In C. elegans there are two sexes: hermaphrodite and male. Sex is determined by the ratio of X chromosomes to haploid sets of autosomes (X/A). An X/A ratio of 1.0 produces a hermaphrodite (XX), and an X/A ratio of 0.5 results in a male (XO). In the 1970s, Jonathan Hodgkin and Sydney Brenner carried out genetic screens to identify mutations in three genes that result in either XX males (tra-1, tra-2) or XO hermaphrodites (her-1). Double-mutant strains were constructed to assess for epistatic interactions between the genes (see table). Propose a genetic model of how the her and tra genes control sex determination.

Genotypeᵃ             XX Phenotype             XO Phenotype
Wild-type               Hermaphrodite            Male
tra-1ʳᵉᶜ                   Male                            Male
tra-2ʳᵉᶜ                   Male                            Male
her-1ʳᵉᶜ                  Hermaphrodite            Hermaphrodite
tra-1ᵈᵒᵐ/+               Hermaphrodite            Hermaphrodite
tra-1ʳᵉᶜ tra-2ʳᵉᶜ        Male                            Male
tra-1ʳᵉᶜ her-1ʳᵉᶜ       Male                            Male
tra-2ʳᵉᶜ her-1ʳᵉᶜ       Male                            Male
tra-2ʳᵉᶜ tra-1ᵈᵒᵐ/+   Hermaphrodite            Hermaphrodite
ᵃrec = recessive mutation; dom = dominant mutation.