Reconstructing phylogenies from noisy quartets in polynomial time with a high success probability

Background: In recent years, quartet-based phylogeny reconstruction methods have received considerable attentions in the computational biology community. Traditionally, the accuracy of a phylogeny reconstruction method is measured by simulations on synthetic datasets with known true phylogenies, while little theoretical analysis has been done. In this paper, we present a new model-based approach to measuring the accuracy of a quartet-based phylogeny reconstruction method. Under this model, we propose three efficient algorithms to reconstruct the true phylogeny with a high success probability. Results: The first algorithm can reconstruct the true phylogeny from the input quartet topology set without quartet errors in O(n(2)) time by querying at most (n - 4) log(n - 1) quartet topologies, where n is the number of the taxa. When the input quartet topology set contains errors, the second algorithm can reconstruct the true phylogeny with a probability approximately 1 - p in O(n(4) log n) time, where p is the probability for a quartet topology being an error. This probability is improved by the third algorithm to approximately, 1/1+q(2)+1/2q(4)+1/16q(5) where q = p/1-p, with running time of O(n(5)), which is at least 0.984 when p < 0.05. Conclusion: The three proposed algorithms are mathematically guaranteed to reconstruct the true phylogeny with a high success probability. The experimental results showed that the third algorithm produced phylogenies with a higher probability than its aforementioned theoretical lower bound and outperformed some existing phylogeny reconstruction methods in both speed and accuracy.