An error-correcting map for quartets can improve the signals for phylogenetic trees

From the DNA sequences for N taxa, the (generally unknown) phylogenetic tree T that gave rise to them is to be reconstructed. Various methods give rise, for each quartet J consisting of exactly four taxa, to a predicted tree L(J) based only on the sequences in J, and these are then used to reconstruct T. The author defines an "error-correcting map" (Ec), which replaces each L(J) with a new tree, Ec(L)(J), which has been corrected using other trees, L(K), in the list L. The "quartet distance" between two trees is defined as the number of quartets J on which the two trees differ, and two distinct trees are shown to always have quartet distance of at least N - 3. If L has quartet distance at most (N - 4)/2 from T, then Ec(L) will coincide with the correct list for T; and this result cannot be improved. In general, Ec can correct many more errors in L. Iteration of the map Ec may produce still more accurate lists. Simulations are reported which often show improvement even when the quartet distance considerably exceeds (N - 4)/2. Moreover, the Buneman tree for Ec(L) is shown to refine the Buneman tree for L, so that strongly supported edges for L remain strongly supported for Ec(L). Simulations show that if methods such as the C-tree or hypercleaning are applied to Ec(L), the resulting trees often have more resolution than when the methods are applied only to L.