In diploid organisms, the rates of mutation and recombination played a pivotal role in the evolution of sex-determining regions and, thus, sex chromosomes. We know quite a bit theoretically and empirically in XY systems in mammals and ZW systems in birds. But, empirical data on the sex-determining regions in haploid organisms are lacking.
Immler and Otto (2015) provide a model and a brief literature review on the evolution of sex chromosomes in organisms with dioecious haploid stages. They focus on two aspects of haploid sex chromosome evolution:
reduced recombination and degeneration due to the accumulation of deleterious mutations.
Their modeling predicts that the decay of recombination, for example, is just as much a part of the evolution of haploid sex chromosomes as it is in diploid systems. However, there are some important differences between diploid and haploid sex determination. The masking of deleterious mutations does not happen in haploid male and females so degeneration of the haploid sex-determining region should be slower than in diploids.
They, then, provide a literature review ranging from algae to bryophytes to fungi. Only a few of the studies had reported sequence information about the sex determining region, but they all confirmed Immler and Otto’s models. In all cases, signs of reduced recombination were found, as well as differentiation in the sex-determining regions of males and females, even in fungi in which anisogamy is limited or absent.