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On the decidability of population size histories from finite allele frequency spectra

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  • Baharian, Soheil
  • Gravel, Simon

Abstract

Understanding the historical events that shaped current genomic diversity has applications in historical, biological, and medical research. However, the amount of historical information that can be inferred from genetic data is finite, which leads to an identifiability problem. For example, different historical processes can lead to identical distribution of allele frequencies. This identifiability issue casts a shadow of uncertainty over the results of any study which uses the frequency spectrum to infer past demography. It has been argued that imposing mild ‘reasonableness’ constraints on demographic histories can enable unique reconstruction, at least in an idealized setting where the length of the genome is nearly infinite. Here, we discuss this problem for finite sample size and genome length. Using the diffusion approximation, we obtain bounds on likelihood differences between similar demographic histories, and use them to construct pairs of very different reasonable histories that produce almost-identical frequency distributions. The finite-genome problem therefore remains poorly determined even among reasonable histories. Where fits to few-parameter models produce narrow parameter confidence intervals, large uncertainties lurk hidden by model assumption.

Suggested Citation

  • Baharian, Soheil & Gravel, Simon, 2018. "On the decidability of population size histories from finite allele frequency spectra," Theoretical Population Biology, Elsevier, vol. 120(C), pages 42-51.
  • Handle: RePEc:eee:thpobi:v:120:y:2018:i:c:p:42-51
    DOI: 10.1016/j.tpb.2017.12.008
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    References listed on IDEAS

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    1. Lukić, Sergio & Hey, Jody & Chen, Kevin, 2011. "Non-equilibrium allele frequency spectra via spectral methods," Theoretical Population Biology, Elsevier, vol. 79(4), pages 203-219.
    2. Myers, Simon & Fefferman, Charles & Patterson, Nick, 2008. "Can one learn history from the allelic spectrum?," Theoretical Population Biology, Elsevier, vol. 73(3), pages 342-348.
    3. Joseph K Pickrell & Jonathan K Pritchard, 2012. "Inference of Population Splits and Mixtures from Genome-Wide Allele Frequency Data," PLOS Genetics, Public Library of Science, vol. 8(11), pages 1-17, November.
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    1. Legried, Brandon & Terhorst, Jonathan, 2022. "Rates of convergence in the two-island and isolation-with-migration models," Theoretical Population Biology, Elsevier, vol. 147(C), pages 16-27.

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