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(n²) 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(n⁴log 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+q²+1/2q⁴ +1/16q⁵, where q=p/1-p with running time of O(n⁵), 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.