Statistical properties of pairwise distances between leaves on a random Yule tree.
A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2015-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC4380457?pdf=render |
| _version_ | 1817982811534000128 |
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| author | Michael Sheinman Florian Massip Peter F Arndt |
| author_facet | Michael Sheinman Florian Massip Peter F Arndt |
| author_sort | Michael Sheinman |
| collection | DOAJ |
| description | A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the n-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species. |
| first_indexed | 2024-04-13T23:26:01Z |
| format | Article |
| id | doaj.art-5df732db76584192a1815512c0f1f0eb |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-04-13T23:26:01Z |
| publishDate | 2015-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-5df732db76584192a1815512c0f1f0eb2022-12-22T02:25:04ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-01103e012020610.1371/journal.pone.0120206Statistical properties of pairwise distances between leaves on a random Yule tree.Michael SheinmanFlorian MassipPeter F ArndtA Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the n-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species.http://europepmc.org/articles/PMC4380457?pdf=render |
| spellingShingle | Michael Sheinman Florian Massip Peter F Arndt Statistical properties of pairwise distances between leaves on a random Yule tree. PLoS ONE |
| title | Statistical properties of pairwise distances between leaves on a random Yule tree. |
| title_full | Statistical properties of pairwise distances between leaves on a random Yule tree. |
| title_fullStr | Statistical properties of pairwise distances between leaves on a random Yule tree. |
| title_full_unstemmed | Statistical properties of pairwise distances between leaves on a random Yule tree. |
| title_short | Statistical properties of pairwise distances between leaves on a random Yule tree. |
| title_sort | statistical properties of pairwise distances between leaves on a random yule tree |
| url | http://europepmc.org/articles/PMC4380457?pdf=render |
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