Jochen Blath , Matthias Hammer , Dave Jacobi , Florian Nie
{"title":"How the interplay of dormancy and selection affects the wave of advance of an advantageous gene","authors":"Jochen Blath , Matthias Hammer , Dave Jacobi , Florian Nie","doi":"10.1016/j.spa.2024.104537","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div><div>We find that the slow-down effect of dormancy on the speed of propagation of beneficial alleles is more serious in variant II (the ‘spore model’) than in variant I (the ‘seed bank model’). Mathematically, this can be understood via probabilistic representations of solutions in terms of (two variants of) ‘on/off branching Brownian motion’. A variety of open research questions are briefly discussed at the end of the paper.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104537"},"PeriodicalIF":1.1000,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S030441492400245X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
We find that the slow-down effect of dormancy on the speed of propagation of beneficial alleles is more serious in variant II (the ‘spore model’) than in variant I (the ‘seed bank model’). Mathematically, this can be understood via probabilistic representations of solutions in terms of (two variants of) ‘on/off branching Brownian motion’. A variety of open research questions are briefly discussed at the end of the paper.
期刊介绍:
Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests.
Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.