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Pathological rate matrices: from primates to pathogens.

Harold W Schranz1, Von Bing Yap, Simon Easteal

  • 1John Curtin School of Medical Research, The Australian National University, Canberra, ACT, Australia. harold.schranz@anu.edu.au

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Summary
This summary is machine-generated.

Pathological rate matrices in evolutionary models are common. The Padé algorithm with scaling and squaring is more robust and faster than eigendecomposition or Taylor series for computing substitution probabilities.

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Area of Science:

  • Evolutionary biology
  • Computational biology
  • Bioinformatics

Background:

  • Continuous-time Markov models offer flexible sequence divergence descriptions.
  • Non-reversible models are biologically realistic but computationally challenging.
  • Matrix exponentiation algorithms can yield significant errors with pathological rate matrices.

Purpose of the Study:

  • To investigate the natural occurrence of pathological rate matrices.
  • To evaluate the performance of different algorithms for computing substitution probabilities.

Main Methods:

  • Comparison of Taylor series, eigendecomposition, and Padé with scaling and squaring algorithms.
  • Analysis of concatenated protein coding gene and intron alignments from microbial and primate genomes.
  • Assessment of nucleotide, dinucleotide, codon, and trinucleotide rate matrices.

Main Results:

  • Pathological dinucleotide and trinucleotide matrices were identified in microbial data.
  • Eigendecomposition and Taylor algorithms showed substantial error rates (~10-100%) with pathological matrices.
  • The Padé algorithm demonstrated robustness and was up to 3x faster than eigendecomposition.

Conclusions:

  • The Padé with scaling and squaring algorithm is essential for robust computation of non-reversible evolutionary models.
  • Implementation of the Padé algorithm is recommended for developing reliable bioinformatics software.