Related papers: Using transient encounter rates to quantify spatia…
Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…
Dryland ecosystems commonly exhibit periodic bands of vegetation, thought to form due to competition between individual plants for heterogeneously distributed water. In this paper, we develop a Fourier method for locally identifying the…
Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces…
Movement is a fundamental behaviour of organisms that brings about beneficial encounters with resources and mates, but at the same time exposes the organism to dangerous encounters with predators. The movement patterns adopted by organisms…
We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
Self-interacting random walks are endowed with long range memory effects that emerge from the interaction of the random walker at time $t$ with the territory that it has visited at earlier times $t'<t$. This class of non Markovian random…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
Unraveling patterns of animals' movements is important for understanding the fundamental basics of biogeography, tracking range shifts resulting from climate change, predicting and preventing biological invansions. Many researchers have…
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a…
Animals foraging alone are hypothesized to optimize the encounter rates with resources through L\'evy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely…
Identifying statistical patterns characterizing human trajectories is crucial for public health, traffic engineering, city planning, and epidemic modeling. Recent developments in global positioning systems and mobile phone networks have…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
Although animal locations gained via GPS, etc. are typically observed on a discrete time scale, movement models formulated in continuous time are preferable in order to avoid the struggles experienced in discrete time when faced with…
We study a simple model of a foraging animal that modifies the substrate on which it moves. This substrate provides its only resource, and the forager manage it by taking a limited portion at each visited site. The resource recovers its…
A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
1. The utilisation distribution describes the relative probability of use of a spatial unit by an animal. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of…
In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed…
A spreading process can be observed when particular information, substances, or diseases spread through a population over time in social and biological systems. It is widely believed that contact interactions among individual entities play…