A general representation of the substitutions involved in changing the heterogametic system, both for model 1 transitions (A) and for model 2 transitions (B). In both models, numerical subscripts reveal regularities in the progression of mutations whose fixations switch the system of heterogamety. (A) For model 1, because the sex chromosome locus does not change, we have used the usual sex chromosome labels X and Y. Transitions between heterogametic systems that involve the arrival and fixation (“substitution”) of new dominant sex determining mutations are labeled
a and
c.
a is from male to female heterogamety, and involves the substitution
c is from female to male heterogamety, and involves the substitution
Transitions that involve the substitution of new recessive sex determining mutations are labeled
b and
d.
b is from female to male heterogamety via the substitution
d is from male to female heterogamety, via the substitution
(B) For model 2, we have used the arbitrary letters A and B to denote the two separate chromosomes/unlinked loci: one switches to a sex chromosome, and the other switches to an autosome, each time the heterogametic system changes. Again,
a and
c are used to label heterogametic transitions involving substitution of new dominant sex-determining mutations;
a from male to female heterogamety via substitution of the mutation
on a previous autosome, and
c from female to male heterogamety via substitution of the mutation
on a previous autosome.
b and
d refer to the reverse transitions, involving substitution of new recessive sex determining mutations;
b from female to male heterogamety via substitution of the mutation
on a previous autosome, and
d from male to female heterogamety via substitution of the mutation
on a previous autosome. We find in both models that, when all sexual genotypes are equally fit, dominant sex-determining mutations substitute at a higher rate than recessive sex-determining mutations—with reference to the present figure, we find a bias toward rightward transitions of the heterogametic system.