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Statistical Properties of the Site-Frequency Spectrum Associated with Λ-Coalescents

机译:与Λ关联的站点频率频谱的统计特性

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摘要

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.
机译:与Λ关联的站点频谱的统计特性是我们的研究对象。特别是,我们推导了光谱的期望值,方差和协方差的递归,扩展了经典金曼合并的早期结果。估计某些Λ联盟引入的联盟参数以获取对于完全似然法而言过大的数据集。我们获得的期望值的递归可用于查找最适合所观察频谱的参数值。预期值还用于估计在给定数量的叶子(DNA序列)的分支上发生(衍生)突变的可能性,从而使我们能够应用拟似然推断来估计与Λ关联的某些子类相关的合并参数。在模拟和真实mtDNA数据集上研究了拟饵似然方法的特性,该数据集用于大西洋大西洋鳕鱼(Gadus morhua)。我们对Λ-coalescent的两个子类的结果表明,即使对于中等大小(可能是几百个)的样本量,也可以区分这些子类与Kingman联合,以及Λ-子类。

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