The Statistics of k-mers from a Sequence Undergoing a Simple Mutation Process Without Spurious Matches

Area of Science:

• Bioinformatics
• Computational Biology
• Statistical Genetics

Background:

• K-mer based methods are crucial in bioinformatics but lack thorough statistical understanding.
• Understanding the impact of sequence mutations on k-mer properties is essential for accurate data analysis.

Purpose of the Study:

• To statistically model the effects of independent nucleotide mutations on k-mer content.
• To derive methods for estimating mutation rates and sequence similarity.
• To provide practical applications in genome analysis and read alignment.

Main Methods:

• Developed a mathematical model for sequence mutation and its effect on k-mers.
• Derived expectation and variance for mutated k-mers, islands, and oceans.
• Formulated hypothesis tests and confidence intervals for mutation rates (r) using k-mer counts and Jaccard similarity.

Main Results:

• Provided theoretical framework for understanding k-mer changes under mutation.
• Derived novel statistical tests and confidence intervals for mutation rate estimation.
• Demonstrated practical utility in applications like Mash distance, read filtering, and alignment quality assessment.

Conclusions:

• The derived statistical methods enhance the reliability of k-mer based analyses in bioinformatics.
• This work offers a robust framework for quantifying sequence divergence and mutation.
• The applications highlight the practical impact of these statistical insights for genomic data interpretation.