Genetic diversity analysis of elite European maize (Zea mays L.) inbred lines using AFLP, SSR, and SNP markers reveals ascertainment bias for a subset of SNPs

Recent advances in high-throughput sequencing technologies have triggered a shift toward single-nucleotide polymorphism (SNP) markers. A systematic bias can be introduced if SNPs are ascertained in a small panel of genotypes and then used for characterizing a larger population (ascertainment bias). With the objective of evaluating a potential ascertainment bias of the Illumina MaizeSNP50 array with respect to elite European maize dent and flint inbred lines, we compared the genetic diversity among these materials based on 731 amplified fragment length polymorphisms (AFLPs), 186 simple sequence repeats (SSRs), 41,434 SNPs of the MaizeSNP50 array (SNP-A), and two subsets of it, i.e., 30,068 Panzea (SNP-P) and 11,366 Syngenta markers (SNP-S). We evaluated the bias effects on major allele frequency, allele number, gene diversity, modified Roger’s distance (MRD), and on molecular variance (AMOVA). We revealed ascertainment bias in SNP-A, compared to AFLPs and SSRs. It affected especially European flint lines analyzed with markers (SNP-S) specifically developed to maximize differences among North American dent germplasm. The bias affected all genetic parameters, but did not substantially alter the relative distances between inbred lines within groups. For these reasons, we conclude that the SNP markers of the MaizeSNP50 array can be employed for breeding purposes in the investigated material. However, attention should be paid in case of comparisons between genotypes belonging to different heterotic groups. In this case, it is advisable to prefer a marker subset with potentially low ascertainment bias, like in our case the SNP-P marker set.     

Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F₂ generation and subsequently among DH lines derived from the selected F₂ individual (Method 1), (2) MAS for augmented F₂ enrichment and subsequently for T among DH lines from the best carrier F₂ individual (Method 2), and (3) MAS for T among DH lines derived from the F₁ generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F₂ ( n₁^* \, n_{1}^{*} ) and DH generations (n - n₁^* ) (n - n_{1}^{*} ) for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F₂ individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F₂ individuals than DH lines ($ n_{1}^{*} :n > 0.5 $ n_{1}^{*} :n > 0.5 ), whereas under Method 2, the optimal ratio n₁^* :n n_{1}^{*} :n was close to 0.5. However, for ratios deviating moderately from the optimum, the mean [`(X)] \overline{X} of T in the finally selected DH line ( T<sub>\textDH</sub><sup>*</sup> T_{\text{DH}}^{*} ) was hardly reduced. Method 3 had always the lowest mean [`(X)] \overline{X} of T_\textDH^* T_{\text{DH}}^{*} except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean [`(X)] \overline{X} and lowest SD of T_\textDH^* T_{\text{DH}}^{*} for the finally selected DH.     

Heterosis for biomass-related traits in Arabidopsis investigated by quantitative trait loci analysis of the triple testcross design with recombinant inbred lines

Arabidopsis thaliana has emerged as a leading model species in plant genetics and functional genomics including research on the genetic causes of heterosis. We applied a triple testcross (TTC) design and a novel biometrical approach to identify and characterize quantitative trait loci (QTL) for heterosis of five biomass-related traits by (i) estimating the number, genomic positions, and genetic effects of heterotic QTL, (ii) characterizing their mode of gene action, and (iii) testing for presence of epistatic effects by a genomewide scan and marker x marker interactions. In total, 234 recombinant inbred lines (RILs) of Arabidopsis hybrid C24 x Col-0 were crossed to both parental lines and their F1 and analyzed with 110 single-nucleotide polymorphism (SNP) markers. QTL analyses were conducted using linear transformations Z1, Z2, and Z3 calculated from the adjusted entry means of TTC progenies. With Z1, we detected 12 QTL displaying augmented additive effects. With Z2, we mapped six QTL for augmented dominance effects. A one-dimensional genome scan with Z3 revealed two genomic regions with significantly negative dominance x additive epistatic effects. Two-way analyses of variance between marker pairs revealed nine digenic epistatic interactions: six reflecting dominance x dominance effects with variable sign and three reflecting additive x additive effects with positive sign. We conclude that heterosis for biomass-related traits in Arabidopsis has a polygenic basis with overdominance and/or epistasis being presumably the main types of gene action.     

