Figure 2 .

Simulated distribution of the number of migration events traced back along the line of descent of a randomly selected gene at the autosomal neutral marker locus in a genome containing two autosomal incompatibility loci, under multiplicative fitnesses and no linkage among any of the loci. For each of 15,000 independent replicates using a modified version of SFS CODE (Hernandez 2008), we simulated 100,000 generations forward in time and then counted the number of migration events in a randomly sampled line of descent traced backward in time. Each of the two populations comprised 1000 genes (500 diploid individuals), with the proportion of migrant genes each generation set to m₁₂ = m₂₁ = 1 × 10⁻⁴. Left, the foreign allele at the incompatibility loci reduced the fitness of their heterozygous male carriers (σ_m,1 = σ_m,2 = 0.3), with no effect on female carriers (σ_f,1 = σ_f,2 = 1). The observed counts (histogram) showed an excellent match (χ² = 12.1, 11 d.f.) to the Poisson distribution determined from our approximation (Equation 1) of the parameter of the exponential waiting time between migration events (g = 3.096, red circles). In contrast, the distribution predicted by assuming multiplicative barriers (black line) showed a poor fit (χ² = 4924, 9 d.f.), predicting too few migration events (g = 2.318). Right, the histogram shows the counts under incompatibility due to loci with discordant relative effects on the sexes: the foreign allele at one locus caused greater detriment to males than to females (σ_m,1 = 0.3, σ_f,1 = 1), with opposite effects at the other locus (σ_m,2 = 1, σ_f,2 = 0.3). Our approximation (g = 1.5916, red circles) again fitted the observations well (χ² = 6.3, 7 d.f.), contrary to the multiplicative prediction (g = 2.318, χ² = 3758, 7 d.f.). Discordance between the incompatibility loci on the relative impairment of males and females induces a greater barrier (fewer migration events) than expected under multiplicativity.