The limits of weak selection and large population size in evolutionary game theory
The limits of weak selection and large population size in evolutionary game theory
复制标题
进化博弈论中弱选择和大群体规模的局限性
DOI：
--
复制
发表时间：
2016
影响因子：
1.9
通讯作者：
Benjamin Allen
中科院分区：
文献类型：
--
作者：
C. Sample;Benjamin Allen
进化博弈论是一种研究社会行为如何演变的数学方法。在最近的许多工作中，策略之间的进化竞争被建模为有限种群中的随机过程。在这种情况下，有两个限制在数学上是方便的，在生物学上也是相关的：弱选择和大种群规模。这些限制可以以不同的方式组合在一起，从而可能导致不同的结果。我们考虑两种排序：wn\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$Wn$\end{Document}限制，和NW\Documentclass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$NW$\end{Document}限制，顺序颠倒。NW\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$NW$\end{Documentclass[12pt]{}\usepackage{amsath}\usepackage{amssfonts}\usepackage{amssy}\usepackage{amssy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$Wn$\end{Document}限制。将这些定义应用到进化博弈论的Moran过程中，我们得到了固定概率的渐近表达式和在这些极限下成功的条件。我们发现，固定概率的渐近表达式，以及策略优先于中性突变的条件，在NW\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$NW$\end{Documentclass[12pt]{}\usepackage{amsmax}\usepackage{amsfonts}\usepackage{amssy}\usepackage{amsbsy}\usepackage{amssy}\usepackage{amsbsy}\usepackage{amsbsy}Usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$Wn$\end{Document}限制。然而，限制的顺序并不影响一种战略优先于另一种战略的条件。
Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the wN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$wN$$\end{document} limit, in which weak selection is applied before the large population limit, and the Nw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Nw$$\end{document} limit, in which the order is reversed. Formal mathematical definitions of the Nw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Nw$$\end{document} and wN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$wN$$\end{document} limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the Nw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Nw$$\end{document} and wN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$wN$$\end{document} limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.
影响因子：
2
作者：
Tarnita, Corina E.;Ohtsuki, Hisashi;Antal, Tibor;Fu, Feng;Nowak, Martin A.
通讯作者：
Nowak, Martin A.
影响因子：
2
作者：
H. Ohtsuki;P. Bordalo;M. Nowak
通讯作者：
H. Ohtsuki;P. Bordalo;M. Nowak
影响因子：
2
作者：
Traulsen, Arne;Pacheco, Jorge M.;Nowak, Martin A.
通讯作者：
Nowak, Martin A.