DipSkmer: Reference-free population genomics with diploid genome skims

Ecologists and conservation biologists rely on genetic diversity as a key essential biodiversity variable (EBV) used to track population health and dynamics, and utilize the population parameter {theta} (estimated by the average pairwise genomic distance) as a key metric of diversity. While whole-genome-sequencing (wgs) is increasingly affordable, it will be considerable time before the full diversity of life is represented by high-quality assembled genomes; even then, constant monitoring will still require repeated sampling of populations. In contrast, genome skimming (low-coverage, short-read wgs) is highly cost-effective but challenging to analyze because the coverage is too low for assembly and reliable error correction. Mature methods, such as Mash, exist for estimating pairwise genomic distances based on the Jaccard similarity of k-mer sets computed using sketching techniques. Some, such as Skmer, additionally model the impacts of low coverage. These methods have been successfully applied to assembly-free species identification and phylogenetics; however, their use in population genetics has been limited. This is because these methods implicitly treat genomes as haploid and heterozygosity confounds true estimates of genomic distance for diploid organisms. In this paper, we address this problem through a number of technical advances. First, we use coalescent theory to mathematically derive how the Jaccard index between two diploid samples changes with the scaled population size parameter ({theta}). Next, we derive an estimator that computes {theta} from the Jaccard index, in addition to several auxiliary variables, which we also estimate from the genome skims. The resulting method, DipSkmer, enables more accurate estimates of coverage, sequencing error, and pairwise nucleotide distance for diploid samples. Analyses of both simulated and empirical datasets show that for diploids and low distances (e.g.,