A predictive relationship between population and genetic sex ratios in clonal species

Sexual reproduction depends on mate availability that is reflected by local sex ratios. In species where both sexes can clonally expand, the population sex ratio describes the proportion of males, including clonally derived individuals (ramets) in addition to sexually produced individuals (genets). In contrast to population sex ratio that accounts for the overall abundance of the sexes, the genetic sex ratio reflects the relative abundance of genetically unique mates, which is critical in predicting effective population size but is difficult to estimate in the field. While an intuitive positive relationship between population (ramet) sex ratio and genetic (genet) sex ratio is expected, an explicit relationship is unknown. In this study, we determined a mathematical expression in the form of a hyperbola that encompasses a linear to a nonlinear positive relationship between ramet and genet sex ratios. As expected when both sexes clonally have equal number of ramets per genet both sex ratios are identical, and thus ramet sex ratio becomes a linear function of genet sex ratio. Conversely, if sex differences in ramet number occur, this mathematical relationship becomes nonlinear and a discrepancy between the sex ratios amplifies from extreme sex ratios values towards intermediate values. We evaluated our predictions with empirical data that simultaneously quantified ramet and genet sex ratios in populations of several species. We found that the data support the predicted positive nonlinear relationship, indicating sex differences in ramet number across populations. However, some data may also fit the null model, which suggests that sex differences in ramet number were not extensive, or the number of populations was too small to capture the curvature of the nonlinear relationship. Data with lack of fit suggest the presence of factors capable of weakening the positive relationship between the sex ratios. Advantages of this model include predicting genet sex ratio using population sex ratios given known sex differences in ramet number, and detecting sex differences in ramet number among populations.