Jensen, R. J.,' and C. D. Barbour. (Department of Biological Sciences, Wright State University, Dayton, Ohio 45435) 1981. A phylogenetic reconstruction of the Mexican cyprinid fish genus Algansea, Syst. Zool., 30:41-57.-Phenetic and cladistic methods have been employed to estimate evolutionary relationships in Algansea, a small genus of Mexican cyprinid fishes. Cluster analyses and ordinations were prepared from various association, correlation, and distance matrices. Cladistic analyses were prepared in the form of a Wagner analysis (after Farris), compatibility analysis (after Estabrook), and a non-numerical phylogeny (after Hennig). All analyses utilized the same set of morphological and ecological characters to allow direct comparisons of estimates of relationships. Cluster analyses produced different views of the relationships between taxa. Ordinations produced generally similar arrays of OTU's in total character space which, of the phenetic methods, were closest to the identical solutions given by Wagner and compatibility analyses. A minimum spanning tree derived from taxonomic distances resulted in a network that also reflected the same relationships indicated by the cladistic methods. A reinvestigation of the relationships among the barbelled species of Algansea based in part on the distribution of shared apomorphies not included in the larger analysis confirmed the existence of a polyphyletic species. Possible solutions to this problem are discussed. [Algansea; Mexico; cladistics; ordination; cluster analysis; polyphyly.] The advent and rapid spread of numerical taxonomy has resulted in a reassessment of taxonomic methodology and philosophy. In an effort to turn the largely intuitive classical systematics into a method of analysis characterized by objectivity and repeatability, pioneering numerical taxonomists separated evolutionary speculation from taxonomic procedure. Their approach was intended to be a strictly phenetic operation utilizing a large number of unweighted characters, and serving as an efficient means of recognition, identification and classification of taxa. The results, which may be expressed as phenograms, were not meant specifically to reflect historical relationships (Sneath and Sokal, 1973). The reluctance of taxonomists to dismiss phylogenetic thinking has been well documented in the pages of this and other journals. Some authors have concluded that the phenetic approach can