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The TMRCA of general genealogies in populations with deterministically varying size
Alejandro H Wences1, Lizbeth Peñaloza2, Matthias Steinrücken3,4
1LAAS - CNRS, Université de Toulouse, France.
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.
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