Matrix-analytical methods in population genetics

Summary

The analysis of genomic data makes it possible to characterize the demographic processes that shaped the genetic diversity of populations. State-of-the-art in genomic data analyses is increasingly simula-tion-based, but disadvantages of simulation-based procedures include that they are (a) highly com-puter intensive, (b) often depend on the choice of summary statistics, and (c) a rather indirect proce-dure for understanding key properties of the model. As an alternative to simulations, I will outline an emerging mathematical framework for genetic diversity based on linear algebra. The main idea is that the ancestral process of a genetic sample can be described using a generalization of the exponential distribution called a phase-type distribution. Phase-type distributions have been used with great suc-cess in the actuarial sciences and in queuing theory, but the distribution is also very well suited for the ancestral process. I will describe important recent results of using phase-type distributions in popula-tion genetics, and discuss the latest progress and future plans for the framework.

Recent publications

1. I Rivas-González, LN Andersen, A Hobolth (2022). PhaseTypeR: phase-type distributions in R with reward transformations and a view to-wards population genetics. bioRxiv.

2. A Hobolth, M Bladt, LN Andersen (2021). Multivariate phase-type theory for the site frequency spectrum. Journal of Mathematical Biology 83 (6), 1-28.

3. A Hobolth, A Siri-Jegousse, M Bladt (2019). Phase-type distributions in population genetics. Theoretical population biology 127, 16-32.