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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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