Lake's evolutionary parsimony (EP) method of constructing a phylogenetic tree is primarily applied to four DNA sequences. In this method, three quantities--X, Y, and Z--that correspond to three possible unrooted trees are computed, and an invariance property of these quantities is used for choosing the best tree. However, Lake's method depends on a number of unrealistic assumptions. We therefore examined the theoretical basis of his method and reached the following conclusions: (1) When the rates of two transversional changes from a nucleotide are unequal, his invariance property breaks down. (2) Even if the rates of two transversional changes are equal, the invariance property requires some additional conditions. (3) When Kimura's two-parameter model of nucleotide substitution applies and the rate of nucleotide substitution varies greatly with branch, the EP method is generally better than the standard maximum-parsimony (MP) method in recovering the correct tree but is inferior to the neighbor-joining (NJ) and a few other distance matrix methods. (4) When the rate of nucleotide substitution is the same or nearly the same for all branches, the EP method is inferior to the MP method even if the proportion of transitional changes is high. (5) When Lake's assumptions fail, his chi2 test may identify an erroneous tree as the correct tree. This happens because the test is not for comparing different trees. (6) As long as a proper distance measure is used, the NJ method is better than the EP and MP methods whether there is a transition/transversion bias or whether there is variation in substitution rate among different nucleotide sites.