Among many higher animals and terrestrial plants, the dominant phase is composed of diploid cells, while the gametes are haploid cells. Classical genetic theories generally assume either a fully haploid or fully diploid life cycle. However, organisms often exhibit more complex life cycles, with both free-living haploid and diploid stages.

To understand the evolutionary process in haploid-diploid populations, here we ask what the probability of fixation will be for selected alleles in such organisms. We develop a genetic model that considers the population dynamics of haploid and diploid individuals. We then derive the fixation probability of mutant alleles, allowing for different fecundities and mortalities in the different ploidy stages.

Applying a branching process approximation gives an accurate fixation probability assuming the net effect of a mutation is beneficial. A diffusion approximation also allows calculation of the fixation probability of deleterious alleles, but it is only accurate when selection is weak and haploids and diploids are similarly abundant. These analytical results are evaluated by comparison to numerical simulations.