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The TMRCA of general genealogies in populations with deterministically varying size

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  • Wences, Alejandro H.
  • Peñaloza, Lizbeth
  • Steinrücken, Matthias
  • Siri-Jégousse, Arno

Abstract

We study the time to the most recent common ancestor (TMRCA) of a sample of finite size in a wide class of genealogical models for populations with deterministically varying size. This is made possible by recently developed results on inhomogeneous phase-type random variables, allowing us to obtain the density and the moments of the TMRCA of time-dependent coalescent processes in terms of matrix formulas. We also provide matrix simplifications permitting a more straightforward calculation. With these results, the TMRCA provides an explanatory variable to distinguish different evolutionary scenarios, and to infer model parameters.

Suggested Citation

  • Wences, Alejandro H. & Peñaloza, Lizbeth & Steinrücken, Matthias & Siri-Jégousse, Arno, 2025. "The TMRCA of general genealogies in populations with deterministically varying size," Theoretical Population Biology, Elsevier, vol. 165(C), pages 1-9.
    • Handle: RePEc:eee:thpobi:v:165:y:2025:i:c:p:1-9
    DOI: 10.1016/j.tpb.2025.06.002
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    References listed on IDEAS

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    1. Hobolth, Asger & Siri-Jégousse, Arno & Bladt, Mogens, 2019. "Phase-type distributions in population genetics," Theoretical Population Biology, Elsevier, vol. 127(C), pages 16-32.
    2. Blath, Jochen & Cronjäger, Mathias Christensen & Eldon, Bjarki & Hammer, Matthias, 2016. "The site-frequency spectrum associated with Ξ-coalescents," Theoretical Population Biology, Elsevier, vol. 110(C), pages 36-50.
    3. Miroshnikov, Alexey & Steinrücken, Matthias, 2017. "Computing the joint distribution of the total tree length across loci in populations with variable size," Theoretical Population Biology, Elsevier, vol. 118(C), pages 1-19.
    4. Kumagai, Seiji & Uyenoyama, Marcy K., 2015. "Genealogical histories in structured populations," Theoretical Population Biology, Elsevier, vol. 102(C), pages 3-15.
    5. Hobolth, Asger & Rivas-González, Iker & Bladt, Mogens & Futschik, Andreas, 2024. "Phase-type distributions in mathematical population genetics: An emerging framework," Theoretical Population Biology, Elsevier, vol. 157(C), pages 14-32.
    6. Heng Li & Richard Durbin, 2011. "Inference of human population history from individual whole-genome sequences," Nature, Nature, vol. 475(7357), pages 493-496, July.
    7. Gautam Upadhya & Matthias Steinrücken, 2022. "Robust inference of population size histories from genomic sequencing data," PLOS Computational Biology, Public Library of Science, vol. 18(9), pages 1-32, September.
    8. Schweinsberg, Jason, 2003. "Coalescent processes obtained from supercritical Galton-Watson processes," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 107-139, July.
    9. Hansjörg Albrecher & Mogens Bladt & Jorge Yslas, 2022. "Fitting inhomogeneous phase‐type distributions to data: the univariate and the multivariate case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 44-77, March.
    10. Blath, Jochen & Buzzoni, Eugenio & Koskela, Jere & Wilke Berenguer, Maite, 2020. "Statistical tools for seed bank detection," Theoretical Population Biology, Elsevier, vol. 132(C), pages 1-15.
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