Understanding evolutionary and ecological dynamics using a continuum limit

被引:13
作者
Czuppon, Peter [1 ,2 ,3 ]
Traulsen, Arne [3 ]
机构
[1] Sorbonne Univ, INRA, Inst Ecol & Environm Sci Paris, UPEC,CNRS,IRD, Paris, France
[2] PSL Res Univ, Coll France, CNRS, Ctr Interdisciplinaire Rech Biol, Paris, France
[3] Max Planck Inst Evolutionary Biol, Dept Evolutionary Theory, Plon, Germany
关键词
continuum limit; diffusion approximation; extinction time; fixation probability; stationary distribution; QUASI-STATIONARY DISTRIBUTIONS; FIXATION; POPULATION; EXTINCTION; SELECTION; MODELS; STRATEGY; PROBABILITY; COOPERATION; STABILITY;
D O I
10.1002/ece3.7205
中图分类号
Q14 [生态学(生物生态学)];
学科分类号
071012 ; 0713 ;
摘要
Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual-based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright-Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi-stationary distribution in a finite population.
引用
收藏
页码:5857 / 5873
页数:17
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