The isometry group of phylogenetic tree space is $S_n$

AbstractTerraces in phylogenetic tree space are, among other things, important for the design of tree space search strategies. While the phenomenon of phylogenetic terraces is already known for unlinked partition models on partitioned phylogenomic data sets, it has not yet been studied if an analogous structure is present under linked and scaled partition models. To this end, we analyze aspects such as the log-likelihood distributions, likelihood-based significance tests, and nearest neighborhood interchanges on the trees residing on a terrace and compare their distributions among unlinked, linked, and scaled partition models. Our study shows that there exists a terrace-like structure under linked and scaled partition models as well. We denote this phenomenon as quasi-terrace. Therefore quasi-terraces should be taken into account in the design of tree search algorithms as well as when reporting results on ‘the’ final tree topology in empirical phylogenetic studies.

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Two C++ Libraries for Counting Trees on a Phylogenetic Terrace

10.1101/211276 ◽

2017 ◽

Cited By ~ 2

Author(s):

R. Biczok ◽

P. Bozsoky ◽

P. Eisenmann ◽

J. Ernst ◽

T. Ribizel ◽

...

Keyword(s):

Maximum Likelihood ◽

Phylogenetic Tree ◽

Phylogenetic Inference ◽

Source Codes ◽

Likelihood Score ◽

Order Of Magnitude ◽

Tree Topologies ◽

Tree Space ◽

Bayesian Phylogenetic Inference ◽

Counting Trees

AbstractMotivationThe presence of terraces in phylogenetic tree space, that is, a potentially large number of distinct tree topologies that have exactly the same analytical likelihood score, was first described by Sanderson et al, (2011). However, popular software tools for maximum likelihood and Bayesian phylogenetic inference do not yet routinely report, if inferred phylogenies reside on a terrace, or not. We believe, this is due to the unavailability of an efficient library implementation to (i) determine if a tree resides on a terrace, (ii) calculate how many trees reside on a terrace, and (iii) enumerate all trees on a terrace.ResultsIn our bioinformatics programming practical we developed two efficient and independent C++ implementations of the SUPERB algorithm by Constantinescu and Sankoff (1995) for counting and enumerating the trees on a terrace. Both implementations yield exactly the same results and are more than one order of magnitude faster and require one order of magnitude less memory than a previous 3rd party python implementation.AvailabilityThe source codes are available under GNU GPL at https://github.com/[email protected]

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Markov Katana: a Novel Method for Bayesian Resampling of Parameter Space Applied to Phylogenetic Trees

10.1101/250951 ◽

2018 ◽

Author(s):

Stephen T. Pollard ◽

Kenji Fukushima ◽

Zhengyuan O. Wang ◽

Todd A. Castoe ◽

David D. Pollock

Keyword(s):

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Statistical Approach ◽

Evolutionary Model ◽

Complex Model ◽

Tree Topology ◽

Added Value ◽

General Idea ◽

Branch Lengths ◽

Tree Space

ABSTRACTPhylogenetic inference requires a means to search phylogenetic tree space. This is usually achieved using progressive algorithms that propose and test small alterations in the current tree topology and branch lengths. Current programs search tree topology space using branch-swapping algorithms, but proposals do not discriminate well between swaps likely to succeed or fail. When applied to datasets with many taxa, the huge number of possible topologies slows these programs dramatically. To overcome this, we developed a statistical approach for proposal generation in Bayesian analysis, and evaluated its applicability for the problem of searching phylogenetic tree space. The general idea of the approach, which we call ‘Markov katana’, is to make proposals based on a heuristic algorithm using bootstrapped subsets of the data. Such proposals induce an unintended sampling distribution that must be determined and removed to generate posterior estimates, but the cost of this extra step can in principle be small compared to the added value of more efficient parameter exploration in Markov chain Monte Carlo analyses. Our prototype application uses the simple neighbor-joining distance heuristic on data subsets to propose new reasonably likely phylogenetic trees (including topologies and branch lengths). The evolutionary model used to generate distances in our prototype was far simpler than the more complex model used to evaluate the likelihood of phylogenies based on the full dataset. This prototype implementation indicates that the Markov katana approach could be easily incorporated into existing phylogenetic search programs and may prove a useful alternative in conjunction with existing methods. The general features of this statistical approach may also prove useful in disciplines other than phylogenetics. We demonstrate that this method can be used to efficiently estimate a Bayesian posterior.

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