# Efficient Estimation of Mutation Rates during Individual Development by Minimization of Chi-Square

## TL;DR

This paper introduces a computationally efficient method to estimate mutation rates during cell divisions in Drosophila melanogaster development.

## Contribution

A new chi-square minimization approach is proposed as a computationally efficient alternative to maximum likelihood estimation for mutation rate inference.

## Key findings

- The chi-square minimization method is asymptotically consistent with maximum likelihood estimation.
- The new method eliminates computational bottlenecks in mutation rate inference.
- Reanalysis of Drosophila mutation data using the new method produced similar mutation rate estimates.

## Abstract

Mutation primarily occurs when cells divide and it is highly desirable to have knowledge of the rate of mutations for each of the cell divisions during individual development. Recently, recessive lethal or nearly lethal mutations which were observed in a large mutation accumulation experiment using Drosophila melanogaster suggested that mutation rates vary significantly during the germline development of male Drosophila melanogaster. The analysis of the data was based on a combination of the maximum likelihood framework with numerical assistance from a newly developed coalescent algorithm. Although powerful, the likelihood based framework is computationally highly demanding which limited the scope of the inference. This paper presents a new estimation approach by minimizing chi-square statistics which is asymptotically consistent with the maximum likelihood method. When only at most one mutation in a family is considered the minimization of chi-square is simplified to a constrained weighted minimum least square method which can be solved easily by optimization theory. The new methods effectively eliminates the computational bottleneck of the likelihood. Reanalysis of the published Drosophila melanogaster mutation data results in similar estimates of mutation rates. The new method is also expected to be applicable to the analysis of mutation data generated by next-generation sequencing technology.