Pierre de Villemereuil, Luis-Miguel Chevin

Many phenotypic traits vary in a predictable way across environments, as captured by their norms of reaction. These reaction norms may be discrete or continuous, and can substantially vary in shape across organisms and traits, making it difficult to compare amounts and types of plasticity among (and sometimes even within) studies. In addition, the evolutionary potential of phenotypic traits in heterogeneous environments critically depends on how reaction norms vary genetically, but there is no consensus on how this should be quantified. 

Here, we propose a partitioning of phenotypic variance across genotypes and environments that jointly address these challenges. We start by distinguishing the components of phenotypic variance arising from the average reaction norm across genotypes, (additive) genetic variation in reaction norms, and a residual that cannot be predicted from the genotype and the environment. We then further partition the (additive) genetic variance of the trait into a component related the marginal (additive) genetic variance in the trait and a component due to (additive) genetic variance in plasticity, including for complex, non-linear reaction norms. The last step involves estimating contributions from different parameters of reaction norm shape to these variance components.

This decomposition is general and we show how to apply it to various modelling approaches, from the character-state to curve-parameter approaches, including polynomial functions, or arbitrary non-linear models. To facilitate the use of this variance decomposition, we provide the Reacnorm R package, including a practical tutorial. Overall the toolbox we develop should serve as a base for an unifying and deeper understanding of the variation and genetics of reaction norms and plasticity, as well as more robust comparative studies of plasticity across organisms and traits.