TY - JOUR
T1 - The statistics of <em>k</em>-mers from a sequence undergoing a simple mutation process without spurious matches
JF - bioRxiv
DO - 10.1101/2021.01.15.426881
SP - 2021.01.15.426881
AU - Blanca, Antonio
AU - Harris, Robert S.
AU - Koslicki, David
AU - Medvedev, Paul
Y1 - 2021/01/01
UR - http://biorxiv.org/content/early/2021/02/09/2021.01.15.426881.abstract
N2 - K-mer-based methods are widely used in bioinformatics, but there are many gaps in our understanding of their statistical properties. Here, we consider the simple model where a sequence S (e.g. a genome or a read) undergoes a simple mutation process whereby each nucleotide is mutated independently with some probability r, under the assumption that there are no spurious k-mer matches. How does this process affect the k-mers of S? We derive the expectation and variance of the number of mutated k-mers and of the number of islands (a maximal interval of mutated k-mers) and oceans (a maximal interval of non-mutated k-mers). We then derive hypothesis tests and confidence intervals for r given an observed number of mutated k-mers, or, alternatively, given the Jaccard similarity (with or without minhash). We demonstrate the usefulness of our results using a few select applications: obtaining a confidence interval to supplement the Mash distance point estimate, filtering out reads during alignment by Minimap2, and rating long read alignments to a de Bruijn graph by Jabba.Competing Interest StatementThe authors have declared no competing interest.
ER -