Dawson K J
Institute of Cell, Animal and Population Biology, University of Edinburgh, King's buildings, Edinburgh, EH9 3JT, United Kingdom.
Theor Popul Biol. 1997 Oct;52(2):137-54. doi: 10.1006/tpbi.1997.1325.
Under the classical Fisher-Bulmer infinitesimal model of quantitative genetics, the within-family distribution for an additive trait with no environmental component is Gaussian with mean at the mid-parent value and a variance which is the same for all families. When an additive trait is determined by unlinked loci, the Fisher-Bulmer model can arise in the limit as the number of loci contributing to variation in the trait increases. However, a counterexample is presented where the Fisher-Bulmer model fails to arise in the infinite locus limit because there is too much linkage disequilibrium. An example is also presented where a degenerate form of the Fisher-Bulmer model arises. Under what conditions does the Fisher-Bulmer model arise in the infinite locus limit? It follows from the central limit theorem that the within-family distribution is Gaussian. But, under what conditions is the within-family distribution the same for almost all families in the population? An alternative population genetic derivation of the Fisher-Bulmer model is presented for a population at linkage equilibrium. This approach is then extended to allow many patterns of linkage disequilibrium. Diallelic models are used to illustrate the type of linkage disequilibrium allowed. The results on the limiting behaviour of population genetic models with many unlinked loci can be regarded as special cases of a more general limiting property of sequences of random variables. A possible application of this more general result to models of cultural inheritance is suggested.
在经典的定量遗传学费希尔 - 布尔默无穷小模型下，对于一个没有环境成分的加性性状，家系内分布呈高斯分布，均值为中亲值，方差对所有家系而言都相同。当一个加性性状由不连锁的基因座决定时，随着对性状变异有贡献的基因座数量增加，在极限情况下会出现费希尔 - 布尔默模型。然而，给出了一个反例，由于存在过多的连锁不平衡，在无穷基因座极限情况下费希尔 - 布尔默模型并未出现。还给出了一个出现费希尔 - 布尔默模型退化形式的例子。在什么条件下费希尔 - 布尔默模型会在无穷基因座极限情况下出现呢？根据中心极限定理，家系内分布是高斯分布。但是，在什么条件下群体中几乎所有家系的家系内分布是相同的呢？针对处于连锁平衡的群体，给出了费希尔 - 布尔默模型的另一种群体遗传学推导。然后将此方法进行扩展，以允许存在多种连锁不平衡模式。使用双等位基因模型来说明所允许的连锁不平衡类型。具有许多不连锁基因座的群体遗传模型的极限行为结果可被视为随机变量序列更一般极限性质的特殊情况。提出了这一更一般结果在文化遗传模型中的一种可能应用。
