The effect of dispersal patterns on stream populations

Individuals in streams are constantly subject to predominantly unidirectional flow. The question of how these populations can persist in upper stream reaches is known as the "drift paradox." We employ a general mechanistic movement-model framework and derive dispersal kernels for this situation. We derive thin-as well as fat-tailed kernels. We then introduce population dynamics and analyze the resulting integrodifferential equation. In particular, we study how the critical domain size and the invasion speed depend on the velocity of the stream flow. We give exact conditions under which a population can persist in a finite domain in the presence of stream flow, as well as conditions under which a population can spread against the direction of the flow. We find a critical stream velocity above which a population cannot persist in an arbitrarily large domain. At exactly the same stream velocity, the invasion speed against the flow becomes zero; for larger velocities, the population retreats with the flow.