Abstract
Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form.
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Notes
While the question of whether the MCMC analysis is sufficiently thorough is of high importance to practitioners, this issue is set aside in this more conceptually minded paper.
If not explicitly stated otherwise, I refer to a tree topology when using the term ‘tree’ or ‘phylogenetic tree’ in this paper.
Hence, the Yule process is also known as ‘pure birth process’ or just a ‘birth process’.
Pinelis refers to the uniform distribution on tree topologies as the ‘proportional-to-distinguishable-arrangements’ (PDA) model.
Since the set of states S is finite these two sums are finite.
For a very sceptical view on Eldredge and Gould’s idea of punctuated equilibrium, see Dennett (1995).
An alternative stochastic process inducing the uniform distribution on tree topologies is the ‘explosive radiation process’ suggested by Steel and McKenzie (2001). In the explosive radiation process ‘stabilization’ (rather than quasi-stabilization) is certain to occur for every species that reach a certain age. That is, in the explosive radiation process a species older than a certain age does not give birth to any new species nor does it change in any way.
Idealizations that involve deliberate distortions are sometimes referred to as ‘Galilean idealizations’ (McMullin 1985).
For more details on the hierarchical Bayesian approach in phylogenetics, see Yang (2006), p. 123.
In fact, applying the full Bayesian approach to some stochastic processes can be very restrictive. Take the Yule process as one, admittedly extreme, example. Applying the full Bayesian approach to this process yields the Yule distribution for any possible prior probability distribution of the model parameter since for any (constant) choice of this parameter the Yule process induces the Yule distribution.
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Acknowledgments
I would like to thank Jason Alexander, Roman Frigg and Elliott Sober as well as two anonymous reviewers for very helpful comments on earlier drafts of this paper.
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Autzen, B. Constraining prior probabilities of phylogenetic trees. Biol Philos 26, 567–581 (2011). https://doi.org/10.1007/s10539-011-9253-7
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DOI: https://doi.org/10.1007/s10539-011-9253-7