H. F. Utz

Effect of population size on the estimation of QTL: a test using resistance to barley stripe rust

The limited population sizes used in many quantitative trait locus (QTL) detection experiments can lead to underestimation of QTL number, overestimation of QTL effects, and failure to quantify QTL interactions. We used the barley/barley stripe rust pathosystem to evaluate the effect of population size on the estimation of QTL parameters. We generated a large (n=409) population of doubled haploid lines derived from the cross of two inbred lines, BCD47 and Baronesse. This population was evaluated for barley stripe rust severity in the Toluca Valley, Mexico, and in Washington State, USA, under field conditions. BCD47 was the principal donor of resistance QTL alleles, but the susceptible parent also contributed some resistance alleles. The major QTL, located on the long arm of chromosome 4H, close to the Mlo gene, accounted for up to 34% of the phenotypic variance. Subpopulations of different sizes were generated using three methods—resampling, selective genotyping, and selective phenotyping—to evaluate the effect of population size on the estimation of QTL parameters. In all cases, the number of QTL detected increased with population size. QTL with large effects were detected even in small populations, but QTL with small effects were detected only by increasing population size. Selective genotyping and/or selective phenotyping approaches could be effective strategies for reducing the costs associated with conducting QTL analysis in large populations. The method of choice will depend on the relative costs of genotyping versus phenotyping.

The Role of Epistasis in the Manifestation of Heterosis: A Systems-Oriented Approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive × additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive × additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.

Analysis of a triple testcross design with recombinant inbred lines reveals a significant role of epistasis in heterosis for biomass-related traits in Arabidopsis

Primary causes of heterosis are still unknown. Our goal was to investigate the extent and underlying genetic causes of heterosis for five biomass-related traits in Arabidopsis thaliana. We (i) investigated the relative contribution of dominance and epistatic effects to heterosis in the hybrid C24 × Col-0 by generation means analysis and estimates of variance components based on a triple testcross (TTC) design with recombinant inbred lines (RILs), (ii) estimated the average degree of dominance, and (iii) examined the importance of reciprocal and maternal effects in this cross. In total, 234 RILs were crossed to parental lines and their F1s. Midparent heterosis (MPH) was high for rosette diameter at 22 days after sowing (DAS) and 29 DAS, growth rate (GR), and biomass yield (BY). Using the F2-metric, directional dominance prevailed for the majority of traits studied but reciprocal and maternal effects were not significant. Additive and dominance variances were significant for all traits. Additive × additive and dominance × dominance variances were significant for all traits but GR. We conclude that dominance as well as digenic and possibly higher-order epistatic effects play an important role in heterosis for biomass-related traits. Our results encourage the use of Arabidopsis hybrid C24 × Col-0 for identification and description of quantitative trait loci (QTL) for heterosis for biomass-related traits and further genomic studies.

QTL analyses of complex traits with cross validation, bootstrapping and other biometric methods

With the development of molecular markers, dissection of complex quantitative traits by mapping the underlying genetic factors has become a major research area in plant breeding. Here, we report results from a vast QTL mapping experiment in maize with testcrosses of N= 976 F4:5 lines evaluated in E= 16 environments. Although the number of detected QTL confirmed the infinitesimal model of quantitative genetics (e.g., 30 QTL detected with LOD ≥ 2.5 for plant height, explaining p= 61% of the genetic variance), cross validation (CV) still revealed an upward bias of about 10% in p. With smaller values of N (122, 244, 488) and E (2, 4), the number of detected QTL decreased, but the estimates of p remained almost the same due to a tremendous increase in the bias. This illustrates that QTL effects obtained from smaller sample sizes are usually highly inflated, leading to an overly optimistic assessment of the prospects of MAS. Moreover, inferences about the genetic architecture (number of QTL and their effects) of complex traits cannot be achieved reliably with smaller sample sizes. Based on simulations, we conclude that CV and one method of bootstrapping (BS) performed well with regard to yielding realistic estimates of p. In addition, we briefly review progress in new biometric methods and approaches to QTL mapping in plants including Bayesian methods that show great promise to overcome the present limitations of QTL mapping.

