Abstract
Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may either split into two or die, and the difference between the birth and death rates is a linear function of the position of the particle. We show that, under certain assumptions, after a sufficiently long time, the empirical distribution of the positions of the particles is approximately Gaussian. This provides mathematically rigorous justification for results in the biology literature indicating that the distribution of the fitness levels of individuals in a population over time evolves like a Gaussian traveling wave.
| Original language | English |
|---|---|
| Article number | 103 |
| Pages (from-to) | 1-76 |
| Number of pages | 76 |
| Journal | Electronic Journal of Probability |
| Volume | 26 |
| Early online date | 14 Jul 2021 |
| DOIs | |
| Publication status | Published - 31 Dec 2021 |
Bibliographical note
Funding Information:*MR was supported by a Royal Society University Research Fellowship, and JS was supported in part by NSF Grant DMS-1707953. †University of Bath, UK. E-mail: [email protected] ‡University of California at San Diego, USA.E-mail: [email protected]
Publisher Copyright:
© 2021, Institute of Mathematical Statistics. All rights reserved.
Keywords
- Branching brownian motion
- Evolution
- Fitness
- Gaussian traveling wave
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty