Chevalet Claude, Nikolic Natacha
Laboratoire de Génétique cellulaire, UMR 444 INRA/ENVT, Centre de Recherche INRA de Toulouse, BP52627, 31326 Castanet Tolosan cedex, France.
Theor Popul Biol. 2010 May;77(3):152-63. doi: 10.1016/j.tpb.2010.01.001. Epub 2010 Jan 18.
We investigate the effects of past changes of the effective population size on the present allelic diversity at a microsatellite marker locus. We first derive the analytical expression of the generating function of the joint probabilities of the time to the Most Recent Common Ancestor for a pair of alleles and of their distance (the difference in allele size). We give analytical solutions in the case of constant population size and the geometrical mutation model. Otherwise, numerical inversion allows the distributions to be calculated in general cases. The effects of population expansion or decrease and the possibility to detect an ancient bottleneck are discussed. The method is extended to samples of three and four alleles, which allows investigating the covariance structure of the frequencies f(k) of pairs of alleles with a size difference of k motifs, and suggesting some approaches to the estimation of past demography.
我们研究了有效种群大小过去的变化对微卫星标记位点当前等位基因多样性的影响。我们首先推导了一对等位基因到最近共同祖先的时间及其距离（等位基因大小差异）的联合概率生成函数的解析表达式。我们给出了恒定种群大小和几何突变模型情况下的解析解。否则，数值反演可在一般情况下计算分布。讨论了种群扩张或减少的影响以及检测古代瓶颈的可能性。该方法扩展到三个和四个等位基因的样本，这使得能够研究大小相差k个基序的等位基因对频率f(k)的协方差结构，并提出一些估计过去种群统计学的方法。
