Improving the Efficiency of p-ECR Moves in Evolutionary TreeSearch Methods Based on Maximum Likelihood by Neighbor Joining

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Inference of evolutionary trees using the maximum likelihood principle is NP-hard. Therefore, all practical methods rely on heuristics. The topological transformations often used in heuristics are nearest neighbor interchange (NNI), sub-tree prune and regraft (SPR) and tree bisection and reconnection (TBR). However, these topological transformations often fall easily into local optima, since there are not many trees accessible in one step from any given tree. Another more exhaustive topological transformation is p-Edge Contraction and Refinement (p-ECR). However, due to its high computation complexity, p-ECR has rarely been used in practice. This paper proposes a method p-ECRNJ with a O(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) time complexity to make the p-ECR move efficient by using neighbor joining (NJ) to refine the unresolved nodes produced in p-ECR. Moreover, the demonstrated topological accuracy for small datasets of NJ can guarantee the accuracy of the p-ECRNJ move. Experiments with simulated and real datasets show that p-ECRNJ can find better trees than the best-known maximum likelihood methods so far and can efficiently improve local topological transforms in reasonable time.