Computing the Distribution of a Tree Metric
Copyright policy )Computing the Distribution of a Tree Metric
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time has yet to be described for computing this distribution (which is also the distribution of trees around a given tree under the popular Robinson-Foulds metric). In this paper we derive a polynomial-time algorithm for this distribution. We show how the distribution can be approximated by a Poisson distribution determined by the proportion of leaves that lie in `cherries' of the given tree. We also describe how our results can be used to derive normalization constants that are required in a recently-proposed maximum likelihood approach to supertree construction.
16 pages, 3 figures
- University of Auckland New Zealand
- University of Canterbury New Zealand
Fields of Research::270000 Biological Sciences::270200 Genetics, Models, Genetic, Populations and Evolution (q-bio.PE), 511, trees, Quantitative Biology - Quantitative Methods, discrete mathematics applications, Fields of Research::230000 Mathematical Sciences::230200 Statistics::230204 Applied statistics, phylogenetics, Robinson-Foulds distance, normalization constant, FOS: Biological sciences, Poisson approximation, Poisson Distribution, biology and genetics, Quantitative Biology - Populations and Evolution, Algorithms, Phylogeny, Quantitative Methods (q-bio.QM)
Fields of Research::270000 Biological Sciences::270200 Genetics, Models, Genetic, Populations and Evolution (q-bio.PE), 511, trees, Quantitative Biology - Quantitative Methods, discrete mathematics applications, Fields of Research::230000 Mathematical Sciences::230200 Statistics::230204 Applied statistics, phylogenetics, Robinson-Foulds distance, normalization constant, FOS: Biological sciences, Poisson approximation, Poisson Distribution, biology and genetics, Quantitative Biology - Populations and Evolution, Algorithms, Phylogeny, Quantitative Methods (q-bio.QM)
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