  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 explore 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. We relate the wavelength and decay length of the
wrinkles to the shape of the interaction kernel. Since these spatial structures
encode details about the interaction among individuals, we discuss how
heterogeneities reveal information that would be hidden in a flat landscape.
