The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population

Appropriate selection of parents for the development of mapping populations is pivotal to maximizing the power of quantitative trait loci detection. Trait genotypic variation within a family is indicative of the family's informativeness for genetic studies. Accurate prediction of the most useful parental combinations within a species would help guide quantitative genetics studies. We tested the reliability of genotypic and phenotypic distance estimators between pairs of maize inbred lines to predict genotypic variation for quantitative traits within families derived from biparental crosses. We developed 25 families composed of ~200 random recombinant inbred lines each from crosses between a common reference parent inbred, B73, and 25 diverse maize inbreds. Parents and families were evaluated for 19 quantitative traits across up to 11 environments. Genetic distances (GDs) among parents were estimated with 44 simple sequence repeat and 2303 single-nucleotide polymorphism markers. GDs among parents had no predictive value for progeny variation, which is most likely due to the choice of neutral markers. In contrast, we observed for about half of the traits measured a positive correlation between phenotypic parental distances and within-family genetic variance estimates. Consequently, the choice of promising segregating populations can be based on selecting phenotypically diverse parents. These results are congruent with models of genetic architecture that posit numerous genes affecting quantitative traits, each segregating for allelic series, with dispersal of allelic effects across diverse genetic material. This architecture, common to many quantitative traits in maize, limits the predictive value of parental genotypic or phenotypic values on progeny variance.     

Genomic mating in outbred species: predicting cross usefulness with additive and total genetic covariance matrices

Diverse crops are both outbred and clonally propagated. Breeders typically use truncation selection of parents and invest significant time, land, and money evaluating the progeny of crosses to find exceptional genotypes. We developed and tested genomic mate selection criteria suitable for organisms of arbitrary homozygosity level where the full-sibling progeny are of direct interest as future parents and/or cultivars. We extended cross variance and covariance variance prediction to include dominance effects and predicted the multivariate selection index genetic variance of crosses based on haplotypes of proposed parents, marker effects, and recombination frequencies. We combined the predicted mean and variance into usefulness criteria for parent and variety development. We present an empirical study of cassava (Manihot esculenta), a staple tropical root crop. We assessed the potential to predict the multivariate genetic distribution (means, variances, and trait covariances) of 462 cassava families in terms of additive and total value using cross-validation. Most variance (89%) and covariance (70%) prediction accuracy estimates were greater than zero. The usefulness of crosses was accurately predicted with good correspondence between the predicted and the actual mean performance of family members breeders selected for advancement as new parents and candidate varieties. We also used a directional dominance model to quantify significant inbreeding depression for most traits. We predicted 47,083 possible crosses of 306 parents and contrasted them to those previously tested to show how mate selection can reveal the new potential within the germplasm. We enable breeders to consider the potential of crosses to produce future parents (progeny with top breeding values) and varieties (progeny with top own performance).     

High Resolution of Quantitative Traits into Multiple Loci via Interval Mapping

A very general method is described for multiple linear regression of a quantitative phenotype on genotype [putative quantitative trait loci (QTLs) and markers] in segregating generations obtained from line crosses. The method exploits two features, (a) the use of additional parental and F(1) data, which fixes the joint QTL effects and the environmental error, and (b) the use of markers as cofactors, which reduces the genetic background noise. As a result, a significant increase of QTL detection power is achieved in comparison with conventional QTL mapping. The core of the method is the completion of any missing genotypic (QTL and marker) observations, which is embedded in a general and simple expectation maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. The method is described in detail for the analysis of an F(2) generation. Because of the generality of the approach, it is easily applicable to other generations, such as backcross progenies and recombinant inbred lines. An example is presented in which multiple QTLs for plant height in tomato are mapped in an F(2) progeny, using additional data from the parents and their F(1) progeny.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

Quantitative trait loci affecting life span in replicated populations of Drosophila melanogaster. I. Composite interval mapping

Composite interval mapping was used to identify life-span QTL in F2 progeny of three crosses between different pairs of inbred lines. Each inbred line was derived from a different outbred population that had undergone long-term selection for either long or short life span. Microsatellite loci were used as genetic markers, and confidence intervals for QTL location were estimated by bootstrapping. A minimum of 10 QTL were detected, nine of which were located on the two major autosomes. Five QTL were present in at least two crosses and five were present in both sexes. Observation of the same QTL in more than one cross was consistent with the hypothesis that genetic variation for life span is maintained by balancing selection. For all QTL except one, allelic effects were in the direction predicted on the basis of outbred source population. Alleles that conferred longer life were always at least partially dominant.     

