Six different methods of cladogram construction were applied to a data set embracing 34 species and subspecies of Pontederiaceae. Nineteen Wagner trees were constructed using dif- ferent combinations of character subsets and outgroups. Although 12 trees were constructed using the largest character cliques uncovered by character compatibility analysis, these were highly un- resolved. Four additional trees were constructed using phenetic methods. Trees resulting from the various procedures were compared using several optimality criteria. Wagner trees based on all 42 characters or on the subset of 27 reproductive characters were most successful according to these criteria. Branch-swapping trials, based upon common features found in the Wagner and other trees produced another 10 trees that were as successful as the Wagner trees. The number of about equally successful trees is partly a function of homoplasy. Two-thirds of the character state changes on the trees are homoplasious. The primitive breeding system of the Pontederiaceae is not clearly resolved, but heterostyly is probably a synapomorphy of only one lineage of the family. A vicariance expla- nation of the biogeography of the family, based on a Gondwanan distribution, seems less parsi- monious than an origin in South America, followed by several eastward dispersals. While Mono- choria and Pontederia are apparently monophyletic under different analyses, Eichhornia and Heteranthera, as presently circumscribed, are probably paraphyletic. We had two main goals in undertaking this study. The first was to examine the evolution- ary history of tristyly and several other system- atic features in the small, aquatic, monocoty- ledonous family Pontederiaceae. The other was to assess the performance of several different numerical cladistic procedures using character distributions in this family as test data. Grow- ing discussion of the theoretical bases of biological classification has spawned a bewil- dering array of individual methods. No com- parative studies have evaluated all proposed methods, but several of the most popular, in- cluding single linkage clustering, UPGMA (av- erage linkage) clustering, character compatibil- ity analysis, and Wagner tree construction
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Eckenwalder et al. (1986) studied this question.