Optimal foraging: Lévy pattern or process?

A guide to area-restricted search: a foundational foraging behaviour

Area-restricted search is the capacity to change search effort adaptively in response to resource encounters or expectations, from directional exploration (global, extensive search) to focused exploitation (local, intensive search). This search pattern is used by numerous organisms, from worms and insects to humans, to find various targets, such as food, mates, nests, and other resources. Area-restricted search has been studied for at least 80 years by ecologists, and more recently in the neurological and psychological literature. In general, the conditions promoting this search pattern are: (1) clustered resources; (2) active search (e.g. not a sit-and-wait predator); (3) searcher memory for recent target encounters or expectations; and (4) searcher ignorance about the exact location of targets. Because area-restricted search adapts to resource encounters, the search can be performed at multiple spatial scales. Models and experiments have demonstrated that area-restricted search is superior to alternative search patterns that do not involve a memory of the exact location of the target, such as correlated random walks or Lévy walks/flights. Area-restricted search is triggered by sensory cues whereas concentrated search in the absence of sensory cues is associated with other forms of foraging. Some neural underpinnings of area-restricted search are probably shared across metazoans, suggesting a shared ancestry and a shared solution to a common ecological problem of finding clustered resources. Area-restricted search is also apparent in other domains, such as memory and visual search in humans, which may indicate an exaptation from spatial search to other forms of search. Here, we review these various aspects of area-restricted search, as well as how to identify it, and point to open questions.

An Embodied Intelligence-Based Biologically Inspired Strategy for Searching a Moving Target

Bacterial chemotaxis in unicellular Escherichia coli, the simplest biological creature, enables it to perform effective searching behaviour even with a single sensor, achieved via a sequence of "tumbling" and "swimming" behaviours guided by gradient information. Recent studies show that suitable random walk strategies may guide the behaviour in the absence of gradient information. This article presents a novel and minimalistic biologically inspired search strategy inspired by bacterial chemotaxis and embodied intelligence concept: a concept stating that intelligent behaviour is a result of the interaction among the "brain," body morphology including the sensory sensitivity tuned by the morphology, and the environment. Specifically, we present bacterial chemotaxis inspired searching behaviour with and without gradient information based on biological fluctuation framework: a mathematical framework that explains how biological creatures utilize noises in their behaviour. Via extensive simulation of a single sensor mobile robot that searches for a moving target, we will demonstrate how the effectiveness of the search depends on the sensory sensitivity and the inherent random walk strategies produced by the brain of the robot, comprising Ballistic, Levy, Brownian, and Stationary search. The result demonstrates the importance of embodied intelligence even in a behaviour inspired by the simplest creature.

Intrinsic and environmental factors modulating autonomous robotic search under high uncertainty

Autonomous robotic search problems deal with different levels of uncertainty. When uncertainty is low, deterministic strategies employing available knowledge result in most effective searches. However, there are domains where uncertainty is always high since information about robot location, environment boundaries or precise reference points is unattainable, e.g., in cave, deep ocean, planetary exploration, or upon sensor or communications impairment. Furthermore, latency regarding when search targets move, appear or disappear add to uncertainty sources. Here we study intrinsic and environmental factors that affect low-informed robotic search based on diffusive Brownian, naive ballistic, and superdiffusive strategies (Lévy walks), and in particular, the effectiveness of their random exploration. Representative strategies were evaluated considering both intrinsic (motion drift, energy or memory limitations) and extrinsic factors (obstacles and search boundaries). Our results point towards minimum-knowledge based modulation approaches that can adjust distinct spatial and temporal aspects of random exploration to lead to effective autonomous search under uncertainty.

Optimal escape-and-feeding dynamics of random walkers: Rethinking the convenience of ballistic strategies

Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dynamics is adaptive, so at short times an area-restricted search is carried out, and a switch to extensive or ballistic motion occurs later if necessary. We derive for this case explicit analytical expressions of the mean escape time and the asymptotic growth of the depleted region in one dimension. These, together with numerical results in two dimensions, provide surprising evidence that ballistic searches are detrimental in such scenarios, a result which could explain why ballistic movement is barely observed in animal searches at microscopic and millimetric scales, therefore providing significant implications for biological foraging.

Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes

Lévy walks are random walk processes whose step lengths follow a long-tailed power-law distribution. Because of their abundance as movement patterns of biological organisms, substantial theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here, we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape. Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent Lévy walk fails to efficiently find either large targets or small ones. Our results shed new light on the Lévy foraging hypothesis and are thus expected to affect future experiments on animals performing Lévy walks.

Foraging behavior in visual search: A review of theoretical and mathematical models in humans and animals

Visual search (VS) is a fundamental task in daily life widely studied for over half a century. A variant of the classic paradigm-searching one target among distractors-requires the observer to look for several (undetermined) instances of a target (so-called foraging) or several targets that may appear an undefined number of times (recently named as hybrid foraging). In these searches, besides looking for targets, the observer must decide how much time is needed to exploit the area, and when to quit the search to eventually explore new search options. In fact, visual foraging is a very common search task in the real world, probably involving additional cognitive functions than typical VS. It has been widely studied in natural animal environments, for which several mathematical models have been proposed, and just recently applied to humans: Lévy processes, composite and area-restricted search models, marginal value theorem, and Bayesian learning (among others). We conducted a systematic search in the literature to understand those mathematical models and study its applicability in human visual foraging. The review suggests that these models might be the first step, but they seem to be limited to fully comprehend foraging in visual search. There are essential variables involving human visual foraging still to be established and understood. Indeed, a jointly theoretical interpretation based on the different models reviewed could better account for its understanding. In addition, some other relevant variables, such as certain individual differences or time perception might be crucial to understanding visual foraging in humans.

Development of swarm behavior in artificial learning agents that adapt to different foraging environments

Collective behavior, and swarm formation in particular, has been studied from several perspectives within a large variety of fields, ranging from biology to physics. In this work, we apply Projective Simulation to model each individual as an artificial learning agent that interacts with its neighbors and surroundings in order to make decisions and learn from them. Within a reinforcement learning framework, we discuss one-dimensional learning scenarios where agents need to get to food resources to be rewarded. We observe how different types of collective motion emerge depending on the distance the agents need to travel to reach the resources. For instance, strongly aligned swarms emerge when the food source is placed far away from the region where agents are situated initially. In addition, we study the properties of the individual trajectories that occur within the different types of emergent collective dynamics. Agents trained to find distant resources exhibit individual trajectories that are in most cases best fit by composite correlated random walks with features that resemble Lévy walks. This composite motion emerges from the collective behavior developed under the specific foraging selection pressures. On the other hand, agents trained to reach nearby resources predominantly exhibit Brownian trajectories.

Multiscale Computation and Dynamic Attention in Biological and Artificial Intelligence

Biological and artificial intelligence (AI) are often defined by their capacity to achieve a hierarchy of short-term and long-term goals that require incorporating information over time and space at both local and global scales. More advanced forms of this capacity involve the adaptive modulation of integration across scales, which resolve computational inefficiency and explore-exploit dilemmas at the same time. Research in neuroscience and AI have both made progress towards understanding architectures that achieve this. Insight into biological computations come from phenomena such as decision inertia, habit formation, information search, risky choices and foraging. Across these domains, the brain is equipped with mechanisms (such as the dorsal anterior cingulate and dorsolateral prefrontal cortex) that can represent and modulate across scales, both with top-down control processes and by local to global consolidation as information progresses from sensory to prefrontal areas. Paralleling these biological architectures, progress in AI is marked by innovations in dynamic multiscale modulation, moving from recurrent and convolutional neural networks-with fixed scalings-to attention, transformers, dynamic convolutions, and consciousness priors-which modulate scale to input and increase scale breadth. The use and development of these multiscale innovations in robotic agents, game AI, and natural language processing (NLP) are pushing the boundaries of AI achievements. By juxtaposing biological and artificial intelligence, the present work underscores the critical importance of multiscale processing to general intelligence, as well as highlighting innovations and differences between the future of biological and artificial intelligence.

