{"title":"Effects of phase separation on extinction times in population models","authors":"Janik Schüttler, Robert L Jack, Michael E Cates","doi":"10.1088/1742-5468/ad5c59","DOIUrl":null,"url":null,"abstract":"We study the effect of phase-separating diffusive dynamics on the mean time to extinction (MTE) in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual particles on two sites undergo on-site reactions and hopping between the sites. In the slow-reaction limit, we project the models’ dynamics onto suitable one-dimensional reaction coordinates, which allows the derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the MTE. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We discuss how Allee effects can be affected by phase separation, including situations where the tendency to phase-separate renders an otherwise stable population unstable.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad5c59","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the effect of phase-separating diffusive dynamics on the mean time to extinction (MTE) in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual particles on two sites undergo on-site reactions and hopping between the sites. In the slow-reaction limit, we project the models’ dynamics onto suitable one-dimensional reaction coordinates, which allows the derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the MTE. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We discuss how Allee effects can be affected by phase separation, including situations where the tendency to phase-separate renders an otherwise stable population unstable.
我们研究了在几种慢反应的反应扩散模型中,相分离扩散动力学对平均消亡时间(MTE)的影响。我们考虑了类似于 AB 模型的连续体理论,以及两个位点上的单个粒子发生现场反应并在位点间跳跃的简单模型。在慢反应极限,我们将模型的动力学投影到合适的一维反应坐标上,从而推导出准平衡有效自由能。对于弱噪声,这就能确定 MTE 的特征。与同质参考情况相比,相分离的加入可以增强或抑制这一时间。我们将讨论相分离如何影响阿利效应,包括相分离趋势使原本稳定的种群变得不稳定的情况。
期刊介绍:
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