Speciation as Pattern Formation by Competition in a Smooth Fitness Landscape

We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasispecies. By suggesting an analogy between the competition among strains and the diffusion of a chemical inhibitor in a reaction-diffusion system, the speciation phenomenon is considered the analogous of chemical pattern formation in genetic space. In the limit of vanishing mutation rate we obtain analytically the conditions for speciation. Using different forms of the competition interaction we show that the speciation is absent for the genetic equivalent of a normal diffusing inhibitor, and is present for shorter-range interactions.