Neighbor-Joining Phylogenetic Tree Builder (2D)

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. This 2D sibling runs the exact same join sequence as the 3D version, laid out flat: each node's angle is the vector-average of its children's angles and its radius is its cumulative branch-length depth from the root, so the whole tree reads as a top-down radial diagram instead of a spinning 3D scene.

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 tree grows a new branch pair at each step.
Drag / scroll — pan and zoom the canvas to inspect a crowded tree.

Taxon (leaf) Ancestral node

drag to pan · scroll to zoom