Chaucer, the Genom, and the Combinatorics of Finite Metric Spaces
CUNY and University of Bielefeld
refreshments at 3:45pm
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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