Evidence of Multiple Maximum Likelihood Points for a Phylogenetic Tree

A Global Maximum Likelihood Super-Quartet Phylogeny Method

“…Theoretical values are obtained by assuming the two subtrees that have been merged in a heuristic merging step are real neighbors in the true tree. Previous experimental results [18] demonstrated that the probability for the correct tree to be included in the small set of generated trees is very high. As shown in Figure 2, the algorithm is able to achieve better results than PHYML when a limited number of trees are constructed.…”

“…Since each vertex may contain more than one taxon, we expect the super-quartet weights are more reliable than weights of simple quartets. After the weights for all possible super-quartets are calculated, the super-quartet weight matrix can be generated the same way as the simple quartet weight matrix [17,18,19] with each row or column corresponding to a subtree rather than a single taxon. Our new super-quartet method shares the same theoretical property of one-to-one tree topology and matrix mapping [17,18].…”

“…Our previous quartet-based algorithm rebuilds the evolutionary tree using quartet weights [17,18]. As shown in Figure 1, the algorithm is a three-stage procedure: 1. generate all the quartets and calculate the quartet weights; 2. accumulate weights to a global quartet weight matrix; 3. iteratively merge subtrees using this matrix.…”

“…Previously we developed a quartet-based algorithm for the reconstruction of evolutionary trees [17,18,19]. Instead of constructing only one tree as output, this algorithm constructs a limited number of trees for a given set of DNA or protein sequences.…”

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Extending the idea of our previous algorithm [17,18] we developed a new sequential quartet-based phylogenetic tree construction method. This new algorithm reconstructs the phylogenetic tree iteratively by examining at each merge step every possible super-quartet which is formed by four subtrees instead of simple quartet in our previous algorithm.

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