Quantitative genetics of sexual plasticity: the environmental threshold model and genotype-by-environment interaction for phallus development in the snail Bulinus truncatus

Sexual polymorphisms are model systems for analyzing the evolution of reproductive strategies. However, their plasticity and other binary traits have rarely been studied, with respect to environmental variables. A possible reason is that, although threshold models offer an adequate quantitative genetics framework for binary traits in a single environment, analyzing their plasticity requires more refined empirical and theoretical approaches. The statistical framework proposed here, based on the environmental threshold model (ETM), should partially fill this gap. This methodology is applied to an empirical dataset on a plastic sexual polymorphism, aphally, in the snail Bulinus truncatus. Aphally is characterized by the co-occurrence of regular hermaphrodites (euphallics) together with hermaphrodites deprived of the male copulatory organ (aphallics). Reaction norms were determined for 40 inbred lines, distributed at three temperatures, in a first experiment. A second experiment allowed us to rule out maternal effects. We confirmed the existence of high broad-sense heritabilities as well as a positive effect of high temperatures on aphally. However a significant genotype-by-environment interaction was detected for the first time, suggesting that sexual plasticity itself can respond to selection. A nested series of four ETM-like models was developed for estimating genetical effects on both mean aphally rate and plasticity. These models were tested using a maximum-likelihood procedure and fitted to aphally data. Although no perfect fit of models to data was observed, the refined versions of ETM models conveniently reduce the analysis of complex reaction norms of binary traits into standard quantitative genetics parameters, such as genetic values and environmental variances.