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

IF 1.1 2区 数学 Q3 STATISTICS & PROBABILITY
Jochen Blath , Matthias Hammer , Dave Jacobi , Florian Nie
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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.
休眠和选择的相互作用如何影响优势基因的进化
我们研究了两个具有休眠的F-KPP模型变体中优势基因的传播。在第一个模型中,休眠的个体不会在空间中移动,而是形成“局部种子库”。在第二个模型中,休眠形式的个体受制于运动,而“活跃”(繁殖)的个体保持空间静态。例如,这可以由真菌的孢子传播引起,其中“休眠”的孢子通过风、水或昆虫传播,而“活跃”的真菌则在局部固定。对于这两个模型,我们建立了单调行波解的存在性,根据模型参数确定了相应的临界波速,并根据初始条件的衰减特性表征了波的渐近形状的各个方面。我们发现休眠对有益等位基因繁殖速度的减缓作用在变异II(“孢子模型”)中比在变异I(“种子库模型”)中更为严重。从数学上讲,这可以通过“开/关分支布朗运动”的(两种变体)解的概率表示来理解。本文最后简要讨论了各种开放性的研究问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Stochastic Processes and their Applications
Stochastic Processes and their Applications 数学-统计学与概率论
CiteScore
2.90
自引率
7.10%
发文量
180
审稿时长
23.6 weeks
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.
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