Hybrid foraging in patchy environments using spatial memory

Efficient random searches are essential to the survival of foragers searching for sparsely distributed targets. Lévy walks have been found to optimize the search over a wide range of constraints. When targets are distributed within patches, generating a spatial memory over the detected targets can be beneficial towards optimizing the search efficiency. Because foragers have limited memory, storing each target location separately is unrealistic. Instead, we propose incrementally learning a spatial distribution in favour of memorizing target locations. We demonstrate that an ensemble of Gaussian mixture models is a suitable candidate for such a spatial distribution. Using this, a hybrid foraging strategy is proposed, which interchanges random searches with informed movement. Informed movement results in displacements towards target locations, and is more likely to occur if the learned spatial distribution is correct. We show that, depending on the strength of the memory effects, foragers optimize search efficiencies by continuous revisitation of non-destructive targets. However, this negatively affects both the target and patch diversity, indicating that memory does not necessarily optimize multi-objective searches. Hence, the benefits of memory depend on the specific goals of the forager. Furthermore, through analysis of the distribution over walking distances of the forager, we show that memory changes the underlying walk characteristics. Specifically, the forager resorts to Brownian motion instead of Lévy walks, due to truncation of the long straight line displacements resulting from memory effects. This study provides a framework that opens up new avenues for investigating memory effects on foraging in sparse environments.

Foraging in Mind

People and other animals can search for information inside their heads. Where does this ability come from, and what does it enable cognitive systems to do? In this article, we address the behavioral and cognitive similarities between search in external environments and internal environments (e.g., memory). These require both maplike representations and the means to navigate them, and the latter involves modulation between exploitation and exploration analogous to a foraging process called area-restricted search. These findings have implications for understanding a number of cognitive abilities commonly considered to be hallmarks of the human species, such as well-developed executive control and goal-directed cognition, autonoetic consciousness (i.e., self-awareness), deliberation, and free will. Moreover, this research extends our conception of what organisms may share these abilities and how they evolved.

Chemokinetic Scattering, Trapping, and Avoidance of Active Brownian Particles

We present a theory of chemokinetic search agents that regulate directional fluctuations according to distance from a target. A dynamic scattering effect reduces the probability to penetrate regions with high fluctuations and thus reduces search success for agents that respond instantaneously to positional cues. In contrast, agents with internal states that initially suppress chemokinesis can exploit scattering to increase their probability to find the target. Using matched asymptotics between the case of diffusive and ballistic search, we obtain analytic results beyond Fox colored noise approximation.

Dynamical modeling of multi-scale variability in neuronal competition

Variability is observed at multiple-scales in the brain and ubiquitous in perception. However, the nature of perceptual variability is an open question. We focus on variability during perceptual rivalry, a form of neuronal competition. Rivalry provides a window into neural processing since activity in many brain areas is correlated to the alternating perception rather than a constant ambiguous stimulus. It exhibits robust properties at multiple scales including conscious awareness and neuron dynamics. The prevalent theory for spiking variability is called the balanced state; whereas, the source of perceptual variability is unknown. Here we show that a single biophysical circuit model, satisfying certain mutual inhibition architectures, can explain spiking and perceptual variability during rivalry. These models adhere to a broad set of strict experimental constraints at multiple scales. As we show, the models predict how spiking and perceptual variability changes with stimulus conditions.

Neurocognitive free will

Free will is an apparent paradox because it requires a historical identity to escape its history in a self-guided fashion. Philosophers have itemized design features necessary for this escape, scaling from action to agency and vice versa. These can be organized into a coherent framework that neurocognitive capacities provide and that form a basis for neurocognitive free will. These capacities include (1) adaptive access to unpredictability, (2) tuning of this unpredictability in the service of hierarchical goal structures, (3) goal-directed deliberation via search over internal cognitive representations, and (4) a role for conscious construction of the self in the generation and choice of alternatives. This frames free will as a process of generative self-construction, by which an iterative search process samples from experience in an adaptively exploratory fashion, allowing the agent to explore itself in the construction of alternative futures. This provides an explanation of how effortful conscious control modulates adaptive access to unpredictability and resolves one of free will's key conceptual problems: how randomness is used in the service of the will. The implications provide a contemporary neurocognitive grounding to compatibilist and libertarian positions on free will, and demonstrate how neurocognitive understanding can contribute to this debate by presenting free will as an interaction between our freedom and our will.

Changing measurements or changing movements? Sampling scale and movement model identifiability across generations of biologging technology

Animal movement patterns contribute to our understanding of variation in breeding success and survival of individuals, and the implications for population dynamics. Over time, sensor technology for measuring movement patterns has improved. Although older technologies may be rendered obsolete, the existing data are still valuable, especially if new and old data can be compared to test whether a behavior has changed over time. We used simulated data to assess the ability to quantify and correctly identify patterns of seabird flight lengths under observational regimes used in successive generations of wet/dry logging technology. Care must be taken when comparing data collected at differing timescales, even when using inference procedures that incorporate the observational process, as model selection and parameter estimation may be biased. In practice, comparisons may only be valid when degrading all data to match the lowest resolution in a set. Changes in tracking technology, such as the wet/dry loggers explored here, that lead to aggregation of measurements at different temporal scales make comparisons challenging. We therefore urge ecologists to use synthetic data to assess whether accurate parameter estimation is possible for models comparing disparate data sets before planning experiments and conducting analyses such as responses to environmental changes or the assessment of management actions.

