Letter to the Editor Nonparametric Phylogenetic Inference from Restriction Cleavage Sites

Nei and Tajima (1985) recently have criticized my algorithms (Templeton 1983a, 19833) that make phylogenetic inference from restriction-site maps. The purpose of this letter is to address their criticisms and to examine the reasons for our difference of opinion concerning the range of validity of my algorithms. These points will also be illustrated by a worked example using Hawaiian Drosophila. Nei and Tajima ( 1985) have suggested that my discrimination between two primate phylogenies (Templeton 19833) might be statistically flawed if the data included a double counting of some restriction sites. Overlap could arise owing to enzymes with multiple recognition sequences that include the recognition sequences of single cutters. However, in generating the scores used to test these hypotheses (table 2 of Templeton 19833), I used only the novel informative patterns revealed by the mutiple cutters. No site was counted twice. Hence, the concern raised by Nei and Tajima does not apply. The primary criticism of Nei and Tajima concerns the range of validity of the algorithms. I have concluded (Templeton 19838) that the algorithms are valid if the average substitution rate (1) times the time of divergence (t) is ~0.05. Nei and Tajima (1985) argue that the much smaller value of 0.01 is necessary. They justify this smaller ht value on the basis of two theoretical arguments. The first concerns the difficulty, in the absence of outgroup data, of distinguishing a single convergent gain of restriction sites from a double loss. (fig. 3 of Nei and Tajima [ 19851 and associated text). However, the criticized algorithms were explicitly limited to data with an outgroup (Templeton 1983b). Hence, this theoretical objection lies outside the inference domain delimited by me (Templeton 1983b) and is therefore completely irrelevant to the validity of the 0.05ht criterion. The second theoretical objection raised by Nei and Tajima is that the probability of three parallel losses of a restriction site (or of one gain followed by two losses) is not necessarily smaller and can be greater than the probability of two parallel gains (or of one loss followed by a gain). These conclusions are sound. However, Nei and Tajima state: “Templeton (1983a) recognized this problem but concluded that if ht < 0.05, the error introduced in a parsimony [emphasis mine] tree is small. . . . [A] lower criterion (ht < 0.01) is necessary.” However, the 0.05 criterion was specifically recommended for the algorithms of Templeton (19833), which are not the same as the parsimony criterion used by Nei and Tajima in arriving at their conclusion (see, in particular, the discussion on pp. 227-229 and 239-240 of my article [Templeton 1983b]). Although I used parsimony (Templeton 1983b), my use of it differed from Nei and Tajima’s use of it in the following two fundamental ways: ( 1) it used compatibility to restrict the application of parsimony to only a subset of the data, and (2) it used a weighting scheme that can assign different weights to patterns that involve the same number of events and the same weight to patterns that involve different numbers of