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Designer invariants for large phylogenies.

D Sankoff1

  • 1Centre de Recherches Mathématiques, Univeristé de Montréal, Québec, Canada.

Molecular Biology and Evolution
|May 1, 1990
PubMed
Summary

New phylogenetic invariants, generalized from binary to k-valued characters, aid in evaluating evolutionary hypotheses. These customized invariants, based on probabilistic independence of character configurations, are applicable to various tree sizes.

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Area of Science:

  • Phylogenetics and Evolutionary Biology
  • Computational Biology
  • Statistical Modeling

Background:

  • Phylogenetic invariants are crucial for evaluating evolutionary hypotheses by analyzing character distributions across species.
  • Existing invariants, like Cavender-Felsenstein, are often limited to specific tree structures and character types.

Purpose of the Study:

  • To develop generalized and customized phylogenetic invariants for evaluating and comparing evolutionary hypotheses.
  • To extend invariants from binary to k-valued characters and apply them to trees of various sizes.

Main Methods:

  • Generalization of Cavender-Felsenstein edge-length invariants for binary characters to k-valued characters.
  • Utilizing probabilistically independent sets of character configurations under symmetric Markov change models.
  • Developing quadratic invariants for 5-trees and edge invariants for 6-trees, and cubic/higher-degree invariants for entire larger trees.

Main Results:

  • Demonstrated the generalization of quadratic invariants for binary characters to k-valued characters.
  • Derived invariants for individual edges in 6-trees and for entire trees (cubic for 6-trees, higher-degree for larger trees).
  • Highlighted the challenge of constructing useful independent event sets for k-valued characters and large trees due to rare configurations.

Conclusions:

  • The developed approach provides a flexible framework for creating customized phylogenetic invariants.
  • This method integrates with statistical contingency table analysis for hypothesis testing.
  • The invariants show potential for analyzing biological data, such as ribosomal RNA, to address evolutionary origins.

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