Recent mathematical approaches to reconstruct phylogenies: A chemosystematist's and botanist's view

Abstract

Some basic problems of mathematical phylogenetics are discussed. While algorithms regularly depend on the principle of parsimony, some features of phylogenesis interfere with that principle. Nonrandomness of the distribution of mutations as well as the inconstancy of the molecular clock in time and within a given sequence can bias the calculated relationships of closely related taxa. True comparability of sequences is difficult to establish, since this requires defining of homology of positions and of functions of amino acids as well. Parallelism and convergence can give rise to errors in establishing homology. Furthermore, they are difficult to be integrated into a consistent mathematical approach. The asymmetry of identity versus difference matrices is discussed. Common mathematical procedures implicate the monophyletic hypothesis as well as strict dichotomy of the final tree. Real phylogeny demands to introduce more flexible approaches with respect to monophyly and dichotomy. Graph theory offers the possibility to prove the minimality of a given tree and to develop more flexible approaches. The consequences of altering the procedures to compare sequences can be tested. This is demonstrated by calculations with a set of 15 cytochromes from various taxa. To interpret a calculated tree requires a sharp distinction between taxonomy and phyletics. This is exemplified for the case of directly linked taxa. The limits of resolving uncertain relationships by accumulating more data are mentioned.