Effective population size of X chromosomes and haplodiploids under cyclical parthenogenesis

Many organisms can reproduce both sexually and asexually. Many such groups also exhibit ploidy differences between males and females during the sexual phase of their life, including aphids, nematodes, wasps, and rotifers. The constraints of combining asexual reproduction with asymmetric ploidy often results in X chromosomes (or haplodiploids) which show distinct transmission genetics from conventional systems. This may be expected to impact the effective population size; however, we currently lack analytical expressions for such life cycles. To remedy this, here we generate expressions for the effective population size of X chromosomes and haplodiploids under cyclical parthenogenesis. By first analysing a purely sexual scenario, we show how these distinct transmission genetics generate an effective population size substantially smaller than that of the autosomes, and how it may be further altered by aspects of sex-specific ecology, inbreeding, and non-random X elimination. Considering this inheritance system in an explicit population structure also demonstrates how genetic differentiation builds up differently between autosomes and X chromosomes. By introducing asexual reproduction into the model, we can see how low frequencies of sex cause these differences between autosomes and X chromosomes to dissipate. We discuss the relevance of these results to some different groups and consider future avenues for both empirical and theoretical work.