The Neognathostomata (comprising the orders Clypeasteroida, Oligopygoida, Neolampadoida, and the paraphyletic Cassiduloida) form one of the three major clades of irregular echinoids. Despite the group's apparent success since the Jurassic and impressive peak diversity in the mid-Cretaceous, most included clades are now severely reduced. A phylogeny is essential for reconstructing the taxonomic, environmental and biogeographic patterns of this decline, and understanding the causal processes responsible for them. I examined the distribution of qualitative morphological characters (including those defining genera) for 97 species from 77 non-clypeasteroid genera and the three clypeasteroid suborders. Following preliminary analyses, I reduced the data to 40 characters (having 60 apomorphic states) and 71 representative genera. Goloboff's data decisiveness, the skewness of tree length distributions, and permutation tests all reveal significant phylogenetic structure in the data. Heuristic searches conducted with PAUP found more than 72 500 trees of 217 steps (CI = 0.276), but only the first 30 000 were evaluated. These exhibit considerable instability in the relationships among taxa. Successive approximations weightings did not reduce the numbers of favoured trees. Analyses using only less homoplasious characters failed to improve the resolution. Fisher's stratigraphic debt provides an objective means of selecting a very few of the morphologically most-parsimonious trees. Most nodes are supported by only one to three character changes, and these are generally reversed or paralleled elsewhere. The results suggest some cassiduloid families can not be separated, and support the reassignment of several genera. Despite the high levels of homoplasy, the most-parsimonious trees require fewer changes than had been previously suggested for evolutionary trends in several characters. Whether the rampant homoplasy present in the data reflects incorrect character analysis, limited structural or developmental options, or the effects of parallel selection, its presence raises severe obstacles to phylogenetic analyses.
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