Marcos G. E. da Luz

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.

Survival in patchy landscapes: the interplay between dispersal, habitat loss and fragmentation

Habitat loss and fragmentation are important factors determining animal population dynamics and spatial distribution. Such landscape changes can lead to the deleterious impact of a significant drop in the number of species, caused by critically reduced survival rates for organisms. In order to obtain a deeper understanding of the threeway interplay between habitat loss, fragmentation and survival rates, we propose here a spatially explicit multi-scaled movement model of individuals that search for habitat. By considering basic ecological processes, such as predation, starvation (outside the habitat area), and competition, together with dispersal movement as a link among habitat areas, we show that a higher survival rate is achieved in instances with a lower number of patches of larger areas. Our results demonstrate how movement may counterbalance the effects of habitat loss and fragmentation in altered landscapes. In particular, they have important implications for conservation planning and ecosystem management, including the design of specific features of conservation areas in order to enhance landscape connectivity and population viability.

Stochastic Optimal Foraging Theory

We present here the core elements of a stochastic optimal foraging theory (SOFT), essentially, a random search theory for ecologists. SOFT complements classic optimal foraging theory (OFT) in that it assumes fully uninformed searchers in an explicit space. Mathematically, the theory quantifies the time spent by a random walker (the forager) on a spatial region delimited by absorbing boundaries (the targets). The walker starts from a given initial position and has no previous knowledge (nor the possibility to gain knowledge) on target/patch locations. Averages on such process can describe the dynamics of an uninformed forager looking for successive targets in a diverse and dynamical spatial environment. The framework provides a means to advance in the study of search uncertainty and animal information use in natural foraging systems.

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.

Perspectives and challenges in statistical physics and complex systems for the next decade

Further Advances in the Analysis of Traditional Problems in Statistical Physics: Comparing Methods and Monte Carlo Algorithms at Phase Transition Regimes: A General Overview (C E Fiore) Elementary Statistical Models for Nematic Transitions in Liquid-Crystalline Systems (D B Liarte & S R Salinas) On Some Experimental Reasons for an Inhomogeneous Structure of Ambient Water on the Nanometer Length Scale (F Mallamace et al.) New Insights Into Traditional Problems in Statistical Physics: Topological and Geometrical Aspects of Phase Transitions (F A N Santos et al.) Exact Solution for a Diffusive Process on a Backbone Structure: Green Function Approach and External Force (E K Lenzi et al.) Applications to Biological Problems: Nanoelectronics of a DNA Molecule (E L Albuquerque et al.) Social Distancing Strategies Against Disease Spreading (L D Valdez et al.) Non-Traditional Problems Related to Complex Systems: Thermodynamics and Kinetic Theory of Granular Materials (G M Kremer) Search Strategy: Hedging Your Bet (M F Shlesinger).

Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior

We propose a Cellular Automata (CA) model in which three ubiquitous and relevant processes in nature are present, namely, spatial competition, distinction between dynamically stronger and weaker agents and the existence of an inner resistance to changes in the actual state S n (=−1,0,+1) of each CA lattice cell n (which we call inertia). Considering ensembles of initial lattices, we study the average properties of the CA final stationary configuration structures resulting from the system time evolution. Assuming the inertia a (proper) control parameter, we identify qualitative changes in the CA spatial patterns resembling usual phase transitions. Interestingly, some of the observed features may be associated with continuous transitions (critical phenomena). However, certain quantities seem to present jumps, typical of discontinuous transitions. We argue that these apparent contradictory findings can be attributed to the inertia parameter’s discrete character. Along the work, we also briefly discuss a few potential applications for the present CA formulation.

Subjective expectation of rewards can change the behavior of smart but impatient foragers.

Search efficiency can be a matter of life and death in biological encounter processes. Animals that fail to explore their environments efficiently suffer heightened risk of earlier death (1). Some theoretical aspects of foraging are closely related to the random search problem of determining the best strategy for optimizing the search when ( i ) targets are distributed in unknown spatial locations and ( ii ) learning and other skills (such as long-range ability to detect prey) do not significantly alter the choice of long-term strategy. Also, it is well known (1) that foragers that learn usually outperform foragers that do not. However, it is not yet well established how foraging patterns change when foragers are cognitively complex. In PNAS, Namboodiri et al. (2) propose an interesting framework to understand possible changes in such spatial patterns. Their plausible premise, assuming a smart forager, is that the searcher can attempt to improve future outcomes by determining, through exploratory trial and error, a good strategy. The forager searches by sampling the environment and using “different step lengths so as to maximize the ability to detect differences in reward distributions associated with each step length.” The model by Namboodiri et al. (2) predicts that animals attempting to learn optimally from their landscapes will have asymptotically power law-distributed move lengths x . Essentially, such a probability density function (PDF) p ( x ) arises as a consequence of a built-in temporal discounting function D ( t ) , which, according to many behavioral experiments (ref. 2 and also below), should have a “hyperbolic-like” functional form proportional to ( 1 + t / c μ ) − μ , where t is the delay time for access to the reward. The case μ = 1 is often called the hyperbolic discounting function and c μ = 1 represents a proper scaling for … [↵][1]1To whom correspondence should be addressed. Email: luz{at}fisica.ufpr.br. [1]: #xref-corresp-1-1

General tracking control of arbitrary N-level quantum systems using piecewise time-independent potentials

Here we propose a tracking quantum control protocol for arbitrary N-level systems. The goal is to make the expected value of an observable

The Physics of Foraging: An Introduction to Random Searches and Biological Encounters

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