Coverage statistics for sequence census methods

Under the mild assumptions that fragment start sites are Poisson distributed and successive fragment lengths are independent and identically distributed, we observe that, regardless of fragment length distribution, the fragments produced in a sequencing experiment can be viewed as resulting from a two-dimensional spatial Poisson process. We then study the successive jumps of the coverage function, and show that they can be encoded as a random tree that is approximately a Galton-Watson tree with generation-dependent geometric offspring distributions whose parameters can be computed.We 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. Our approach leads to explicit determinations of the null distributions of certain test statistics, while for others it greatly simplifies the approximation of their null distributions by simulation. Our focus on fragments also leads to a new approach to visualizing sequencing data that is of independent interest.The classic "Lander-Waterman model" [1] provides statistical estimates for the read depth in a whole genome shotgun (WGS) sequencing experiment via the Poisson approximation to the Binomial distribution. Although originally intended for estimating the redundancy when mapping by fingerprinting random clones, the Lander-Waterman model has served as an essential tool for estimating sequencing requirements for modern WGS experiments [2]. Further-more, although it makes a number of simplifying assumptions (e.g. fixed fragment length and uniform fragment selection) that are violated in actual experiments, extensions and generalizations [3-9] have continued to be developed and applied in a variety of settings.The advent of "high-throughput sequencing", which refers to massively parallel sequencing technologies has greatly increased the scope and applicability of