A phylogenetic mixture model for the evolution of gene expression

Microarray platforms are used increasingly to make comparative inferences through genome-wide surveys of gene expression. Although recent studies focus on describing the evidence for natural selection using estimates of the within- and between-taxa mutational variances, these methods do not explicitly or flexibly account for predicted nonindependence due to phylogenetic associations between measurements. In the interest of parsing the effects of selection: we introduce a mixture model for the comparative analysis of variation in gene expression across multiple taxa. This class of models isolates the phylogenetic signal from the nonphylogenetic and the heritable signal from the nonheritable while measuring the proper amount of correction. As a result, the mixture model resolves outstanding differences between existing models, relates different ways to estimate the across taxa variance, and induces a likelihood ratio test for selection. We investigate by simulation and application the feasibility and utility of estimation of the required parameters and the power of the proposed test. We illustrate analysis under this mixture model with a gene duplication family data set.

The Phylogenetic Mixed Model

The phylogenetic mixed model is an application of the quantitative-genetic mixed model to interspecific data. Although this statistical framework provides a potentially unifying approach to quantitative-genetic and phylogenetic analysis, the model has been applied infrequently because of technical difficulties with parameter estimation. We recommend a reparameterization of the model that eliminates some of these difficulties, and we develop a new estimation algorithm for both the original maximum likelihood and new restricted maximum likelihood estimators. The phylogenetic mixed model is particularly rich in terms of the evolutionary insight that might be drawn from model parameters, so we also illustrate and discuss the interpretation of the model parameters in a specific comparative analysis.