Waxman D, Peck J R
Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Brighton, UK.
Theor Popul Biol. 2006 Jun;69(4):409-18. doi: 10.1016/j.tpb.2006.01.004. Epub 2006 Mar 10.
We consider a large population of asexual organisms characterised by a number of quantitative traits that are subject to stabilising selection. Mutation is taken to act pleiotropically, with every mutation generally changing all of the traits under selection. We focus on the equilibrium distribution of the population, where mutation and selection are in balance. It has been previously established that the equilibrium distribution of genotypic effects may be anomalous, as it may contain a singular spike--a Dirac delta function--corresponding to a non-zero proportion of the population having exactly optimal genotypic values. In the present work, we present exact results for the case where three traits are under selection. These results give the equilibrium genetic variance of the population, and the proportion of the population that have the optimal genotype. This is achieved for two different spherically symmetric distributions of mutant effects. Additionally, a simple and robust numerical approach is also presented that allows the treatment of some other mutation distributions, where there are an arbitrary number of selected traits.
我们考虑大量无性生物群体，其具有多个受稳定选择作用的数量性状。假定突变具有多效性，每个突变通常会改变所有受选择的性状。我们关注群体的平衡分布，此时突变和选择处于平衡状态。先前已经确定，基因型效应的平衡分布可能是异常的，因为它可能包含一个奇异尖峰——狄拉克δ函数——对应于具有恰好最优基因型值的非零比例群体。在本工作中，我们给出了三个性状受选择情况下的精确结果。这些结果给出了群体的平衡遗传方差以及具有最优基因型的群体比例。这是针对突变效应的两种不同球对称分布实现的。此外，还提出了一种简单且稳健的数值方法，该方法允许处理存在任意数量选择性状的其他一些突变分布。
