How to make a kin selection model when marginal fitness is non-linear?
How to make a kin selection model when marginal fitness is non-linear?
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当边际适应度是非线性时，如何建立亲缘选择模型？
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Vicente
中科院分区：
文献类型：
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作者：
R. Schonmann;R. Boyd;R. Vicente
我们观察到，当适应度w是连续参与者的表型y的非线性函数并且其社会环境中的平均表型z要求w(y，z)是可微的(作为两个变量的函数，即联合在y和z中)时，建立亲子选择模型的Taylor-Frank方法。这意味着即使w(y，z)在全局上是非线性的，但在局部上它一定是接近线性的，这意味着它的图形一定被平面很好地逼近。当两个以上的个体相互作用时，只有当参与者的边际适应度是其社会环境中共享其表型的个体比例的线性函数时，这一假设才被满足。这一假设有时不适用于生物学上重要的适应度函数，例如在微生物数据和重复n人游戏理论中。在这些情况下，不能使用泰勒-弗兰克方法，而必须用一种更一般的直接适应度形式来取代它，以决定社会突变等位基因何时可以入侵单态种群。
We observe that the Taylor-Frank method for making kin selection models when fitness w is a nonlinear function of a continuous actor’s phenotype y and the average phenotype z in its social environment requires w(y, z) to be differentiable (as a function of two variables, i.e., jointly in y and z). This means that even if w(y, z) is non-linear globally, locally it must be close to linear, meaning that its graph must be well approximated by a plane. When more than two individuals interact, this assumption is only satisfied when the marginal fitness of the actor is a linear function of the fraction of individuals in its social environment that share its phenotype. This assumption sometimes fails for biologically important fitness functions, for instance in microbial data and the theory of repeated n-person games. In these cases, the Taylor-Frank methodology cannot be used, and a more general form of direct fitness must replace it, to decide when a social mutant allele can invade a monomorphic population.