DandD: efficient measurement of sequence growth and similarity

Genome assembly databases are growing rapidly. The sequence content in each new assembly can be largely redundant with previous ones, but this is neither conceptually nor algorithmically easy to measure. We propose new methods and a new tool called DandD that addresses the question of how much new sequence is gained when a sequence collection grows. DandD can describe how much human structural variation is being discovered in each new human genome assembly and when discoveries will level off in the future. DandD uses a measure called δ ("delta"), developed initially for data compression. Computing δ directly requires counting k-mers, but DandD can rapidly estimate it using genomic sketches. We also propose δ as an alternative to k-mer-specific cardinalities when computing the Jaccard coefficient, avoiding the pitfalls of a poor choice of k. We demonstrate the utility of DandD's functions for estimating δ, characterizing the rate of pangenome growth, and computing all-pairs similarities using k-independent Jaccard. DandD is open source software available at: https://github.com/jessicabonnie/dandd.