Statistical geometry on sequence space.

Publisher Summary This chapter describes methods of comparative sequence analysis that combine horizontal and vertical criteria. They are used to construct geometries that are more complex, but at the same time also more informative than simple distance dendrograms. Geometrical representations of sequence space diagrams become less lucid if more than four symbol classes which are not equivalent in their substitution behavior are involved. The true distance between any two points in this space depends on historical details of the interplay of mutation and selection. Dendrograms that refer to distances usually do not reflect these uncertainties correctly, even if the correlation between segment length and time is taken as having a statistical nature. With increasing divergence, the chance increases that a position that has mutated once will undergo another mutation. For binary sequences, this will always mean a reversal of the first mutation and will thus reduce the distance. If more than two symbols are involved such a substitution may leave the distance unchanged.