A Lévy-flight diffusion model to predict transgenic pollen dispersal

The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

Search in patchy media: Exploitation-exploration tradeoff

How to best exploit patchy resources? We introduce a minimal exploitation-migration model that incorporates the coupling between a searcher's trajectory, modeled by a random walk, and ensuing depletion of the environment by the searcher's consumption of resources. The searcher also migrates to a new patch when it takes S consecutive steps without finding resources. We compute the distribution of consumed resources F_{t} at time t for this non-Markovian searcher and show that consumption is maximized by exploring multiple patches. In one dimension, we derive the optimal strategy to maximize F_{t}. This strategy is robust with respect to the distribution of resources within patches and the criterion for leaving the current patch. We also show that F_{t} has an optimum in the ecologically relevant case of two-dimensional patchy environments.

Multifractal anisotropic swimming: the optimal foraging behaviour of grouper larvae

It was hypothesized that the Malabar grouper Ephinephelus malabaricus larvae have developed search patterns adapted to the distribution of their prey to maximise their net energy intake per unit time. Analysis of the swimming behaviour of E. malabaricus larvae in both the presence and absence of Artemia sp. nauplii is presented to test this hypothesis. A method derived from turbulence studies (the moment function of the displacements) was used to characterize the behaviour. The results revealed that larval swimming pattern was multifractal (intermittent and long-range-correlated) and isotropic (i.e. uniform in all directions) in the presence of prey, but multifractal and anisotropic (i.e. more frequent long displacement on the vertical axis) in the absence of prey. It is suggested that the search behaviour observed in the absence of prey is an adaptive response to prey distribution pattern, which is often characterised by multifractality and anisotropy (i.e. larger patches on the horizontal axes). In the presence of prey, E. malabaricus shifted to intensive search behaviour. Other possible contributors to the observed patterns are discussed. It is concluded that multifractality and anisotropy of swimming patterns observed in the experiment are mainly explained in an optimal foraging theory framework.

Experimental evidence for inherent Lévy search behaviour in foraging animals

Recently, Lévy walks have been put forward as a new paradigm for animal search and many cases have been made for its presence in nature. However, it remains debated whether Lévy walks are an inherent behavioural strategy or emerge from the animal reacting to its habitat. Here, we demonstrate signatures of Lévy behaviour in the search movement of mud snails (Hydrobia ulvae) based on a novel, direct assessment of movement properties in an experimental set-up using different food distributions. Our experimental data uncovered clusters of small movement steps alternating with long moves independent of food encounter and landscape complexity. Moreover, size distributions of these clusters followed truncated power laws. These two findings are characteristic signatures of mechanisms underlying inherent Lévy-like movement. Thus, our study provides clear experimental evidence that such multi-scale movement is an inherent behaviour rather than resulting from the animal interacting with its environment.

Ringed Seal Search for Global Optimization via a Sensitive Search Model

The efficiency of a metaheuristic algorithm for global optimization is based on its ability to search and find the global optimum. However, a good search often requires to be balanced between exploration and exploitation of the search space. In this paper, a new metaheuristic algorithm called Ringed Seal Search (RSS) is introduced. It is inspired by the natural behavior of the seal pup. This algorithm mimics the seal pup movement behavior and its ability to search and choose the best lair to escape predators. The scenario starts once the seal mother gives birth to a new pup in a birthing lair that is constructed for this purpose. The seal pup strategy consists of searching and selecting the best lair by performing a random walk to find a new lair. Affected by the sensitive nature of seals against external noise emitted by predators, the random walk of the seal pup takes two different search states, normal state and urgent state. In the normal state, the pup performs an intensive search between closely adjacent lairs; this movement is modeled via a Brownian walk. In an urgent state, the pup leaves the proximity area and performs an extensive search to find a new lair from sparse targets; this movement is modeled via a Levy walk. The switch between these two states is realized by the random noise emitted by predators. The algorithm keeps switching between normal and urgent states until the global optimum is reached. Tests and validations were performed using fifteen benchmark test functions to compare the performance of RSS with other baseline algorithms. The results show that RSS is more efficient than Genetic Algorithm, Particles Swarm Optimization and Cuckoo Search in terms of convergence rate to the global optimum. The RSS shows an improvement in terms of balance between exploration (extensive) and exploitation (intensive) of the search space. The RSS can efficiently mimic seal pups behavior to find best lair and provide a new algorithm to be used in global optimization problems.

