A fast algorithm for computing multilocus recombination

A fast algorithm for computing recombination is developed for model organisms with selection on haploids. Haplotype frequencies are transformed to marginal frequencies; random mating and recombination are computed; marginal frequencies are transformed back to haplotype frequencies. With LL diallelic loci, this algorithm is theoretically a factor of a constant times (3/8)L(3/8)L faster than standard computations with selection on diploids, and up to 16 recombining loci have been computed. This algorithm is then applied to model the opposing evolutionary forces of multilocus epistatic selection and recombination. Selection is assumed to favor haplotypes with specific alleles either all present or all absent. When the number of linked loci exceeds a critical value, a jump bifurcation occurs in the two-dimensional parameter space of the selection coefficient ss and the recombination frequency rr. The equilibrium solution jumps from high to low mean fitness with increasing rr or decreasing ss. These numerical results display an unexpected and dramatic nonlinear effect occurring in linkage models with a large number of loci.