Chaucer, the Genom, and the Combinatorics of Finite Metric Spaces

Andreas Dress

CUNY and University of Bielefeld

November 18,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

Comparative phylogenetic analysis generally reveals a large array of similarities and dissimilarities between the various species under consideration. To derive phylogenetic branching patterns from that array (so that e.g. the kinship relation between horse, cow and whale could be elucidated), a rather "brutal", yet amazingly successful procedure has been to rally all the observed similarities and dissimilarities, for any two species, in just one number -- then called the (dis)similarity index of those two species. The resulting structure then -- in most cases -- is a finite metric space, and the associated task is to detect the branching pattern in question from analysing this space. While statistician have designed many useful procedures for analysing such spaces, most of these methods (like e.g. principal component analysis) perceive euclidean n-space as the "standard of truth" and are designed to construct "good", if not (somehow) optimal embeddings of the given space into euclidean space. Clearly, this is inadeqate if phylogenetic branching patterns (and migration or diffusion in some large (state)space accompanying these branching processes) are considered to be the cause for the observed dissimilarity patterns. In the lecture, it will be shown that tools for a completely unprejudiced abstract, "combinatorial" analysis of finite metric spaces provide amazingly usable means for phylogenetic reconstruction. The basic concepts and the resulting mathematical theory will be reviewed, and illustrative examples including a discussion of the still somehow mysterious evolution of mammals and of a recent application of the resulting computer program regarding "The Phylogeny of The Canterbury Tales" -- NATURE, August 27, 1998 will be presented.


Speaker's Contact Info: dress(at-sign)chs1ce.engr.ccny.cuny.edu


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