Role of depletion on the dynamics of a diffusing forager

  title={Role of depletion on the dynamics of a diffusing forager},
  author={Olivier B'enichou and Marie Chupeau and Sidney Redner},
  journal={Journal of Physics A: Mathematical and Theoretical},
We study the dynamics of a starving random walk in general spatial dimension d. This model represents an idealized description for the fate of an unaware forager whose motion is not affected by the presence or absence of resources. The forager depletes its environment by consuming resources and dies if it wanders too long without finding food. In the exactly solvable case of one dimension, we explicitly derive the average lifetime of the walk and the distribution for the number of distinct… 

Impact of food distribution on lifetime of a forager with or without sense of smell.

This paper analyzes how the distribution of food in space affects the forager's lifetime in several different scenarios and finds based on analytical considerations that the lifetime scales with the starving time and food density as T∼S^{4}f^{3/2}.

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

This work explores 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, providing surprising evidence that ballistic searches are detrimental in such scenarios.

Lifetime of a greedy forager with long-range smell

A greedy forager who consumes food throughout a region is studied and it is found that for this case the forager always dies within finite time, however, in 2D there are indications of an optimal α (and λ) for which the foragers has the longest lifetime.

Depletion of resources by a population of diffusing species

Depletion of natural and artificial resources is a fundamental problem and a potential cause of economic crises, ecological catastrophes, and death of living organisms. Understanding the depletion

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs.

An effective reduction of the random walk dimensionality is found due to the ballistic behavior of the surviving particles induced by the mortality constraint for experiments involving travel times of particles in diffusion-decay systems.

The dynamics of starvation and recovery

A nutritional state-structured model that incorporates two classes of consumer: nutritionally replete, reproducing consumers, and undernourished, non-reproducing consumers is introduced and it is found that population dynamics are typically driven to a steady state.

Optimally frugal foraging.

The frugal foraging model is introduced and it is shown that there exists an optimal strategy, namely, an optimal frugality threshold k^{*} that maximizes the forager lifetime.

Dynamics of starvation and recovery predict extinction risk and both Damuth’s law and Cope’s rule

A nutritional state-structured model that predicts population size as a function of body mass known as Damuth's law, and a mechanism for Cope’s rule, the evolutionary trend towards larger body mass is developed.

Dimensionality-dependent crossover in motility of polyvalent burnt-bridges ratchets

This work investigates the kinetic characteristics of simple polyvalent BBRs as they move on tracks of increasing width, and finds there exists a tradeoff in BBR track association time and superdiffusivity in the BBR design parameter space of span, polyvalency and track width.



Depletion-controlled starvation of a diffusing forager.

We study the starvation of a lattice random walker in which each site initially contains one food unit and the walker can travel S steps without food before starving. When the walker encounters food,

Universality classes of foraging with resource renewal.

This work determines the impact of resource renewal on the lifetime of a forager that depletes its environment and starves if it wanders too long without eating and outlines an enumeration method to determine the mean lifetime of the forager in the mortal regime.

Exploration and trapping of mortal random walkers.

This work analytically calculates a number of basic and broadly used quantities for evanescent random walkers, which can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps.

Diffusion-Limited Reactions and Mortal Random Walkers in Confined Geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact

Lévy flight search patterns of wandering albatrosses

LéVY flights are a special class of random walks whose step lengths are not constant but rather are chosen from a probability distribution with a power-law tail. Realizations of Lévy flights in

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the

Evanescent continuous-time random walks.

This work studies how an evanescence process affects the number of distinct sites visited by a continuous-time random walker in one dimension by considering three different forms of the waiting time distribution between jumps, namely, exponential, long tailed, and ultraslow.

Multi-excited random walks on integers

We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a

The Behavioral Ecology of Intermittent Locomotion1

Although intermittent locomotion is usually expected to increase energetic costs as a result of additional expenditure for acceleration and deceleration, a variety of energetic benefits can arise when forward movement continues during pauses, and Endurance also can be improved by partial recovery from fatigue during pauses.