Ultimate failure of the Lévy Foraging Hypothesis: Two-scale searching strategies outperform scale-free ones even when prey are scarce and cryptic

The "Lévy Foraging Hypothesis" promotes Lévy walk (LW) as the best strategy to forage for patchily but unpredictably located prey. This strategy mixes extensive and intensive searching phases in a mostly cue-free way through strange, scale-free kinetics. It is however less efficient than a cue-driven two-scale Composite Brownian walk (CBW) when the resources encountered are systematically detected. Nevertheless, it could be assumed that the intrinsic capacity of LW to trigger cue-free intensive searching at random locations might be advantageous when resources are not only scarcely encountered but also so cryptic that the probability to detect those encountered during movement is low. Surprisingly, this situation, which should be quite common in natural environments, has almost never been studied. Only a few studies have considered "saltatory" foragers, which are fully "blind" while moving and thus detect prey only during scanning pauses, but none of them compared the efficiency of LW vs. CBW in this context or in less extreme contexts where the detection probability during movement is not null but very low. In a study based on computer simulations, we filled the bridge between the concepts of "pure continuous" and "pure saltatory" foraging by considering that the probability to detect resources encountered while moving may range from 0 to 1. We showed that regularly stopping to scan the environment can indeed improve efficiency, but only at very low detection probabilities. Furthermore, the LW is then systematically outperformed by a mixed cue-driven/internally-driven CBW. It is thus more likely that evolution tends to favour strategies that rely on environmental feedbacks rather than on strange kinetics.

Patterns of interaction-dominant dynamics in individual versus collaborative memory foraging

The extent to which a cognitive system's behavioral dynamics fit a power law distribution is considered indicative of the extent to which that system's behavior is driven by multiplicative, interdependent interactions between its components. Here, we investigate the dynamics of memory processes in individual and collaborating participants. Collaborative dyads showed the characteristic collaborative inhibition effect when compared to nominal groups in terms of the number of items retrieved in a categorical recall task, but they also generate qualitatively different patterns of search behavior. To categorize search behavior, we used multi-model inference to compare the degree to which five candidate models (normal, exponential, gamma, lognormal, and Pareto) described the temporal distribution of each individual and dyad's recall processes. All individual and dyad recall processes were best fit by interaction-dominant distributions (lognormal and Pareto), but a clear difference emerged in that individual behavior is more power law, and collaborative behavior was more lognormal. We discuss these results in terms of the cocktail model (Holden et al. in Psychol Rev 116(2):318-342, 2009), which suggests that as a task becomes more constrained (such as through the necessity of collaborating), behavior can shift from power law to lognormal. This shift may reflect a decrease in the dyad's ability to flexibly shift between perseverative and explorative search patterns. Finally, our results suggest that a fruitful avenue for future research would be to investigate the constraints modulating the shift from power law to lognormal behavior in collaborative memory search.

Hidden processes in structural representations: A reply to Abbott, Austerweil, and Griffiths (2015)

In recent work exploring the semantic fluency task, we found evidence indicative of optimal foraging policies in memory search that mirror search in physical environments. We determined that a 2-stage cue-switching model applied to a memory representation from a semantic space model best explained the human data. Abbott, Austerweil, and Griffiths demonstrate how these patterns could also emerge from a random walk applied to a network representation of memory based on human free-association norms. However, a major representational issue limits any conclusions that can be drawn about the process model comparison: Our process model operated on a memory space constructed from a learning model, whereas their model used human behavioral data from a task that is quite similar to the behavior they attempt to explain. Predicting semantic fluency (e.g., how likely it is to say cat after dog in a sequence of animals) from free association (how likely it is to say cat when given dog as a cue) should be possible with a relatively simple retrieval mechanism. The 2 tasks both tap memory, but they also share a common process of retrieval. Assuming that semantic memory is a network from free-association behavior embeds variance due to the shared retrieval process directly into the representation. A simple process mechanism is then sufficient to simulate semantic fluency because much of the requisite process complexity may already be hidden in the representation. (PsycINFO Database Record

