Intrinsic inference difficulties for trait evolution with Ornstein‐Uhlenbeck models

Abstract

Summary1. For the study of macroevolution, phenotypic data are analysed across species on a dated phylogeny using phylogenetic comparative methods. In this context, the Ornstein-Uhlenbeck (OU) process is now being used extensively to model selectively driven trait evolution, whereby a trait is attracted to a selection optimum l. 2. We report here theoretical properties of the maximum-likelihood (ML) estimators for these parameters, including their non-uniqueness and inaccuracy, and show that theoretical expectations indeed apply to real trees. We provide necessary conditions for ML estimators to be well defined and practical implications for model parametrization. 3. We then show how these limitations carry over to difficulties in detecting shifts in selection regimes along a phylogeny. When the phylogenetic placement of these shifts is unknown, we identify a 'large p -small n' problem where traditional model selection criteria fail and favour overly complex scenarios. Instead, we propose a modified criterion that is better adapted to change-point models. 4. The challenges we identify here are inherent to trait evolution models on phylogenetic trees when observations are limited to present-day taxa, and require the addition of fossil taxa to be alleviated. We conclude with recommendations for empiricists.

Post-molecular systematics and the future of phylogenetics

“…Then, comparative methods are applied to the dated tree, for aims such as estimating diversification rates, ancestral areas, community assembly processes, ancestral character states, and models of character evolution or some interaction between these, such as the effect of a trait on diversification. However, recent results suggest that many of these methods are underpowered, biased, and suffer from nonindependence in ways not easily fixable, which may affect significant proportions of studies using them [9][10][11][12].In general, as more groups approach phylogenetic completeness and stability, and comparative methods grow more complex, the era of molecular systematics as an end unto itself is ending. Now, I suggest we are entering an age of post-molecular systematics that will: (i) critically examine the utility and dimensionality of genomic data above and below the species level; (ii) reexamine the use of phylogenetic comparative methods in terms of scale and power; and (iii) place a renewed emphasis on total-evidence phylogenetics, including fossil species based on morphological data.…”

“…Then, comparative methods are applied to the dated tree, for aims such as estimating diversification rates, ancestral areas, community assembly processes, ancestral character states, and models of character evolution or some interaction between these, such as the effect of a trait on diversification. However, recent results suggest that many of these methods are underpowered, biased, and suffer from nonindependence in ways not easily fixable, which may affect significant proportions of studies using them [9][10][11][12].…”

“…Even a simple bivariate correlation needs a phylogenetic term when it involves multiple species [52]. Such methods have become increasingly complex, including models of trait evolution [9], character correlation [53], estimation of speciation and extinction rates [54], and the association of traits and diversification rates [54]. These models permit sophisticated statistical analyses based on traditional modelfitting techniques such as analysis of variance (ANOVA) as well as situations (such as diversification rate estimation) specific to a phylogenetic context [55].…”

“…For instance, the power to reconstruct a character at the root of placental mammals using a tree of 4507 species modeled using Brownian motion (BM) is equivalent to a measurement from five data points [9]. For more complex models such as Ornstein-Uhlenbeck (OU), current approaches are non-unique or unidentifiable, often inaccurate, and pathologically biased toward excessively complex scenarios [9]. In general, available models such as BM and OU appear to be relatively inadequate and poor absolute fits to real clades when examined from an empirical perspective [10,63].…”

“…While tedious, it seems absolutely necessary for future investigations of complex evolutionary dynamics, given the frequent and substantial failings that many commonly used comparative methods exhibit. Furthermore, the potential for exhausting the available degrees of freedom in a phylogeny through numerous tests of different rates, characters, and scenarios should not be overlooked [9,12] and, if possible, should be simulated and assessed jointly. Clearly [11], it is often possible to retrieve strong significance from comparative analysis of large-scale phylogenies.…”