具有任意空间和遗传结构的natural selection的数学形式
A mathematical formalism for natural selection with arbitrary spatial and genetic structure
摘要：
我们定义了一个一般类的模型代表两个等位基因之间的自然选择。种群规模和空间结构是任意的，但却是固定的。遗传学可以是单倍体、二倍体或其他;生殖可以是无性或有性的。生物事件（例如~出生、死亡、交配、扩散）以任意的方式取决于当前的人口状况。我们的形式主义是基于遗传位点的概念。每个基因位点位于特定的基因座上，并容纳单个等位基因。每个个体含有与其倍性相等的位点数（一个用于单倍体，两个用于二倍体，等等）。选择通过替换事件发生，其中一些位点中的等位基因被其他位点的拷贝替换。替换事件随机地依赖于种群状态，导致自然选择的马尔可夫链表示。在这种形式主义，我们定义生殖值，健身，中性漂移，固定概率，并证明它们之间的关系。我们确定了四个标准，用于评估等位基因的选择，并表明这些成为等价的低突变的限制。然后，我们形式化弱选择方法。我们的形式主义的力量说明与应用程序的进化游戏的图形和选择在一个haplodiploid人口。
英文摘要：
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g.~births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). Selection occurs via replacement events, in which alleles in some sites are replaced by copies of others. Replacement events depend stochastically on the population state, leading to a Markov chain representation of natural selection. Within this formalism, we define reproductive value, fitness, neutral drift, and fixation probability, and prove relationships among them. We identify four criteria for evaluating which allele is selected and show that these become equivalent in the limit of low mutation. We then formalize the method of weak selection. The power of our formalism is illustrated with applications to evolutionary games on graphs and to selection in a haplodiploid population.
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