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DOI10.1088/1742-5468/2013/01/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
ISSN1742-5468
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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