A novel analytical framework to quantify co-gradient and countergradient variation

Spatial covariance between genotypic and environmental influences on phenotypes (Cov_GE ) can result in the nonrandom distribution of genotypes across environmental gradients and is a potentially important factor driving local adaptation. However, a framework to quantify the magnitude and significance of Cov_GE has been lacking. We develop a novel quantitative/analytical approach to estimate and test the significance of Cov_GE from reciprocal transplant or common garden experiments, which we validate using simulated data. We demonstrate how power to detect Cov_GE changes over a range of experimental designs. We confirm an inverse relationship between gene-by-environment interactions (GxE) and Cov_GE , as predicted by first principles, but show how phenotypes can be influenced by both. The metric provides a way to measure how phenotypic plasticity covaries with genetic differentiation and highlights the importance of understanding the dual influences of Cov_GE and GxE on phenotypes in studies of local adaptation and species' responses to environmental change.