Conditional repeatability and the variance explained by reaction norm variation in random slope models

Abstract

Individuals differ in average phenotypes, but also in sensitivity to environmental variation. Such variation is biologically relevant, because it reflects variation in reaction norms. Between-individual variation in average phenotypes is typically quantified as random-intercept variation in linear mixed-effects models or as intra-class correlations (also known as repeatability). Similarly, context-sensitivity can be modelled as random-slope variation. However, random-slope variation implies that between-individual variation varies across the range of a covariate (environment, context, time or age) and has thus been called ‘conditional’ repeatability. While studies fitting random-slope models are on a rapid increase, there is a lack of a general concept for the quantification of context-sensitive between-individual variation. We here propose to put reaction-norm (random-slope) variation in perspective of the total phenotypic variance and suggest a way of standardization that we call random-slope coefficient of determination . Furthermore, we illustrate that instead of the random-intercept variance, the average repeatability across an environmental gradient will be a biologically more relevant description of between-individual variation and we call this the marginalized repeatability R_mar. We provide simple equation to calculated key descriptors of conditional repeatabilities, clarify the difference between random-intercept variation and average between-individual variation and make recommendations for comprehensive reporting. Most importantly, reporting should include means and variances of covariates. While we introduce the concept with individual-variation in mind, the framework is equally applicable to other type of between-group/cluster variation that varies across some (environmental) gradient.