Instability of spatial patterns and its ambiguous impact on species diversity

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.