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This study introduces two Markov models for sequence evolution on pedigrees, exploring if pedigrees can be reconstructed from extant sequence data. Results show certain pedigrees are distinguishable by counting spanning subgraph sequences.

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Area of Science:

  • Population Genetics
  • Computational Biology
  • Statistical Genetics

Background:

  • Pedigrees, as directed acyclic graphs, model ancestral relationships.
  • Sequence evolution on pedigrees is influenced by recombination and mutation processes.
  • A key challenge is reconstructing pedigrees from observed genetic data.

Purpose of the Study:

  • To investigate the identifiability of pedigrees from the joint probability distribution of extant sequences.
  • To develop and analyze Markov models for sequence evolution on pedigrees.
  • To determine if distinct pedigrees can be differentiated using sequence data.

Main Methods:

  • Development of two Markov models: Model R (recombinations only) and Model RM (recombinations with mutations).
  • Analysis of sequence evolution dynamics on general pedigrees.
  • Mathematical formulation to count spanning subgraph sequences from extant sequence distributions.

Main Results:

  • Partial identifiability results for general pedigrees are established.
  • When crossover probabilities are small, specific spanning subgraph sequences can be counted.
  • This counting method distinguishes between pedigrees previously considered difficult to differentiate.

Conclusions:

  • The joint probability distribution of extant sequences contains information about the underlying pedigree structure.
  • Counting spanning subgraph sequences offers a method for pedigree reconstruction and differentiation.
  • The developed models and methods advance the understanding of genetic data's utility in inferring evolutionary history.