Introduction
Sex determination and sex ratio are intrinsically linked. In organisms where sex is determined solely by sex chromosome, the sex ratio for the offspring of a parent is determined on the basis of Mendelian inheritance and can be predicted simply from a binomial distribution (Krackow et al. 2002). Where multiple sex factor genes or other genes that affect sex tendency are present, sex ratio of offspring may be less straightforward, as has now been observed in a variety of fish species (Vandeputte et al. 2007; Liew et al. 2012; Faggion et al. 2019). In addition, environmental effects, including maternal effects, can modify sex tendency in an individual (Bull et al. 1982; Bull 1985; Sarre et al. 2004; Radder et al. 2008).
Historically, sex determination tended to be labelled as genetic (GSD) or environmental (ESD), but it is increasingly clear that this traditional view of sex determination is unreasonably simple (Uller and Helanterä 2011; Beukeboom and Perrin 2014). A variety of recent studies suggest that in species with sex chromosomes, sex of individuals can be strongly influenced by modifier autosomal genes and/or environmental effects. Notably, this has been observed in a variety of fish when reared in captivity, with aquaculturists often intentionally modifying population sex ratios to increase production of the more profitable sex (Vandeputte and Piferrer 2019; Zhou et al. 2020). In sea bass, Vandeputte (2007) showed that both a polygenic model with environmental variance and a two-locus gene model with environmental variance fit data from a crossing design.
Regardless of the sex determining mechanism, theory predicts that, where male and female offspring are equally costly to produce, population sex ratio should be stable at 50% males and females (Fisher 1930; Shaw and Mohler 1953; Shaw 1958; Karlin and Lessard 1983) and unstable at biased sex ratios. Further, theory predicts polygenic determination of sex should never be stable (Rice 1986). Yet the harpacticoid copepod,Tigriopus californicus , a benthic species inhabiting high-intertidal pools along the west coast of North America, is well documented to have highly variable sex ratios (Ar-Rushdi 1958; Ar-rushdi 1963; Voordouw and Anholt 2002b; Voordouw et al. 2005) that, while affected by environment, are also highly heritable in a manner that suggests polygenic inheritance (Alexander et al. 2014, 2015).
The developmental process of sex determination in Tigriopus californicus is not known, but as males engaging in precopulatory mate-guarding will clasp females as early as copepodite stage CII (Burton 1985), sex is presumably determined by this stage. (Sexes cannot be differentiated morphologically until copepodite stage CIV.) Work on delineating sex determination and sex ratio processes in T. californicus is ongoing. Foley et al. (2013) crossed isofemale lines from two different populations and found that sex and mitochondrial background are significantly associated with genetic markers in nine of 12 chromosomes. In previous studies (Alexander et al. 2014, 2015), we selected on brood sex ratio to create male- and female-biased lines, showing that brood sex ratio responded to artificial truncation selection (Alexander et al. 2014). Using a California population ofT. californicus with a published linkage map of SNP markers, we conducted crosses between that population (Foley et al. 2011) and a British Columbia population to identify quantitative genetic loci associated with brood sex ratio, finding that at least six QTL for brood sex ratio exist on five different chromosomes (Alexander et al. 2015). Here, we take advantage of the selected lines from the local population to conduct a diallel cross, followed by backcrosses to parental lines, and use an animal model analysis to assess the quantitative genetics of sex determination in T. californicus . Using pedigree data for F1 crosses and F2 backcrosses, we look at the heritability of an individual to become male and further explore the nature of polygenic sex determination in T. californicus .