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Finding optimal evolutionary trees from sequence data is typically anintractable problem, and there is usually no way of knowing how close tooptimal the best tree from some search truly is. The problem would seem to beparticularly acute when we have many taxa and when that data has high levels ofhomoplasy, in which the individual characters require many changes to fit onthe best tree. However, a recent mathematical result has provided a precisetool to generate a short number of high-homoplasy characters for any giventree, so that this tree is provably the optimal tree under the maximumparsimony criterion. This provides, for the first time, a rigorous way to testtree search algorithms on homoplasy-rich data, where we know in advance whatthe `best' tree is. In this short note we consider just one search program(TNT) but show that it is able to locate the globally optimal tree correctlyfor 32,768 taxa, even though the characters in the dataset requires, onaverage, 1148 state-changes each to fit on this tree, and the number ofcharacters is only 57.

Hide and seek: placing and finding an optimal tree for thousands of homoplasy-rich sequences