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A Linear-Time Algorithm for Gaussian and Non-Gaussian Trait Evolution Models

We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylog... Full description

Journal Title: Systematic biology 2014, Vol.63 (3), p.397-408
Main Author: Ho, Lam si Tung
Other Authors: Ané, Cécile
Format: Electronic Article Electronic Article
Language: English
Subjects:
Quelle: Alma/SFX Local Collection
Publisher: England: Oxford University Press
ID: ISSN: 1063-5157
Link: https://www.ncbi.nlm.nih.gov/pubmed/24500037
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title: A Linear-Time Algorithm for Gaussian and Non-Gaussian Trait Evolution Models
format: Article
creator:
  • Ho, Lam si Tung
  • Ané, Cécile
subjects:
  • Algorithms
  • Biological Evolution
  • Classification - methods
  • Computer Simulation
  • Covariance
  • Covariance matrices
  • Evolution
  • Modeling
  • Models
  • Normal distribution
  • Parametric models
  • Phenotypic traits
  • Phylogenetics
  • Plant roots
  • Regression analysis
  • Software - standards
  • Systematic biology
  • Taxa
ispartof: Systematic biology, 2014, Vol.63 (3), p.397-408
description: We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.
language: eng
source: Alma/SFX Local Collection
identifier: ISSN: 1063-5157
fulltext: fulltext
issn:
  • 1063-5157
  • 1076-836X
url: Link


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descriptionWe developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.
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subjectAlgorithms ; Biological Evolution ; Classification - methods ; Computer Simulation ; Covariance ; Covariance matrices ; Evolution ; Modeling ; Models ; Normal distribution ; Parametric models ; Phenotypic traits ; Phylogenetics ; Plant roots ; Regression analysis ; Software - standards ; Systematic biology ; Taxa
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0Copyright © 2014 Society of Systematic Biologists
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abstractWe developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.
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