The Differential Geometry of Population Genetics and Evolutionary Games
The Differential Geometry of Population Genetics and Evolutionary Games
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群体遗传学和进化博弈的微分几何
DOI：
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发表时间：
1990
期刊：
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通讯作者：
E. Akin
中科院分区：
文献类型：
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作者：
E. Akin
通过Shahshahani和Conley引入的黎曼度量，微分几何中的一些基本思想在数学生物学中被证明是广泛有用的。数学是不是很深，但它是不熟悉的许多，所以我们开始的调查元素的线性代数的欧几里德向量空间和微积分的黎曼流形。然后，我们将Shahshahani度量应用于群体遗传学，推导出两个位点，两个等位基因模型中循环的发生。然后我们转向进化博弈，并将ESS条件与其他稳定性概念进行比较。
Via the Riemannian metric introduced by Shahshahani and Conley, some elementary ideas from differential geometry have proved broadly useful in mathematical biology. The mathematics is not very deep but it is unfamiliar to many, so we begin with a survey of the elements of linear algebra on Euclidean vector spaces and of calculus on Riemannian manifolds. We then apply the Shahshahani metric to population genetics, deriving the occurrence of cycling in the two locus, two allele model. Then we turn to evolutionary games and compare the ESS condition with other notions of stability.