Journal of Mathematical Biology

, Volume 67, Issue 5, pp 1141-1161

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Coverage theories for metagenomic DNA sequencing based on a generalization of Stevens’ theorem

  • Michael C. WendlAffiliated withThe Genome Institute, Washington UniversityDepartment of Genetics, Washington UniversityDepartment of Mathematics, Washington University Email author 
  • , Karthik KotaAffiliated withThe Genome Institute, Washington University
  • , George M. WeinstockAffiliated withThe Genome Institute, Washington UniversityDepartment of Genetics, Washington University
  • , Makedonka MitrevaAffiliated withThe Genome Institute, Washington UniversityDepartment of Genetics, Washington University


Metagenomic project design has relied variously upon speculation, semi-empirical and ad hoc heuristic models, and elementary extensions of single-sample Lander–Waterman expectation theory, all of which are demonstrably inadequate. Here, we propose an approach based upon a generalization of Stevens’ Theorem for randomly covering a domain. We extend this result to account for the presence of multiple species, from which are derived useful probabilities for fully recovering a particular target microbe of interest and for average contig length. These show improved specificities compared to older measures and recommend deeper data generation than the levels chosen by some early studies, supporting the view that poor assemblies were due at least somewhat to insufficient data. We assess predictions empirically by generating roughly 4.5 Gb of sequence from a twelve member bacterial community, comparing coverage for two particular members, Selenomonas artemidis and Enterococcus faecium, which are the least (\(\sim \)3 %) and most (\(\sim \)12 %) abundant species, respectively. Agreement is reasonable, with differences likely attributable to coverage biases. We show that, in some cases, bias is simple in the sense that a small reduction in read length to simulate less efficient covering brings data and theory into essentially complete accord. Finally, we describe two applications of the theory. One plots coverage probability over the relevant parameter space, constructing essentially a “metagenomic design map” to enable straightforward analysis and design of future projects. The other gives an overview of the data requirements for various types of sequencing milestones, including a desired number of contact reads and contig length, for detection of a rare viral species.


DNA sequencing Coverage Microbiome Metagenomics

Mathematics Subject Classification (2000)

05A10 60D05 62K05 92B99