Highly fit ancestors of a partly sexual haploid population

Earlier, using the semi-deterministic solitary wave approach, we have investigated accumulation of pre-existing beneficial alleles in genomes consisting of a large number of simultaneously evolving sites in the presence of selection and infrequent recombination with small rate r per genome. Our previous results for the dynamics of the fitness distribution of genomes are now interpreted in terms of the life cycle of recombinant clones. We show that, at sufficiently small r, the clones dominating fitness classes, at the moment of their birth, are nearly the best fit in a population. New progeny clones are mostly generated by parental genomes whose fitness falls within a narrow interval in the middle of the high-fitness tail of fitness distribution. We also derive the fitness distribution for the distant ancestors of sites of a randomly sampled genome and show that its form is controlled by a single composite model parameter proportional to r. The ancestral fitness distribution differs dramatically from the fitness distribution of the entire ancient population: it is much broader and localized in the high-fitness tail of the ancient population. We generalize these results to the case of moderately small r to conclude that, regardless of fitness of an individual, all its distant ancestors are exceptionally well fit.