Application of a new IBD-based QTL mapping method to common wheat breeding population: analysis of kernel hardness and dough strength

Mapping quantitative trait loci (QTL) in plants is usually conducted using a population derived from a cross between two inbred lines. The power of such QTL detection and the estimation of the effects highly depend on the choice of the two parental lines. Thus, the QTL found represent only a small part of the genetic architecture and can be of limited economical interest in marker-assisted selection. On the other hand, applied breeding programmes evaluate large numbers of progeny derived from multiple-related crosses for a wide range of agronomic traits. It is assumed that the development of statistical techniques to deal with pedigrees in existing plant populations would increase the relevance and cost effectiveness of QTL mapping in a breeding context. In this study, we applied a two-step IBD-based-variance component method to a real wheat breeding population, composed of 374 F₆ lines derived from 80 different parents. Two bread wheat quality related traits were analysed by the method. Results obtained show very close agreement with major genes and QTL already known for those two traits. With this new QTL mapping strategy, inferences about QTL can be drawn across the breeding programme rather than being limited to the sample of progeny from a single cross and thus the use of the detected QTL in assisting breeding would be facilitated.     

Modeling additive and non-additive effects in a hybrid population using genome-wide genotyping: prediction accuracy implications

Hybrids are broadly used in plant breeding and accurate estimation of variance components is crucial for optimizing genetic gain. Genome-wide information may be used to explore models designed to assess the extent of additive and non-additive variance and test their prediction accuracy for the genomic selection. Ten linear mixed models, involving pedigree- and marker-based relationship matrices among parents, were developed to estimate additive (A), dominance (D) and epistatic (AA, AD and DD) effects. Five complementary models, involving the gametic phase to estimate marker-based relationships among hybrid progenies, were developed to assess the same effects. The models were compared using tree height and 3303 single-nucleotide polymorphism markers from 1130 cloned individuals obtained via controlled crosses of 13 Eucalyptus urophylla females with 9 Eucalyptus grandis males. Akaike information criterion (AIC), variance ratios, asymptotic correlation matrices of estimates, goodness-of-fit, prediction accuracy and mean square error (MSE) were used for the comparisons. The variance components and variance ratios differed according to the model. Models with a parent marker-based relationship matrix performed better than those that were pedigree-based, that is, an absence of singularities, lower AIC, higher goodness-of-fit and accuracy and smaller MSE. However, AD and DD variances were estimated with high s.es. Using the same criteria, progeny gametic phase-based models performed better in fitting the observations and predicting genetic values. However, DD variance could not be separated from the dominance variance and null estimates were obtained for AA and AD effects. This study highlighted the advantages of progeny models using genome-wide information.     

Estimation of quantitative trait locus allele frequency via a modified granddaughter design

A method is described on the basis of a modification of the granddaughter design to obtain estimates of quantitative trait loci (QTL) allele frequencies in dairy cattle populations and to determine QTL genotypes for both homozygous and heterozygous grandsires. The method is based on determining the QTL allele passed from grandsires to their maternal granddaughters using haplotypes consisting of several closely linked genetic markers. This method was applied to simulated data of 10 grandsire families, each with 500 granddaughters, and a QTL with a substitution effect of 0.4 phenotypic standard deviations and to actual data for a previously analyzed QTL in the center of chromosome 6, with substitution effect of 1 phenotypic standard deviation on protein percentage. In the simulated data the standard error for the estimated QTL substitution effect with four closely linked multiallelic markers was only 7% greater than the expected standard error with completely correct identification of QTL allele origin. The method estimated the population QTL allelic frequency as 0.64 +/- 0.07, compared to the simulated value of 0.7. In the actual data, the frequency of the allele that increases protein percentage was estimated as 0.63 +/- 0.06. In both data sets the hypothesis of equal allelic frequencies was rejected at P < 0.05.     

