Neighbor-joining revealed

It is nearly 20 years since the landmark paper (Saitou and Nei 1987) in Molecular Biology and Evolution introducing Neighbor-Joining (NJ). The method has become the most widely used method for building phylogenetic trees from distances, and the original paper has been cited about 13,000 times (Science Citation Index). Yet the question "what does the NJ method seek to do?" has until recently proved somewhat elusive, leading to some imprecise claims and misunderstanding. However, a rigorous answer to this question has recently been provided by further mathematical investigation, and the purpose of this note is to highlight these results and their significance for interpreting NJ. The origins of this story lie in a paper by Pauplin (2000) though its continuation has unfolded in more mathematically inclined literature. Our aim here is to make these findings more widely accessible.