Pattern formation in populations with density-dependent movement and two interaction scales

© 2015 Martínez-García et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological organisms (like mussels) that tend to cluster at short ranges as a defensive strategy, and strongly disperse if there is a high population pressure at large ranges for optimizing foraging. We perform stochastic simulations of a particle-level model of the system, and derive and analyze a continuous density description (a nonlinear diffusion equation). In both cases we show that this interplay of scaledependent- behaviors gives rise to a rich formation of spatial patterns ranging from labyrinths to periodic cluster arrangements. In most cases these clusters have the very peculiar appearance of ring-like structures, i.e., organisms arranging in the perimeter of the clusters, which we discuss in detail.RMG was supported by the JAEPredoc program of Consejo Superior de Investigacion Cientificas. CM was supported by the IFISC-Intro program of Instituto de Fisica Interdisciplinar y Sistemas Complejos. EHG and CL are supported by Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional through grant no. FIS2012-30634 (INTENSE@COSYP) and no. CTM2012-39025-C02-01 (ESCOLA).Peer Reviewe