Rare sex or out of reach equilibrium? The dynamics of FIS in partially clonal organisms

Katja Reichel, Jean-Pierre Masson, Florent Malrieu, Sophie Arnaud-Haond, Solenn Stoeckel

Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient [Formula: see text]. Yet in partially clonal species, both F IS  < 0 and F IS  > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F IS over time under increasing rates of clonality. Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F IS  = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean [Formula: see text] value expected at equilibrium. Our results argue for a dynamical interpretation of F IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean [Formula: see text] values deviating from zero and/or a large variation of F IS over loci are observed.