A simulation study on the accuracy of position and effect estimates of linked QTL and their asymptotic standard deviations using multiple interval mapping in an F2 scheme

Approaches like multiple interval mapping using a multiple-QTL model for simultaneously mapping QTL can aid the identification of multiple QTL, improve the precision of estimating QTL positions and effects, and are able to identify patterns and individual elements of QTL epistasis. Because of the statistical problems in analytically deriving the standard errors and the distributional form of the estimates and because the use of resampling techniques is not feasible for several linked QTL, there is the need to perform large-scale simulation studies in order to evaluate the accuracy of multiple interval mapping for linked QTL and to assess confidence intervals based on the standard statistical theory. From our simulation study it can be concluded that in comparison with a monogenetic background a reliable and accurate estimation of QTL positions and QTL effects of multiple QTL in a linkage group requires much more information from the data. The reduction of the marker interval size from 10 cM to 5 cM led to a higher power in QTL detection and to a remarkable improvement of the QTL position as well as the QTL effect estimates. This is different from the findings for (single) interval mapping. The empirical standard deviations of the genetic effect estimates were generally large and they were the largest for the epistatic effects. These of the dominance effects were larger than those of the additive effects. The asymptotic standard deviation of the position estimates was not a good criterion for the accuracy of the position estimates and confidence intervals based on the standard statistical theory had a clearly smaller empirical coverage probability as compared to the nominal probability. Furthermore the asymptotic standard deviation of the additive, dominance and epistatic effects did not reflect the empirical standard deviations of the estimates very well, when the relative QTL variance was smaller/equal to 0.5. The implications of the above findings are discussed.     

Statistical issues in the analysis of quantitative traits in combined crosses.

We consider some practical statistical issues in QTL analysis where several crosses originate in multiple inbred parents. Our results show that ignoring background polygenic variation in different crosses may lead to biased interval mapping estimates of QTL effects or loss of efficiency. Threshold and power approximations are derived by extending earlier results based on the Ornstein-Uhlenbeck diffusion process. The results are useful in the design and analysis of genome screen experiments. Several common designs are evaluated in terms of their power to detect QTL.     

Molecular marker-based prediction of hybrid performance in maize using unbalanced data from multiple experiments with factorial crosses

In hybrid breeding, the prediction of hybrid performance (HP) is extremely important as it is difficult to evaluate inbred lines in numerous cross combinations. Recent developments such as doubled haploid production and molecular marker technologies have enhanced the prospects of marker-based HP prediction to accelerate the breeding process. Our objectives were to (1) predict HP using a combined analysis of hybrids and parental lines from a breeding program, (2) evaluate the use of molecular markers in addition to phenotypic and pedigree data, (3) evaluate the combination of line per se data with marker-based estimates, (4) study the effect of the number of tested parents, and (5) assess the advantage of haplotype blocks. An unbalanced dataset of 400 hybrids from 9 factorial crosses tested in different experiments and data of 79 inbred parents were subjected to combined analyses with a mixed linear model. Marker data of the inbreds were obtained with 20 AFLP primer–enzyme combinations. Cross-validation was used to assess the performance prediction of hybrids of which no or only one parental line was testcross evaluated. For HP prediction, the highest proportion of explained variance (R ²), 46% for grain yield (GY) and 70% for grain dry matter content (GDMC), was obtained from line per se best linear unbiased prediction (BLUP) estimates plus marker effects associated with mid-parent heterosis (TEAM-LM). Our study demonstrated that HP was efficiently predicted using molecular markers even for GY when testcross data of both parents are not available. This can help in improving greatly the efficiency of commercial hybrid breeding programs.     

