Wagner Networks and Ancestors

Lundberg, J. G. (Dept. of Zoology, Duke University, Durham, North Carolina 27706) 1972. Wagner Networks and Ancestors. Syst. Zool. 21:398-413.-Differences between Wagner Networks and Wagner Trees, and, the general problems encountered in estimating ancestral character states are briefly reviewed. The relation between Wagner Network structure and probable ancestral state combinations is illustrated with a hypothetical case and a real case of seven species of bullhead catfishes (genus Ictalurus, subgenus Amiurus). The relation between Wagner Networks and paraphyletic classifications is also noted. A new concept in quantitative phyletic cluster analysis, the Wagner Network was recently introduced into the literature of systematic biology by Farris (1970). Although it appears that the method holds a promise of great utility in phyletic systematics, there has been just one published study which has employed the Wagner Network as a major analytical tool (Baird and Eckardt, 1972). In this paper I will illustrate, through hypothetical and re,al examples, the application of Wagner Networks to the problem of constructing evolutionary trees. Historically the Wagner Network (hereafter termed Network) is an extension of the Wagner Tree (hereafter termed Tree). The theoretical bases of Wagner methods in evolutionary systematics have been outlined in detail by Kluge and Farris (1969) and Farris, Kluge, and Eckardt (1970). Computational details and formalization of the methods are covered by Farris (1970). Briefly, a Network or Tree is a most parsimonious, or minimum total length set of connections among a series of OTUs (Operational Taxonomic Units) that is based on an OTU by OTU distance matrix. The measure of distance is a lattice metric, D(A, B) = X IX(A,i) -X(B,i)I where X(A, i) and X(B, i) are the states of character i in OTUs A and B respectively and D (A, B) is the distance between A and B (Kluge and Farris, 1969). Generally in both Networks and Trees real OTUs are connected through hypothetical intermediate ancestors (or Hypothetical Taxonomic Units, HTUs). HTUs are constructed one character at a time from the median character state values of any three OTUs (or other HTUs). They serve to eliminate the need for many homoplasious steps (parallelisms and reversals) and, therefore, reduce the total number of implied evolutionary steps. For example, consider a case of three OTUs which possess states for three characters: A(O, 0, 1), B(1, 2, 0) and C(2, 1, 0). The OTUs can be arranged in a simple Network in which they are connected through a single HTU. This HTU would be described by the states 1, 1, 0, i.e., the median states of each of the three characters over A, B and C. This construct involves no homoplasious steps whereas any other form of the Network (direct connections between real OTUs) or any other HTU would involve assumptions about parallel evolution. There is a single major difference between the Network and Tree. A Tree is an estimated evolutionary tree or phylogeny. It is a hypothesis on both the patristic and cladistic relationships among a set of OTUs. Patristic relationship is measured as the amount of evolutionary steps or degree of divergence between taxa. Taxa may be more or less patristically related depending on the number of evolutionary steps that have taken place between them since their separation. Cladistic relationship is relationship due to common ancestry and thus involves only the branching events in