Thanks to the reduced cost of RNA-Sequencing and other advanced methods for quantifying expression levels, accurate and expansive comparative expression data sets including data from multiple individuals per species are emerging. Comparative genomics has been greatly facilitated by the availability of statistical methods considering both between and within species variation for testing hypotheses regarding the evolution of DNA sequences. Similar methods are now needed to fully leverage comparative expression data. In this paper, we describe the β model which parameterizes the ratio of population to evolutionary expression variance, facilitating a wide variety of analyses, including a test for expression divergence or diversity for a single gene or a class of genes. The β model can also be used to test for lineage-specific shifts in expression level, amongst other applications. We use simulations to explore the functionality of these tests under a variety of circumstances. We then apply them to a mammalian phylogeny of 15 species typed in liver tissue. We identify genes with high expression divergence between species as candidates for expression level adaptation, and genes with high expression diversity within species as candidates for expression level conservation and plasticity. Using the test for lineage-specific expression shifts, we identify several candidate genes for expression level adaptation on the catarrhine and human lineages, including genes possibly related to dietary changes in humans. We compare these results to those reported previously using the species mean model which ignores population expression variance, uncovering important differences in performance.