The measurement of test severity, significance tests for resolution, and a unified philosophy of phylogenetic inference

摘要

The philosopher Karl Popper described a concept termed degree of corroboration, C, for evaluating and comparing hypotheses according to the results of their tests. C is, fundamentally, a comparison of two likelihoods: p(ehb), the likelihood of the hypothesis (h) in conjunction with the background knowledge (b), and p(e), the likelihood of b alone. C is closely related to the likelihood ratio of nested hypotheses. When phylogenetic analysis is interpreted as an attempt to assess C for a phylogenetic tree (the hypothesis, h), several interpretations have been given for p(e). Here I describe a new interpretation that equates p(e) with the probability of the data in the absence of a hypothesis of phylogenetic resolution, that is with the likelihood of an unresolved or polytomous tree. Under this interpretation, C for a fully or partially resolved phylogenetic tree is the likelihood of that tree minus the likelihood of the corresponding unresolved tree. These same two likelihoods can be used in a likelihood ratio test (LRT) to assess the significance of the degree of corroboration of the hypothesis of phylogenetic resolution. This LRT for resolution is closely related to permutation tests for phylogenetic structure in the data, because data that evolved on a true polytomous tree are expected to be phylogenetically randomized. It therefore reconciles the interpretation of the evidence (e) as the distribution of character states among taxa (rather than the score of the optimal tree) with the interpretation of permutation tests as methods for assessing C. Likelihood methods are (contrary to the views of some commentators) central to understanding how Popper's C applies to phylogenetic hypotheses, and they form the foundation of a unified and inclusive philosophy of phylogenetic inference.