The effect of population size and recombination on delayed evolution of polymorphism and speciation in sexual populations

Recent theory suggests that absolute population size may qualitatively influence the outcome of evolution under disruptive selection in asexual populations. Large populations are predicted to undergo rapid evolutionary branching; however, in small populations, the waiting time to branching increases steeply with decreasing abundance, and below a critical size, the population remains monomorphic indefinitely. Here, we (1) extend the theory to sexual populations and (2) confront its predictions with empirical data, testing statistically whether lake size affects the level of resource polymorphism in arctic char (Salvelinus alpinus) in 22 lakes of different sizes. For a given level of recombination, our model predicts qualitatively similar relations between population size and time to evolutionary branching (either speciation or evolution of genetic polymorphism) as the asexual model, while recombination further increases the delay to branching. The loss of polymorphism at certain loci, an inherent aspect of multilocus-trait evolution, may increase the delay to speciation, resulting in stable genetic polymorphism without speciation. The empirical analysis demonstrates that the occurrence of resource polymorphism depends on both lake size and the number of coexisting fish species. For a given number of coexisting species, the level of polymorphism increases significantly with lake size, thus confirming our model prediction.