Is the "small world" effect relevant to evolution?

Mutations and selection are the driving forces of biological evolution. We model here the simplest case: an evolving population of asexual organisms. We consider two kinds of mutations: point mutations, corresponding to local displacements in the genotypic space, and all the other genotypic rearrangements, equivalent to long-range jumps. We show that a small-world effect is present in evolution: even a small fraction of quenched long-range jumps makes the results indistinguishable from those obtained by assuming all mutations equiprobable. We apply this result to the evolution of a population on a smooth fitness landscape, showing that the equilibrium distribution is a Boltzmann one, in which the fitness plays the role of an energy, and mutations that of a temperature.