Transformation Series Analysis

Mickevich, M. F. (Department of Ichthyology, American Museum of Natural History, Central Park West at 79th St., New York 10024) 1982. Transformation series analysis. Syst. Zool., 31:461-478.-The interpretation of two state features on a cladogram presents no problem in that Farris optimization (Farris, 1970) produces the simplest (most parsimonious) explanation of a set of changes. The only methods which produce parsimonious explanations for multistate characters either require theories of character evolution or assume that any transformation between different states is always possible. A method-Transformation Series Analysis (TSA)for obtaining the cladogram which best explains all the data including multistate characters is developed. TSA derives parsimonious interpretations of character change (cladistic characters) from a cladogram, and the cladogram iteratively until a stable point is reached. It is demonstrated that the cladograms resulting from TSA do not depend on the initial classification. Further, the solution (stable) cladogram results in a set of characters of greater consistency that the original Wagner tree for the 20 multistate data sets examined. Sometimes this stable cladogram is the same as the original "best" (parsimonious) cladogram. When Transformation Series Analysis (TSA) gives results different from the original Wagner trees, the cladograms from the former show greater taxonomic congruence between data sets. Therefore, TSA is an improvement on existing phylogenetic methods. Because the cladistic characters are different from the original characters, "theories" for character evolution are not so well verified as has been presumed. Cladogram characters resulting from TSA are powerful systematic tools to be used in the study of character evolution. [Phylogenetic systematics; cladistics; classification; congruence; parsimony; character evolution; Wagner trees; transition series; character state trees; transformation series.] Thus the question of whether kinship relations based on a single character or a single presumed transformation series of characters correspond to the actual phylogenetic relationships of the species is tested by means of other series of characters by trying to bring the relationships indicated by the several series of characters into congruence. In the final analysis this is again the method of "checking, correcting and rechecking." (Hennig, 1966:112) A character phylogeny (Hennig, 1966), character state tree (Farris et al., 1970) or transformation series (Hennig, 1966) is a hypothesis that specifies which states of a character may evolve directly into which other states. All existing taxonomic methods make tacit use of such rules. For example, 0 -1 -2 specifies that the evolutionary sequence of state 0 to state 2 proceeds through state 1. Therefore, taxa with state 0 are considered to be more similar to taxa with state 1 than those taxa which have state 2. If the roles of states 1 and 2 were interchanged, the implied relationship of the taxa would be invert' Present address: 41 Admiral St., Port Jefferson Station, New York 11776. ed. If a character has only two conditions, there is only one possible transformation, but there are many possible transitions for characters with multiple conditions. Transformation series for multiple character states are usually (and optimistically) derived from more general theories of character transformation, or what were called in a more naive era, Rules of Evolution. Examples of such theories abound. Theories for transformation of morphological features include Haeckel's Law, Cope's Rule, Bergmann's Rule, Allometry, and Orthogenesis (see Rensch, 1961). Molecular features are also the subject of such theories. Some are: the theory of minimum allelic turnover for allozyme data (Mickevich and Mitter, 1982) and minimum codon mutation in protein sequences (Fitch, 1971). All of these are now, or have been in the past, targets for scepticism. To avoid the justified criticism of these theories, some systematists claim to eschew all transformational theories, either by dealing with so few taxa that the prob-