On Theoretical Models of Gene Expression Evolution with Random Genetic Drift and Natural Selection

Background: The relative contributions of natural selection and random genetic drift are a major source of debate in the study of gene expression evolution, which is hypothesized to serve as a bridge from molecular to phenotypic evolution. It has been suggested that the conflict between views is caused by the lack of a definite model of the neutral hypothesis, which can describe the long-run behavior of evolutionary change in mRNA abundance. Therefore previous studies have used inadequate analogies with the neutral prediction of other phenomena, such as amino acid or nucleotide sequence evolution, as the null hypothesis of their statistical inference. Methodology/Principal Findings: In this study, we introduced two novel theoretical models, one based on neutral drift and the other assuming natural selection, by focusing on a common property of the distribution of mRNA abundance among a variety of eukaryotic cells, which reflects the result of long-term evolution. Our results demonstrated that (1) our models can reproduce two independently found phenomena simultaneously: the time development of gene expression divergence and Zipf's law of the transcriptome; (2) cytological constraints can be explicitly formulated to describe long-term evolution; (3) the model assuming that natural selection optimized relative mRNA abundance was more consistent with previously published observations than the model of optimized absolute mRNA abundances. Conclusions/Significance: The models introduced in this study give a formulation of evolutionary change in the mRNA abundance of each gene as a stochastic process, on the basis of previously published observations. This model provides a foundation for interpreting observed data in studies of gene expression evolution, including identifying an adequate time scale for discriminating the effect of natural selection from that of random genetic drift of selectively neutral variations.