Additive evolutionary trees

Abstract

Metric trees are dendrograms which show the phylogenetic relationships for a set of contemporary species. These dendrograms have numerical values attached to the branches. If the sum of these values on the branches between any two contemporary species is equal to the dissimilarity between these two species, the metric tree is said to be additive and possess an additive dissimilarity matrix. Metric trees and additive matrices are discussed and the uniqueness of the metric tree for an additive dissimilarity matrix is shown. A simple algorithm is given to generate the metric tree for an additive dissimilarity matrix. This algorithm is extended to non-additive dissimilarity matrices through the use of linear programming. Finally, some results for cytochrome c sequences are presented. © 1977.