Modeling Gene Expression Evolution with an Extended Ornstein–Uhlenbeck Process Accounting for Within-Species Variation

Abstract

Much of the phenotypic variation observed between even closely related species may be driven by differences in gene expression levels. The current availability of reliable techniques like RNA-Seq, which can quantify expression levels across species, has enabled comparative studies. Ornstein-Uhlenbeck (OU) processes have been proposed to model gene expression evolution as they model both random drift and stabilizing selection and can be extended to model changes in selection regimes. The OU models provide a statistical framework that allows comparisons of specific hypotheses of selective regimes, including random drift, constrained drift, and expression level shifts. In this way, inferences may be made about the mode of selection acting on the expression level of a gene. We augment this model to include within-species expression variance, allowing for modeling of nonevolutionary expression variance that could be caused by individual genetic, environmental, or technical variation. Through simulations, we explore the reliability of parameter estimates and the extent to which different selective regimes can be distinguished using phylogenies of varying size using both the typical OU model and our extended model. We find that if individual variation is not accounted for, nonevolutionary expression variation is often mistaken for strong stabilizing selection. The methods presented in this article are increasingly relevant as comparative expression data becomes more available and researchers turn to expression as a primary evolving phenotype.

Resolving the backbone of the Brassicaceae phylogeny for investigating trait diversity

“…Employing Ornstein–Uhlenbeck process modeling (Rohlfs et al ., ) using our explicit phylogenetic framework, we identified 64 genes exhibiting significant directional change in expression from neutral expectations in the core Brassicaceae (the clade sister to Aethionema ), where diversity in leaf margin geometry is pronounced ( q ‐value < 0.05) (Dataset S3). These genes included the developmental regulators AUXIN RESPONSE TRANSCRIPTION FACTOR 3 / ETTIN ( AT2G33860 ), CYCLIN D6;1 ( AT4G03270 ), CHROMATIN REMODELING 9 / SWITCH 2 ( AT1G03750 ), Enhancer of polycomb‐like transcription factor ( AT4G32620 ) and the ethylene receptor ETHYLENE RESPONSIVE 2 ( AT3G23150 ) (Table S11).…”

A cautionary note on the use of Ornstein Uhlenbeck models in macroevolutionary studies

“…Several approaches for accounting for error have been proposed and warrant wider implementation for OU models and other models of trait evolution (e.g. Lynch, ; Martins & Hansen, ; Ives, Midford & Garland, ; Hansen & Bartoszek, ; Rohlfs, Harrigan & Nielsen, ), but it is outside our scope to explore these here.…”

Intrinsic inference difficulties for trait evolution with Ornstein‐Uhlenbeck models

“…For example, Brawand et al . () detected evolutionary shifts in gene expression in testes for a large number of mammalian genes, by comparing a single‐regime OU model to a two‐regime OU model in which the optimal gene expression level μ undergoes a shift on a specific lineage (see also Rohlfs, Harrigan & Nielsen ). In this section, we use simulations to study the power to detect such shifts.…”