Peischl Stephan
Department of Mathematics, University of Vienna, A-1090 Wien, Austria.
Theor Popul Biol. 2010 Aug;78(1):12-25. doi: 10.1016/j.tpb.2010.03.006. Epub 2010 Apr 2.
The maintenance of genetic variation in a spatially heterogeneous environment has been one of the main research themes in theoretical population genetics. Despite considerable progress in understanding the consequences of spatially structured environments on genetic variation, many problems remain unsolved. One of them concerns the relationship between the number of demes, the degree of dominance, and the maximum number of alleles that can be maintained by selection in a subdivided population. In this work, we study the potential of maintaining genetic variation in a two-deme model with deme-independent degree of intermediate dominance, which includes absence of G x E interaction as a special case. We present a thorough numerical analysis of a two-deme three-allele model, which allows us to identify dominance and selection patterns that harbor the potential for stable triallelic equilibria. The information gained by this approach is then used to construct an example in which existence and asymptotic stability of a fully polymorphic equilibrium can be proved analytically. Noteworthy, in this example the parameter range in which three alleles can coexist is maximized for intermediate migration rates. Our results can be interpreted in a specialist-generalist context and (among others) show when two specialists can coexist with a generalist in two demes if the degree of dominance is deme independent and intermediate. The dominance relation between the generalist allele and the specialist alleles play a decisive role. We also discuss linear selection on a quantitative trait and show that G x E interaction is not necessary for the maintenance of more than two alleles in two demes.
在空间异质环境中维持遗传变异一直是理论群体遗传学的主要研究主题之一。尽管在理解空间结构环境对遗传变异的影响方面取得了相当大的进展，但许多问题仍未解决。其中一个问题涉及亚群的数量、显性程度以及在细分群体中通过选择可以维持的等位基因的最大数量之间的关系。在这项工作中，我们研究了在具有与亚群无关的中间显性程度的双亚群模型中维持遗传变异的潜力，其中包括不存在基因与环境互作作为一种特殊情况。我们对双亚群三等位基因模型进行了全面的数值分析，这使我们能够识别出具有稳定三等位基因平衡潜力的显性和选择模式。然后，通过这种方法获得的信息被用于构建一个例子，在这个例子中可以通过解析证明完全多态平衡的存在性和渐近稳定性。值得注意的是，在这个例子中，对于中间迁移率，三个等位基因可以共存的参数范围最大。我们的结果可以在专家 - 通才的背景下进行解释，并且（除其他外）表明，如果显性程度与亚群无关且为中间程度，那么在两个亚群中两个专家何时可以与一个通才共存。通才等位基因和专家等位基因之间的显性关系起着决定性作用。我们还讨论了对数量性状的线性选择，并表明在两个亚群中维持两个以上等位基因并不一定需要基因与环境互作。
