T. californicus.
T. californicus gives every indication of having true polygenic inheritance of sex, with many genes of small effect contributing to the underlying liability trait value for the threshold trait of sex. The data presented in the current study confirms previous work done on sex ratio in this organism using different populations and estimation methods (Voordouw and Anholt 2002b; Voordouw et al. 2005, 2008; Foley et al. 2013; Alexander et al. 2014, 2015). Using a Bayesian pedigree analysis (i.e., the animal model), we show that the tendency for an individual T. californicus to become male has a significant genetic component, with a heritability estimate of 0.09, after removing variance due to fixed effects of breeding lines and blocks. Note that in this study, breeding lines were different isofemale lines and thus clearly also included a genetic component; thus, our heritability estimates are likely to be underestimates. By including the fixed effects in our Bayesian model, the credible interval of our estimate of heritability was decreased to one-third the size (Appendix Figure 2). We initially ran the model using a standard uninformative prior distribution, but as we had estimates of heritability from previous studies (Voordouw and Anholt 2002b; Alexander et al. 2014), we were in a position to use an informed prior and Bayesian analysis to update our prior knowledge. Using an informed prior did allow us to minimally reduce credible intervals around our heritability estimates but did not affect analysis results and had far less of an effect than adding in the ancestral selection line information (Appendix Figure 2).
The maintenance of variability, and continued presence of extra-binomial variation, when crossing offspring of two individuals from the same selection line provides strong evidence for many genes of small effect controlling sex determination in T. californicus . Further, the increase in phenotypic variation for F1s that occurred when different lines from the same selection type population were crossed suggests selection lines were achieved using different genes among lines. If lines were genetically similar, we would not expect much change between crosses within each selection type by block. This result is further corroborated through consideration of the phenotypic variance in brood sex ratio across generations under selection for biased sex ratios. While the sex ratios responded strongly to selection, the variance in brood sex ratio was essentially unchanging over the seven generations of selection (Figure 3). This also matches observations in the field of extensive variance in brood sex ratio both within and among sites (Voordouw et al. 2008) and models showing polygenic sex determination is maintained indefinitely when combined with seasonal fluctuations of alternating selection (Bateman and Anholt 2017).
Several other aspects of T. californicus biology are likely to contribute to maintenance of genetic variance in the species.Tigriopus live in supralittoral marine splash pools that are both ephemeral and highly variable environments and form a complex metapopulation, with each splash pool representing a subpopulation and migration occurring between splash pools. Charnov and Bull (1989) demonstrated that in patchy environments, if females do relatively better in one patch, then the primary sex ratio is male-biased (the sex coming from the poorer habitat). In addition, environmental sex determination (ESD) is also known to play role in Tigriopus sex determination (Voordouw and Anholt 2002a). In contrast, the failure ofT. californicus to develop heterogametic sex determination is perhaps surprising given that females have achiasmatic meiosis (Ar-rushdi 1963), and with achiasmata in one sex any sex-determining gene that evolves should quickly lead to differentiated sex chromosomes (Wright et al. 2016).
A recent simulation by Butka and Freedberg (2019) reveals that when environmental sex determination is present and controlled by many loci (≥10), limited dispersal rates (<0.5) among multiple subpopulations lead to a male-biased sex ratio equilibrium. Population genetic studies do suggest that Tigriopus dispersal among rocky outcrops is limited (Burton and Feldman 1981). At least six QTL exist for sex determination (Alexander et al. 2015) and recent research suggests such QTLs likely represent many separate genes each (Walsh and Lynch 2021). In nature, T. californicus populations do tend to be male-biased (Voordouw et al. 2008). The combination of the modelling and field data thus suggest one possible explanation for male-biased sex ratios observed in T. californicus and further reinforces the idea that the species has polygenic sex determination. Environmental variance represents only a minor portion of sex ratio variance inT. californicus (Voordouw and Anholt 2002a,b) and genetic influence on pivotal temperature has not been considered; it is possible that selection for sex ratio bias is in fact selecting for changes in pivotal temperature (Wright et al. 2016).
Variance for threshold traits on the observed scale contains additional variance and this reduces maximum heritability. For example, while the liability trait, on the latent scale, has a continuous range of values, the observed phenotype has only one of two values, determined by the latent scale breeding value and the threshold value. Thus, if the threshold value is 0.4, whether the individual’s breeding value is 0.2 or 0.01 they will be male on the observed scale. This has the effect of increasing the non-additive genetic variance for the trait on the observed scale, thereby limiting the maximum heritability possible. In particular, heritability on the observed scale will always be lower than that on the latent scale (Dempster and Lerner 1950; de Villemereuil et al. 2016; de Villemereuil 2020). This is one reason why the heritability observed here, given on the observed scale, is lower than the realized heritability estimated on the latent scale by Alexander et al. (2014). Nonetheless, a strong response to truncation selection for biased sex ratios clearly indicates some aspect of sex determination in the species is sufficiently heritable to respond to selection. We speculate that epistatic effects may also limit our ability to estimate true heritability.
The difference in estimated heritabilities may also reflect violation of any one of the many assumptions of the threshold model. In particular, the model assumes allelic effects at the many loci contributing to liability are multivariate normal. This is both unlikely to be true and difficult to assess. Benchek and Morris (2013), using simulated data to test heritability estimates when true liability included a common environmental effect that was not normally distributed, found that heritability estimates can be highly biased in this case and that the direction of bias was not consistent. The model also assumes no pleiotropic or epigenetic effects, but environment is known to influence sex determination in Tigriopus . Temperature effects on sex may well be influenced by genes and alleles affecting sex determination and temperature effects on sex determination seem likely to interact with each other as well as with the environment. At the heart of the challenge is that selection acts on the multivariate phenotype and any one component in isolation may have low heritability although the combined traits have high heritability (Walsh and Lynch 2018).
Regardless of the underlying genetic mechanism, it seems likely that the complex metapopulation dynamics of Tigriopus (Dethier 1980; Burton and Swisher 1984; Powlik 1999; Johnson 2001) may be an important component to understanding the unusual maintenance of polygenic sex determination in the species. The highly unpredictable nature of the splash pools these copepods inhabit may further provide insight into why this species has failed to evolve a single gene of large effect for sex tendency. Pools that are washed out by wave action will cause large-scale mortality unrelated to phenotype, as most individuals washed into the ocean are likely to be consumed by fish (Dethier 1980).
While the presence of multiple genes affecting sex has recently been observed in many animals, particularly in fish species (Martínez et al. 2014), in most of these cases a sex chromosome or gene with large effect on sex is present in the species. The case for polygenic sex determination has perhaps been most strongly made for the model organism zebrafish (Liew et al. 2012), where only two to three (depending on strain) sex determining regions (compared to six in Tigriopus ) have been identified in domesticated zebrafish (Wilson et al. 2014) and wild zebrafish have a ZZ/ZW sex determining system (Wilson et al. 2014). Similarly in European sea bass, while genetic components for sex determination are present and suggest polygenic sex determination (Vandeputte et al. 2007), sex determination is also strongly influenced by temperature and wild populations do not show the same sex ratio biases seen in farmed populations (Vandeputte et al. 2012). We suggest that T. californicus represents a unique polygenic system in that there is no indication that any one gene has a large effect on sex determination nor that such a gene has ever existed in the species. The species thus continues to present an interesting case study that appears to defy theoretical expectations.