Interfacing Mind and Environment: The Central Role of Search in Cognition

Search can be found in almost every cognitive activity, ranging across vision, memory retrieval, problem solving, decision making, foraging, and social interaction. Because of its ubiquity, research on search has a tendency to fragment into multiple areas of cognitive science. The proposed topic aims at providing integrative discussion of the central role of search from multiple perspectives. We focus on controlled search processes, which require (a) a goal, (b) uncertainty about the nature, location, or acquisition method of the objects to be searched for, and (c) a method for sampling through the search environment. While this definition of search is general and applicable to different domains, the specific mechanisms in the search process will likely differ. The goal of this issue is to compare and contrast how these search processes are similar and differ in different cognitive activities, with the goal of understanding the general nature of search in terms of the three characteristics stated above. We expect that given its cross-domain nature, the topic on search will be of broad interest to cognitive scientists, including psychologists, behavioral ecologists, computer scientists, neuroscientists, linguists, and sociologists.

Apparent power-law distributions in animal movements can arise from intraspecific interactions

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.

Stochastic optimal foraging: tuning intensive and extensive dynamics in random searches

Recent theoretical developments had laid down the proper mathematical means to understand how the structural complexity of search patterns may improve foraging efficiency. Under information-deprived scenarios and specific landscape configurations, Lévy walks and flights are known to lead to high search efficiencies. Based on a one-dimensional comparative analysis we show a mechanism by which, at random, a searcher can optimize the encounter with close and distant targets. The mechanism consists of combining an optimal diffusivity (optimally enhanced diffusion) with a minimal diffusion constant. In such a way the search dynamics adequately balances the tension between finding close and distant targets, while, at the same time, shifts the optimal balance towards relatively larger close-to-distant target encounter ratios. We find that introducing a multiscale set of reorientations ensures both a thorough local space exploration without oversampling and a fast spreading dynamics at the large scale. Lévy reorientation patterns account for these properties but other reorientation strategies providing similar statistical signatures can mimic or achieve comparable efficiencies. Hence, the present work unveils general mechanisms underlying efficient random search, beyond the Lévy model. Our results suggest that animals could tune key statistical movement properties (e.g. enhanced diffusivity, minimal diffusion constant) to cope with the very general problem of balancing out intensive and extensive random searching. We believe that theoretical developments to mechanistically understand stochastic search strategies, such as the one here proposed, are crucial to develop an empirically verifiable and comprehensive animal foraging theory.

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Ecological sampling of gaze shifts

Visual attention guides our gaze to relevant parts of the viewed scene, yet the moment-to-moment relocation of gaze can be different among observers even though the same locations are taken into account. Surprisingly, the variability of eye movements has been so far overlooked by the great majority of computational models of visual attention. In this paper we present the ecological sampling model, a stochastic model of eye guidance explaining such variability. The gaze shift mechanism is conceived as an active random sampling that the foraging eye carries out upon the visual landscape, under the constraints set by the observable features and the global complexity of the landscape. By drawing on results reported in the foraging literature, the actual gaze relocation is eventually driven by a stochastic differential equation whose noise source is sampled from a mixture of α-stable distributions. This way, the sampling strategy proposed here allows to mimic a fundamental property of the eye guidance mechanism: where we choose to look next at any given moment in time, it is not completely deterministic, but neither is it completely random To show that the model yields gaze shift motor behaviors that exhibit statistics similar to those displayed by human observers, we compare simulation outputs with those obtained from eye-tracked subjects while viewing complex dynamic scenes.

Spatial foraging in free ranging bearded sakis: traveling salesmen or Lévy Walkers?

