Collective adaptation in a statistical model of an evolving population.

We simulate asexually and sexually reproducing model populations evolving in a rugged fitness landscape where fit and unfit genotypes are distributed at random, and where all fit genotypes have the same a priori probability of reproduction. Varying the fraction chi of unfit genotypes at a fixed mutation rate we observe a strikingly different behavior for the two reproduction mechanisms. For the asexually reproducing population, the effective mutation rate lambda decreases roughly proportionally to (1-chi), and the fraction delta of sterile individuals--processing an unfit genotype--accordingly increases roughly proportionally to chi. On the other hand, lambda remains approximately constant (and delta increases proportionally to chi) for small values of chi:but, at a critical value chi*, both lambda and delta suddenly drop. This corresponds to the transition to an adaptive regime where the average fitness of the population is enhanced. We show how this transition can be interpreted in terms of an improvement of the collective fitness of the population.