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Review: The Neighbor-Joining Method: A New Method for Reconstructing Phylogenetic Trees

Citation

  • Saitou, N. & Nei, M. (1987). The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular Biology and Evolution, 4(4), 406–425.
  • DOI

Abstract

The neighbor-joining method reconstructs a phylogenetic tree from a matrix of pairwise evolutionary distances. Starting from a starlike tree, it repeatedly joins the pair of operational taxonomic units that minimizes the total branch length of the resulting tree, producing both the topology and the branch lengths of a unique final tree. Computer simulations show that it recovers the correct unrooted topology more efficiently than several other distance methods.

Neighbor-joining is a distance method: it takes a matrix of pairwise evolutionary distances \( D_{ij} \) and returns a tree, following the principle of minimum evolution. A pair of neighbors is a pair of taxa joined through a single interior node of an unrooted binary tree.

The algorithm starts from a starlike tree with no internal structure. At each step it considers joining each candidate pair \( (i, j) \), computes the total branch length \( S_{ij} \) of the tree that results from treating that pair as neighbors, and selects the pair with the smallest \( S_{ij} \). That pair is merged into one combined unit, the distance matrix is reduced by

\[D_{(ij),k} = \tfrac{1}{2}\bigl(D_{ik} + D_{jk}\bigr),\]

and the step repeats until three units remain, which fix a single unrooted tree. Branch lengths are estimated by a least-squares (Fitch-Margoliash) formula as the joins are made. The procedure is deterministic, runs in polynomial time, and yields one tree. For a purely additive distance matrix it recovers the correct topology and branch lengths exactly; the necessary four-taxon condition \( D_{12} + D_{34} < D_{13} + D_{24} \) and \( < D_{14} + D_{23} \) (with 1, 2 as neighbors) is the four-point condition. On real data, where distances are not additive because of backward and parallel substitutions, simulations show neighbor-joining recovers the correct topology more often than UPGMA and the other distance methods tested.

The distances themselves come from a model: the paper's simulations convert nucleotide differences to distances with the Jukes-Cantor (1969) correction. The raw proportion of differing sites \( p \) is a metric but is not additive; the model correction \( d \) restores additivity.

Relevance to Hifuku

Neighbor-joining builds the anchor trees that fix Hifuku's chart. Each of the three anchors \( r_1, r_2, r_3 \) is a neighbor-joining tree, computed by nj_tree from a corrected pairwise distance matrix: the Jukes-Cantor (1969) correction for DNA and the Kimura (1983) correction for protein (see Jukes & Cantor 1969 and Kimura 1983). The three anchors' pairwise distances are embedded in the plane to give the two-dimensional chart (Section 6).

Neighbor-joining suits this role because it is fast, deterministic, and returns a single unrooted tree with branch lengths, so the chart rests on a stable, cheaply computed reference frame. The anchors are coordinate references, not claimed optima; the maximum-likelihood tree can sit anywhere on the chart the anchors span.