genetics - How does sex differentiation work in Paracerceis sculpta, the sexually tetramorphic isopod?

Shuster, SM & C Sassaman (1997)
Genetic interaction between male mating strategy and sex ratio in a marine isopod. Nature 388: 373-377

As described in this paper, the chromosomal system of sex determination in Paracerceis sculpta is ZW=females, ZZ=males. Genetic evidence indicates that the morph of a ZZ male is determined by a second locus, Ams (alternative mating strategy) which exists in three allelic forms whose dominance relationship is Ams^β > Ams^γ > Ams^α. So for example, to be an α type male, an individual must be ZZ Ams^α / Ams^α.

That's the end of the answer, what follows is supplementary information.

The paper also describes an additional layer of complexity in the sex-determining system of P. sculpta involving sex changes in both directions. This is explained by a model in terms of two other factors: an autosomal locus Tfr (transformer) and a cytoplasmic factor ECF (extra-chromosomal factor) which interact as shown in the Table below (taken from the paper). However, this doesn't really add anything to the Ams story as far as male morphs are concerned, except that some of them start as females.