Bürger Reinhard
Department of Mathematics, University of Vienna, Austria.
J Math Biol. 2005 Apr;50(4):355-96. doi: 10.1007/s00285-004-0294-2. Epub 2004 Dec 20.
The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.
推导了一个加性、双等位基因多基因座定量性状模型在频率和密度依赖选择下的平衡结构。该性状处于稳定选择之下，并介导种内竞争，例如由资源利用差异引起的竞争。假设稳定选择较弱，但竞争强度相对于它可以是任意的。密度依赖是由种群调节引起的，种群调节可能是非常一般的类型。基因座的数量和效应是任意的，并且稳定选择不一定关于表型值范围对称。如果总体选择较弱，作者所知的所有先前研究的连续资源种内竞争模型都简化为本模型的一个特殊情况。因此，在这种情况下，我们的结果可作为所有这些模型的近似值应用。我们的核心结果是根据所有参数对平衡和稳定性结构进行（近乎）完整的刻画。它是在唯一的假设下推导出来的，即相对于重组而言选择足够弱以至于可以忽略连锁不平衡。特别地，找到了关于竞争强度相对于稳定选择的必要和充分条件，这些条件确保了多基因座多态性的维持和间断选择的发生。在这种情况下，得到了平衡时多态基因座数量、等位基因频率、遗传方差和间断选择强度的显式公式。对于两个基因座，通过解析方法研究连锁效应；对于多个基因座，则通过数值方法进行研究。
