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 repro ductive strategies. However, their plasticity and other binary traits have rarely been studied, with respect to environmental variables. A possible re ason is that, although threshold models offer an adequate quantitative gene tics framework for binary traits in a single environment, analyzing their p lasticity requires more refined empirical and theoretical approaches. The s tatistical framework proposed here, based on the environmental threshold mo del (ETM), should partially fill this gap. This methodology is applied to a n empirical dataset on a plastic sexual polymorphism, aphally, in the snail Bulinus truncatus. Aphally is characterized by the co-occurrence of regula r hermaphrodites (euphallics) together with hermaphrodites deprived of the male copulatory organ (aphallics). Reaction norms were determined for 40 in bred lines, distributed at three temperatures, in a first experiment. A sec ond experiment allowed us to rule out maternal effects. We confirmed the ex istence 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 plasti city itself can respond to selection. A nested series of four ETM-like mode ls was developed for estimating genetical effects on both mean aphally rate and plasticity. These models were tested using a maximum-likelihood proced ure and fitted to aphally data. Although no perfect fit of models to data w as observed, the refined versions of ETM models conveniently reduce the ana lysis of complex reaction norms of binary traits into standard quantitative genetics parameters, such as genetic values and environmental variances.