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

Martínez-García R, Murgui C, Hernández-García E, López C - PLoS ONE (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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

Spatial distribution of the population from the particle-level model.Spatial distribution at long times of a population of 104 individuals using the dynamics of Eq (1) with a short interaction range Rs = 0.05 and a long interaction length Rl = 0.1. D0 = 10−4, a = 1 in all the panels. Every individual is plotted as a small black dot. The system is a square area of lateral size L = 1 with periodic boundary conditions. Upper panel: b = 3.5 × 10−4, c = 7.0 × 10−4 (homogeneous distribution). Left bottom panel: b = 8.5 × 10−4, c = 7 × 10−4 (labyrinth pattern). Right bottom panel: b = 4.3 × 10−4, c = 3.9 × 10−4 (spot pattern). Note the rings with higher density in the border.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4493154&req=5

pone.0132261.g002: Spatial distribution of the population from the particle-level model.Spatial distribution at long times of a population of 104 individuals using the dynamics of Eq (1) with a short interaction range Rs = 0.05 and a long interaction length Rl = 0.1. D0 = 10−4, a = 1 in all the panels. Every individual is plotted as a small black dot. The system is a square area of lateral size L = 1 with periodic boundary conditions. Upper panel: b = 3.5 × 10−4, c = 7.0 × 10−4 (homogeneous distribution). Left bottom panel: b = 8.5 × 10−4, c = 7 × 10−4 (labyrinth pattern). Right bottom panel: b = 4.3 × 10−4, c = 3.9 × 10−4 (spot pattern). Note the rings with higher density in the border.

Mentions: A direct exploration of pattern formation in the model starts from Monte Carlo numerical simulations of the individual-based dynamics given by Eq 1. To unveil the relationships between the two spatial scales that promote the formation of spatial structures, we isolate in our analysis the relative importance of the short and long-range densities fixing all the parameters of the model (Rs, Rl, D0, N, a; see caption of Fig 2 for details), except b and c, that weight the influence of and on the diffusivity.


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

Martínez-García R, Murgui C, Hernández-García E, López C - PLoS ONE (2015)

Spatial distribution of the population from the particle-level model.Spatial distribution at long times of a population of 104 individuals using the dynamics of Eq (1) with a short interaction range Rs = 0.05 and a long interaction length Rl = 0.1. D0 = 10−4, a = 1 in all the panels. Every individual is plotted as a small black dot. The system is a square area of lateral size L = 1 with periodic boundary conditions. Upper panel: b = 3.5 × 10−4, c = 7.0 × 10−4 (homogeneous distribution). Left bottom panel: b = 8.5 × 10−4, c = 7 × 10−4 (labyrinth pattern). Right bottom panel: b = 4.3 × 10−4, c = 3.9 × 10−4 (spot pattern). Note the rings with higher density in the border.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493154&req=5

pone.0132261.g002: Spatial distribution of the population from the particle-level model.Spatial distribution at long times of a population of 104 individuals using the dynamics of Eq (1) with a short interaction range Rs = 0.05 and a long interaction length Rl = 0.1. D0 = 10−4, a = 1 in all the panels. Every individual is plotted as a small black dot. The system is a square area of lateral size L = 1 with periodic boundary conditions. Upper panel: b = 3.5 × 10−4, c = 7.0 × 10−4 (homogeneous distribution). Left bottom panel: b = 8.5 × 10−4, c = 7 × 10−4 (labyrinth pattern). Right bottom panel: b = 4.3 × 10−4, c = 3.9 × 10−4 (spot pattern). Note the rings with higher density in the border.
Mentions: A direct exploration of pattern formation in the model starts from Monte Carlo numerical simulations of the individual-based dynamics given by Eq 1. To unveil the relationships between the two spatial scales that promote the formation of spatial structures, we isolate in our analysis the relative importance of the short and long-range densities fixing all the parameters of the model (Rs, Rl, D0, N, a; see caption of Fig 2 for details), except b and c, that weight the influence of and on the diffusivity.

Bottom Line: 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.

View Article: PubMed Central - PubMed

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