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The wide array of currently available genomes displays a wonderful diversity in size, composition, and structure and is quickly expanding thanks to several global biodiversity genomics initiatives. However, sequencing of genomes, even with the latest technologies, can still be challenging for both technical (e.g., small physical size, contaminated samples, or access to appropriate sequencing platforms) and biological reasons (e.g., germline-restricted DNA, variable ploidy levels, sex chromosomes, or very large genomes). In recent years,k-mer-based techniques have become popular to overcome some of these challenges. They are based on the simple process of dividing the analyzed sequences (e.g., raw reads or genomes) into a set of subsequences of lengthk, calledk-mers, and then analyzing the frequency or sequences of thosek-mers. Analyses based onk-mers allow for a rapid and intuitive assessment of complex sequencing data sets. Here, we provide a comprehensive review to the theoretical properties and practical applications ofk-mers in biodiversity genomics with a special focus on genome modeling. 

Haplodiploidy and paternal genome elimination (HD/PGE) are common in invertebrates, having evolved at least two dozen times, all from male heterogamety (i.e., systems with X chromosomes). However, why X chromosomes are important for the evolution of HD/PGE remains debated. The Haploid Viability Hypothesis posits that X-linked genes promote the evolution of male haploidy by facilitating purging recessive deleterious mutations. The Intragenomic Conflict Hypothesis holds that conflict between genes drives genetic system turnover; under this model, X-linked genes could promote the evolution of male haploidy due to conflicts with autosomes over sex ratios and genetic transmission. We studied lineages where we can distinguish these hypotheses: species with germline PGE that retain an XX/X0 sex determination system (gPGE+X). Because evolving PGE in these cases involves changes in transmission without increases in male hemizygosity, a high degree of X linkage in these systems is predicted by the Intragenomic Conflict Hypothesis but not the Haploid Viability Hypothesis. To quantify the degree of X linkage, we sequenced and compared 7 gPGE+X species’ genomes with 11 related species with typical XX/XY or XX/X0 genetic systems, representing three transitions to gPGE. We find highly increased X linkage in both modern and ancestral genomes of gPGE+X species compared to non-gPGE relatives and recover a significant positive correlation between percent X linkage and the evolution of gPGE. These empirical results substantiate longstanding proposals for a role for intragenomic conflict in the evolution of genetic systems such as HD/PGE.