Coalescence times of ancestral lineages in two-dimensional logistic branching random walks | Vidéo | Carmin.tv

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Coalescence times of ancestral lineages in two-dimensional logistic branching random walks

By Matthias Birkner

Appears in collection : Stochastic Processes in Evolutionary Biology / Processus Stochastiques en Biologie Evolutive

Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that it agrees with well known results for a suitably scaled two-dimensional stepping stone model and also with Malécot's continuous-space approximation for the probability of identity by descent as a function of sampling distance. This can be viewed as a justification for the replacement of locally fluctuating population sizes by fixed effective sizes. Our main tool is a joint regeneration construction for the spatial embeddings of the two ancestral lineages.

Information about the video

Date of recording 21/05/2024
Date of publication 11/06/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20180403
Cite this video Birkner, Matthias (21/05/2024). Coalescence times of ancestral lineages in two-dimensional logistic branching random walks. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20180403
URL https://dx.doi.org/10.24350/CIRM.V.20180403

Domain(s)

Probability

Bibliography

BIRKNER, Matthias, DEPPERSCHMIDT, Andrej, et SCHLÜTER, Timo. Pair coalescence times of ancestral lineages of two-dimensional logistic branching random walks. arXiv preprint arXiv:2405.02090, 2024. - https://arxiv.org/abs/2405.02090

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/3000/Slides/2024-05-21_Birkner.pdf

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