Abstract
AbstractWe derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497–507, 2014). In that paper, it was noted that the speed of invasion by the mutant trait is faster when the resident population is expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman–Kac representation to provide rigorous estimates that confirm these predictions.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Modeling and Simulation
Reference22 articles.
1. Arguin L-P, Bovier A, Kistler N (2011) Genealogy of extremal particles of branching Brownian motion. Commun Pure Appl Math 64(12):1647–1676
2. Aurzada F, Schickentanz DT (2022) Brownian motion conditioned to spend limited time below a barrier. Stoch Process Appl 146:360–381
3. Beghin L, Orsingher E (1999) On the maximum of the generalized Brownian bridge. Liet Mat Rink 39(2):200–213
4. Blath J, Hammer M, Nie F (2022) The stochastic Fisher-KPP equation with seed bank and on/off branching coalescing Brownian motion. Stoch Partial Differ Equ Anal Comput 11(2):773–818
5. Bramson MD (1983) Convergence of solutions of the Kolmogorov equation to travelling waves. Mem Am Math Soc 44(285):iv+190