On Theoretical Models of Gene Expression Evolution with Random Genetic Drift and Natural Selection Osamu Ogasawara*, Kousaku Okubo Center for Information Biology and DNA Data Bank of Japan, National Institute of Genetics, Mishima, Shizuoka, Japan Abstract 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 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. Citation: Ogasawara O, Okubo K (2009) On Theoretical Models of Gene Expression Evolution with Random Genetic Drift and Natural Selection. PLoS ONE 4(11): e7943. doi:10.1371/journal.pone.0007943 Editor: Justin C. Fay, Washington University, United States of America Received August 10, 2009; Accepted October 26, 2009; Published November 20, 2009 Copyright: 2009 Ogasawara, Okubo. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by a Grant-in-Aid for Scientific Research in Priority Areas (Genome Information Science) 17017037 from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) http://www.mext.go.jp/english/. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: oogasawa@genes.nig.ac.jp Introduction It has long been hypothesized that phenotypic evolution is more often based on evolutionary changes in gene expression regulation than on sequence changes in proteins [1]. Prompted by this hypothesis and the advent of genome-wide gene expression profiling techniques, an increasing number of studies have investigated the pattern of evolutionary change in gene expression profiles and the evolutionary forces governing the process. Recently, it has become evident that heritable variations in the mRNA abundance are commonly seen in a variety of species, such as yeast [2–5], Drosophila [6–10], mice [11,12], and humans [13–16], along with variations between species [7,9,17–25]. This has raised the question of how those variations are maintained in populations and what evolutionary forces affect the pattern of variations within and among species. In particular, the main conflict between researchers over gene expression evolution is the relative contribution of random genetic drift and natural selection to evolutionary changes in mRNA abundance. Some researchers have argued that the majority of evolutionary changes in the mRNA abundance is selectively neutral and likely to be of little or no functional significance (neutral hypothesis) [17,18,21,22,24–26], while others have argued that natural selection has a substantial effect on gene expression evolution [7,23]. According to Whitehead and Crawford (2006) [30], among studies which provide quantita- tive estimates, the proportion of genes which are supposed to be subject to stabilizing selection, for example, varies from 7% to 100%. In a comparison of populations of the marine killifish Fundulus adapting to different habitat temperatures, much of the variation in expression level was correlated with phylogeny regardless of the habitat temperature they adapted to [17,18,24,25]. This result can be explained by the neutral hypothesis. On the other hand, Lemos et al. (2005) [23] argued that more than 96% of genes were subject to stabilizing selection in primates, rodents, and Drosophila lineages by using the mutation- drift equilibrium model [27–29] in which the variance in expression levels of a given gene among species was scaled by the divergence time. As for the cause of this conflict, Whitehead and Crawford (2006) [30] suggested that the linearity between gene expression divergence and phylogenetic distance, which is expected from the neutral hypothesis, might be lost when the divergence time PLoS ONE | www.plosone.org 1 November 2009 | Volume 4 | Issue 11 | e7943