Editing Neighbor joining (section)

== Neighbor joining as minimum evolution ==
Neighbor joining may be viewed as a [[greedy algorithm|greedy heuristic]] for the [[minimum evolution|balanced minimum evolution]]<ref name="gascuel">{{cite journal |author=Gascuel O, [[Mike Steel (mathematician)|Steel M]] |title=Neighbor-joining revealed |journal=Mol Biol Evol |volume=23 |issue=11 |pages=1997–2000 |year=2006 |doi=10.1093/molbev/msl072 |pmid=16877499|url=https://hal-lirmm.ccsd.cnrs.fr/lirmm-00136653/document |doi-access=free }}</ref> (BME) criterion. For each topology, BME defines the tree length (sum of branch lengths) to be a particular weighted sum of the distances in the distance matrix, with the weights depending on the topology. The BME optimal topology is the one which minimizes this tree length. NJ at each step greedily joins that pair of taxa which will give the greatest decrease in the estimated tree length. This procedure does not guarantee to find the optimum for the BME criterion, although it often does and is usually quite close.<ref name="gascuel"/>