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A comparative method for both discrete and continuous characters using the threshold model.

Joseph Felsenstein1

  • 1Department of Genome Sciences, University of Washington, Seattle, Washington 98195, USA. joe@gs.washington.edu

The American Naturalist
|January 6, 2012
PubMed
Summary
This summary is machine-generated.

Sewall Wright's threshold model analyzes discrete character evolution using unobserved liability. This method, enhanced with Markov chain Monte Carlo, integrates discrete and continuous traits for comparative analyses.

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Area of Science:

  • Evolutionary biology
  • Quantitative genetics
  • Phylogenetics

Background:

  • The threshold model, developed by Sewall Wright in 1934, provides a framework for modeling the evolution of discrete characters.
  • This model posits an underlying, unobserved quantitative trait (liability) that determines the discrete state based on a threshold.
  • Extending this model allows for the integration of both discrete and continuous characters in evolutionary studies.

Purpose of the Study:

  • To adapt and apply Sewall Wright's threshold model for inferring evolutionary covariances of liabilities for discrete characters.
  • To develop a comparative-methods analysis framework that can simultaneously accommodate both discrete and continuous characters.
  • To evaluate the model's performance and limitations through simulations.

Main Methods:

  • Utilizing a Markov chain Monte Carlo (MCMC) algorithm to sample liability values consistent with phylogenetic data and observed discrete character states.
  • Applying the MCMC approach to continuous characters by treating observed tip species values as the liability values.
  • Conducting simulations to assess the accuracy and precision of estimated liability covariances.

Main Results:

  • The MCMC algorithm successfully estimates the evolutionary covariances of liabilities for discrete characters.
  • The approach allows for a unified comparative-methods analysis combining discrete and continuous traits.
  • Simulation results demonstrate successful estimation of covariances, with precision contingent on species number.

Conclusions:

  • Sewall Wright's threshold model, implemented with MCMC, is effective for inferring evolutionary covariances and integrating discrete and continuous character analyses.
  • The model's flexibility allows for extensions to incorporate within-species variation and quantitative genetics models.
  • While effective, accurate covariance estimation requires substantial species data, and model applicability across diverse groups warrants consideration.