PT  - JOURNAL ARTICLE
AU  - Schielzeth, Holger
AU  - Nakagawa, Shinichi
TI  - Conditional repeatability and the variance explained by reaction norm variation in random slope models
AID  - 10.1101/2020.03.11.987073
DP  - 2020 Jan 01
TA  - bioRxiv
PG  - 2020.03.11.987073
4099  - http://biorxiv.org/content/early/2020/03/11/2020.03.11.987073.short
4100  - http://biorxiv.org/content/early/2020/03/11/2020.03.11.987073.full
AB  - 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 Rmar. 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.