Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the sma ll- and large-time evolution of a species distribution within a bounded dom ain. These expressions are compared with the results of numerical simulatio ns and are found to be satisfactory within appropriate temporal regimes. Th e solutions presented can be used to describe existing observations of nema tode distributions, can be used as the basis for further work on nematode m igration, and may also be interpreted more generally.