Genes underlying mutant phenotypes can be isolated by combining marker discovery, genetic mapping and resequencing, but a more straightforward strategy for mapping mutations would be the direct comparison of mutant and wild-type genomes. Applying such an approach, however, is hampered by the need for reference sequences and by mutational loads that confound the unambiguous identification of causal mutations. Here we introduce NIKS (needle in the k-stack), a reference-free algorithm based on comparing k-mers in whole-genome sequencing data for precise discovery of homozygous mutations. We applied NIKS to eight mutants induced in nonreference rice cultivars and to two mutants of the nonmodel species Arabis alpina. In both species, comparing pooled F 2 individuals selected for mutant phenotypes revealed small sets of mutations including the causal changes. Moreover, comparing M 3 seedlings of two allelic mutants unambiguously identified the causal gene. Thus, for any species amenable to mutagenesis, NIKS enables forward genetics without requiring segregating populations, genetic maps and reference sequences. Forward genetic screens have been of fundamental importance in elucidating biological mechanisms in model species 1 . Their success, however, has relied on the feasibility of mutant gene isolation. Identification of causal mutations typically begins with genetic mapping, followed by candidate gene sequencing and complementation studies using transformation. Advances in DNA sequencing technologies have tremendously accelerated genetic mapping by combining bulk segregant analysis, that is, pooling recombinant genomes, with whole-genome sequencing, usually referred to as mapping by sequencing 2,3 . This approach is now becoming standard for mutation mapping and identification in many model species 3-12 and has even been applied to decipher quantitative traits with complex genetic architectures 13, 14 . Recently, mutagen-induced changes have been used as novel markers, allowing mapping of mutations using isogenic mapping populations 10, 15 . Nevertheless, all mapping-by-sequencing methods rely on resequencing, a method for whole-genome reconstruction based on aligning sequences to a reference sequence. Therefore, this requirement restricts the application of the technique to species for which such a reference genome sequence is available. Many reference-sequence assembly projects are currently in progress, including ones for most of the major crop species and breeding animals. However, even with an existing reference sequence, extending mapping-by-sequencing methods beyond the sequenced reference accessions has proved technically challenging. Mutant alleles of genes that are not present in the reference sequence cannot be identified within resequencing data alone. In particular, fast-evolving genes, such as those involved in disease resistance, might not always be represented in the reference sequence 16, 17 . Alternative solutions for mapping-by-sequencing in species without reference sequences have been proposed, such as mappingby-sequencing based on reference sequences of related species or expressed sequence tag collections 11, 18 . However, all of these methods greatly rely on low sequence divergence and high levels of synteny between the mutant genome and alignment target. Recently, methods for direct genome comparison of multiple samples without a reference sequence were introduced, but none has proven to be accurate and precise enough for the identification of mutations [19] [20] [21] . NIKS is a method for reference-free genome comparison based solely on the frequencies of short subsequences within whole-genome sequencing data. It is geared toward identifying mutagen-induced, small-scale, homozygous differences between two highly related genomes, independent of their inbred or outbred background, and provides a route to identification of mutations without requiring any prior information about reference sequences or genetic maps. Principles and performance of NIKS NIKS relies on the analysis of k-mers, which are defined as subsequences of length k of a sequencing read. NIKS starts by assessing the frequency of each k-mer within the sequencing data of each sample using the k-mer-counting software Jellyfish 22 . K-mers that overlap with sequencing errors will be of low frequency, as these errors are not present in all reads from the corresponding region, and it is therefore possible to separate them from reads that are error free (Fig. 1) .
NIKS REF is designed for whole-genome sequencing protocols.
Mutation identification by direct comparison of whole-genome sequencing data from mutant and wild-type individuals using k-mers
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