Proving phylogenetic trees minimal with l-clustering and set partitioning

Abstract

The problem of determining a minimal length phylogenetic (evolutionary) tree from a set of aligned protein sequences is defined mathematically. Although this is an example of the Steiner problem in graphs (S.P.G.), we exploit the special nature of the character sequences to solve it more efficiently than by using S.P.G. algorithms. This is done by using a key theorem concerning partitions of the data. All optimal solutions for problems with less than six species are classified. In problems where optimality is not immediately achieved, the data must be partitioned. Methods for obtaining useful partitions are explained, and some simple cases are classified. It is concluded that the techniques presented are often powerful enough to find minimal trees for the data of a significant biological study.