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We describe techniques for assessing evolutionary trees constructed by the parsimony criteria, when sequences exhibit irregular base compositions. In particular, we extend a recently described frequencydependent significance test to handle any number of taxa and describe a modification of the KishinoHasegawa sites test. These modifications are useful for detecting historical signals beyond those patterns which arise purely from irregular base compositions between the compared sequences. We apply the test to extend our earlier studies on chloroplast origins using 168 rDNA sequences, where a failure to compensate for irregular base compositions between the compared sequences provides statistically significant support for unjustified phylogenetic inferences. We also describe how the techniques can be modified to determine how "tree-like" data are, given independent variation in the base frequencies. © 1995 Academic Press, Inc.One of the earliest, and still most widely used, methods for constructing phylogenetic trees is the maximum parsimony technique. Given a tree T, each of whose leaves correspond to an aligned sequence, and a collection C of aligned sequences, the length of T for C-denoted L(C, T)-is the least number of point mutations (substitutions) that needs to occur across the edges of T to account for the observed variation in the sequences.To make this notion more precise, it is useful to regard a collection C of k parsimony sites in n aligned sequences as k functions XI' . . . , Xk' where each Xj assigns sequence i (i = 1, ... , n) one of r possible states (r = 4 for DNA sequences; r = 2 for purine/ pyrimidine sequences; r = 20 for amino acid sequences). For any tree T whose leaves (degree one vertices) are numbered 1, ... , n, let L(Xj, T) be the minimal number of edges of T which must have different states assigned to their ends in order to extend the function Xj to all the vertices of T (an extension which realizes this minimization is said to be minimal).
We describe techniques for assessing evolutionary trees constructed by the parsimony criteria, when sequences exhibit irregular base compositions. In particular, we extend a recently described frequencydependent significance test to handle any number of taxa and describe a modification of the KishinoHasegawa sites test. These modifications are useful for detecting historical signals beyond those patterns which arise purely from irregular base compositions between the compared sequences. We apply the test to extend our earlier studies on chloroplast origins using 168 rDNA sequences, where a failure to compensate for irregular base compositions between the compared sequences provides statistically significant support for unjustified phylogenetic inferences. We also describe how the techniques can be modified to determine how "tree-like" data are, given independent variation in the base frequencies. © 1995 Academic Press, Inc.One of the earliest, and still most widely used, methods for constructing phylogenetic trees is the maximum parsimony technique. Given a tree T, each of whose leaves correspond to an aligned sequence, and a collection C of aligned sequences, the length of T for C-denoted L(C, T)-is the least number of point mutations (substitutions) that needs to occur across the edges of T to account for the observed variation in the sequences.To make this notion more precise, it is useful to regard a collection C of k parsimony sites in n aligned sequences as k functions XI' . . . , Xk' where each Xj assigns sequence i (i = 1, ... , n) one of r possible states (r = 4 for DNA sequences; r = 2 for purine/ pyrimidine sequences; r = 20 for amino acid sequences). For any tree T whose leaves (degree one vertices) are numbered 1, ... , n, let L(Xj, T) be the minimal number of edges of T which must have different states assigned to their ends in order to extend the function Xj to all the vertices of T (an extension which realizes this minimization is said to be minimal).
Sir Karl Popper is well known for explicating science in falsificationist terms, for which his degree of corroboration formalism, C(h,e,b), has become little more than a symbol. For example, de Queiroz and Poe in this issue argue that C(h,e,b) reduces to a single relative (conditional) probability, p(e,hb), the likelihood of evidence e, given both hypothesis h and background knowledge b, and in reaching that conclusion, without stating or expressing it, they render Popper a verificationist. The contradiction they impose is easily explained--de Queiroz and Poe fail to take account of the fact that Popper derived C(h,e,b) from absolute (logical) probability and severity of test, S(e,h,b), where critical evidence, p(e,b), is fundamental. Thus, de Queiroz and Poe's conjecture that p(e,hb) = C(h,e,b) is refuted. Falsificationism, not verificationism, remains a fair description of the parsimony method of inference used in phylogenetic systematics, not withstanding de Queiroz and Poe's mistaken understanding that "statistical" probability justifies that method. Although de Queiroz and Poe assert that maximum likelihood has the power "to explain data", they do not successfully demonstrate how causal explanation is achieved or what it is that is being explained. This is not surprising, bearing in mind that what is assumed about character evolution in the accompanying likelihood model M cannot then be explained by the results of a maximum likelihood analysis.
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