WAITING WITH AND WITHOUT RECOMBINATION - THE TIME TO PRODUCTION OF A DOUBLE MUTANT

R. A. Fisher and H. J. Muller argued in the 1930s that a major evoluti onary advantage of recombination is that it allows favorable mutations to be combined within an individual even when they first appear in di fferent individuals. This effect is evaluated in a two-locus, two-alle le model by calculating the average waiting time until a new genotypic combination first appears in a haploid population. Three approximatio ns are developed and compared with Monte Carlo simulations of the Wrig ht-Fisher process of random genetic drift in a finite population. Firs t, a crude method, based on the deterministic accumulation of single m utants, produces a waiting time of 1/root N mu(2) with no recombinatio n and 1/ (3)root 1/3RN mu(2) with recombination between the two loci, where mu is the mutation rate, N is the haploid population size, and R is the recombination rate. Second, the waiting time is calculated as the expected value of a heterogeneous geometric distribution obtained from a branching process approximation. This gives accurate estimates for N mu large. The estimates for small values of N mu are considerabl y lower than the simulated values. Finally, diffusion analysis of the Wright-Fisher process provides accurate estimates for N mu small, and the time scales of the diffusion process show a difference between R = 0 and for R >> 0 of the same order of magnitude as seen in the determ inistic analysis. In the absence of recombination, accurate approximat ions to the waiting time are obtained by using the branching process f or high N mu and the diffusion approximation for low N mu. For low N m u the waiting time is well approximated by 1/root 8N(2)mu(3). With R > > 0, the following dependence on N mu is observed: For N mu > 1 the wa iting time is virtually independent of recombination and is well descr ibed by the branching process approximation. For N mu approximate to 1 the waiting time is well described by a simplified diffusion approxim ation that assumes symmetry in the frequencies of single mutants. For N mu << 1 the waiting time is well described by the diffusion approxim ation allowing asymmetry in the frequencies of single mutants, Recombi nation lowers the waiting time until a new genotypic combination first appears, but the effect is small compared to that of the mutation rat e and population size. For large N mu, recombination has a negligible effect, and its effect is strongest for small N mu, in which case the waiting time approaches a fixed fraction of the waiting time for R=0. Free recombination lowers the waiting time to about 45% of the waiting time for absolute linkage for small N mu. Selection has little effect on the importance of recombination in general. (C) 1998 Academic Pres s.