Landscape-induced spatial oscillations in population dynamics

We study the effect that disturbances in the ecological landscape exert on the spatial distribution of a population that evolves according to the nonlocal FKPP equation. Using both numerical and analytical techniques, we characterize, as a function of the interaction kernel, the three types of stationary profiles that can develop near abrupt spatial variations in the environmental conditions vital for population growth: sustained oscillations, decaying oscillations and exponential relaxation towards a flat profile. Through the mapping between the features of the induced wrinkles and the shape of the interaction kernel, we discuss how heterogeneities can reveal information that would be hidden in a flat landscape.

Automated summary

The study analyzes the impact of disturbances in the ecological landscape on the spatial distribution of a population evolving according to the nonlocal FKPP equation. It characterizes the three types of stationary profiles that can develop near abrupt spatial variations in environmental conditions, and discusses how heterogeneities can reveal hidden information in a flat landscape through mapping between induced wrinkles and the shape of the interaction kernel.