Figure 1.

Neutral and adaptive models of a transition from male to female heterogamety. The two panels illustrate the change of the gamete frequencies of the ancestral (horizontal axes) and novel (vertical axes) sex-determining alleles during a transition from XX♀/XY♂ GSD (male heterogamety) to ZZ♂/ZW♀ GSD (female heterogamety). For each panel, genetic assumptions are illustrated by means of schematic representations of the ancestral sex chromosome pair (gray) with the sex-determining locus, and a pair of autosomes (white) carrying a sex-determination mutation (A,B) and a sexually antagonistic locus (B only). (A) Invasion of an autosomal, epistatically dominant feminizing mutation W. In the absence of intrinsic fitness differences between sex-determination genotypes, the allele W can drift to fixation as the population moves stochastically along a line of equilibria (thick gray line) (Bull and Charnov 1977), away from the ancestral state in the lower left corner of the diagram. By the time variation at the ancestral sex-determining locus is lost and the allele W reaches fixation (in the upper right corner of genotype space), the former X chromosome has disappeared from the population. Populations initialized with arbitrary combinations of allele frequencies quickly evolve toward the line of equilibria (thin gray trajectories), under the influence of selection for a balanced sex ratio. The process of drift along the line of equilibria is illustrated by the results from a stochastic, individual-based implementation of the population-genetic model (black trajectory with open circles; gamete frequencies are plotted every 50 generations for a population of 1000 individuals). (B) A sexually antagonistic gene located on the same autosome pair as the feminizing mutation causes the W allele to spread as a result of indirect selection, supported by the development of linkage disequilibrium between W and the female beneficial allele B (van Doorn and Kirkpatrick 2010). A simulation of a large population of 1 · 10⁶ individuals illustrates the slow deterministic movement of the allele frequencies along a nearly neutral path close to the former line of equilibria (thick grey line). Small insets in A and B present a close-up view of evolutionary trajectories in the vicinity of the line of equilibria, confirming that movement along the line is no longer neutral in B.