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]. Furthermore, we illustrate that the marginalized repeatability Rmar 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.