*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.