Fixation Time for Competing Beneficial Mutations and Their Genomic Footprint

For a highly beneficial mutation A at locus 1 spreading in a very large population, we have analyzed the scenario that at a closely linked locus 2 a second beneficial mutant B arises in repulsion; i.e. on a chromosome carrying the wildtype a at locus 1. Under the assumptions that the fitness of B is greater than that of A and that A- and B-carrying chromosomes can recombine at some rate r, recombinants AB may form and eventually fix. We present explicit formulas for the fixation time of AB under additive fitness of the mutants as a function of the frequency X_2 (0) of A at the time when B is introduced. Our analysis suggests that the effect of interference between the beneficial mutations is most pronounced for small values of X_2 (0)< 0.1. Furthermore, we identify a threshold value for r, above which recombination speeds up fixation. Using published simulation data we also describe the genomic footprint of competing beneficial mutations. At neutral sites between the two linked selected loci an excess of intermediate-frequency variants may occur when interference is strong; i.e. X_2 (0) small. Finally, we discuss under which circumstances this scenario may be encountered in real data.