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We study the spatial patterns formed by a system of interacting particleswhere the mobility of any individual is determined by the population crowdingat two different spatial scales. In this way we model the behavior of somebiological organisms (like mussels) that tend to cluster at short ranges as adefensive strategy, and strongly disperse if there is a high populationpressure at large ranges for optimizing foraging. We perform stochasticsimulations of a particle-level model of the system, and derive and analyze acontinuous density description (a nonlinear diffusion equation). In both caseswe show that this interplay of scale-dependent-behaviors gives rise to a richformation of spatial patterns ranging from labyrinths to periodic clusterarrangements. In most cases these clusters have the very peculiar appearance ofring-like structures, i.e., organisms arranging in the perimeter of theclusters, that we discuss in detail.

Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales