An approach to estimate short-term, long-term and reaction norm repeatability

Abstract

Evolutionary ecologists increasingly study reaction norms that are expressed repeatedly within the same individual's lifetime. For example, foragers continuously alter anti-predator vigilance in response to moment-to-moment changes in predation risk. Variation in this form of plasticity occurs both among and within individuals. Among-individual variation in plasticity (individual by environment interaction or I × E) is commonly studied; by contrast, despite increasing interest in its evolution and ecology, within-individual variation in phenotypic plasticity is not. We outline a study design based on repeated measures and a multilevel extension of random regression models that enables quantification of variation in reaction norms at different hierarchical levels (such as among and within individuals). The approach enables the calculation of repeatability of reaction norm intercepts (average phenotype) and slopes (level of phenotypic plasticity); these indices are not specific to measurement or scaling and are readily comparable across data sets. The proposed study design also enables calculation of repeatability at different temporal scales (such as short- and long-term repeatability), thereby answering calls for the development of approaches enabling scale-dependent repeatability calculations. We introduce a simulation package in the R statistical language to assess power, imprecision and bias for multilevel random regression that may be utilised for realistic data sets (unequal sample sizes across individuals, missing data, etc). We apply the idea to a worked example to illustrate its utility. We conclude that consideration of multilevel variation in reaction norms deepens our understanding of the hierarchical structuring of labile characters and helps reveal the biology in heterogeneous patterns of within-individual variance that would otherwise remain 'unexplained' residual variance.