Asymptotic behavior of the scaled mutation rate estimators

Area of Science:

• Population genetics
• Evolutionary biology
• Genomics

Background:

• Nucleotide sequences are crucial for understanding population evolution.
• The scaled mutation rate is a key parameter in population genetics, representing new mutations per generation under the neutral Wright-Fisher model.

Purpose of the Study:

• To present and analyze various methods for estimating the scaled mutation rate.
• To compare the asymptotic behavior and distributional properties of these estimators.
• To apply and assess bias correction for the maximum likelihood estimator (MLE) using real data.

Main Methods:

• Analytical studies of estimator asymptotic behavior.
• Simulations to compare estimator distributions.
• Application of the maximum likelihood estimator (MLE) with bias correction using jackknife on real genetic data.

Main Results:

• Analytical proof of asymptotic equivalence between Waterson's estimator and the MLE with identical convergence rates to normality.
• Demonstration that the MLE exhibits a superior convergence rate compared to Waterson's estimator for parameter values greater than one.
• Identification of the reversed relationship in convergence rates when the parameter is less than one.

Conclusions:

• Waterson's estimator and the MLE are asymptotically equivalent for scaled mutation rate estimation.
• The MLE offers advantages in convergence rate depending on the parameter's value, with implications for analyzing population evolution from genetic data.