Information entropy as a measure of genetic diversity and evolvability in colonization

In recent years, several studies have examined the relationship between genetic diversity and establishment success in colonizing species. Many of these studies have shown that genetic diversity enhances establishment success. There are several hypotheses that might explain this pattern, and here I focus on the possibility that greater genetic diversity results in greater evolvability during colonization. Evaluating the importance of this mechanism first requires that we quantify evolvability. Currently, most measures of evolvability have been developed for quantitative traits whereas many studies of colonization success deal with discrete molecular markers or phenotypes. The purpose of this study is to derive a suitable measure of evolvability for such discrete data. I show that under certain assumptions, Shannon's information entropy of the allelic distribution provides a natural measure of evolvability. This helps to alleviate previous concerns about the interpretation of information entropy for genetic data. I also suggest that information entropy provides a natural generalization to previous measures of evolvability for quantitative traits when the trait distributions are not necessarily multivariate normal.