The Evolution of Polygenic Sex Determination with Potential for Environmental Manipulation

We present a formal account of a genetic mechanism for Environmental Sex Determination (ESD) using a probabilistic process algebra (WSCCS). We exploit the process algebra to demonstrate that a single chromosome pair based polyfactorial system is intrinsically unstable. The system evolves, with a deterministic relationship between an animal's sex and its polyfactor count, to three possible forms of genetic mechanism: pure ESD; pure genetic sex determination (GSD) (both XY and ZW being possible outcomes); or a mixed solution with a 50/50 division between ESD and GSD. With a probabilistic dependence between gene count and sex we observe the rst and last of the above solutions (no pure GSD), but with population gene frequencies that can be far from Hardy-Weinberg equilibrium. A model of the systemic behaviour in the presence of recombination is presented, and the e ect of the relative recombination and evolution rates is discussed. Our process algebraic model is extended to account for the polyfactors being distributed over many possible chromosome pairs and demonstrates that only one essentially new stable solution is reachable. We demonstrate that within a multichromosome system there will almost always be a `leading' chromosome pair which determines sex, other chromosome pairs will have identical sex determining information upon both members of the pair, but not necessarily none.