On the optimal sex-ratio: a stability analysis based on a characterization for one-locus multiallele viability models

Theoretical one-locus multiallele sex-determination models are found to admit even sex ratio equilibrium surfaces besides the equilibria for corresponding one-locus multiallele viability models. Both types of equilibria can be defined in terms of a single spectral radius function, the former corresponding to level surfaces and the latter to critical points. The stable equilibria in the corresponding viability models are associated with the local maxima, and the equilibrium structures for the sex-determination models can be fully described. Several optimality properties of the even-sex-ratio equilibrium surfaces can be deduced.