Extended Data Fig. 7: Polynesian ancestry-specific shared drift ordination plot with principal curve.

A principal coordinate analysis (PCoA) projection of the pairwise shared drift distances (the Polynesian ancestry-specific outgroup-F3) between each Pacific island population using Taiwan as an outgroup (Supplementary Fig. 12). This PCoA projection uses only the pairwise distance matrix and is fully unsupervised; that is, it does not presuppose that Rapa Nui is a terminal island along some settlement path. Nevertheless, it shows the same ordering as in Supplementary Fig. 9, confirming that Rapa Nui is indeed the terminal island in our dataset along the longest drift path, and confirming the drift ordering along that path. For further confirmation, a principal curve was also fit to the full dimensional space (Supplementary Fig. 12) and then projected into the two-dimensional PCoA space for visualization. The orthogonal projections of each island onto the principal curve are shown as thinner grey lines. This fully unsupervised principal curve confirms the visually apparent path from Island Southeast Asia (Sumatra, far right) through Samoa, Fiji, Tonga and ending in Raivavae, Mangareva, and Rapa Nui (far left) in that order (cf. migration map in Fig. 2a). This projection of the high dimensional principal curve does not double back on itself, showing that the apparent ordering in this projection is consistent with the original high dimensional ordering. Note that this principal curve is able to fit only one settlement path (the principal one, that is, the longest drift path), which ends in Rapa Nui. Other settlement paths that branch away from this principal (longest) path appear simply as clusters projected onto the principal curve, since islands on those paths share no further drift with the principal path. That is, islands settled along secondary branching paths appear as clusters lying very close to one another along the principal curve. For example, Rapa Iti, which branches off from Rarotonga separately from the main settlement path (Fig. 2a), appears here as coincident with Rarotonga along the principal curve. The eigenvalue for PC1 over the sum of eigenvalues is .997 and for PC 2 is .002 (all eigenvalues are non-negative).