Figure 1.
Schematic representation of the models developed here for exploring the maintenance of sexual reproduction.
a: Model without competition. pS and pA are the speciation probabilities of sexual and asexual lineages, respectively, eS and eA are extinction probabilities for sexual and asexual lineages, respectively, and uS is the probability of transition from sexual to asexual states. While pS, pA, eS and eA are fixed over generations, the transition rate uS can evolve. b: Model with competition. The parameters are explained on the figure. For the two models, all simulations start with a single sexual lineage.
Table 1.
List and description of the parameters used in the two models.
Figure 2.
Proportion of sexual lineages at the end of simulations for the model without competition, for different values of the initial transition rate (uinit, rows), the rate of change of this transition rate (σu, columns), the speciation rate of sexual (pS, x-axis on each plot) and the extinction rate of sexual (eS, y-axis on each plot).
Plots a and b differ by the value of α, a parameter that controls the difference between sexual and asexual lineages in terms of extinction rate (asexual lineages have an extinction probability α-times greater than that of sexual lineages). α = 2 in a and α = 5 in b. The shading represents the mean proportion of sexual lineages at the end of the runs (after 3000 generations, 50 repetitions). Cells with crosses (×) represent cases in which all simulations ended prematurely.
Figure 3.
Effect of different parameters on the proportion of sexual lineages at the end of simulations (a) and the evolution of the transition rate of sexual (b) for the model without competition.
a. Effect of increasing the difference in the rate of extinction between asexual and sexual lineages (controlled by the α parameter, see Table 1; x-axis) on the proportion of sexual lineages at the end of simulations. The vertical bars indicate the standard deviation around the mean. The parameters used are as follows: Extinction rate of sexual lineages: eS = 0.002; Speciation rate of sexual lineages: pS = 0.004; initial transition rate: uinit = 10−3; Rate of change in the rate of transition: σu = 10−5. b. Changes in transition rate over 3000 generations. Mean and SD were calculated for 50 repetitions for the same set of parameters as in a. and with α = 10.
Figure 4.
Effect of the initial transition rate (a) and of the rate of change in transition rate (b) on the sexual and asexual lineages formed during simulations, for the model with competition.
Black lines represent sexual forms and red lines represent asexual forms. Extinct lineages are not represented. The tree with a star (*) in a is the same as the tree with a star (*) in b (same set of parameters).
Figure 5.
Illustration of lineage selection favouring sexual lineages with the model with competition.
The circles represent the probability of transition from sexuality to asexuality. Black and grey lines represent sexual forms, and red lines represent asexual forms. Lineages without circles can no longer lose sex. After 100 generations, the lineages present are all sexual and have lost the ability to become asexual; all the asexual lineages have become extinct.
Figure 6.
Heatmaps showing the mean proportion (top panel) and mean number (bottom panel) of sexual lineages at the end of simulations (500 generations) over 10 repetitions, for various values of initial transition rate (uinit), rate of change in the transition rate (σu) and the “exploratory ability” of asexuals on the horizontal axis (σA). σS is fixed at 100.