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A mathematical formalism for natural selection with arbitrary spatial and genetic structure

机译：采用任意空间和遗传结构的自然选择数学形式主义

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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.
机译：我们定义了代表两位等位基因之间的自然选择的一般模型。人口规模和空间结构是任意的，而是固定的。遗传学可以是单倍体，二倍体或其他方式;复制可以是无性的或性的。生物事件（例如，死亡，死亡，交配，分散）取决于当前人口州的任意时尚。我们的形式主义是基于遗传网站的想法。每个遗传部位都存在于特定的轨迹并容纳单个等位基因。每个人包含许多等于其倍性的网站（一个用于单倍体，两倍用于二倍体等）。通过替换事件发生选择，其中一些站点中的等位基因被其他网站的副本所取代。替代事件随机依赖于人口状态，导致自然选择的马尔可夫链表示。在这种形式主义中，我们定义生殖价值，健身，中性漂移和固定概率，并证明它们之间的关系。我们确定四个评价哪种标准，并表明这些等位基因在低突变的极限中变得等同。然后，我们正式化选择弱的方法。我们的形式主义的力量用应用于图形的进化游戏并在单层脂素种群中选择。

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