The Statistics of Parametrized Syncmers in a Simple Mutation Process Without Spurious Matches

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• Bioinformatics frequently uses summary sketches for analyzing next-generation sequencing data.
• Most existing sketching methods lack thorough statistical understanding.
• Previous work by Blanca et al. analyzed complete k-mer sketches to estimate evolutionary distance (θ) under a simple mutation model.

Purpose of the Study:

• To extend the statistical analysis of complete sketches to parametrized syncmer sketches with downsampling.
• To develop methods for estimating evolutionary distance and sequence length using syncmer counts.
• To provide statistical guarantees and hypothesis testing capabilities for sequence analysis.

Main Methods:

• Utilized a simple mutation model (independent nucleotide mutations, no insertions/deletions).
• Applied parametrized syncmer sketches with downsampling to analyze sequences.
• Derived approximate Gaussian distributions for syncmer counts to estimate parameters.
• Developed p-value tests for sequence length comparisons based on syncmer counts.

Main Results:

• Syncmer counts alone yield approximate Gaussian distributions for estimating the point mutation parameter (θ).
• Syncmer counts also provide an approximate Gaussian distribution for estimating mutated sequence length.
• The methods allow for estimation of θ and sequence length with known sampling error.
• Results offer insights into the sampling error of the Mash containment index for syncmer counts.

Conclusions:

• Approximate Gaussian distributions enable hypothesis tests and confidence intervals for phylogenetic distance and sequence length.
• The developed methods offer a statistically sound approach for analyzing sequencing data with syncmer sketches.
• These findings are likely generalizable to other sketching methods and beneficial for read assembly and related applications.