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-scaled mutation parameter θ 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 across time and space. 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. Among other limitations, these methods implicitly treat genomes as haploid, and heterozygosity confounds estimates of genomic distance for diploid organisms. In this paper, we address this problem through several technical advances. First, we use coalescent theory to mathematically derive how the Jaccard index between the k-mer sets of two diploid samples changes with θ under a neutral Kingman's coalescent model. Next, we model the impact of coverage and sequencing error to derive an estimate of θ 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 θ for diploid samples. Analyses of both simulated and empirical datasets show that for diploids and low distances (e.g., < 2%), DipSkmer's estimate outperforms existing alignment-free methods such as Mash and Skmer, and closely approximates ANGSD, a reference and alignment-based tool.