arXiv subjects

Lizbeth Peñaloza

Publications and source records attributed to Lizbeth Peñaloza.

2 recordsLinked to original sources

arXiv2023

Seed bank Cannings Graphs: How dormancy smoothes random genetic drift

In this article, we introduce a random (directed) graph model for the simultaneous forwards and backwards description of a rather broad class of Cannings models with a seed bank mechanism. This provides a simple tool to establish a sampling duality in the finite population size, and obtain a path-wise embedding of the forward frequency process and the backward ancestral process. Further, it allows the derivation of limit theorems that generalize celebrated results by Möhle to models with seed banks, and where it can be seen how the effect of seed banks affects the genealogies. The explicit graphical construction is a new tool to understand the subtle interplay of seed banks, reproduction and genetic drift in population genetics.

math.PR↗

arXiv2020

The shape of a seed bank tree

We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations evolving under some seed bank effects, such as plants and bacteria, and for some cases of structured populations like metapopulations. The proof relies on the study of the tree at a stopping time corresponding to the first time that a deactivated lineage reactivates. We also give conditional sampling formulas for the random partition and we study the system at the time of the first deactivation of a lineage. All these results provide a good picture of the different regimes and behaviors of the block-counting process of the seed bank coalescent.

math.PR↗