DOI: 10.5061/dryad.jwstqjqc1
title: A cautionary note on: A cautionary note on the use of Ornstein-Uhlenbeck models in macroevolutionary studies

description: 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.
description: Data was simulated in R with known parameter values and analyzed
 using the R packages motmot, Slouch, and phylolm.
description: Microsoft Word and Microsoft Excel but Google Docs and Google
 Sheets can be used.
description: # 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-likelihood of the BM model (logL OU - logL BM), and if that difference
 exceeds the likelihood ratio as in Cooper et al. (2016). Individual runs
 that were rejected were inspected using the Replicate Index column. All
 runs were also inspected using SLOUCH and here we show the phylogenetic
 half-life (t1/2) in units of tree height (=1 here) with 2-unit support
 interval shown in brackets. Also shown in the "Uncertain Inference
 Test" column - whether the half-life &gt; 1 (BM), if the half-life
 &lt; 1 and the upper limit of the 2-unit support surface is &lt;1 (OU), if
 the best estimate of the half-life &lt;1 but the  2-unit support surface
 from SLOUCH includes infinity (Includes BM), or if the best estimate of
 the half-life is &lt;1 and the upper limit of the 2-unit support surface
 falls between 1 and 3 (Uncertain). ## Uploaded to Zenodo 1. Grabowski et
 al Supp Text S1.docx - Supplementary Text S1 referred to in the article -
 Simulation of dataset including measurement error and results of
 correcting for this error for various tree sizes. **Dataset citation**:
 Mark Grabowski and others, A Cautionary Note on “A Cautionary Note on the
 Use of Ornstein Uhlenbeck Models in Macroevolutionary Studies”, Systematic
 Biology, 2023;, syad012,
 [https://doi.org/10.1093/sysbio/syad012](https://doi.org/10.1093/sysbio/syad012)