Changes in the heterogametic mechanism of sex determination

Abstract

SUMMARYThis paper attempts to explain how the different hetcrogametic mechanisms of sex determination, such as male and female heterogamety, can arise from a single ancestor. We study this problem by first building and analysing some models and then comparing the models to relevant data from animals. Based on these comparisons, the models appear to be useful for understanding how sex determining mechanisms evolve. Some results of the models include:(1) A mutant sex determiner invading a population of male or female heterogamety creates the potential for the evolution of a new heterogametic sex determining mechanism.(2) Certain mutants will lead to a new system of male heterogamety whereas others will lead to a new system of female heterogamety.(3) These changes take place through an intermediate population charactensed by multigenic sex determination. In some cases the multigenic mechanism is stable and will not revert to male or female heterogamety. The success of the invading mutant depends upon both (i) the relative viabilities of the different genotypes, and (ii) the segregation ratio of the X and Y in males; the population primary sex ratio is otherwise maintained at 1/2. (4) The models show how the different systems of genie balance arise and how sex determiners can become inherited autosomally.

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

“…Mechanistic Approach We want to build a similar model, but more mechanistically using the genotype frequencies. We will denote their numbers n (1) (A (1) A (1) ), n (2) (A (1) A (2) ) and n (3) (A (2) A (2) ), so that the fixed size of the population is n (1) + n (2) + n (3) = N . (Note the slight difference in notation with the main text; n (A (1) A (1) ) ≡ n (1) , n (A (1) A (2) ) ≡ n (2) and n (A (2) A (2) ) ≡ n (3) ).…”

“…As we discussed in the Introduction, the validity of our methods and approximations are checked via computer simulations, and these use the microscopic model defined by Eqs. (1) and (3). The simulations use the Gillepsie algorithm [25,26] which is developed within the same formalism discussed in this section.…”

“…To use these we need to introduce what are in effect stoichiometric vectors corresponding to the four "reactions" in Eq. (3). In other words we write the final state, n , in terms of the initial state, n, as n = n + ν μ , where μ = 1, .…”

“…Let the frequency of XX, X X and X Y (female) and XY and YY genotypes (male) be respectively given by x = (x (1) , x (2) , x (3) , x (4) , x (5) ). Due to the condition of fixed population size, we can then express x (5) (4) .…”

“…Due to the condition of fixed population size, we can then express x (5) (4) . If all genotypes are equally fit, then this four-dimensional system exhibits a one-dimensional CM that connects the absorbing states, characterised in [3]. It is given by…”