Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales.
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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 scale-dependent-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.
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Affiliation: IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), CSIC-UIB, Campus UIB, Palma de Mallorca, Spain; Department of Ecology and Evolutionary Biology, Princeton University, Princeton NJ, 08544-1003, United States of America.
ABSTRACT
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 scale-dependent-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. No MeSH data available. Related in: MedlinePlus |
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Mentions: The dynamics of each particle i = 1, … N is then given byr˙i=2D(ri,ρ˜s,ρ˜l)ηi(t),(1)where the diffusivity D is, in general, a positive continuous function of and . ηi(t) is a white Gaussian vector noise with zero mean and with time-correlation matrix given by 〈ηi(t)ηj(t′)〉 = 1δijδ(t − t′). 1 is the identity matrix. Eq (1) should be interpreted within the Itô calculus, since the stop/movement behavior is assumed to occur at the beginning of each time step [25]. The mean densities are defined as:ρ˜μ(r)=NμπRμ2,(2)with μ ≡ s, l. Ns and Nl are the number of individuals found in a near and far neighborhood of the particle at r, respectively (see Fig 1). Note that, since the number of individuals does not change, the global density ρ0 = N/L2 remains constant in time. |
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Affiliation: IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), CSIC-UIB, Campus UIB, Palma de Mallorca, Spain; Department of Ecology and Evolutionary Biology, Princeton University, Princeton NJ, 08544-1003, United States of America.
No MeSH data available.