Central limit theorems describing isolation by distance under various forms of power-law dispersal
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913784980832256 |
|---|---|
| author | Forien, Raphaël Wiederhold, Bastian |
| author_facet | Forien, Raphaël Wiederhold, Bastian |
| contents | In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which this information was obtained from forwards-in-time dynamics using a novel stochastic partial differential equations approach for spatial $Λ$-Fleming-Viot models. The latter were introduced by Barton, Etheridge and Véber as a framework to model the evolution of the genetic composition of a spatially structured population. Reproduction takes place through extinction-recolonisation events driven by a Poisson point process. During an event, in certain ball-shaped areas, a parent is sampled and a proportion of the population is replaced. We generalize the previous approach of the first author by allowing the area from which a parent is sampled during events to differ from the area in which offspring are dispersed, and the radii of these regions follow power-law distributions. In particular, while in previous works the motion of ancestral lineages and coalescence behaviour were closely linked, we demonstrate that local and non-local coalescence is possible for ancestral lineages governed by both fractional and standard Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16286 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Central limit theorems describing isolation by distance under various forms of power-law dispersal Forien, Raphaël Wiederhold, Bastian Probability 60F17, 60G60, 60J90, 60G52, 92D15 In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which this information was obtained from forwards-in-time dynamics using a novel stochastic partial differential equations approach for spatial $Λ$-Fleming-Viot models. The latter were introduced by Barton, Etheridge and Véber as a framework to model the evolution of the genetic composition of a spatially structured population. Reproduction takes place through extinction-recolonisation events driven by a Poisson point process. During an event, in certain ball-shaped areas, a parent is sampled and a proportion of the population is replaced. We generalize the previous approach of the first author by allowing the area from which a parent is sampled during events to differ from the area in which offspring are dispersed, and the radii of these regions follow power-law distributions. In particular, while in previous works the motion of ancestral lineages and coalescence behaviour were closely linked, we demonstrate that local and non-local coalescence is possible for ancestral lineages governed by both fractional and standard Laplacians. |
| title | Central limit theorems describing isolation by distance under various forms of power-law dispersal |
| topic | Probability 60F17, 60G60, 60J90, 60G52, 92D15 |
| url | https://arxiv.org/abs/2211.16286 |