Send to

Choose Destination
Am Nat. 2013 Mar;181(3):291-300. doi: 10.1086/669158. Epub 2013 Jan 28.

Selection gradients, the opportunity for selection, and the coefficient of determination.

Author information

Duke Population Research Institute and Department of Biology, Duke University, Durham, NC 27708, USA.


We derive the relationship between R(2) (the coefficient of determination), selection gradients, and the opportunity for selection for univariate and multivariate cases. Our main result is to show that the portion of the opportunity for selection that is caused by variation for any trait is equal to the product of its selection gradient and its selection differential. This relationship is a corollary of the first and second fundamental theorems of natural selection, and it permits one to investigate the portions of the total opportunity for selection that are involved in directional selection, stabilizing (and diversifying) selection, and correlational selection, which is important to morphological integration. It also allows one to determine the fraction of fitness variation not explained by variation in measured phenotypes and therefore attributable to random (or, at least, unknown) influences. We apply our methods to a human data set to show how sex-specific mating success as a component of fitness variance can be decoupled from that owing to prereproductive mortality. By quantifying linear sources of sexual selection and quadratic sources of sexual selection, we illustrate that the former is stronger in males, while the latter is stronger in females.

[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for University of Chicago Press Icon for PubMed Central
Loading ...
Support Center