A regular decomposition of the edge-product space of phylogenetic trees

Gill, Jonna; Linusson, Svante; Moulton, Vincent; Steel, Mike

doi:10.1016/j.aam.2006.07.007

Cited by 18 publications

(28 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Much work is needed for these spaces— both theoretically (such as defining medians and averages when there are multiple shortest paths between points) as well as algorithmic tools (such as algorithms and software that can compute distances for more than 3-leaf trees). Given the huge complexity in computing even small examples and the topology of the underlying space ( Moulton and Steel 2004 ; Gill et al 2008 ; Engström et al 2013) , this is a daunting task. We briefly explain these spaces as well as their links to the phylogenetic orange space (defined below) that includes probabilistic models of evolution ( Kim 2000) .…”

Section: Continuous Treespacesmentioning

confidence: 99%

“…The space has nice mathematical properties but lacks unique geodesics and is difficult to visualize for even small trees ( Figure 1 of Engström et al (2013) illustrates the curved subspace corresponding to a rooted 3-leaf tree). As Moulton and Steel (2004) and Gill et al (2008) note, this space is related to the “phylogenetic orange” space of Kim (2000) . In the orange space, the points are probability distributions on the possible leaf labelings or site patterns.…”

Section: Continuous Treespacesmentioning

confidence: 99%

See 1 more Smart Citation

Review Paper: The Shape of Phylogenetic Treespace

John

2016

Syst Biol

View full text Add to dashboard Cite

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths.

show abstract

Section: Continuous Treespacesmentioning

confidence: 99%

Section: Continuous Treespacesmentioning

confidence: 99%

Review Paper: The Shape of Phylogenetic Treespace

John

2016

Syst Biol

View full text Add to dashboard Cite

show abstract

“…By characterising the covariance space related to Gaussian latent tree models, we can better assess the suitability of trees or the fit of a particular tree for a data set. In this paper we present the complete description of this model class by relating this to the space of phylogenetic oranges (Engström et al, 2012;Gill et al, 2008;Kim, 2000;Moulton & Steel, 2004). Such a complete description had been known for a simple tree with only four leaves (see Pearl & Xu (1987, Theorem 2)) or for a star tree (see Bekker & de Leeuw (1987)).…”

Section: Introductionmentioning

confidence: 99%

The correlation space of Gaussian latent tree models and model selection without fitting

et al. 2016

View full text Add to dashboard Cite

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian latent tree model. Our method does not require us first to fit such a tree. We demonstrate the usefulness of the inverse-Wishart distribution for performing preliminary assessments of tree-compatibility using semialgebraic constraints. Using results from Drton et al. (2008) we then provide the appropriate moments required for test statistics for assessing adherence to these equality constraints. These are shown to be effective even for small sample sizes and can be easily adjusted to test either the entire model or only certain macrostructures hypothesized within the tree. We illustrate our exploratory tetrad analysis using a linguistic application and our confirmatory tetrad analysis using a biological application.

show abstract

“…This idea was first considered by Kim ( 2000 ), and then developed more formally in subsequent papers (Moulton and Steel 2004 ; Gill et al. 2008 ). The space is known as the phylogenetic orange space or edge-product space.…”

Section: Introductionmentioning

confidence: 99%

Information geometry for phylogenetic trees

et al. 2021

View full text Add to dashboard Cite

We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than existing spaces: in wald space, trees are close if they induce similar distributions on genetic sequence data. As a point set, wald space contains the previously developed Billera–Holmes–Vogtmann (BHV) tree space; it also contains disconnected forests, like the edge-product (EP) space but without certain singularities of the EP space. We investigate two related geometries on wald space. The first is the geometry of the Fisher information metric of character distributions induced by the two-state symmetric Markov substitution process on each tree. Infinitesimally, the metric is proportional to the Kullback–Leibler divergence, or equivalently, as we show, to any f-divergence. The second geometry is obtained analogously but using a related continuous-valued Gaussian process on each tree, and it can be viewed as the trace metric of the affine-invariant metric for covariance matrices. We derive a gradient descent algorithm to project from the ambient space of covariance matrices to wald space. For both geometries we derive computational methods to compute geodesics in polynomial time and show numerically that the two information geometries (discrete and continuous) are very similar. In particular, geodesics are approximated extrinsically. Comparison with the BHV geometry shows that our canonical and biologically motivated space is substantially different.

show abstract

A regular decomposition of the edge-product space of phylogenetic trees

Cited by 18 publications

References 5 publications

Review Paper: The Shape of Phylogenetic Treespace

Review Paper: The Shape of Phylogenetic Treespace

The correlation space of Gaussian latent tree models and model selection without fitting

Information geometry for phylogenetic trees

Contact Info

Product

Resources

About