Estimating the number of sexual events per generation in a facultatively sexual haploid population

Abstract

In populations of facultatively sexual organisms, the proportion of sexually produced offspring contributed to each generation is a critical determinant of their evolutionary potential. However, estimating this parameter in natural populations has proved difficult. Here we develop a population genetic model for estimating the number of sexual events occurring per generation for facultatively sexual haploids possessing a biallelic mating-type locus (e.g., Chlamydomonas, ascomycete fungi). Our model treats the population as two subpopulations possessing opposite mating-type alleles, which exchange genes only when a sexual event takes place. Where mating types are equally abundant, we show that, for a neutral genetic marker, genetic differentiation between mating-type subpopulations is a simple function of the effective population size, the frequency of sexual reproduction, and the recombination fraction between the genetic marker and the mating-type locus. We employ simulations to examine the effects of linkage of markers to the mating-type locus, inequality of mating-type frequencies, mutation rate, and selection on this relationship. Finally, we apply our model to estimate the number of sexual reproduction events per generation in populations of four species of facultatively sexual ascomycete fungi, which have been jointly scored for mating type and a range of polymorphic molecular markers. Relative estimates are in line with expectations based on the known reproductive biology of these species.

Fig. 1

The life cycle and modes of reproduction of the haploid organisms considered in the model. Sexually produced individuals are shown as solid, asexually reproduced as hatched. F_stM measures genetic differentiation between the mating-type subpopulations

Fig. 2

Estimates of F_stM under different frequencies of sexual reproduction (s). a Mean and standard deviation of simulated F_stM at steady state; b standard deviation for linkage disequilibrium (LD) at steady state. The steady-state results at each point are derived from 1000 independent simulations each for 1300 generations. Parameter settings are the total population size N_e = 400, proportion of the population with mating MT-1 type p = 0.5, the recombination rate r = 0.5 and the scaled mutation rates N_eµ = 1.0 and N_ev = 0.8

Fig. 3

Effects of effective population size (N_e) on estimation of F_stM. a Mean and standard deviation of simulated F_stM at steady state; b standard deviation for linkage disequilibrium (LD) at steady state. The steady-state results at each point are derived from 1000 independent simulations each for 1300 generations. Parameter settings are the proportion of the population with mating MT-1 type p = 0.5, the recombination rate r = 0.5, the probability of sexual reproduction s = 0.05 and the mutation rates µ = 2.5 × 10⁻³ and v = 2.0 × 10⁻³

Fig. 4

Effects of recombination rate (r) on estimation of F_stM. a. Mean and standard deviation of simulated F_stM at steady state; b. standard deviation for linkage disequilibrium (LD) at steady state. Results are derived from 1000 independent simulations with parameters of the total population size N_e = 400, proportion of the population with mating MT-1 type p = 0.5, probability of sexual reproduction s = 0.05 and scaled mutation rate N_eµ = 1.0 and N_ev = 0.8

Fig. 5

Effects of the frequency of mating types (p) on genetic differentiation between mating-type subpopulations F_stM. a Mean and standard deviation of simulated F_stM at steady state; b standard deviation for linkage disequilibrium (LD) at steady state. Results are derived from 1000 independent simulations, with parameter settings of the total population size N_e = 400, the recombination rate between A and mating-type loci r = 0.5, probability of sexual reproduction s = 0.05 and scaled mutation rate N_eµ = 1.0 and N_ev = 0.8

Fig. 6

Effects of mutation rate on estimation of F_stM. a Mean and standard deviation of simulated F_stM at steady state; b standard deviation for linkage disequilibrium (LD) at steady state. The steady-state results at each point are derived from 1000 independent simulations each for 1300 generations. Parameter settings are the proportion of the population with mating MT-1 type p = 0.5, the recombination rate r = 0.5, the probability of sexual reproduction s = 0.05, and the effective population size N_e = 1000

Fig. 7

Effects of various forms of selection (selection coefficients x_i = 0.002, 0.02 and 0.05) on estimates of population genetic differentiation between mating-type subpopulations (F_stM) at a locus A linked to the MT locus with recombination rates r = 0.05 (left) and r = 0.05 (right). Values are derived from 1000 independent simulations at their steady-state distributions. a Directional selection. b Disruptive selection. c Stochastic selection with probability of an allele being favoured set at 0.2 or 0.8 (open squares) or 0.5 (filled squares). Expectations under neutrality (x_i = 0) are given for comparison