Environmental coupling of heritability and selection is rare and of minor evolutionary significance in wild populations.

Predicting the rate of adaptation to environmental change in wild populations is important for understanding evolutionary change. However, predictions may be unreliable if the two key variables affecting the rate of evolutionary change-heritability and selection-are both affected by the same environmental variable. To determine how general such an environmentally induced coupling of heritability and selection is, and how this may influence the rate of adaptation, we made use of freely accessible, open data on pedigreed wild populations to answer this question at the broadest possible scale. Using 16 populations from 10 vertebrate species, which provided data on 50 traits (relating to body mass, morphology, physiology, behaviour and life history), we found evidence for an environmentally induced relationship between heritability and selection in only 6 cases, with weak evidence that this resulted in an increase or decrease in the expected selection response. We conclude that such a coupling of heritability and selection is unlikely to strongly affect evolutionary change, even though both heritability and selection are commonly postulated to be dependent on the environment.