Prey patchiness, predator survival and fish recruitment

A simple mathematical model is presented for the population dynamics of fish larvae when the main food supply, in this case copepods, is spatially patchy in its distribution. Encounters by an individual predator (larva) with prey patches, and with individual prey within patches, are represented by Poisson processes. It is demonstrated analytically, and confirmed by numerical experiments, that prey patchiness fails to alter mean predator-prey encounter rates from their values for homogeneous prey distributions. Individual variance in encounter rate is, however, much affected. This has significant consequences for the (small) numbers of larvae surviving to metamorphosis and recruitment to the adult fish population.