Genetic basis of heterosis for growth-related traits in Arabidopsis investigated by testcross progenies of near-isogenic lines reveals a significant role of epistasis

Epistasis seems to play a significant role in the manifestation of heterosis. However, the power of detecting epistatic interactions among quantitative trait loci (QTL) in segregating populations is low. We studied heterosis in Arabidopsis thaliana hybrid C24 x Col-0 by testing near-isogenic lines (NILs) and their triple testcross (TTC) progenies. Our objectives were to (i) provide the theoretical basis for estimating different types of genetic effects with this experimental design, (ii) determine the extent of heterosis for seven growth-related traits, (iii) map the underlying QTL, and (iv) determine their gene action. Two substitution libraries, each consisting of 28 NILs and covering approximately 61 and 39% of the Arabidopsis genome, were assayed by 110 single-nucleotide polymorphism (SNP) markers. With our novel generation means approach 38 QTL were detected, many of which confirmed heterotic QTL detected previously in the same cross with TTC progenies of recombinant inbred lines. Furthermore, many of the QTL were common for different traits and in common with the 58 QTL detected by a method that compares triplets consisting of a NIL, its recurrent parent, and their F(1) cross. While the latter approach revealed mostly (75%) overdominant QTL, the former approach allowed separation of dominance and epistasis by analyzing all materials simultaneously and yielded substantial positive additive x additive effects besides directional dominance. Positive epistatic effects reduced heterosis for growth-related traits in our materials.     

Variance of the parental genome contribution to inbred lines derived from biparental crosses

The expectation of the parental genome contribution to inbred lines derived from biparental crosses or backcrosses is well known, but no theoretical results exist for its variance. Our objective was to derive the variance of the parental genome contribution to inbred lines developed by the single-seed descent or double haploid method from biparental crosses or backcrosses. We derived formulas and tabulated results for the variance of the parental genome contribution depending on the chromosome lengths and the mating scheme used for inbred line development. A normal approximation of the probability distribution function of the parental genome contribution fitted well the exact distribution obtained from computer simulations. We determined upper and lower quantiles of the parental genome contribution for model genomes of sugar beet, maize, and wheat using normal approximations. These can be employed to detect essentially derived varieties in the context of plant variety protection. Furthermore, we outlined the application of our results to predict the response to selection. Our results on the variance of the parental genome contribution can assist breeders and geneticists in the design of experiments or breeding programs by assessing the variation around the mean parental genome contribution for alternative crossing schemes.     

An incomplete enumeration algorithm for an exact test of Hardy–Weinberg proportions with multiple alleles

Testing of Hardy–Weinberg proportions (HWP) with asymptotic goodness-of-fit tests is problematic when the contingency table of observed genotype counts has sparse cells or the sample size is low, and exact procedures are to be preferred. Exact p-values can be (1) calculated via computational demanding enumeration methods or (2) approximated via simulation methods. Our objective was to develop a new algorithm for exact tests of HWP with multiple alleles on the basis of conditional probabilities of genotype arrays, which is faster than existing algorithms. We derived an algorithm for calculating the exact permutation significance value without enumerating all genotype arrays having the same allele counts as the observed one. The algorithm can be used for testing HWP by (1) summation of the conditional probabilities of occurrence of genotype arrays with smaller probability than the observed one, and (2) comparison of the sum with a nominal Type I error rate α. Application to published experimental data from seven maize populations showed that the exact test is computationally feasible and reduces the number of enumerated genotype count matrices about 30% compared with previously published algorithms.     

Recovering Power in Association Mapping Panels with Variable Levels of Linkage Disequilibrium

Association mapping has permitted the discovery of major QTL in many species. It can be applied to existing populations and, as a consequence, it is generally necessary to take into account structure and relatedness among individuals in the statistical model to control false positives. We analytically studied power in association studies by computing noncentrality parameter of the tests and its relationship with parameters characterizing diversity (genetic differentiation between groups and allele frequencies) and kinship between individuals. Investigation of three different maize diversity panels genotyped with the 50k SNPs array highlighted contrasted average power among panels and revealed gaps of power of classical mixed models in regions with high linkage disequilibrium (LD). These gaps could be related to the fact that markers are used for both testing association and estimating relatedness. We thus considered two alternative approaches to estimating the kinship matrix to recover power in regions of high LD. In the first one, we estimated the kinship with all the markers that are not located on the same chromosome than the tested SNP. In the second one, correlation between markers was taken into account to weight the contribution of each marker to the kinship. Simulations revealed that these two approaches were efficient to control false positives and were more powerful than classical models.