A Cautionary Note on "A Cautionary Note on the Use of Ornstein Uhlenbeck Models in Macroevolutionary Studies"

Abstract

Models based on the Ornstein-Uhlenbeck process have become standard for the comparative study of adaptation. Cooper et al. (2016) have cast doubt on this practice by claiming statistical problems with fitting Ornstein-Uhlenbeck models to comparative data. Specifically, they claim that statistical tests of Brownian motion may have too high Type I error rates and that such error rates are exacerbated by measurement error. In this note, we argue that these results have little relevance to the estimation of adaptation with Ornstein-Uhlenbeck models for three reasons. First, we point out that Cooper et al. (2016) did not consider the detection of distinct optima (e.g. for different environments), and therefore did not evaluate the standard test for adaptation. Second, we show that consideration of parameter estimates, and not just statistical significance, will usually lead to correct inferences about evolutionary dynamics. Third, we show that bias due to measurement error can be corrected for by standard methods. We conclude that Cooper et al. (2016) have not identified any statistical problems specific to Ornstein-Uhlenbeck models, and that their cautions against their use in comparative analyses are unfounded and misleading. [adaptation, Ornstein-Uhlenbeck model, phylogenetic comparative method.].

Figure 1.

Support (log-likelihood) surfaces for phylogenetic half-lives (t_1/2 = ln(2)/α) and stationary variances ($v={\sigma }^2/2\alpha$) for four replicates. The trait data were simulated under a Brownian-motion model and fitted as an Ornstein–Uhlenbeck process on 25-tip trees simulated under a birth–death model (d/b ratio = 0.75). All trees were scaled to unit height. In each figure, the black dot is the maximum-likelihood estimate. The distance between the dot and the surrounding line, and the lines relative to each other, is 0.5 log-likelihood units. Run (a) depicts support for the Brownian-motion model. Runs (b)–(d) show increasing support for the Ornstein–Uhlenbeck model. A half-life above one indicates that the process is approaching Brownian motion and a half-life of three means that the model is dynamically similar to Brownian motion. The non-shaded parts of the figure correspond to estimates that were more than two support units worse than the best estimate. The cases a, b, c, and d correspond to simulation replicates 151, 164, 194, and 189, respectively, in Table S1.