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

Abstract

Phylogenetic comparative methods are increasingly used to give new insights into the dynamics of trait evolution in deep time. For continuous traits the core of these methods is a suite of models that attempt to capture evolutionary patterns by extending the Brownian constant variance model. However, the properties of these models are often poorly understood, which can lead to the misinterpretation of results. Here we focus on one of these models - the Ornstein Uhlenbeck (OU) model. We show that the OU model is frequently incorrectly favoured over simpler models when using Likelihood ratio tests, and that many studies fitting this model use datasets that are small and prone to this problem. We also show that very small amounts of error in datasets can have profound effects on the inferences derived from OU models. Our results suggest that simulating fitted models and comparing with empirical results is critical when fitting OU and other extensions of the Brownian model. We conclude by making recommendations for best practice in fitting OU models in phylogenetic comparative analyses, and for interpreting the parameters of the OU model.

Keywords: OU; comparative methods; macroevolutionary models; phylogeny; stabilizing selection.

Figure 1

The number of ecology, evolutionary biology and palaeontology papers published between 2005 and 2014 containing the phrase ‘Ornstein Uhlenbeck’, as a proportion of the total number of ecology, evolutionary biology or palaeontology papers published that year. See Supporting Information for details.

Figure 2

Examples of profile likelihoods for selected simulated datasets for tippy (A), rooty (B) and Yule (C) simulated trees of 50 taxa. Each solid black line represents one simulated dataset selected at random. Tippy trees are those with branching events distributed disproportionately late in the clade's history (i.e. nearer to the present). Rooty trees are those with branching events distributed disproportionately early in the clade's history (i.e. nearer to the root). In all cases the ‘true’ value of α is 0 (black dashed line). The red dashed line represents −1.92 log‐likelihood units from the maximum: using log‐Likelihood ratio tests, values of α yielding values higher than this would be considered statistically indistinguishable from the Maximum Likelihood value.

Figure 3

The number of taxa in phylogenies used to fit Ornstein Uhlenbeck models in ecology, evolutionary biology and palaeontology papers published between 2005 and 2014. Two studies with > 3000 taxa have been omitted for clarity. See Supporting Information for details.

Figure 4

Scaling of expected trait similarity with time since evolutionary divergence predicted by the Ornstein Uhlenbeck model. The covariance between species’ trait values is scaled by the intra‐specific trait variance (i.e. equal to correlation between species’ traits). This is plotted against the relative time of shared history (time at which species branched from each other, divided by the total tree height: t _ij/T). Different panels show different ranges of ?: (A) α = 0 to 0.5; (B) α = 1 to 5; and (C) α = 10‐50. In (A) trait evolution is essentially Brownian; in (C) it is independent of phylogeny.