Autopolyploid establishment through polygenic adaptation.

We define the infinitesimal model of quantitative genetics for the inheritance of an additive quantitative trait in a mixed-ploidy population consisting of diploid, triploid and autotetraploid individuals producing haploid and diploid gametes. We implement efficient simulation methods and use these to study the quantitative genetics of mixed-ploidy populations and the establishment of autotetraploids in a new habitat. We show that, when migration from the source population is rare, autotetraploids are more likely to establish in the new habitat than diploids under a very broad range of conditions, but that this is unlikely to sufficiently counter the scarcity of tetraploid founders when the source is predominantly diploid. We assess in more detail how minority cytotype exclusion interacts with migration load in the establishment process and evaluate the impact of additional sources of prezygotic isolation, specifically selfing and assortative mating, on the relative establishment probabilities of the different cytotypes in the presence of maladaptive migration. In the discussion we consider how inbreeding depression may impact our findings.