Flow spatial structure determines pattern instabilities in nonlocal models of population dynamics

Abstract

Environmental flows shape spatial patterns and population dynamics; however, we do not fully understand how they influence the onset of pattern formation and population abundance. By combining numerical simulations and analytical approximations, we show that the spatial structure of the flow’s velocity field determines the pattern formation instability in two nonlocal models of population dynamics. For a simple shear flow, where one of the primary axes of the population pattern can align with the flow, the onset of pattern formation remains unaffected. In contrast, a vortex flow delays the pattern instability relative to the no-flow case. The velocity field, therefore, interacts with the spatial feedbacks driving pattern formation in complex ways, which also leads to different oscillatory time series of population abundance. Depending on the flow, population abundance may exhibit regular oscillations with a characteristic frequency or long, erratic transients before settling into a more stable regime.