An evolutionary relationship between genetic variation and phenotypic fluctuation

The relevance of phenotype fluctuations among clones (i.e., organisms with identical genes) to evolution has recently been recognized both theoretically and experimentally. By considering the stability of the distributions of genetic variations and phenotype fluctuations, we derive a general inequality between the phenotype variance due to genetic differences and the intrinsic phenotype variance of clones. For a given mutation rate, an approximately linear relationship between the two is obtained which elucidates the consistency between the fundamental theorem of natural selection by Fisher and the evolutionary fluctuation-response relationship (fluctuation dissipation theorem) proposed recently. A general condition for the error catastrophe is also derived as the violation of the inequality, which sets up the limit to the speed of stable evolution. All of these theoretical results are confirmed by a numerical evolution experiment of a cell that consists of a catalytic reaction network. Based on the relationships proposed here, relevance of the phenotypic plasticity to evolution as well as the genetic assimilation is discussed.