On the Matrix Condition of Phylogenetic Tree
Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element c ij in C represent...
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| Format: | Article |
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SAGE Publishing
2020-02-01
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| Series: | Evolutionary Bioinformatics |
| Online Access: | https://doi.org/10.1177/1176934320901721 |
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doaj-40597fbd02d340a78bcf4705812e84e62021-08-20T13:03:20ZengSAGE PublishingEvolutionary Bioinformatics1176-93432020-02-011610.1177/1176934320901721On the Matrix Condition of Phylogenetic TreeDwueng-Chwuan Jhwueng0Brian C O’Meara1Department of Statistics, Feng Chia University, Taichung, Taiwan R.O.CDepartment of Ecology and Evolutionary Biology, The University of Tennessee, Knoxville, Knoxville, TN, USAPhylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element c ij in C represents the affinity between extant species i and extant species j . This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if κ , defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C , is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.https://doi.org/10.1177/1176934320901721 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dwueng-Chwuan Jhwueng Brian C O’Meara |
| spellingShingle |
Dwueng-Chwuan Jhwueng Brian C O’Meara On the Matrix Condition of Phylogenetic Tree Evolutionary Bioinformatics |
| author_facet |
Dwueng-Chwuan Jhwueng Brian C O’Meara |
| author_sort |
Dwueng-Chwuan Jhwueng |
| title |
On the Matrix Condition of Phylogenetic Tree |
| title_short |
On the Matrix Condition of Phylogenetic Tree |
| title_full |
On the Matrix Condition of Phylogenetic Tree |
| title_fullStr |
On the Matrix Condition of Phylogenetic Tree |
| title_full_unstemmed |
On the Matrix Condition of Phylogenetic Tree |
| title_sort |
on the matrix condition of phylogenetic tree |
| publisher |
SAGE Publishing |
| series |
Evolutionary Bioinformatics |
| issn |
1176-9343 |
| publishDate |
2020-02-01 |
| description |
Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element c ij in C represents the affinity between extant species i and extant species j . This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if κ , defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C , is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue. |
| url |
https://doi.org/10.1177/1176934320901721 |
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