### Fixation in facultatively sexual populations

With increasing outcrossing rate, the competition between mutations decreases and the fixation probability increases. With more recombination, the fate of a mutation also depends less on the fitness of the original background since a mutation will hop backgrounds often. Both effects can be readily explored in simulations.As before, we use FFPopSim in a mode in which we can specify the number of segregating sites and calculate the fixation probability and study how it depends on the number of segregating sites and the background fitness.

The script fixation_probability_sex.py loops over different outcrossing rates while keeping all other parameters fixed (download here). After repeating this for many samples and all our choices for the outcrossing rate, we find for the fixation probability

The fixation probability is divided by the independent sites expectation 2s. We see that it increases strongly with increasing outcrossing rate and asymptotes to the expected value 2s.

The next graph shows the fitness distribution of the entire population (solid) and of the mutations that fixed (dashed) on the left. The right panel shows the probability of fixation conditional on arising on a genome with fitness indicated on the x-axis. For low outcrossing rates, this function is very step. The more rapidly backgrounds are switched, the less does the background matter. Consequently, the fixation probability curves flatten out as r increases.

The increasing fitness variance with increasing outcrossing rate is a consequence of reduced interference between mutations and hence faster adaptation.