PS 45-7
Quantifying variation in individual reaction norms: a practical guide and power analysis for GLMM
Correlations between environment and phenotype are often attributed to the ability of individual organisms to alter labile traits in response to environmental conditions. While such phenotypic plasticity at the population level has long been the focus of ecological research, a torrent of recent studies has illustrated significant variation among individuals in both average responses (reaction norm intercepts) and direction and magnitude of plasticity (reaction norm slopes). These studies take advantage of the powerful machinery offered by the use of generalized mixed effects models (GLMM) for decomposing total phenotypic variation into among group and among individual components. Indeed, these recent advancements have greatly enhanced our understanding of the importance of individual variation in phenotypic responses. Here present a framework for examining how variation in conditions experienced by individuals during their lifetimes can also drive differences in among individual variation across treatments (i.e. variation around individual reaction norms). For example, individuals experiencing more variable environments may have more variable traits than individuals experiencing the same average, but less variable conditions. In this study we provide a primer on how to specify mixed models for examining whether among-individual variance differs among treatments; and present power analyses to guide experimental designs.
Results/Conclusions
Utilizing the recently introduced simulation capabilities of the lme4package in the R statistical programing environment, we evaluate power of GLMMs for detecting treatment differences in individual variation. With logistically feasible sample sizes, modest (e.g. high vs. low variation environments) differences in among-individual variance could be detected with high power (>80%) even in cases with no detectable differences in population mean responses. The relative distribution of total observations to repeated samples of individuals over time, versus replicate individuals, also affects power. Power is highest when the number of individuals/number of observations per individual is ~0.5. Using mixed effects models to test hypotheses about whether among-individual variance differs among treatments opens up new avenues for research.
Most previous discussions of labile traits and phenotypic plasticity have focused on the average phenotypic response of populations across environments, and more recently about how variation in individual phenotypic responses can influence population levels patterns. However, variability in individual responses across environments may itself be a form of phenotypic plasticity that has implication for the evolution of labile traits. These power analyses will provide a guide for empiricists for quantifying and testing hypotheses about the drivers of individual variation in phenotypic responses in changing environments.