# Spectral analysis of phylogenetic data

@article{Hendy1993SpectralAO, title={Spectral analysis of phylogenetic data}, author={Michael D. Hendy and David Penny}, journal={Journal of Classification}, year={1993}, volume={10}, pages={5-24} }

The spectral analysis of sequence and distance data is a new approach to phylogenetic analysis. For two-state character sequences, the character values at a given site split the set of taxa into two subsets, a bipartition of the taxa set. The vector which counts the relative numbers of each of these bipartitions over all sites is called a sequence spectrum. Applying a transformation called a Hadamard conjugation, the sequence spectrum is transformed to the conjugate spectrum. This conjugationâ€¦Â

## 196 Citations

### Phylogenetic analysis based on spectral methods.

- BiologyMolecular biology and evolution
- 2012

Through simulations, it is shown that the covariance-based methods effectively capture phylogenetic signal even when structural information is not fully retained, and Comparisons of simulation results with the bootstrap permutation results indicate that the covariances are fairly robust under perturbation in sequence similarity but more sensitive to perturbations in structural similarity.

### The sampling distributions and covariance matrix of phylogenetic spectra

- Mathematics
- 1994

Recent advances in computing variance-covariance matrices from genetic distances to a sequence method of phylogenetic analysis are extended and the bias induced by the delta method, a convenient approximation in deriving V[y], is evaluated and found to be acceptable in the first case and very good in the second.

### Generalizing Phylogenetic Parsimony from the Tree to the Forest

- Biology
- 1998

This multitree approach is a simple generalization of cladistic parsimony to reticulate systems of common ancestry, which can be attributed to the algorithmic and conceptual simplicity of trees and the expecta- tion that certain evolutionary processes gener- ate treelike descent patterns.

### Distinguishing Convergence on Phylogenetic Networks

- Biology
- 2016

It is shown how methods from algebraic geometry, such as Grobner bases, can be used to solve the polynomial equations in phylogenetics and some four-taxon trees and networks can be distinguished from each other.

### Application of Phylogenetic Network

- Biology
- 2012

The phylogenetic network revealed the following pattern: a recombinant allele had a short external branch and was located on a diagonal with the outgroup allele and the two parental alleles were located on another diagonal with long external branches.

### Building trees, hunting for trees, and comparing trees : theory and methods in phylogenetic analysis

- Computer Science
- 1997

It is proved that there exist rules of every order that cannot be reduced to lower order rules, and several new NPcompleteness results and a list of standard NP-complete phylogenetic problems are discussed.

### Measuring the fit of sequence data to phylogenetic model: allowing for missing data.

- BiologyMolecular biology and evolution
- 2005

It is fundamentally important to assess the fit of data to model in phylogenetic and evolutionary studies. Phylogenetic methods using molecular sequences typically start with a multiple alignment. Itâ€¦

### d Plots: A Tool for Analyzing Phylogenetic Distance Data

- Biology

The method is shown to be capable of identifying single recombinant taxa on the basis of distance information alone, provided the parents of the recombinant sequence are sufficiently divergent and the mixture of tree histories is not strongly skewed toward a single tree.

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