Pinheiro Hildete P, Kiihl Samara F, Pinheiro Aluísio, dos Reis Sérgio F
Department of Statistics, University of Campinas, IMECC, CEP, SP, Brazil.
Biom J. 2010 Jun;52(3):400-16. doi: 10.1002/bimj.200900014.
Important aspects of population evolution have been investigated using nucleotide sequences. Under the neutral Wright-Fisher model, the scaled mutation rate represents twice the average number of new mutations per generations and it is one of the key parameters in population genetics. In this study, we present various methods of estimation of this parameter, analytical studies of their asymptotic behavior as well as comparisons of the distribution's behavior of these estimators through simulations. As knowledge of the genealogy is needed to estimate the maximum likelihood estimator (MLE), an application with real data is also presented, using jackknife to correct the bias of the MLE, which can be generated by the estimation of the tree. We proved analytically that the Waterson's estimator and the MLE are asymptotically equivalent with the same rate of convergence to normality. Furthermore, we showed that the MLE has a better rate of convergence than Waterson's estimator for values of the parameter greater than one and this relationship is reversed when the parameter is less than one.
人们已经利用核苷酸序列对种群进化的重要方面进行了研究。在中性的赖特 - 费希尔模型下，标度突变率代表每代新突变平均数量的两倍，它是群体遗传学中的关键参数之一。在本研究中，我们提出了估计该参数的各种方法，对其渐近行为进行了分析研究，并通过模拟比较了这些估计量的分布行为。由于估计最大似然估计量（MLE）需要系谱知识，因此还给出了一个实际数据的应用，使用刀切法来校正MLE的偏差，该偏差可能由树的估计产生。我们通过分析证明，沃特森估计量和MLE渐近等价，具有相同的正态收敛速率。此外，我们表明，对于大于1的参数值，MLE的收敛速率比沃特森估计量更好，而当参数小于1时，这种关系则相反。
