The Ornstein-Uhlenbeck model (OU model) is a commonly used model for studying trait evolution. It extends the Brownian motion model by adding a term for “pull” toward the optimum trait value. The OU model reasonably models the trait evolution under natural selection, which is often the main focus of evolutionary studies, and is widely used to test if selection acts on a studied trait. This paper reports that the inference with OU model has limitations which are often ignored.
Several limitations of the OU model are discussed. For example, the optimum trait values and its ancestral states can not be simultaneously estimated. You can not separately estimate the optimal trait value, μ and ancestral state, y0 because the likelihood surface forms a “ridge”. This unidentifiablity issue appears when the shift of selection optimum occurs once on a tree and the group under the same selection forms a connected subtree. (I don’t fully understand the maths behind the unidentifiability, but I can intuitively understand that the left tree is bad and the right is OK.)
Other points include: Model selection with AIC, often used to find shifts of selection regime, can be misleading because parameter-rich models are not correctly penalized. Also, the power of model selection is limited and adding more taxa do not readily improve the accuracy.
I was shocked when I first saw this paper. I have been playing with the OU model recently for my new project. If the OU model were useless, my ideas would be all ruined. Fortunately, it is not useless though it is limited. It is still possible to estimate useful parameters. For example, the optimum trait value can not be estimated, but the expected difference between 2 selection regimes can be.
Authors gave recommendations to handle the limitations of the OU, including adding fossil records and re-parameterization techniques. These are very useful guidelines to check the feasibility of the OU-based analysis, and we should carefully consider the conditions when the OU model is misleading before using it.