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.