Reproductive strategies are diverse and a whole continuum of mixed systems lies between strict sexuality and strict clonality (apomixis), including automixis, a parthenogenetic mode of reproduction involving a meiosis and increasing homozygosity over generations. These various systems impact the genetic structure of populations, which can therefore be used to infer reproductive strategies in natural populations. Here, we first develop a mathematical model, validated by simulations, to predict

heterozygosity and inbreeding in mixed sexual-automictic populations. It highlights the predominant role of the rate of heterozygosity loss experienced during automixis ( ), which is locus dependent. When is low, mixed populations behave like purely sexual ones until sex becomes rare. In contrast, when is high, the erosion of genetic diversity is tightly correlated to the rate of sex, so that the individual inbreeding coefficient can inform on the ratio of sexual/asexual reproduction. In the second part of this study, we used our model to test the presence of cryptic sex in a hybridogenetic Cataglyphis ant where new queens are produced parthenogenetically, leaving males with an apparent null fitness while they are essential to colony development as sperm is required to produce workers. Occasional sexual production of queens could resolve this paradox by providing males some fertile progeny. To determine whether this occurs in natural populations, we simulated genotypic datasets in a  population under various regimes of sexual vs. asexual reproduction for queen production and compared the distribution of inbreeding, expected heterozygosity and inter-individual relatedness coefficients with those observed in a natural population of Cataglyphis mauritanica using microsatellites. Our simulations show that the distribution of inter-individual relatedness coefficients was particularly informative to assess the relative rate of sexual/asexual reproduction, and our dataset was compatible with pure parthenogenesis but also with up to 2% sexual reproduction. Our approach, implemented in an R script, should be useful to assess reproductive strategies in other biological models.

Keywords: cryptic sex, mixed reproductive system, population genetic model, automixis, Cataglyphis, social hybridogenesis