On the path length of binary trees
Journal of the ACM (JACM)
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The deep coalescence consensus tree problem is Pareto on clusters
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
From Gene Trees to Species Trees II: Species Tree Inference by Minimizing Deep Coalescence Events
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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In the minimizing-deep-coalescences (MDC) approach for species tree inference, a tree that has the minimal deep coalescence cost for reconciling a collection of gene trees is taken as an estimate of the species tree topology. The MDC method possesses the desirable Pareto property, and in practice it is quite accurate and computationally efficient. Here, in order to better understand the MDC method, we investigate some properties of the deep coalescence cost. We prove that the unit neighborhood of either a rooted species tree or a rooted gene tree under the deep coalescence cost is exactly the same as the tree's unit neighborhood under the rooted nearest-neighbor interchange (NNI) distance. Next, for a fixed species tree, we obtain the maximum deep coalescence cost across all gene trees as well as the number of gene trees that achieve the maximum cost. We also study corresponding problems for a fixed gene tree.