Fig. 2

How quartet queries vote. Each node u in the tree t is associated with a triplet \(u_1, u_2, u_3\) from each of the three subtrees around u (see text for details). When adding new taxon x, we make quartet queries, such as the one on \(\{u_1, u_2, u_3, x\},\) which potentially contribute to the vote for where to place x. Only those quartets whose diameter is below a specified threshold are allowed to vote, and these are referred to as “valid quartets”. Trees are computed on these valid quartets using the Four Point Method. Each valid quartet query then votes using the corresponding quartet tree by identifying a subset of the tree in to which x can be placed without violating the quartet tree. In this figure, FPM returns quartet tree \(u_1x|u_2u_3,\) and then votes for all the edges in the subtree off u containing \(u_1\) (edges dashed). With high probability, given polynomial sequence lengths, valid queries make correct votes