The E ects of Recombination on a Haploid Quasispecies Evolving on a Single-peak Fitness Landscape

In this paper we investigate the eeects of (uniform) recombination on the evolution of a haploid quasispecies on a single-peak \spike" tness landscape. It is found that at low mutation rates the long-term behaviour of the quasispecies exhibits one stable and one unstable equilibrium. At a critical mutation rate which we identify as an error threshold, the stable and unstable equilibria coalesce. Beyond the error threshold there is no (biologically meaningful) equilibrium; errors accumulate and the optimum genotype is inevitably lost. In contrast to the asexual case where the error threshold is discontinuous, the sexual error threshold represents a 2nd order (continuous) phase transition. It is mooted that the unstable equilibrium could act as a barrier to the xation of a favourable mutant. We derive analytic approximations for the equilibrium concentrations of the optimum genotype and for the error threshold. We also analyse the stability of the equilibria.