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DOI | 10.1088/1742-5468/2013/01/P01007 |
Stochastic delocalization of finite populations | |
Geyrhofer, Lukas; Hallatschek, Oskar | |
通讯作者 | Geyrhofer, Lukas |
来源期刊 | JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
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ISSN | 1742-5468 |
出版年 | 2013 |
英文摘要 | The localization of populations of replicating bacteria, viruses or autocatalytic chemicals arises in various contexts, such as ecology, evolution, medicine or chemistry. Several deterministic mathematical models have been used to characterize the conditions under which localized states can form, and how they break down due to convective driving forces. It has been repeatedly found that populations remain localized unless the bias exceeds a critical threshold value, and that close to the transition the population is characterized by a diverging length scale. These results, however, have been obtained upon ignoring number fluctuations (’genetic drift’), which are inevitable given the discreteness of the replicating entities. Here, we study the localization/delocalization of a finite population in the presence of genetic drift. The population is modeled by a linear chain of subpopulations, or demes, which exchange migrants at a constant rate. Individuals in one particular deme, called ’oasis’, receive a growth rate benefit, and the total population is regulated to have constant size N. In this ecological setting, we find that any finite population delocalizes on sufficiently long time scales. Depending on parameters, however, populations may remain localized for a very long time. The typical waiting time to delocalization increases exponentially with both population size and distance to the critical wind speed of the deterministic approximation. We augment these simulation results by a mathematical analysis that treats the reproduction and migration of individuals as branching random walks subject to global constraints. For a particular constraint, different from a fixed population size constraint, this model yields a solvable first moment equation. We find that this solvable model approximates very well the fixed population size model for large populations, but starts to deviate as population sizes are small. Nevertheless, the qualitative behavior of the fixed population size model is properly reproduced. In particular, the analytical approach allows us to map out a phase diagram of an order parameter, characterizing the degree of localization, as a function of the two driving parameters, inverse population size and wind speed. Our results may be used to extend the analysis of delocalization transitions to different settings, such as the viral quasi-species scenario. |
英文关键词 | models for evolution (theory) mutational and evolutionary processes (theory) population dynamics (theory) |
类型 | Article |
语种 | 英语 |
国家 | Germany |
收录类别 | SCI-E |
WOS记录号 | WOS:000315410500008 |
WOS关键词 | FISHER EQUATION ; EVOLUTION ; EXTINCTION ; MELTDOWN ; GENETICS |
WOS类目 | Mechanics ; Physics, Mathematical |
WOS研究方向 | Mechanics ; Physics |
资源类型 | 期刊论文 |
条目标识符 | http://119.78.100.177/qdio/handle/2XILL650/178687 |
作者单位 | Max Planck Inst Dynam & Self Org, Biophys & Evolutionary Dynam Grp, D-37077 Gottingen, Germany |
推荐引用方式 GB/T 7714 | Geyrhofer, Lukas,Hallatschek, Oskar. Stochastic delocalization of finite populations[J],2013. |
APA | Geyrhofer, Lukas,&Hallatschek, Oskar.(2013).Stochastic delocalization of finite populations.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT. |
MLA | Geyrhofer, Lukas,et al."Stochastic delocalization of finite populations".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2013). |
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