Coverage statistics for sequence census methods

TL;DR

This paper extends the classic Lander-Waterman model to include fragment length distributions, modeling coverage as a Poisson process, and introduces methods to detect coverage aberrations in high-throughput sequencing data.

Contribution

It provides a new theoretical framework for modeling sequencing coverage considering fragment length variability and introduces a novel approach for visualizing sequencing data.

Findings

Coverage modeled as a 2D Poisson process regardless of fragment length distribution.

Coverage function's jump skeleton forms Galton-Watson trees with computable parameters.

Provides a null model for detecting deviations in high-throughput sequencing coverage.

Abstract

Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce the notion of the shape of a coverage function, which can be used to detect abberations in coverage. The probability theory underlying these problems is essential for constructing models of current high-throughput sequencing experiments, where both sample preparation protocols and sequencing technology particulars can affect fragment length distributions. Results: We show that regardless of fragment length distribution and under the mild assumption that fragment start sites are Poisson distributed, the fragments produced in a sequencing experiment can be viewed as resulting from a two-dimensional spatial Poisson process. We then study the jump skeleton of the the coverage function, and show that the induced trees are Galton-Watson trees whose parameters can be computed. Conclusions: Our results extend standard analyses of shotgun sequencing that focus on coverage statistics at individual sites, and provide a null model for detecting deviations from random coverage in high-throughput sequence census based experiments. By focusing on fragments, we are also led to a new approach for visualizing sequencing data that should be of independent interest.