Autosomal admixture levels are informative about sex bias in admixed populations

Sex-biased admixture has been observed in a wide variety of admixed populations. Genetic variation in sex chromosomes and functions of quantities computed from sex chromosomes and autosomes have often been examined to infer patterns of sex-biased admixture, typically using statistical approaches that do not mechanistically model the complexity of a sex-specific history of admixture. Here, expanding on a model of Verdu and Rosenberg (2011) that did not include sex specificity, we develop a model that mechanistically examines sex-specific admixture histories. Under the model, multiple source populations contribute to an admixed population, potentially with their male and female contributions varying over time. In an admixed population descended from two source groups, we derive the moments of the distribution of the autosomal admixture fraction from a specific source population as a function of sex-specific introgression parameters and time. Considering admixture processes that are constant in time, we demonstrate that surprisingly, although the mean autosomal admixture fraction from a specific source population does not reveal a sex bias in the admixture history, the variance of autosomal admixture is informative about sex bias. Specifically, the long-term variance decreases as the sex bias from a contributing source population increases. This result can be viewed as analogous to the reduction in effective population size for populations with an unequal number of breeding males and females. Our approach suggests that it may be possible to use the effect of sex-biased admixture on autosomal DNA to assist with methods for inference of the history of complex sex-biased admixture processes.