Líffræðifélag Íslands - biologia.is
Líffræðiráðstefnan 2019

Erindi/veggspjald / Talk/poster E6

Multiple-merger coalescents, bounded juvenile numbers, and large sample sizes

Höfundar / Authors: Jonathan A. Chetwynd-Diggle(1), Bjarki Eldon(2), Alison M. Etheridge(1)

Starfsvettvangur / Affiliations: 1. University of Oxford, 2. Museum fuer Naturkunde

Kynnir / Presenter: Bjarki Eldon

Natural highly fecund populations abound. Coalescent theory, which models the random gene genealogies of genetic samples, provides powerful statistical inference methods to distinguish between certain evolutionary histories.
We consider the impact of large sample size on gene genealogies in a highly fecund haploid population with sweepstakes reproduction. To this end we consider a modified Schweinsberg model of genetic reproduction, which applies a cutoff to the random number of juveniles contributed by a given individual. Depending on how the cutoff behaves relative to the total population size, we obtain the Kingman-coalescent, or variants of the original Beta-coalescent of (Schweinsberg, 2003). Applying a cutoff enables us to estimate the error of the coalescent approximation. The error estimates reveal that convergence can be very slow, and very small sample size can be sufficient to invalidate convergence, especially if the bound is of a specific form.
However, the impact on the site-frequency spectrum will only be noticed at larger sample size than that at which convergence breaks down. However, the timescale of these models may be too short to be able to recover observed genetic variation. To rectify this, we consider variants of the model of (Schweinsberg, 2003), which include a random cutoff. The resulting coalescent process is a multiple-merger coalescent, with a timescale more in agreement with observed genetic variation.