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

Spatial covariance between genotypic and environmental influences on phenotypes (CovGE ) 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 CovGE has been lacking. We develop a novel quantitative/analytical approach to estimate and test the significance of CovGE from reciprocal transplant or common garden experiments, which we validate using simulated data. We demonstrate how power to detect CovGE changes over a range of experimental designs. We confirm an inverse relationship between gene-by-environment interactions (GxE) and CovGE , 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 CovGE and GxE on phenotypes in studies of local adaptation and species' responses to environmental change.