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Graph-based algorithms for Laplace transformed coalescence time distributions.

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  • 1University of Edinburgh, Institute of Evolution and Ecology, Edinburgh, United Kingdom.

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This study introduces a new computational graph algorithm to efficiently analyze population genetics data from genome sequences. The method speeds up the analysis of demographic history and selective sweeps, aiding in understanding population past.

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Area of Science:

  • Population Genetics
  • Computational Biology
  • Genomics

Background:

  • Understanding population history from genome sequences requires analyzing genealogical distributions.
  • Previous methods faced computational bottlenecks due to repeated differentiation in calculating probabilities.
  • Existing composite likelihood approaches for demographic and selection inference require efficient computation of branch length distributions.

Purpose of the Study:

  • To develop a computationally efficient method for extracting demographic and selective information from genome sequences.
  • To overcome the computational limitations of previous approaches for analyzing genealogical distributions.
  • To accelerate the fitting of isolation with migration models and the estimation of selective sweep parameters.

Main Methods:

  • Utilized the Laplace transform and a recursive procedure to generate the distribution of genealogies.
  • Transformed the state space diagram into a computational graph for efficient Laplace transform evaluation.
  • Employed a graph traversal algorithm for rapid computation of probabilities of linked variant configurations.

Main Results:

  • Developed a general algorithm for efficient evaluation of the Laplace transform of the joint distribution of branch lengths.
  • Demonstrated the algorithm's applicability to tabulating likelihoods of mutational configurations in non-recombining blocks.
  • Achieved a significant speed-up for composite likelihood methods used in population genetics inference.

Conclusions:

  • The novel computational graph approach significantly enhances the efficiency of analyzing population genomic data.
  • This acceleration is crucial for fitting complex demographic models and inferring selection.
  • The associated open-source Python library, 'agemo', facilitates the application of these methods.