Abstract
While Bayesian methods have become very popular in phylogenetic systematics, the foundations of this approach remain controversial. The star-tree paradox in Bayesian phylogenetics refers to the phenomenon that a particular binary phylogenetic tree sometimes has a very high posterior probability even though a star tree generates the data. I argue that this phenomenon reveals an unattractive feature of the Bayesian approach to scientific inference and discuss two proposals for how to address the star-tree paradox. In particular, I defend the polytomy prior as a solution (or rather dissolution) of the paradox and argue that it is preferable to a data-size dependent branch lengths prior from a methodological perspective. However, while this reply dissolves the star-tree paradox, the general challenge to Bayesian confirmation theory remains unmet.
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Notes
The external nodes of the tree represent present-day species (e.g., human, chimpanzee and gorilla), whereas internal nodes represent extinct ancestors (i.e., ancestors for which no sequence data are available). The degree of a node is the number of branches connected to the node. The root of tree T 1 has degree 2; the tree is therefore called binary. If the root of a tree has a degree larger than 2 or a non-root node has a degree larger than 3, the node represents a polytomy. Also note that the terms ‘tree’ and ‘tree topology’ will be used interchangeably.
While here ‘branch length’ is understood as measuring physical time, this term also has a different meaning in the biological literature. In graphical representations of a phylogenetic tree the length of a branch is seen as a measure of the amount of evolutionary change occurring along the branch. In that case ‘branch length’ means the expected number of substitutions, which is a function of time and the rate of substitutions.
A resolved tree does not contain any multifurcations (or, to use a different term for the same phenomenon, polytomies).
Yang also points out that the polytomy prior is difficult to code in current computer algorithms for Bayesian phylogenetic inference, such as ‘MrBayes’ (Huelsenbeck and Ronquist 2001; Ronquist and Huelsenbeck 2003). The focus of this paper, however, is on conceptual issues in Bayesian methodology rather than on practical issues associated with the coding of Bayesian phylogenetic methods. So, when assessing proposals of how to assign prior probabilities in Bayesian phylogenetics, only conceptual aspects will be taken into account and questions of how to practically implement these priors in current computer software are set aside.
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Acknowledgments
I would like to thank Samir Okasha and two anonymous reviewers for their helpful comments on earlier versions of the article. Financial support from the British Academy Postdoctoral Fellowship scheme is gratefully acknowledged.
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Autzen, B. Dissolving the star-tree paradox. Biol Philos 31, 409–419 (2016). https://doi.org/10.1007/s10539-015-9502-2
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DOI: https://doi.org/10.1007/s10539-015-9502-2