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More recently, ( Earle et al., 2016 ) proposed a method for mapping associations to lineages when associations can not be accurately mapped to loci and ( Lees et al., 2016 ) showed that use of variable length k -mers leads to an increase in power.

The reliance on prior sequencing of a reference genome limits the scope of association studies, and also precludes mapping associations outside of the reference.

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We present an alignment free method for association studies of categorical phenotypes based on counting k -mers in whole-genome sequencing reads, testing for associations directly between k -mers and the trait of interest, and local assembly of the statistically significant k -mers to identify sequence differences.

An analysis of the 1000 genomes data show that sequences identified by our method largely agree with results obtained using the standard approach.

However, unlike standard GWAS, our method identifies associations with structural variations and sites not present in the reference genome.

We also demonstrate that population stratification can be inferred from k -mers.

Finally, application to an E.coli dataset on ampicillin resistance validates the approach.

Individuals are genotyped at a set of known SNP locations using a SNP array.

Then each SNP is tested for statistically significant association with the phenotype.

In recent years thousands of genome-wide association studies have been performed and regions associated with traits and diseases have been located.

First, designing SNP arrays requires knowledge about the genome of the organism and where the SNPs are located in the genome.

This makes it hard to apply to study organisms other than human.

Even the human reference genome was shown to be incomplete ( Altemose et al., 2014 ) and association mapping to regions not in the reference is difficult.

Second, structural variations such as insertion-deletions (indels) and copy number variations are usually ignored in these studies.

Despite the many GWA studies that have been performed a significant amount of heritability is yet to be explained.

This is known as the missing heritability problem ( Zuk et al., 2012 ).

Third, the phenotype might be caused by rare variants which are not on the SNP chip.

In last two cases, follow up work is required to find the causal variant even if association is detected in the GWAS.

As sequencing gets cheaper association mapping using next generation sequencing is becoming feasible.

The current approach to doing this is to map all the reads to a reference genome followed by variant calling.

But this again requires a reference genome and it may induce biases in variant calling and regions not in the reference genome will not be included in the study.

Moreover, sequencing errors make genotype calling difficult when sequencing depth is low ( Nielsen et al., 2012 ) and in repetitive regions.

Methods have been proposed to do population genetics analyses that avoid the genotype calling step ( Fumagalli et al., 2013, 2014 ) but these methods still require reads to be aligned to a reference genome.

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