Estimators for Substitution Rates in Genomes from Read Data

TL;DR

This work tackles estimating the substitution mutation rate $p$ between two genomes from noisy sequencing reads under an i.i.d. model. It develops two estimator families based on $k$-mer statistics: a $k=1$ estimator with theoretical concentration guarantees and a large-$k$ estimator that relies on a Wu-style simplification for scalability, both extended to sequencing reads with error rate $ s $. The paper analyzes performance via concentration bounds for the $k=1$ and reads-based estimators and validates the approaches through simulations on real and synthetic sequences, highlighting regimes where each estimator excels and how sequencing errors and coverage affect accuracy. The results offer practical pathways for alignment-free mutation-rate estimation directly from read data, with implications for comparative genomics and evolutionary studies.

Abstract

We study the problem of estimating the mutation rate between two sequences from noisy sequencing reads. Existing alignment-free methods typically assume direct access to the full sequences. We extend these methods to the sequencing framework, where only noisy reads from the sequences are observed. We use a simple model in which both mutations and sequencing errors are substitutions. We propose multiple estimators, provide theoretical guarantees for one of them, and evaluate the others through simulations.

Figures (2)

• Figure 1: Real genomic sequences
• Figure 2: Randomly generated synthetic sequences

Theorems & Definitions (2)

• Theorem 1
• proof