According to optimal foraging theory and most current models of primate socioecology, primate foraging involves a series of decisions concerning when is the most optimal time to leave a food patch, how to travel to the next patch in an efficient manner, and how to minimize the time and distance traveled to all patches throughout the course of the day. In this study, I assess how bearded sakis solve these challenges by presenting data on their patch use, distance minimization, and by comparing their movements with non-deterministic foraging patterns. The study group, composed of 38 ± 15 individuals, fed significantly longer in higher quality patches (quality defined by patch size and productivity) and in those that contained ripe fruit pulp. However, group size was not a significant predictor of patch occupancy. Bearded sakis traveled relatively directly between food patches, sometimes over distances > 300 m. In addition, they chose the optimal daily path among all patches visited on 9 of 17 occasions, and on average traveled only 21% more than the least distance route. Bearded saki step lengths were consistent with a Brownian rather than a Lévy Walk pattern while waiting times were consistent with a Lévy pattern. However, the distribution of their turning angles indicated a high degree of directional persistence between patches. These results suggest that bearded sakis exploit food patches that are randomly distributed spatially but heterogenous in patch quality. They appear to encode the locations of high quality food patches and minimize travel between them, despite opportunistically feeding from more abundant and randomly distributed, lower quality patches en route.

Adaptive Lévy processes and area-restricted search in human foraging

A considerable amount of research has claimed that animals’ foraging behaviors display movement lengths with power-law distributed tails, characteristic of Lévy flights and Lévy walks. Though these claims have recently come into question, the proposal that many animals forage using Lévy processes nonetheless remains. A Lévy process does not consider when or where resources are encountered, and samples movement lengths independently of past experience. However, Lévy processes too have come into question based on the observation that in patchy resource environments resource-sensitive foraging strategies, like area-restricted search, perform better than Lévy flights yet can still generate heavy-tailed distributions of movement lengths. To investigate these questions further, we tracked humans as they searched for hidden resources in an open-field virtual environment, with either patchy or dispersed resource distributions. Supporting previous research, for both conditions logarithmic binning methods were consistent with Lévy flights and rank-frequency methods–comparing alternative distributions using maximum likelihood methods–showed the strongest support for bounded power-law distributions (truncated Lévy flights). However, goodness-of-fit tests found that even bounded power-law distributions only accurately characterized movement behavior for 4 (out of 32) participants. Moreover, paths in the patchy environment (but not the dispersed environment) showed a transition to intensive search following resource encounters, characteristic of area-restricted search. Transferring paths between environments revealed that paths generated in the patchy environment were adapted to that environment. Our results suggest that though power-law distributions do not accurately reflect human search, Lévy processes may still describe movement in dispersed environments, but not in patchy environments–where search was area-restricted. Furthermore, our results indicate that search strategies cannot be inferred without knowing how organisms respond to resources–as both patched and dispersed conditions led to similar Lévy-like movement distributions.

Prey field switching based on preferential behaviour can induce Lévy flights

Using the foraging movements of an insectivorous bat, Myotis mystacinus, we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion

Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

Conditions under which a superdiffusive random-search strategy is necessary

Intuitively, lower target densities and lower detection capabilities should demand more sophisticated search strategies for a random search reasonable outcome. In contrast, when targets are easily found, a simple Brownian random walk strategy is enough. But where is the threshold between these two scenarios and when is optimization really necessary? We address this considering the interplay between two essential scales in random search, the average distance between neighbor targets l(0) and the detection capability r(v). In the limit cases the ratio β=r(v)/l(0) suffices to characterize the problem. For low (high) β a superdiffusive behavior is (is not) crucial for the process optimization. However, there is a crossover range, which is a nontrivial function of r(v) and l(0), separating the two regimes. We analyze this intermediate region, common in nature, and discuss the often overlooked important trade between resources availability and the searcher location power. Our results highlight contexts where efficient random search is a key factor for survival, such as in animal foraging.

Intermittent motion in desert locusts: behavioural complexity in simple environments

Animals can exhibit complex movement patterns that may be the result of interactions with their environment or may be directly the mechanism by which their behaviour is governed. In order to understand the drivers of these patterns we examine the movement behaviour of individual desert locusts in a homogenous experimental arena with minimal external cues. Locust motion is intermittent and we reveal that as pauses become longer, the probability that a locust changes direction from its previous direction of travel increases. Long pauses (of greater than 100 s) can be considered reorientation bouts, while shorter pauses (of less than 6 s) appear to act as periods of resting between displacements. We observe power-law behaviour in the distribution of move and pause lengths of over 1.5 orders of magnitude. While Lévy features do exist, locusts' movement patterns are more fully described by considering moves, pauses and turns in combination. Further analysis reveals that these combinations give rise to two behavioural modes that are organized in time: local search behaviour (long exploratory pauses with short moves) and relocation behaviour (long displacement moves with shorter resting pauses). These findings offer a new perspective on how complex animal movement patterns emerge in nature.

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.