The Optimum Recombination Rate That Realizes the Fastest Evolution of a Novel Functional Combination of Many Genes

The effect of genetic recombination (or crossover) by sexual reproduction on the time until a novel set of genes performing a combined function appears, spreads, and becomes fixed is studied. First, we study a haploid finite population with many binary loci, in which only one sequence (called a functional gene set) is significantly advantageous over the others. The time for evolution of the function (Td) is defined as the mean number of generations until the advantageous sequence dominates in an initially random population. When the sequence diversity is initially stored sufficiently, the evolution time Td is roughly the product of the waiting time until the appearance of the advantageous sequence (creation time Tc) and the average number of appearances of the advantageous sequence from its absence until its fixation (destruction number Nd). Mutation and crossover reduce the former but enlarge the latter. If the mutation rate is low, there is an intermediate optimal rate of crossover that achieves the minimum Td. In contrast, if the mutation rate is sufficiently high, Td is smallest without crossover. Second, the breakdown of established functions by recurrent deleterious mutation in an infinite population is examined. The number of functional genes maintained decreases monotonically with the recurrent deleterious mutation rate. Thus in higher organisms having many functional sets of genes in the genome, the mutation rate must be kept very low to preserve them, and hence a high crossover rate made possible by sexual reproduction is important in accelerating the evolution of novel functional sets of genes. Implications of this long-term advantage of recombination in the maintenance of sexual reproduction in higher organisms are discussed.