Lewontin and Kojima Meet Fisher: Linkage in a Symmetric Model of Sex Determination

The effect of linkage and epistasis on the evolution of the sex-ratio is studied in a symmetric two-locus model of autosomal sex determination closely related to the symmetric viability model of R. C. Lewontin and K. Kojima. R. A. Fisher's expectation of an even sex ratio for autosomal sex determination by a single gene governs the dynamics when the loci are tightly linked. However, recombination may preclude optimization of the sex ratio just as occurs in viability selection models. Many of the evolutionary phenomena known for the symmetric viability model also occur here. In addition, we exhibit a series of new phenomena related to the presence of surfaces of even sex ratio.