*3.2. Population Structure and Linkage Disequilibrium*

When the main factors accounting for population subdivision correlate with a trait under study (i.e., geographic distribution and flowering time), then marker–trait associations will undergo a more accentuated inflation of observed *p*-values as effect of the structure confounding factor [39]. In flaxseed, population structure has been assessed in varying numbers of accessions, where geographic origin and flax morphotype seemed to have been the main factors underlying population subdivisions [40–42]. In our association panel, the "red" and "blue" clusters were slightly differentiated (*FST* = 0.08), with a weak morphotypic effect on dendrogram topology, possibly due to the small number of fiber types (*n* = 33) compared to the larger number of oilseed type accessions (*n* = 153).

Linkage disequilibrium (LD) is the main factor influencing marker density requirement and mapping resolution in GWAS. Mating system and genetic diversity influence LD decay. LD decays more rapidly in outcrossing plant species than in self-pollinated plants [43] and, similarly, in wild relatives and landraces compared to modern cultivars [44]. Here, we observed a rapid LD decay for most of the chromosomes, comparable to some maize commercial elite inbred lines [45] and faster than winter-type *Brassica napus* (480 to 1283 kb, *r* <sup>2</sup> = 0.1) [46]. Therefore, the 200 flaxseed accessions of our diversity panel are expected to contain plentiful allelic diversity, as suggested by the generally short LD blocks for the 15 chromosomes, thereby assisting the search for candidate genes through efficient narrowing of the putative QTL regions.
