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

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 f..., Data was simulated in R with known parameter values and analyzed using the R packages motmot, Slouch, and phylolm., Microsoft Word and Microsoft Excel but Google Docs and Google Sheets can be used., # Supplementary Material associated with Grabowski et al. (2023) - A Cautionary Note on “A Cautionary Note on the Use of Ornstein Uhlenbeck Models in Macroevolutionary Studies”

## Description of the data and file structure

1. **Table S1.xlsx** - Table S1: Results of individual simulation runs summarized in Table 1 given a phylogeny with 25 tips with a relative extinction rate (d/b) of 0.75. Runs in bold are those where the Ornstein-Uhlenbeck (OU) model is preferred over the Brownian-motion (BM) model. Iteration 1 shows result for run below rejection threshold and the likelihood surface is shown in Fig. 1a. For each iteration, results show the unscaled tree height (Original TH), the rate of adaptation (⍺) and ⍺ reparametrized as the phylogenetic half-life (t1/2) from the R Package motmot (Thomas and Freckleton, 2012) in units of tree height (=1 here), the components of the \"Rejection Rate\" of Cooper et al. (2016) including the difference in ​log-likelihood of the OU model and log-like...