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

We investigate how environmental flows influence spatial pattern formation and population dynamics using two nonlocal models of population dynamics, which we couple to two different stationary flows. Combining numerical simulations and analytical approximations, we show that the spatial structure of the flow's velocity field determines the pattern formation instability. For a simple shear flow, where one of the primary axes of the population pattern can become aligned 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 responsible for pattern formation in complex ways, which also leads to different oscillatory time series of population abundance. In some cases, the population undergoes regular oscillations with a characteristic frequency, while in others, the dynamics exhibits long erratic transients with no well-defined period before settling into a more regular behavior.