Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters

Blomberg, Simon P.; Rathnayake, Suren I.; Moreau, Cheyenne M

doi:10.1086/706339

Cited by 57 publications

(56 citation statements)

References 146 publications

(153 reference statements)

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“…To explore these patterns, we pruned simulated datasets to yield ultrametric trees comprising only ex-tant taxa (i.e., lineages in existence at the end of the simulation). We applied commonly used likelihood phylogenetic comparative models of trait evolution to these pruned data: Brownian motion (Felsenstein 1973(Felsenstein , 1985 to represent the null model; evolution under a constraint using an Ornstein-Uhlenbeck (OU) model (Hansen 1997;Butler and King 2004;Blomberg et al 2020) in which variance was constrained to the ancestral value according to the strength of α; and the Early Burst model, in which the rate variance exponentially decreased through time (Blomberg et al 2003;Harmon et al 2010).…”

Section: Phylogenetic Comparative Models Of Trait Distributions That mentioning

confidence: 99%

The complex effects of mass extinctions on morphological disparity

2020

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Studies of biodiversity through deep time have been a staple for biologists and paleontologists for over 60 years. Investigations of species richness (diversity) revealed that at least five mass extinctions punctuated the last half billion years, each seeing the rapid demise of a large proportion of contemporary taxa. In contrast to diversity, the response of morphological diversity (disparity) to mass extinctions is unclear. Generally, diversity and disparity are decoupled, such that diversity may decline as morphological disparity increases, and vice versa. Here, we develop simulations to model disparity changes across mass extinctions using continuous traits and birth-death trees. We find no simple null for disparity change following a mass extinction but do observe general patterns. The range of trait values decreases following either random or trait-selective mass extinctions, whereas variance and the density of morphospace occupation only decline following trait-selective events. General trends may differentiate random and trait-selective mass extinctions, but methods struggle to identify trait selectivity. Long-term effects of mass extinction trait selectivity change support for phylogenetic comparative methods away from the simulated Brownian motion toward Ornstein-Uhlenbeck and Early Burst models. We find that morphological change over mass extinction is best studied by quantifying multiple aspects of morphospace occupation.

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Section: Phylogenetic Comparative Models Of Trait Distributions That mentioning

confidence: 99%

The complex effects of mass extinctions on morphological disparity

2020

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“…If all, or very many, of the haplotypes have the same effect, the distribution may be quite different from Gaussian, which breaks the model assumptions and perhaps other models should be proposed. Blomberg et al (2019) describe the underlying theory behind the common Gaussian processes, such as Brownian motion and Ornstein-Uhlenbeck process, and present general methods for deriving new stochastic models, including non-Gaussian models of quantitative trait macroevolution. See also (Landis et al, 2012;Schraiber and Landis, 2015;Duchen et al, 2017;Bastide et al, 2020).…”

Section: Limitationsmentioning

confidence: 99%

“…A potentially important modelling aspect with respect to across and within species modelling is that the phylogenetic mixed model assumes Brownian motion for evolution of phenotypes along a phylogeny (Felsenstein, 1988;Huey et al, 2019). Brownian motion is a continuous random-walk process with variance that grows over time (is non-stationary) (Gardiner, 2009;Blomberg et al, 2019), which makes it a plausible model of evolution due to mutation and drift. There are alternatives to Brownian motion, in particular the Ornstein-Uhlenbeck process that can accommodate various forms of selection (Lande, 1976;Hansen and Martins, 1996;Martins and Hansen, 1997;Paradis, 2014).…”

Section: Introductionmentioning

confidence: 99%

“…There are alternatives to Brownian motion, in particular the Ornstein-Uhlenbeck process that can accommodate various forms of selection (Lande, 1976;Hansen and Martins, 1996;Martins and Hansen, 1997;Paradis, 2014). The Ornstein-Uhlenbeck process is also a continuous random-walk, but with an additional parameter that reverts the process to the mean (is a stationary process; e.g., Gardiner, 2009;Blomberg et al, 2019). Both of these models imply Gaussian distributions for the initial state and increments.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Modelling of Haplotype Effects on a Phylogeny

et al. 2021

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We introduce a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations, and leveraging similarities can improve the estimation of effects. We build on extensive literature and develop an autoregressive model of order one that models haplotype effects by leveraging phylogenetic relationships described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network, and we refer to the model as the haplotype network model. The model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. Our key contribution is that we obtain a sparse model, and by using hierarchical autoregression, the flow of information between similar haplotypes is estimated from the data. A simulation study shows that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially with few observations for a specific haplotype. We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a study of mitochondrial haplotype effects on milk yield in cattle. We provide R code to fit the model with the INLA package.

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“…a) The Fokker-Plank-Kolmogorov (FPK) model (Boucher et al 2018;Blomberg et al 2020) is a flexible modelling framework that can be used to estimate the shape of a macroevolutionary landscape that has one or more optima, using a parameter called the 'evolutionary potential'. This framework is distinct from the multi-peak OU models above where switches between macroevolutionary regimes are modelled; instead it fits a model of trait change in a single macroevolutionary regime, but that regime can have multiple optima, and be bounded or unbounded.…”

Section: Other New Approachesmentioning

confidence: 99%

Phylogenetic Comparative Methods: A User’s Guide for Paleontologists

Soul¹,

Wright²

2020

Preprint

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Recent advances in statistical approaches called Phylogenetic Comparative Methods (PCMs) have provided paleontologists with a powerful set of analytical tools for investigating evolutionary tempo and mode in fossil lineages. However, attempts to integrate PCMs with fossil data often present workers with practical challenges or unfamiliar literature. In this paper, we present guides to the theory behind, and application of, PCMs with fossil taxa. Based on an empirical dataset of Paleozoic crinoids, we present example analyses to illustrate common applications of PCMs to fossil data, including investigating patterns of correlated trait evolution, and macroevolutionary models of morphological change. We emphasize the importance of accounting for sources of uncertainty, and discuss how to evaluate model fit and adequacy. Finally, we discuss several promising methods for modelling heterogenous evolutionary dynamics with fossil phylogenies. Integrating phylogeny-based approaches with the fossil record provides a rigorous, quantitative perspective to understanding key patterns in the history of life.

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Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters

Cited by 57 publications

References 146 publications

The complex effects of mass extinctions on morphological disparity

The complex effects of mass extinctions on morphological disparity

Hierarchical Modelling of Haplotype Effects on a Phylogeny

Phylogenetic Comparative Methods: A User’s Guide for Paleontologists

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