A note on Sattath and Tversky's, Saitou and Nei's, and Studier and Keppler's algorithms for inferring phylogenies from evolutionary distances.

Agglomerative algorithms iteratively pick a pair of taxa, create a new node that represents the cluster of these taxa, and compute a new distance matrix with reduced size where both taxa are replaced by this node. The cycle is repeated until the number of taxa becomes three (or two for rooted trees). This general scheme was first applied to additive unrooted trees by Sattath and Tversky (ADDTREE method; 1977) in the context of mathematical psychology. The neighbor-joining (NJ) method of Saitou and Nei ( 1987) widely popularized this approach in the phylogenetic study. This method is based on the minimum evolution principle and provides trees with near-minimal sum of branch-length estimates. An alternative formulation of the NJ method with reduced computational complexity was given by Studier and Keppler (SK method; 1988), while Rzhetsky and Nei ( 1992, 1993) clarified the theoretical foundation of the minimum evolution principle. Several simulations (Saitou and Nei 1987; Nei 199 1) have shown a high relative efficiency of ADDTREE and of the NJ method in recovering the true topology. These studies have also shown that ADDTREE and the NJ method, whose principles seem very different, are in fact close and usually provide identical or similar trees. For example, they obtain the same tree with Case’s ( 1978) data. The explanation for this proximity was given by Saitou and Nei ( 1987) for four taxa. In this note, we account for this proximity regardless of the number of taxa, and we show that the minimum evolution principle, as employed in the NJ method, is very close to the neighborliness used by Sattath and Tversky ( 1977) and by Fitch ( 198 1) in a nonagglomerative way. In the following, we recall the principles of the ADDTREE, NJ, and SK methods and explain why they are so close. We will only be concerned with the construction of the tree shape, and not with branch-lengths estimation. For the latter aspect, we refer the reader to the original papers and to