Re-evaluation of the prospects of marker-assisted selection for improving insect resistance against Diatraea spp. in tropical maize by cross validation and independent validation

Abstract Cross validation (CV) and validation with an independent sample (IV) are new biometric approaches in QTL analysis to obtain unbiased estimates of QTL effects and the proportion of the genetic variance explained by the detected marker-QTL association (p). Our objective with these methods was to obtain a realistic picture on the prospects of marker-assisted selection (MAS) for improving the resistance of maize against the tropical stem borer species Diatraea grandiosella (SWCB) and Diatraea saccharalis (SCB). Published QTL mapping studies on leaf-damage ratings (LDR) with populations of F2:3 lines and recombinant inbred lines (RIL) from crosses CML131×CML67 and Ki3× CML139 of tropical maize inbreds were re-analyzed with CV and IV. With CV, the reduction in p for LDR compared to p obtained with the whole data set varied between 41.0 and 79.6% in the populations of F2:3 lines and between 30.1 and 65.2% in the two populations of RIL. Estimates of p for SCB LDR were similar for CV and IV. For SWCB LDR, p estimates obtained with IV were larger than those obtained with CV in CML131× CML67. The reverse was observed for Ki3×CML139. Under the assumption of identical selection intensities, and based on the re-estimates of p, MAS using only molecular marker information is less-efficient than conventional phenotypic selection (CPS). MAS combining marker and phenotypic data increases the relative efficiency by only 4% in comparison to CPS. In conclusion, MAS for improving SWCB and SCB LDR seems not-promising unless additional QTLs with proven large effects are available or the costs of marker assays are considerably reduced.

QTL mapping for European corn borer resistance ( Ostrinia nubilalis Hb.), agronomic and forage quality traits of testcross progenies in early-maturing European maize ( Zea mays L.) germplasm.

In hybrid breeding the performance of lines in hybrid combinations is more important than their performance per se. Little information is available on the correlation between individual line and testcross (TC) performances for the resistance to European corn borer (ECB, Ostrinia nubilalis Hb.) in maize (Zea mays L.). Marker assisted selection (MAS) will be successful only if quantitative trait loci (QTL) found in F2 derived lines for ECB resistance are still expressed in hybrid combinations. The objectives of our study were: (1) to identify and characterize QTL for ECB resistance as well as agronomic and forage quality traits in a population of testcrossed F2:3 families; (2) to evaluate the consistency of QTL for per se and TC performances; and (3) to determine the association between per se and TC performances of F2:3 lines for these traits. Two hundred and four F2:3 lines were derived from the cross between maize lines D06 (resistant) and D408 (susceptible). These lines were crossed to D171 and the TC progenies were evaluated for ECB resistance and agronomic performance in two locations in 2000 and 2001. Using these TC progenies, six QTL for stalk damage rating (SDR) were found. These QTL explained 27.4% of the genotypic variance in a simultaneous fit. Three QTL for SDR were detected consistently for per se and TC performance. Phenotypic and genotypic correlations were low for per se and TC performance for SDR. Correlations between SDR and quality traits were not significant. Based on these results, we conclude that MAS will not be an efficient method for improving SDR. However, new molecular tools might provide the opportunity to use QTL data as a first step to identify genes involved in ECB resistance. Efficient MAS procedures might then be based on markers designed to trace and to combine specific genes and their alleles in elite maize breeding germplasm.

