The consequences of non-passive advection and directed motion for population dynamics

A. R. Robinson has proposed a method for studying population growth and adv ection in the sea. The assumption made by Robinson of a non-divergent veloc ity field for the biological tracer may not be valid for many situations. W hen the assumption is valid the biological dynamics of an advected patch ar e no different from those of a stationary patch, unless a greater degree of spatial structure is incorporated than he considers. The generality and ap plicability of the model are increased if the assumption of non-divergence can be relaxed. If the velocity field associated with a patch is convergent , as can occur for many biological tracers, then new dynamics arise, both i n a Lagrangian sense and when working at the whole-patch level. These new d ynamics are explored for four fundamental examples, which could provide new paradigms for spatially explicit models in mathematical ecology.