Neighbor-Joining Phylogenetic Tree Builder

Distance Matrix

Taxa 6

Build the Tree

Press Step or Play to run neighbor-joining.

Join step

0 / 0

Lineages left

Tree length built (Σ branch lengths)

0.00

How it works

Neighbor-joining (Saitou & Nei, 1987) builds a tree bottom-up from a pairwise distance matrix D, without assuming a constant mutation rate. At each step, with n active lineages, it picks the pair (i,j) minimizing the Q-criterion:

Q(i,j) = (n-2)·d(i,j) - Σ_k d(i,k) - Σ_k d(j,k)

That pair is joined under a new internal node u, with branch lengths computed from the row sums r(i) = Σ_k d(i,k):

len(i,u) = ½·d(i,j) + [r(i) - r(j)] / [2(n-2)]
len(j,u) = d(i,j) - len(i,u)

Distances from every remaining lineage k to the new node u are then recomputed:

d(u,k) = ½·[d(i,k) + d(j,k) - d(i,j)]

i and j are removed from the active set, u is added, and the process repeats until one lineage remains — the root. Unlike UPGMA, neighbor-joining does not assume a molecular clock, so branch lengths can differ freely between sister lineages, which is why it is the workhorse algorithm behind most real phylogenetic trees built from DNA or protein distance data.

Taxa slider — how many lineages seed the distance matrix (4–9).
Randomize — scatters new taxa in an abstract trait space and recomputes all pairwise distances, then resets the build.
Step / Play — advances the neighbor-joining algorithm one join at a time, or auto-plays through every join; the 3D tree grows a new branch pair at each step.

Taxon (leaf) Ancestral node

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