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

Finding optimal evolutionary trees from sequence data is typically an intractable problem, and there is usually no way of knowing how close to optimal the best tree from some search truly is. The problem would seem to be particularly acute when we have many taxa and when that data has high levels of homoplasy, in which the individual characters require many changes to fit on the best tree. However, a recent mathematical result has provided a precise tool to generate a short number of high-homoplasy characters for any given tree, so that this tree is provably the optimal tree under the maximum parsimony criterion. This provides, for the first time, a rigorous way to test tree search algorithms on homoplasy-rich data, where we know in advance what the '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 correctly for 32,768 taxa, even though the characters in the dataset require, on average, 1148 state-changes each to fit on this tree, and the number of characters is only 57.