How the interplay of dormancy and selection affects the wave of advance of an advantageous gene

Jochen Blath, Matthias Hammer, Dave Jacobi and Florian Nie

Stochastic Processes and their Applications, 2025, vol. 181, issue C

Abstract: We investigate the spread of advantageous genes in two variants of the F-KPP model with dormancy. In the first model, dormant individuals do not move in space and instead form ‘localized seed banks’. In the second model, dormant forms of individuals are subject to motion, while the ‘active’ (reproducing) individuals remain spatially static. This can be motivated e.g. by spore dispersal of fungi, where the ‘dormant’ spores are distributed by wind, water or insects, while the ‘active’ fungi are locally fixed. For both models, we establish existence of monotone travelling wave solutions, determine the corresponding critical wave speed in terms of the model parameters, and characterize aspects of the asymptotic shape of the waves depending on the decay properties of the initial condition.

Keywords: Fisher–Kolmogorov–Petrovsky–Piscounov equation; Travelling wave; Dormancy; Seed bank; On/off branching Brownian motion; Advantageous gene (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104537

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