Abstract
An integro-differential reaction-diffusion equation is proposed as a model for populations
where local aggregation is advantageous but intraspecific competition increases as global populations
increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model
for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered,
(i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic
travelling wave solutions. These correspond to aggregation and motion of populations.
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