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A Practical Guide to Phylogenetics for Nonexperts
Published on: February 5, 2014
Fair-balance paradox, star-tree paradox, and Bayesian phylogenetics
1Department of Biology, Galton Laboratory, University College London, London, UK. z.yang@ucl.ac.uk
Molecular Biology and Evolution
|May 10, 2007
Summary
The star-tree paradox shows that Bayesian phylogenetic methods can yield misleadingly high probabilities for incorrect evolutionary trees. This study analyzes the paradox and proposes solutions by adjusting prior probabilities.
Area of Science:
- Phylogenetics and Evolutionary Biology
- Computational Biology
- Statistical Modeling
Background:
- The star-tree paradox describes the tendency of Bayesian phylogenetic inference to assign high posterior probabilities to incorrect evolutionary trees.
- This phenomenon is linked to the sensitivity of Bayesian model selection to prior probability distributions on model parameters.
- Previous analysis has been limited by the mathematical complexity of the integrals involved in posterior probability calculations.
Purpose of the Study:
- To analyze the star-tree paradox in phylogenetic reconstruction using binary characters and a molecular clock.
- To approximate posterior tree probabilities for large datasets and investigate the behavior of these probabilities.
- To explore and evaluate strategies for resolving the star-tree paradox in Bayesian phylogenetics.
Main Methods:
- Utilized Laplacian expansion to approximate posterior probabilities for rooted trees with three species.
- Employed theoretical analysis of analogous probability problems (fair-coin, fair-balance) and computer simulations.
- Investigated two strategies: assigning prior probability to the star tree and using informative priors on branch lengths.
Main Results:
- Confirmed the existence of the star-tree paradox, demonstrating that posterior probabilities do not converge to 1/3 for all trees.
- Showed that posterior tree probabilities vary according to a statistical distribution for large datasets.
- Found that both proposed strategies effectively resolve the paradox, with informative priors on branch lengths being simpler to implement.
Conclusions:
- The star-tree paradox is a real phenomenon in Bayesian phylogenetics, highlighting the impact of prior specifications.
- Posterior probabilities in phylogenetic reconstruction are highly sensitive to the choice of prior distributions.
- Adjusting prior probabilities offers viable solutions to mitigate the effects of the star-tree paradox.
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