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, genetic variation and evolutionary potential 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 first derive components of phenotypic variance arising from the average reaction norm across genotypes, genetic variation in reaction norms (including additive genetic variance), and a residual that cannot be predicted by reaction norms. We then further partition the first two terms into contributions from parameters of reaction norm shape, such as the mean and variance of reaction norm slope and curvature. We show how to implement this approach in practice in various contexts, including the character-state approach, polynomial functions, or arbitrary non-linear models. We also show how the combination of character-state and curve-parameter approaches can provide a metric of goodness of fit of a given model of reaction norm shape. Overall the toolbox we develop, summarized in an online tutorial, should serve as a base for more robust comparative studies of plasticity across organisms and traits.