A Periodic Reaction-Advection-Diffusion Model for a Stream Population

We study a reaction-advection-diffusion system with a nonlinear term representing the average per capita growth rate and time-periodic growth rate of the benthic population.This model represents a trait-structured stream population in a time-periodic reaction-advection-diffusion environment.After showing the solution to the bounded unique and periodic solution of the problem, we study the influence of different factors on the population.This motivates us to consider the existence of the leftward and rightward spreading speeds for a stream population whenever the periodic population growth rate function and the advection velocity function are under additional assumptions.Therefore, we discuss the coincidence of the leftward and rightward spreading speeds with minimal wave speeds for bounded monotone periodic traveling waves for the problem of a nonlinear reaction-advection-diffusion system.