**1. Introduction**

Flax (*Linum usitatissimum* L., 2*n* = 2*x* = 30) is a self-pollinating annual crop from the Linaceae family. It is a dual-purpose crop grown for its seed oil or stem fiber, resulting in two morphotypes: linseed and fiber. The linseed or flaxseed morphotype is rich in oil (40–50%) containing five main fatty acids: palmitic (PAL, C16:0, ~6%), stearic (STE, C18:0, ~2.5%), oleic (OLE, C18:1∆<sup>9</sup> , ~19%), linoleic (LIO, C18:2∆9, 12, ~13%), and linolenic (LIN, C18:3∆9, 12, 15, ~55%) [1,2]. Because of its high LIN content, linseed is the richest plant source of omega-3 fatty acid which is beneficial for reducing blood cholesterol levels and mitigating heart diseases in humans [3,4]. The same attributes make it ideal as industrial oil for use in paints, linoleum flooring, inks, soaps and varnishes [4].

Linseed breeding has focused on high seed yield (YLD), high oil content (OIL), and either high or low LIN content. Low LIN (2–4%) and high LIO (65–70%) lines have been developed through mutation breeding. NuLin™ 50 with 67.8% LIN (http://www.viterra.ca) and Omégalin with 65.8% (http://www.terredelin.com) are examples of high LIN linseed cultivars currently registered. Extremely low LIN lines such as LinolaTM or SolinTM improve oxidative stability, making such cultivars suitable for the fabrication of margarine [3]. Since 1910, a total of 82 flax cultivars have been released in Canada [5]. These cultivars and elite breeding lines provide diverse genetic materials for dissecting the genetic architecture of oil biosynthesis and yield related traits in linseed.

Several methods can be used to dissect the genetic architecture of crop traits. QTL or linkage mapping uses bi-parental populations to identify loci responsible for trait variation between parents based on a recombination-based genetic linkage map [6]. Bi-parental populations, such as F2, recombinant inbred line (RIL), doubled haploid (DH) and backcross (BC) populations, are the most widely used genetic resources for mapping QTL for traits of interest in self-fertilizing crops, including flax [7–12]. While bi-parental populations are easy to develop and have power for QTL detection, only the a limited number of alleles from the parental genotypes are analyzed in a single population, resulting in a narrow genetic base and low representation of allelic diversity [13]. In addition, genetic recombination is limited in these populations [14]. To increase the QTL dissection power, attempts have been made to expand the genetic diversity through other multiple-parent population types, such as nested association mapping (NAM) populations [15–17] and multi-parent advanced generation intercross (MAGIC) populations [18–25], while retaining the advantages of association mapping and bi-parental populations. However, the development of such populations requires careful planning and time. Natural populations that possess tremendous phenotypic diversity can be advantageous in genome-wide association study (GWAS) with various molecular markers in plants and animals [26–31]. Association mapping using a diverse germplasm panel overcomes the phenotypic diversity limitation of bi-parental populations, thereby increasing the QTL mapping power [32] but is impeded by low detection power of association of rare alleles. GWAS usually uses a natural population to investigate wider phenotypic variation for complex traits by taking advantage of ancient genetic recombination events in populations [33].

GWAS may be complemented by performing genome-wide selective sweep scan (GW3S) which identifies selection signatures that are beneficial for plant adaptation. A selective sweep is the reduction or elimination of variation among the nucleotides near a new beneficial mutation. Following strong positive natural selection or artificial selection during domestication or breeding, selective sweeps affect nearby linked alleles [34]. Ancient selective sweeps are relevant to natural evolution and domestication of crop species that are subjected to natural and artificial selective pressures and forced to adapt rapidly to new environments and thus drive speciation [35]. Breeding selects favorable alleles and retains them in new cultivars. These signatures of selection can be detected by a cross-population comparison approach [34]. Recent studies demonstrated that genomic regions that exhibit selection signatures are also enriched for genes associated with biologically important traits [36–40]. Thus, detection of selection signatures is emerging as an additional approach to identify and validate novel gene-trait associations [41].

Genetic regions associated with storage oil biosynthesis in flax have been studied based on QTL mapping using bi-parental populations. Several QTL responsible for oil content and fatty acid composition have been mapped in independent studies including the three populations used herein. The first population (BM) of 243 F2:6 recombinant inbred lines (RILs) from a cross between the Canadian

linseed varieties CDC Bethune and Macbeth was used for a linkage mapping study and detected three QTL each for OLE and STE, two each for LIO and IOD, and one each for PAL, LIN and OIL with several QTL co-locating at the same locus [8]. The second population (EV) was a cross between E1747 and Viking. The third population (SU) was a cross between SP2047 (a yellow-seeded SolinTM line with 2–4% LIN) and UGG5-5 (a brown-seeded flax line with 63–66% LIN) and comprised of 78 lines generated through DH method. It was used in a linkage mapping study using simple sequence repeat (SSR) markers which identified QTL for LIO, LIN and iodine value (IOD) co-locating on LG7 and LG16, and a QTL for PAL on LG9 [7]. The linkage-based studies from these populations provided numerous QTL for important traits but the QTL were generally far from the markers and poorly delimited because of the low resolution of the genetic maps [18,19,42].The three bi-parental populations were also used to construct a consensus genetic map [43], and to perform genomic selection [44] primarily using SSR markers. Because the three populations have been simultaneously phenotyped for several common agronomic and seed oil quality traits in the same environments (years/locations), we designed the present study to test the efficiency of the combined bi-parental population approach for GWAS and GW3S to detect genomic regions associated with seed yield and seed oil quality traits using genotyping by sequencing (GBS).
