Nectar-collecting bumblebees are hypothesized to employ rules of movement which result in the maximum net rate of energy gain (i.e., are optimal). The optimal movement rules are derived from a mathematical model and are used to generate predicted patterns of movement. The predicted patterns are compared with field observations. These observations support the hypothesis. An important component of the mathematical model is the memory of the foraging animal. The field data have implications concerning the memory capabilities of the bumblebees.     

Swimming response of goldfish,Carassius auratus,and the tetra,Hemigrammus caudovittatus,larvae to individual food items and patches

Synopsis Swimming speed and swimming path of goldfish and tetra larvae were studied in aquaria containing food patches composed of decapsulated cysts and immobilized nauplii of Artemia salina or sparsely distributed prey. The mean swimming speed of starved larvae in the medium without food was about four times higher than the speed of larvae feeding in a patch. Satiated larvae swam about 1.5 times slower than hungry fish. Consumption of single prey items by starved larvae caused the following sequence of swimming responses: handling pause (cessation of swimming), slow swimming in a restricted area, and fast swimming (approximately twice as fast as hungry larvae before encountering food) accompanied by a widening of the area searched (area increased searching). Mean swimming speed was constant over a broad range (10¹–10³ ind·1^–1 of food density, although at extreme (high or low) values of food density it depended on swimming responses of the predator. Frequency of visits to the different parts of the aquarium strongly depended on encounters of hungry fish with food particles or patches.     

Interactive effects of haloclines and food patches on the vertical distribution of 3 species of temperate invertebrate larvae

In laboratory experiments, we examined the effect of haloclines and determined whether the presence of food patches overrides this effect on larval vertical distribution of the sea star Asterias rubens, the sea urchin Strongylocentrotus droebachiensis and the mussel Mytilus edulis. We experimentally constructed haloclines in which the salinity of the bottom water layer was 35 and that of the top layer was 21, 24, 27, and 30 (21/35, 24/35, 27/35, and 30/35) for A. rubens and S. droebachiensis, and 24, 27, 30 and 32 (24/35, 27/35, 30/35, and 32/35) for M. edulis. For each species and stage, additional halocline treatments (A. rubens: 24/32 and 27/32; 4-arm S. droebachiensis: 21/29 and 24/32; 6-arm S. droebachiensis: 24/29 and 24/32; M. edulis: 27/32 and 30/32) were used to determine whether the larval response to inhibitory salinity gradients was due to the absolute salinity of the top layer or the relative salinity difference between the two layers. Also, we measured the density of A. rubens and M. edulis to determine whether the specific gravity of larvae can explain the observed vertical distributions. Larvae aggregated at and below the halocline and these aggregations were more pronounced with increasing strength of the vertical salinity gradient. Threshold salinities in the top layer which inhibited ~ 100% of the larvae from crossing the halocline were 24 for A. rubens and M. edulis, and 21 for S. droebachiensis. These distributional patterns were not the result of larval density, which was greater than all treatment water densities for M. edulis and S. droebachiensis and lower for A. rubens. The effect of the presence of a food patch at inhibitory haloclines (A. rubens: 24/35 and 27/35; 4-arm S. droebachiensis: 21/34 and 24/34; M. edulis: 27/35) was determined by using three algal densities: 0, 5000 or 10 000 cells ml^- 1Thalassiosira pseudonana in either the top or the bottom water layer. For both A. rubens and M. edulis, the number of larvae at the halocline increased in the presence of a food patch, but this effect did not depend on algal density in the patch. For 4-arm S. droebachiensis, there was no effect of the presence of a food patch on larval vertical distribution. Our results suggest that low salinity may act as a barrier to vertical movement and that the presence of food patches above the halocline may strengthen the larval aggregation response to inhibitory haloclines.     

Optimal foraging in hummingbirds: Rule of movement between inflorescences

The movements of hummingbirds between inflorescences of scarlet gilia (Ipomopsis aggregata) were studied. These movements exhibited the following patterns: (1) Although the hummingbirds appeared to avoid moving to the previous inflorescence, no significant correlation was found between the directions of successive inter-inflorescence movements. (2) The frequency distribution of inter-inflorescence flight distances was found to be leptokurtic. (3) The hummingbirds were more likely to move to an inflorescence the larger and/or closer it was. (4) The hummingbirds moved to inflorescences of greatest apparent size (i.e. ratio of number of flowers available to distance from present inflorescence) more often than they moved to the largest inflorescence, the closest infloresence, or the inflorescence estimated to yield the greatest rate of energy gain. (5) The frequency distribution of moves to the inflorescence having the ith greatest apparent size is well fitted by a geometric distribution. This is consistent with the hummingbrids choosing the inflorescence of greatest apparent size (excluding the previous inflorescence) from within some scanning sector. These movement patterns are consistent with the expectations of optimal foraging theory only if the hummingbirds cannot or do not determine the directions of possible inflorescences relative to the direction of arrival at the present inflorescence and if they cannot assess independently the sizes and distances of possible inflorescences.     

