Molecular Evolution, Mutation Size and Gene Pleiotropy: A Geometric Reexamination

Abstract The influence of phenotypic effects of genetic mutations on molecular evolution is not well understood. Neutral and nearly neutral theories of molecular evolution predict a negative relationship between the evolutionary rate of proteins and their functional importance; nevertheless empirical studies seeking relationships between evolutionary rate and the phenotypic role of proteins have not produced conclusive results. In particular, previous studies have not found the expected negative correlation between evolutionary rate and gene pleiotropy. Here, we studied the effect of gene pleiotropy and the phenotypic size of mutations on the evolutionary rate of genes in a geometrical model, in which gene pleiotropy was characterized by n molecular phenotypes that affect organismal fitness. For a nearly neutral process, we found a negative relationship between evolutionary rate and mutation size but pleiotropy did not affect the evolutionary rate. Further, for a selection model, where most of the substitutions were fixed by natural selection in a randomly fluctuating environment, we also found a negative relationship between evolutionary rate and mutation size, but interestingly, gene pleiotropy increased the evolutionary rate as $\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\sqrt{n}\) \end{document}$. These findings may explain part of the disagreement between empirical data and traditional expectations.