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This study develops algorithms to detect dependent biological evolution, even without knowing the evolutionary tree structure. It establishes bounds for efficiently identifying evolutionary character dependence across various models.

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Area of Science:

  • Evolutionary biology
  • Statistical modeling
  • Computational biology

Background:

  • Biological evolution models often assume character independence.
  • Detecting dependence is crucial for accurate evolutionary inference.
  • Existing methods typically require knowledge of the phylogenetic tree topology.

Purpose of the Study:

  • To determine the asymptotic complexity of detecting dependence in biological evolution models.
  • To develop algorithms that detect dependence without prior knowledge of tree topology.
  • To establish bounds for efficient dependence detection across diverse evolutionary and dependence models.

Main Methods:

  • Analysis of stochastic models for biological evolution, including Cavender-Farris-Neyman and Jukes-Cantor.
  • Consideration of general models with state-dependent transition matrices on each edge.
  • Development of algorithms for detecting dependence under various perturbation models.
  • Application of a new concentration result for Markov random fields on trivalent trees.

Main Results:

  • Nearly tight bounds on transition matrix norms for efficient dependence detection.
  • Algorithms effective across a range of evolutionary and dependence models.
  • Demonstration that dependence can be detected without knowing the tree topology.
  • A novel concentration result showing subquadratic variance for leaf state counts.

Conclusions:

  • Efficient detection of evolutionary character dependence is achievable using the developed methods.
  • The algorithms are robust across various evolutionary models and dependence structures.
  • The findings advance the statistical analysis of evolutionary processes, particularly in the absence of complete topological information.