How and why to quantify pairwise pleiotropy and genotype-by-environment interactions

Pleiotropy is when a single locus affects two or more traits. The magnitude and direction of pleiotropy can constrain or faciliate phenotypic evolution. Investigations of pleiotropy have typically relied on null-hypothesis tests to classify cases into discrete categories based on the direction of effects. This discrete approach ignores the quantitative nature of pleiotropy, and systematically underestimates pleiotropic interactions. I describe a simple method to quantify the direction and magnitude of pleiotropic effects to alleviate these issues for pairs of traits. I illustrate how genotype-by-environment interactions can be viewed as a special case of pleiotropy and described in the same way. I provide an R package, psiotropy, to apply these methods.