Genetic Expectations of Quantitative Trait Loci Main and Interaction Effects Obtained With the Triple Testcross Design and Their Relevance for the Analysis of Heterosis

Interpretation of experimental results from quantitative trait loci (QTL) mapping studies on the predominant type of gene action can be severely affected by the choice of statistical model, experimental design, and provision of epistasis. In this study, we derive quantitative genetic expectations of (i) QTL effects obtained from one-dimensional genome scans with the triple testcross (TTC) design and (ii) pairwise interactions between marker loci using two-way analyses of variance (ANOVA) under the F2- and the F∞-metric model. The theoretical results show that genetic expectations of QTL effects estimated with the TTC design are complex, comprising both main and epistatic effects, and that genetic expectations of two-way marker interactions are not straightforward extensions of effects estimated in one-dimensional scans. We also demonstrate that the TTC design can partially overcome the limitations of the design III in separating QTL main effects and their epistatic interactions in the analysis of heterosis and that dominance × additive epistatic interactions of individual QTL with the genetic background can be estimated with a one-dimensional genome scan. Furthermore, we present genetic expectations of variance components for the analysis of TTC progeny tested in a split-plot design, assuming digenic epistasis and arbitrary linkage.

Optimum design of family structure and allocation of resources in association mapping with lines from multiple crosses

Family mapping is based on multiple segregating families and is becoming increasingly popular because of its advantages over population mapping. Athough much progress has been made recently, the optimum design and allocation of resources for family mapping remains unclear. Here, we addressed these issues using a simulation study, resample model averaging and cross-validation approaches. Our results show that in family mapping, the predictive power and the accuracy of quatitative trait loci (QTL) detection depend greatly on the population size and phenotyping intensity. With small population sizes or few test environments, QTL results become unreliable and are hampered by a large bias in the estimation of the proportion of genotypic variance explained by the detected QTL. In addition, we observed that even though good results can be achieved with low marker densities, no plateau is reached with our full marker complement. This suggests that higher quality results could be achieved with greater marker densities or sequence data, which will be available in the near future for many species.

Heterosis and gene effects of multiplicative characters: theoretical relationships and experimental results from Vicia faba L.

Theoretical results were derived to relate the heterosis and the hybrid factor (ratio of hybrid performance to parental mean) of a complex character (seed yield) with the respective parameters of component subcharacters in a multiplicative model. A multiplication factor, which is a function of differences in the parents for subcharecters, was introduced to arrive at multiplicative relationships between the parameters in the model. Under certain assumptions, gene effects of a complex multiplicative trait can be expressed in terms of gene effects for the subcharacters. Data on seed yield and its components in two crosses between Vicia faba minor and major cultivars were used as a numerical example. Theoretical and experimental results indicate that with large complementary differences for subcharacters in the parents, it is possible to find substantial heterosis in the complex character without significant heterosis in its component traits. However, a review of results from the literature shows that multiplication effects are only of minor importance in most crops. Implications for the use of multiplication effects in the breeding of hybrid, synthetic, and line cultivars are discussed.

Effect of recombination in the parent populations on the means and combining ability variances in hybrid populations of maize ( Zea mays L.).

Abstract.Recombination of selected genotypes plays a key role in plant breeding for generating new base populations. We investigated the influence of recombination in two parent populations on the means and combining ability variances of their hybrid population by (1) quantitative genetic theory and (2) experiments with maize. The two parent populations were founded by four early flint and four early dent inbred lines, respectively. Each population was studied in three generations: Syn-0, the four inbred lines themselves; Syn*-1, the six intrapool single crosses (SC); and Syn*-2, the three intrapool double crosses (DC). Four interpool hybrid populations were created: (1) all 16 SC and (2) all 36 DC were produced from generations Syn-0 and Syn*-1, respectively, (3) 168 biparental progenies (BIP) of type flint × dent (female × male), and (4) 168 BIP of type dent × flint were produced according to NC-design I with randomly sampled plants of generation Syn*-2. The half-sib and full-sib families obtained in this manner were evaluated for grain yield, dry matter concentration and plant height. According to theoretical results, differences in the population means of these hybrid populations indicate the presence of various types of epistasis. Changes in combining ability variances from SC to DC reflect different levels of parental inbreeding (F = 1 vs F = 0), whereas changes from DC to BIP only reflect the effects of recombination and are attributable to covariances between additive and dominance effects caused by linkage disequilibrium in the Syn-0 generations. The experimental results showed a significant decline in yield from DC to BIP due to a loss of gene combinations with favourable epistatic effects. Estimates of