On the frequency response of prestin charge movement in membrane patches

Outer hair cell (OHC) nonlinear membrane capacitance derives from voltage-dependent sensor charge movements within the membrane protein prestin (SLC26a5) that drive OHC electromotility. The ability of the protein to influence hearing depends on its reaction to membrane receptor potentials across auditory frequency. Estimates of prestin’s frequency response have been evaluated by several groups out to tens of kHz in voltage-clamped macro-patches of OHC membrane. The response is a power function of frequency that is down 40 dB at 77 kHz. Despite these observations, concerns remain that the macro-patch approach is flawed due to mechanical constraints of pipette solution column load or patch size itself. In the absence of these influences, prestin’s frequency response is posited by some to be ultrasonic in nature. Here we evaluate the influence of these putative confounding factors on prestin’s frequency response. We show that neither pipette column height nor negative or positive pipette pressure substantially influence total sensor charge frequency response. Additionally, patch surface area has negligible influence. We conclude that the speed of voltage-driven conformational changes in prestin within the plasma membrane is accurately assessed with the macro-patch technique, permitting investigations of membrane characteristics that can substantially alter prestin’s performance bandwidth. We illustrate significant alterations in bandwidth by perturbation of membrane fluidity and chloride anion concentration. Finally, we speculate that OHC membrane characteristics may differ along the tonotopic axis of the cochlea to tune nonlinear membrane capacitance frequency cutoffs.     

Posture and support use of old world monkeys (Cercopithecidae): The influence of foraging strategies,activity patterns,and the spatial distribution of preferred food items

A common objective in field studies of positional behavior is to establish functional links between locomotion, body size, habitat use, foraging strategies, and maintenance activities. In contrast, there has been relatively little effort to examine posture in a similar, comparative context. Although various studies have shown that particular postures are employed in specific contexts, the theory which could provide the basis for understanding posture on a more general level has not been explicitly stated. This is particularly true for primates lacking specializations such as prehensile tails, claws for clinging, or adaptations for forelimb suspension. Consequently, there are few a priori reasons for predicting postural differences among generalized arboreal quadrupeds. Six sympatric cercopithecid monkeys were studied for 14 months in the Ivory Coast's Tai Forest to determine if more general relationships do exist between posture and other aspects of behavior. The results demonstrate that the postural diversity with these primates can, to varying degrees, be understood within the context of differences in the spatial distribution of preferred food items, activity patterns, support use, and foraging strategies. Am. J. Primatol. 46:229–250, 1998. © 1998 Wiley-Liss, Inc.     

The information of food distribution realizes an ideal free distribution: Support of perceptual limitation

Previous tests of ideal free distribution (IFD) under continuous input conditions have demonstrated that more profitable patches tend to be relatively underused compared to that predicted by the theory. We tested the hypothesis that competitors’ perceptual constraints of resource distribution cause this deviation from the IFD. A laboratory experiment was conducted to determine whether additional information on food distribution by a light cue that indicates the food input point improves the IFD theory’s fit to the distribution of clone red-spotted masu salmons (Salmonids),Oncorhynchus masou ishikawai, that had been conditioned to the light as a cue indicating the site with a higher input rate. In the treatments without a light cue, the distribution of fish was closer to a random pattern than an IFD. In contrast, in the treatments with light cue, the distribution of fish was closer to the expected value of an IFD rather than to a random pattern, supporting the perception-limit hypothesis. The distribution and the pattern of resource use by fish in the treatments without the light cue were best explained by the perception-limit model. Our results suggest that it is perceptual constraints that cause deviation from the IFD.     

Integrating the roles of information and competitive ability on the spatial distribution of social foragers

Understanding and predicting the spatial distribution of social foragers among patchily distributed resources is a problem that has been addressed with numerous approaches over the 30 yr since the ideal free distribution (IFD) was first introduced. The two main approaches involve perceptual constraints and unequal competitors. Here we present a model of social foragers choosing among resource patches. Each forager makes a probabilistic choice on the basis of the information acquired through past foraging experiences. Food acquisition is determined by the forager's competitive ability. This model predicts that perceptual constraints have a greater influence on the spatial distribution of foragers than unequal competitive abilities but that competitive ability plays an important role in determining an individual's information state and behavior. Better competitors have access to more information; consequently, we find that competitive abilities and perceptual constraints are integrated through the social environment occupied by individual foragers. Relative competitive abilities influence the forager's information state, and the ability to use information determines the resulting spatial distribution.     

Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell

It is widely believed that synaptic modifications underlie learning and memory. However, few studies have examined what can be deduced about the learning process from the distribution of synaptic weights. We analyze the perceptron, a prototypical feedforward neural network, and obtain the optimal synaptic weight distribution for a perceptron with excitatory synapses. It contains more than 50% silent synapses, and this fraction increases with storage reliability: silent synapses are therefore a necessary byproduct of optimizing learning and reliability. Exploiting the classical analogy between the perceptron and the cerebellar Purkinje cell, we fitted the optimal weight distribution to that measured for granule cell-Purkinje cell synapses. The two distributions agreed well, suggesting that the Purkinje cell can learn up to 5 kilobytes of information, in the form of 40,000 input-output associations.