### Fixation in asexual populations

The fixation probability of beneficial mutations decreases with an increasing number of competing beneficial mutations. The fate of a mutation also depends very strongly on the fitness of the individual that first carried the mutations. Both effects can be readily explored in simulations.To this end, we use FFPopSim in a mode in which we can specify the number of segregating sites. The program will then keep these sites polymorphic and inject a novel mutation in a random individual whenever a locus is monomorphic, i.e., the previous mutation at this locus went extinct or fixed.

For each mutation, the fitness of the original individual and the time of injection is recorded. In addition, FFPopSim keeps a record of the total number of mutations that where injected and all mutation that fixed. From this, we can calculate the fixation probability and study how it depends on the number of segregating sites and the background fitness.

The script discussed here is called fixation_probability_asex and can be downloaded here . We first specify a list of numbers of segregating sites which we want to simulate, along with the population size and the adaptive effect of individual mutations.

Lvalues = [10,30,100,300, 1000] s = 1e-2 #single site effect N = 10000 #population size

tmp_dis = np.asarray(zip(pop.get_clone_sizes(), pop.get_fitnesses()-pop.get_fitness_statistics().mean)) fit_dis,x = np.histogram(tmp_dis[:,1], weights=tmp_dis[:,0], bins=fit_bins, normed=True)

fixed_mutations = np.asarray([(a.birth+a.sweep_time, a.fitness) for a in pop.fixed_mutations]) late_fixed_mutations = fixed_mutations[fixed_mutations[:,0]>burnin,:] total_mutations = np.sum(pop.number_of_mutations[burnin:])

The fixation probability is divided by the independent sites expectation 2s. We see that it decreases dramatically with an increasing number of segregating sites. The next graph shows the fitness distribution of the entire population (solid) and of the mutations that fixed (dashed).

With increasing number of segregating sites, the fitness distribution broadens and the fixed mutations originate more and more from the tail of the distribution.