Small world effects in evolution - art. no. 021914

For asexual organisms point mutations correspond to local displacements in the genotypic space, while other genotypic rearrangements represent long-ra nge jumps. We investigate the spreading properties of an initially homogene ous population in a flat fitness landscape, and the equilibrium properties on a smooth fitness landscape. We show that a small-world effect is present : even a small fraction of quenched long-range jumps makes the results indi stinguishable from those obtained by assuming all mutations equiprobable. M oreover, we find that the equilibrium distribution is a Boltzmann one, in w hich the fitness plays the role of an energy, and mutations that of a tempe rature.