We study a reaction-diffusion equation model for population dynamics. By focusing on the diffusive behavior expected in a population that seeks to avoid over-crowding, we derive a nonlinear-diffusion porous-Fisher's equation. Using explicit traveling wave solutions, initially-separated, expanding populations are studied as they first coalesce. The nonlinear interactions of the merging populations are examined using perturbation theory and the method of matched asymptotic expansions. Results are also extended to the axisymmetric case. © 1995.