Jordan Scott Martin , Yimen G Araya-Ajoy, Niels J Dingemanse, Alastair J. Wilson, David Westneat

Individual reaction norms describe how labile phenotypes vary as a function of organisms’ expected trait values (intercepts) and plasticity across environments (slopes), as well as their degree of stochastic phenotypic variability or predictability (residuals). These reaction norms can be estimated empirically using multilevel, mixed-effects models and play a key role in ecological research on a variety of behavioral, physiological, and morphological traits. Many evolutionary models have also emphasized the importance of understanding reaction norms as a target of selection in heterogeneous and dynamic environments. However, it remains difficult to empirically estimate nonlinear selection on reaction norms, inhibiting robust tests of adaptive theory and accurate predictions of phenotypic evolution. To address this challenge, we propose generalized multilevel models for estimating stabilizing, disruptive, and correlational selection on the reaction norms of labile traits, which can be applied to any repeatedly measured phenotype using a flexible Bayesian framework. These models avoid inferential bias by accounting for uncertainty in reaction norm parameters and their potentially nonlinear fitness effects. We validate these models in a Bayesian framework using multiple simulation techniques, demonstrating unbiased inference across a broad range of effect sizes and desirable power for large sample sizes. Coding tutorials are further provided to aid empiricists in applying these models to any phenotype of interest using the Stan statistical programming language in R.