title: A likelihood-based method for testing for nonstochastic variation of diversification rates in phylogenies.
abstract: Observed variations in rates of taxonomic diversification have been attributed to a range of factors including biological innovations, ecosystem restructuring, and environmental changes. Before inferring causality of any particular factor, however, it is critical to demonstrate that the observed variation in diversity is significantly greater than that expected from natural stochastic processes. Relative tests that assess whether observed asymmetry in species richness between sister taxa in monophyletic pairs is greater than would be expected under a symmetric model have been used widely in studies of rate heterogeneity and are particularly useful for groups in which paleontological data are problematic. Although one such test introduced by Slowinski and Guyer a decade ago has been applied to a wide range of clades and evolutionary questions, the statistical behavior of the test has not been examined extensively, particularly when used with Fisher's procedure for combining probabilities to analyze data from multiple independent taxon pairs. Here, certain pragmatic difficulties with the Slowinski-Guyer test are described, further details of the development of a recently introduced likelihood-based relative rates test are presented, and standard simulation procedures are used to assess the behavior of the two tests in a range of situations to determine: (1) the accuracy of the tests' nominal Type I error rate; (2) the statistical power of the tests; (3) the sensitivity of the tests to inclusion of taxon pairs with few species; (4) the behavior of the tests with datasets comprised of few taxon pairs; and (5) the sensitivity of the tests to certain violations of the null model assumptions. Our results indicate that in most biologically plausible scenarios, the likelihood-based test has superior statistical properties in terms of both Type I error rate and power, and we found no scenario in which the Slowinski-Guyer test was distinctly superior, although the degree of the discrepancy varies among the different scenarios. The Slowinski-Guyer test tends to be much more conservative (i.e., very disinclined to reject the null hypothesis) in datasets with many small pairs. In most situations, the performance of both the likelihood-based test and particularly the Slowinski-Guyer test improve when pairs with few species are excluded from the computation, although this is balanced against a decline in the tests' power and accuracy as fewer pairs are included in the dataset. The performance of both tests is quite poor when they are applied to datasets in which the taxon sizes do not conform to the distribution implied by the usual null model. Thus, results of analyses of taxonomic rate heterogeneity using the Slowinski-Guyer test can be misleading because the test's ability to reject the null hypothesis (equal rates) when true is often inaccurate and its ability to reject the null hypothesis when the alternative (unequal rates) is true is poor, particularly when small taxon pairs are included. Although not always perfect, the likelihood-based test provides a more accurate and powerful alternative as a relative rates test.
authors.affiliation: Department of Statistics, The Open University, Milton Keynes MK7 6AA, United Kingdom. k.j.mcconway@open.ac.uk
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: McConway
authors.forename: Hallie J
authors.initials: HJ
authors.lastname: Sims
mesh_terms: D044822:Biodiversity; D003627:Data Interpretation, Statistical; D016013:Likelihood Functions; D008954:Models, Biological; D010802:Phylogeny; D012107:Research Design; D018401:Sample Size