A mathematical formalism for natural selection with arbitrary spatial and genetic structure
A mathematical formalism for natural selection with arbitrary spatial and genetic structure
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DOI：
10.1007/s00285-018-1305-z
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发表时间：
2019-03-01
影响因子：
1.9
通讯作者：
McAvoy, Alex
中科院分区：
文献类型：
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作者：
Allen, Benjamin;McAvoy, Alex
我们定义了一类代表两个等位基因之间自然选择的一般模型。人口规模和空间结构是任意的，但是固定的。遗传学可以是单倍体、二倍体或其他；生殖可以是无性的，也可以是有性的。生物事件(如出生、死亡、交配、迁徙)以任意方式取决于当前的种群状态。我们的形式主义是基于基因位点的想法。每个遗传位点都位于一个特定的基因座上，只有一个等位基因。每个个体含有与其倍性相同的数量的位置(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，其中一些位置的等位基因被其他位置的副本替换。替换事件随机地依赖于种群状态，导致了自然选择的马尔科夫链表示。在这种形式主义中，我们定义了再生值、适应度、中性漂移和注视概率，并证明了它们之间的关系。我们确定了评估哪个等位基因被选择的四个标准，并表明在低突变的限制下，这些标准是相等的。然后，我们将弱选择的方法形式化。我们的形式主义的力量通过在图上的进化博弈和在单倍体种群中的选择的应用来说明。
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.