Asymptotic behavior of the scaled mutation rate estimators

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,...

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Bibliographic Details
Published in:Biometrical journal 2010-06, Vol.52 (3), p.400-416
Main Authors: Pinheiro, Hildete P., Kiihl, Samara F., Pinheiro, Aluísio, dos Reis, Sérgio F.
Format: Article
Language:English
Subjects:
Algorithms
Applications
Asymptotic theory
Base Sequence
Biology, psychology, social sciences
Biometrics
Convergence
Data processing
Discrete distribution
Distribution theory
DNA - genetics
Evolution
Evolution, Molecular
Exact sciences and technology
genealogy
General topics
Genetics, Population - methods
Likelihood Functions
Markov processes
Mathematics
Maximum likelihood estimate
Models, Genetic
Mutagenesis
Mutation
Mutation rates
Phylogeny
Population genetics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistical genetics
Statistics
Trees
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Summary: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.
ISSN:0323-3847
1521-4036
1521-4036
DOI:10.1002/bimj.200900014