Complex characters of plants such as starch and sugar content of seeds, fruits, tubers and roots are controlled by multiple genetic and environmental factors. Understanding their molecular basis will facilitate diagnosis and combination of superior alleles in crop improvement programs (''precision breeding''). Association genetics based on candidate genes is one approach toward this goal. Tetraploid potato varieties and breeding clones related by descent were evaluated for 2 years for chip quality before and after cold storage, tuber starch content, yield and starch yield. Chip quality is inversely correlated with tuber sugar content. A total of 36 loci on 11 potato chromosomes were evaluated for natural DNA variation in 243 individuals. These loci included microsatellites and genes coding for enzymes that function in carbohydrate metabolism or transport (candidate loci). The markers were used to analyze population structure and were tested for association with the tuber quality traits. Highly significant and robust associations of markers with 1-4 traits were identified. Most frequent were associations with chip quality and tuber starch content. Alleles increasing tuber starch content improved chip quality and vice versa. With two exceptions, the most significant and robust associations (q \ 0.01) were observed with DNA variants in genes encoding enzymes that function in starch and sugar metabolism or transport. Comparing linkage and linkage disequilibrium between loci provided evidence for the existence of large haplotype blocks in the breeding materials analyzed. IntroductionMost characters important for crop quality show quantitative phenotypic variation, due to the fact that they are controlled by natural DNA variation at multiple loci and by environmental factors. Knowing the molecular basis of the genetic components of this variation will facilitate the selection of improved cultivars with DNA-based markers, which are diagnostic for superior alleles of the underlying genes.Communicated by J. Yu. Electronic supplementary materialThe online version of this article

Key message The number of SNPs required for QTL discovery is justified by the distance at which linkage disequilibrium has decayed. Simulations and real potato SNP data showed how to estimate and interpret LD decay. AbstractThe magnitude of linkage disequilibrium (LD) and its decay with genetic distance determine the resolution of association mapping, and are useful for assessing the desired numbers of SNPs on arrays. To study LD and LD decay in tetraploid potato, we simulated autotetraploid genotypes and used it to explore the dependence on: (1) the number of haplotypes in the population (the amount of genetic variation) and (2) the percentage of haplotype specific SNPs (hs-SNPs). Several estimators for short-range LD were explored, such as the average r 2, median r 2, and other percentiles of r 2 (80, 90, and 95 %). For LD decay, we looked at LD½,90, the distance at which the short-range LD is halved when using the 90 % percentile of r 2 at short range, as estimator for LD. Simulations showed that the performance of various estimators for LD decay strongly depended on the number of haplotypes, although the real value of LD decay was not influenced very much by this number. The estimator LD½,90 was chosen to evaluate LD decay in 537 tetraploid varieties. LD½,90 values were 1.5 Mb for varieties released before 1945 and 0.6 Mb in varieties released after 2005. LD½,90 values within three different subpopulations ranged from 0.7 to 0.9 Mb. LD½,90 was 2.5 Mb for introgressed regions, indicating large haplotype blocks. In pericentromeric heterochromatin, LD decay was negligible. This study demonstrates that several related factors influencing LD decay could be disentangled, that no universal approach can be suggested, and that the estimation of LD decay has to be performed with great care and knowledge of the sampled material.Electronic supplementary materialThe online version of this article (doi:10.1007/s00122-016-2798-8) contains supplementary material, which is available to authorized users.

To exploit the diversity in Arabidopsis thaliana, eight founder accessions were crossed to produce six recombinant inbred line (RIL) subpopulations, together called an Arabidopsis multiparent RIL (AMPRIL) population. Founders were crossed pairwise to produce four F1 hybrids. These F1s were crossed according to a diallel scheme. The resulting offspring was then selfed for three generations. The F4 generation was genotyped with SNP and microsatellite markers. Data for flowering time and leaf morphology traits were determined in the F5 generation. Quantitative trait locus (QTL) analysis for these traits was performed using especially developed mixed-model methodology, allowing tests for QTL main effects, QTL by background interactions, and QTL by QTL interactions. Because RILs were genotyped in the F4 generation and phenotyped in the F5 generation, residual heterozygosity could be used to confirm and fine-map a number of the QTLs in the selfed progeny of lines containing such heterozygosity. The AMPRIL population is an attractive resource for the study of complex traits.