Selective advantage of sexual over asexual reproduction (r
= 0, r
= 0, r
= 0.1) in the standard model for different interaction matrices, simulated deterministically (a) and stochastically with populations sizes N = 1000 (b), N = 10 000 (c), and N = 100 000 (d). The color of each of the points on a graph shows the frequency change during a simulation run (i.e. 1000 host generations after introduction of the modifier allele M), averaged over 10000 simulation runs (100 for the deterministic model) with different random initial conditions. The number of host alleles, n, matched by the parasite determines the corresponding fitness w
in the following way: for hosts, w2 = 1-s2, w1 = 1 - s1, w0 = 1, for parasites w2 = 1, w1 = (1 - s2)/(1 - s1), w0 = 1 - s2. This generalized model reflects the biological characteristic that host and parasite fitness are inversely correlated. The matrix can be continually varied as a function of the parameters s1 and s2, and contains the MA and the MMA as special cases (MA: s1 = 0; MMA, s2 = 1-(1-s1)2, yellow dashed line). Only fitness matrices with s1 ≦ s2 are shown. The parameters s1 and s2 range from 0 to 1 with 0.01 gradation.