Toward a neutral evolutionary model of gene expression.

We introduce a stochastic model that describes neutral changes of gene expression over evolutionary time as a compound Poisson process where evolutionary events cause changes of expression level according to a given probability distribution. The model produces simple estimators for model parameters and allows discrimination between symmetric and asymmetric distributions of evolutionary expression changes along an evolutionary lineage. Furthermore, we introduce two measures, the skewness of expression difference distributions and relative difference of evolutionary branch lengths, which are used to quantify deviation from clock-like behavior of gene expression distances. Model-based analyses of gene expression profiles in primate liver and brain samples yield the following results: (1) The majority of gene expression changes are consistent with a neutral model of evolution; (2) along evolutionary lineages, upward changes in expression are less frequent but of greater average magnitude than downward changes; and (3) the skewness measure and the relative branch length difference confirm that an acceleration of gene expression evolution occurred on the human lineage in brain but not in liver. We discuss the latter result with respect to a neutral model of transcriptome evolution and show that a small number of genes expressed in brain can account for the observed data.