Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts

Mitov, Venelin; Bartoszek, Krzysztof; Asimomitis, Georgios; Stadler, Tanja

doi:10.1016/j.tpb.2019.11.005

Cited by 42 publications

(69 citation statements)

References 47 publications

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“…Starting with Felsenstein’s 11 pruning algorithm, there are many extensions in many contexts. 12-19 These approaches have been implemented in several popular R packages such as , 14 , 19 , 20 , 21 , 22 , 23 and 24 where Felsenstein’s pruning algorithm is extended to support all other Gaussian models assuming independently evolving branches. Overall, using these kind of efficient pruning algorithms, the phylogenetic community indeed have come up with more robust and efficient solutions than the matrix inversion.…”

Section: Introductionmentioning

confidence: 99%

On the Matrix Condition of Phylogenetic Tree

Jhwueng

O’Meara

2020

Evol Bioinform Online

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Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element [Formula: see text] in C represents the affinity between extant species i and extant species j. This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if [Formula: see text], defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C, is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.

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Section: Introductionmentioning

confidence: 99%

On the Matrix Condition of Phylogenetic Tree

Jhwueng

O’Meara

2020

Evol Bioinform Online

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“…The likelihood calculation was implemented in the R-package PCMBase (https://github.com/venelin/PCMBase), using internal calls to its Rcpp companion PCMBaseCpp (https://github.com/venelin/PCMBaseCpp) (24) and the SPLITT C++ library (https://github.com/venelin/SPLITT) (37). The RCP algorithm was implemented in the R-package PCMFit (https://github.com/venelin/PCMFit) (38).…”

Section: Methodsmentioning

confidence: 99%

“…The scriptGitalicLInv family includes the multivariate BM and OU processes, as well as many of their variants widely used in phylogenetic comparative methods (24). In ref.…”

Section: Approachesmentioning

confidence: 99%

“…In ref. 24, we have proved that for any tree and any phylogenetic model satisfying the Definition , it is possible to calculate the likelihood of the model, given multitrait data for the tips with some tips possibly missing some trait values, through a pruning algorithm, based on analytical integration over the unobserved trait values at the internal nodes of the tree. Here, we have extended this algorithm to support mixed phylogenetic models over the scriptGitalicLInv family, meaning the type of model may change at intermodel shift points.…”

Section: Approachesmentioning

confidence: 99%

“…Our approach relies on a subfamily, hereby denoted scriptGitalicLInv, of the Gaussian phylogenetic models, with the transition density exhibiting the properties that the expectation depends linearly on the ancestral trait value and the variance is invariant with respect to the ancestral value. In a related work, we have shown that the likelihood of such models can be calculated in time proportional to the number of nodes in the tree (24). Here, we generalize this fast likelihood calculation algorithm to mixed phylogenetic models over the scriptGitalicLInv family, which we denote mixed Gaussian phylogenetic models (MGPMs).…”

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confidence: 99%

See 2 more Smart Citations

Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models

Mitov

Bartoszek

Stadler

2019

Proc. Natl. Acad. Sci. U.S.A.

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Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein–Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are “intramodel,” meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters “global” for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body- and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain–body-mass allometry over the past 160 million y.

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