Instability of spatial patterns and its ambiguous impact on species diversity
arXiv:0807.0122 · doi:10.1103/PhysRevLett.101.058102
Abstract
Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a bifurcation point. In its vicinity, an Eckhaus instability occurs, leading to convectively unstable "blurred" patterns. At the bifurcation point, stochastic effects dominate and induce counterintuitive effects on diversity: Large patterns, emerging for medium values of individuals' mobility, lead to rapid species extinction, while small patterns (low mobility) promote diversity, and high mobilities render spatial structures irrelevant. We provide a quantitative analysis of these phenomena, employing a complex Ginzburg-Landau equation.
4 pages, 3 figures and supplementary information. To appear in Phys. Rev. Lett.
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