Abstract
The phylogenetic Mean Pairwise Distance (MPD) is one of the most popular measures for computing the phylogenetic distance between a given group of species. More specifically, for a phylogenetic tree \(\mathcal{T}\) and for a set of species R represented by a subset of the leaf nodes of \(\mathcal{T}\), the MPD of R is equal to the average cost of all possible simple paths in \(\mathcal{T}\) that connect pairs of nodes in R.
Among other phylogenetic measures, the MPD is used as a tool for deciding if the species of a given group R are closely related. To do this, it is important to compute not only the value of the MPD for this group but also the expectation, the variance, and the skewness of this metric. Although efficient algorithms have been developed for computing the expectation and the variance the MPD, there has been no approach so far for computing the skewness of this measure.
In the present work we describe how to compute the skewness of the MPD on a tree \(\mathcal{T}\) optimally, in Θ(n) time; here n is the size of the tree \(\mathcal{T}\). So far this is the first result that leads to an exact, let alone efficient, computation of the skewness for any popular phylogenetic distance measure. Moreover, we show how we can compute in Θ(n) time several interesting quantities in \(\mathcal{T}\) that can be possibly used as building blocks for computing efficiently the skewness of other phylogenetic measures.
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References
Cooper, N., Rodríguez, J., Purvis, A.: A Common Tendency for Phylogenetic Overdispersion in Mammalian Assemblages. In: Proceedings of the Royal Society B: Biological Sciences, vol. 275, pp. 2031–2037 (2008)
Harmon-Threatt, A.N., Ackerly, D.D.: Filtering Across Spatial Scales: Phylogeny, Biogeography and Community Structure in Bumble Bees. PLoS ONE 8, e60446 (2013)
Pontarp, M., Canbäck, B., Tunlid, A., Lundberg, P.: Phylogenetic Analysis Suggests that Habitat Filtering Is Structuring Marine Bacterial Communities Across the Globe. Microbial Ecology 64, 8–17 (2012)
Swenson, N.G.: Phylogenetic Beta Diversity Metrics. Trait Evolution and Inferring the Functional Beta Diversity of Communities. PLoS ONE 6(6), e21264 (2011)
Tsirogiannis, C., Sandel, B., Cheliotis, D.: Efficient Computation of Popular Phylogenetic Tree Measures. In: Raphael, B., Tang, J. (eds.) WABI 2012. LNCS, vol. 7534, pp. 30–43. Springer, Heidelberg (2012)
Vamosi, J.C., Vamosi, S.M.: Body Size, Rarity, and Phylogenetic Community Structure: Insights from Diving Beetle Assemblages of Alberta. Diversity and Distributions 13, 1–10 (2007)
Webb, C.O., Ackerly, D.D., McPeek, M.A., Donoghue, M.J.: Phylogenies and Community Ecology. Annual Review of Ecology and Systematics 33, 475–505 (2002)
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Tsirogiannis, C., Sandel, B. (2013). Computing the Skewness of the Phylogenetic Mean Pairwise Distance in Linear Time. In: Darling, A., Stoye, J. (eds) Algorithms in Bioinformatics. WABI 2013. Lecture Notes in Computer Science(), vol 8126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40453-5_14
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DOI: https://doi.org/10.1007/978-3-642-40453-5_14
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