| Abstract | There has been great interest in the persistence and invasion of algal and insect populations in rivers. Most recent modeling approaches assume that the flow speed of the river is constant. In reality, however, flow speeds in rivers vary significantly on various temporal scales due to seasonality, weather conditions, or human generated disturbance such as hydroelectric dams. In this talk, I consider a simple reaction-advection-diffusion model with variable flow speed chosen to be a periodic step function. The density of the population at discrete times turns into an integrodifference equation. Without Allee effect, the asymptotic speed of spread is obtained by the minimum traveling wave speed of a linearized equation. The key idea to derive the minimum traveling wave speed is to take a Laplace transform with respect to space. I apply the same technique to revisit some known results for constant flow speed. Our results can provide informative management strategies for water release schedules to maintain populations downstream of dams. |
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