Extensive theory exists regarding population sex ratio evolution that predicts equal sex ratio (when parental investment is equal). In most animals, sex chromosomes determine the sex of offspring, and this fixed genotype for sex has made theory difficult to test since genotypic variance for the trait (sex) is lacking. It has long been argued that the genotype has become fixed in most animals due to the strong selection for equal sex ratios. The marine copepod Tigriopus californicus has no sex chromosomes, multiple genes affecting female brood sex ratio and a brood sex ratio that responds to selection. The species thus provides an opportune system in which to test established sex ratio theory. In this paper, we further our exploration of polygenic sex determination in T. californicus using an incomplete diallel crossing design for analysis of the variance components of sex determination in the species. Our data confirm the presence of extra-binomial variance for sex, further confirming that sex is not determined through simple Mendelian trait inheritance. In addition, our crosses and backcrosses of isofemale lines selected for biased brood sex ratios show intermediate phenotypic means, as expected if sex is a threshold trait determined by an underlying “liability” trait controlled by many genes of small effects. Furthermore, crosses between families from the same selection line had similar increases in phenotypic variance as crosses between families from different selection lines, suggesting families from artificial selection lines responded to selection pressure through different underlying genetic bases. Finally, we estimate heritability of an individual to be male or female on the observed binary scale as 0.09 (95% CI: 0.034-0.14). This work furthers our accumulating evidence for polygenic sex determination in T. californicus laying the foundation for this as a model species in future studies of sex ratio evolution theory.

Tigriopus californicus are tidal pool copepods with unusual variance in brood sex ratio. Field-caught individuals were used to create two artificial selection lines using truncation selection to select for highly male-biased broods in one line and highly female-biased broods in another line. After six generations, these lines were used to do a diallel cross of families within and between lines, generating an F1 generation, followed by backcrosses to the parental lines. Crosses were done using eight families from each parental line in two blocks of crosses between four families for F1 generation. The sex of all individuals from each brood in the crosses was observed and a pedigree used to an "Animal Model" analysis to estimate the quantitative genetic variance in sex of individuals in a generalized linear model using Bayesian analysis. Sex in this model was treated as a threshold trait - a binary phenotype driven by an underlying (unobservable) continuous 'liability' phenotype of many genes of small effect, with sex determined based on some threshold value in this underlying trait. This analysis allowed estimation of heritability of sex in Tigriopus californicus, a species with polygenic sex determination. 

Data are provided in comma-delimited text files.

Analysis code are provided for use with R.