Fig. 3

Using quartet queries to place new taxa. When adding a taxon x into the tree t, all valid quartet queries are allowed to vote for the edges in the tree (see Fig. 2) and x is then added to the edge that receives the most votes. In this figure, we show x being placed into edge uv, based on the following possible vote outcomes: The query at p returns tree ab|xc and so votes for \(\{pu, uc, uv, vd, vq, qe, qf\},\) and similarly the queries at u and v vote for \(\{uv, vd, vq, qe, qf\}\) and \(\{uv, uc, up, pb, pa\},\) respectively. The query at q is not valid and does not get to vote. Our algorithm guarantees that queries at u, v are valid with high probability. Note that internal nodes are boxed and taxon nodes are circled