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

Abstract

Individuals differ in average phenotypes and in sensitivity to environmental variation. Such context sensitivity can be modelled as random slope variation. Random slope variation implies that the proportion of between-individual variation varies across the range of a covariate (environment/context/time/age) and has thus been called ‘conditional’ repeatability. We propose to put conditional repeatabilities in perspective of the total phenotypic variance and suggest a way of standardization using the random slope coefficient of determination (Formula presented.). Furthermore, we illustrate that the marginalized repeatability (Formula presented.) averaged across an environmental gradient offers a biologically relevant description of between-individual variation. We provide simple equations for calculating key descriptors of conditional repeatabilities, clarify the difference between random intercept variation and average between-individual variation and make recommendations for comprehensive reporting. 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.