Small world effects in evolution

For asexual organisms point mutations correspond to local displacements in the genotypic space, while other genotypic rearrangements represent long-range jumps. We investigate the spreading properties of an initially homogeneous 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 indistinguishable from those obtained by assuming all mutations equiprobable. Moreover, we find that the equilibrium distribution is a Boltzmann one, in which the fitness plays the role of an energy, and mutations that of a temperature.