Invasions and Persistence in flow-through systems

Individuals in streams and rivers are constantly subject to predominantly unidirectional flow in their environment. Some individuals, such as fishes, have mechanisms to actively swim against the water current. Many other species, such as stream insects, lack appropriate mechanisms, and their movement in the water column is determined largely by the flow. The question of how these populations can persist in upper stream reaches is known as the ``drift paradox''. In this talk, we model a population of stream insects using an integrodifferential equation for non-local dispersal, and analyze conditions for persistence and for upstream spread of the population. This work is closely related to models for the plug-flow reactor and biofilms.