Intermittent Precipitation-Dependent Interactions, Encompassing Allee Effect, May Yield Vegetation Patterns in a Transitional Parameter Range

We construct a spatial model that incorporates Allee-type and competition interactions for vegetation as an evolving random field of biomass density. The cumulative effect of close-range precipitation-dependent interactions is controlled by a parameter defining precipitation frequency. We identify a narrow parameter range in which the behavior of the system changes from survival of vegetation to extinction, via a transitional aggregation pattern. The aggregation pattern is tied to the initial configuration and appears to arise differently from Turing’s diffusion and differential flow patterns of other models. There is close agreement of our critical transition parameter range with that of the corresponding evolving random mean-field model.