Failed refutations: further comments on parsimony and likelihood methods and their relationship to Popper's degree of corroboration.
Kluge's (2001, Syst. Biol. 50:322-330) continued arguments that phylogenetic methods based on the statistical principle of likelihood are incompatible with the philosophy of science described by Karl Popper are based on false premises related to Kluge's misrepresentations of Popper's philosophy. Contrary to Kluge's conjectures, likelihood methods are not inherently verificationist; they do not treat every instance of a hypothesis as confirmation of that hypothesis. The historical nature of phylogeny does not preclude phylogenetic hypotheses from being evaluated using the probability of evidence. The low absolute probabilities of hypotheses are irrelevant to the correct interpretation of Popper's concept termed degree of corroboration, which is defined entirely in terms of relative probabilities. Popper did not advocate minimizing background knowledge; in any case, the background knowledge of both parsimony and likelihood methods consists of the general assumption of descent with modification and additional assumptions that are deterministic, concerning which tree is considered most highly corroborated. Although parsimony methods do not assume (in the sense of entailing) that homoplasy is rare, they do assume (in the sense of requiring to obtain a correct phylogenetic inference) certain things about patterns of homoplasy. Both parsimony and likelihood methods assume (in the sense of implying by the manner in which they operate) various things about evolutionary processes, although violation of those assumptions does not always cause the methods to yield incorrect phylogenetic inferences. Test severity is increased by sampling additional relevant characters rather than by character reanalysis, although either interpretation is compatible with the use of phylogenetic likelihood methods. Neither parsimony nor likelihood methods assess test severity (critical evidence) when used to identify a most highly corroborated tree(s) based on a single method or model and a single body of data; however, both classes of methods can be used to perform severe tests. The assumption of descent with modification is insufficient background knowledge to justify cladistic parsimony as a method for assessing degree of corroboration. Invoking equivalency between parsimony methods and likelihood models that assume no common mechanism emphasizes the necessity of additional assumptions, at least some of which are probabilistic in nature. Incongruent characters do not qualify as falsifiers of phylogenetic hypotheses except under extremely unrealistic evolutionary models; therefore, justifications of parsimony methods as falsificationist based on the idea that they minimize the ad hoc dismissal of falsifiers are questionable. Probabilistic concepts such as degree of corroboration and likelihood provide a more appropriate framework for understanding how phylogenetics conforms with Popper's philosophy of science. Likelihood ratio tests do not assume what is at issue but instead are methods for testing hypotheses according to an accepted standard of statistical significance and for incorporating considerations about test severity. These tests are fundamentally similar to Popper's degree of corroboration in being based on the relationship between the probability of the evidence e in the presence versus absence of the hypothesis h, i.e., between p(e|hb) and p(e|b), where b is the background knowledge. Both parsimony and likelihood methods are inductive in that their inferences (particular trees) contain more information than (and therefore do not follow necessarily from) the observations upon which they are based; however, both are deductive in that their conclusions (tree lengths and likelihoods) follow necessarily from their premises (particular trees, observed character state distributions, and evolutionary models). For these and other reasons, phylogenetic likelihood methods are highly compatible with Karl Popper's philosophy of science and offer several advantages over parsimony methods in this context.