EXPERIMENTAL STUDIES OF PONDEROSA PINE. II. QUANTITATIVE GENETICS OF MORPHOLOGICAL TRAITS

We studied fourteen morphological attributes of 511 seedling stage progeny involving crosses between Pinus ponderosa ponderosa parents as well as intervarietal crosses of P. p. ponderosa × P. p. scopulorum. Intravarietal progeny were distinctly differentiated genetically from intervarietal sibships in seven of the fourteen characters examined. The patterns of differentiation observed strongly suggest a syndrome of selective responses to increased water stress in the progeny with a scopulorum parent and for comparatively more rapid, columnar growth in the progeny of the intravariety crosses which involved only P. p. ponderosa parents. These differences are consistent with known ecological distinctions between the habitats of the two varieties. Narrow-sense heritability estimates, obtained from half-sib progeny analysis, indicated that considerable levels of additive genetic variance remain present in several traits. We could detect no relationship between the amount of additive genetic variance present for a particular character and its presumed relevance to fitness.     

A simple regression method for mapping quantitative trait loci in line crosses using flanking markers

The use of flanking marker methods has proved to be a powerful tool for the mapping of quantitative trait loci (QTL) in the segregating generations derived from crosses between inbred lines. Methods to analyse these data, based on maximum-likelihood, have been developed and provide good estimates of QTL effects in some situations. Maximum-likelihood methods are, however, relatively complex and can be computationally slow. In this paper we develop methods for mapping QTL based on multiple regression which can be applied using any general statistical package. We use the example of mapping in an F(2) population and show that these regression methods produce very similar results to those obtained using maximum likelihood. The relative simplicity of the regression methods means that models with more than a single QTL can be explored and we give examples of two lined loci and of two interacting loci. Other models, for example with more than two QTL, with environmental fixed effects, with between family variance or for threshold traits, could be fitted in a similar way. The ease, speed of application and generality of regression methods for flanking marker analysis, and the good estimates they obtain, suggest that they should provide the method of choice for the analysis of QTL mapping data from inbred line crosses.     

Mapping quantitative trait loci using naturally occurring genetic variance among commercial inbred lines of maize (Zea mays L.)

Many commercial inbred lines are available in crops. A large amount of genetic variation is preserved among these lines. The genealogical history of the inbred lines is usually well documented. However, quantitative trait loci (QTL) responsible for the genetic variances among the lines are largely unexplored due to lack of statistical methods. In this study, we show that the pedigree information of the lines along with the trait values and marker information can be used to map QTL without the need of further crossing experiments. We develop a Monte Carlo method to estimate locus-specific identity-by-descent (IBD) matrices. These IBD matrices are further incorporated into a mixed-model equation for variance component analysis. QTL variance is estimated and tested at every putative position of the genome. The actual QTL are detected by scanning the entire genome. Applying this new method to a well-documented pedigree of maize (Zea mays L.) that consists of 404 inbred lines, we mapped eight QTL for the maize male flowering trait, growing degree day heat units to pollen shedding (GDUSHD). These detected QTL contributed >80% of the variance observed among the inbred lines. The QTL were then used to evaluate all the inbred lines using the best linear unbiased prediction (BLUP) technique. Superior lines were selected according to the estimated QTL allelic values, a technique called marker-assisted selection (MAS). The MAS procedure implemented via BLUP may be routinely used by breeders to select superior lines and line combinations for development of new cultivars.     

Selection and subsequent analysis of sib pair data for QTL detection.

Haseman and Elston (1972) developed a robust regression method for the detection of linkage between a marker and a quantitative trait locus (QTL) using sib pair data. The principle underlying this method is that the difference in phenotypes between pairs of sibs becomes larger as they share a decreasing number of alleles at a particular QTL identical by descent (IBD) from their parents. In this case, phenotypically very different sibs will also on average share a proportion of alleles IBD at any marker linked to the QTL that is lower than the expected value of 0.5. Thus, the deviation of the proportion of marker alleles IBD from the expected value in pairs of sibs selected to be phenotypically different (i.e. discordant) can provide a test for the presence of a QTL. A simple regression method for QTL detection in sib pairs selected for high phenotypic differences is presented here. The power of the analytical method was found to be greater than the power obtained using the standard analysis when samples of sib pairs with high phenotypic differences were used. However, the use of discordant sib pairs was found to be less powerful for QTL detection than alternative selective genotyping schemes based on the phenotypic values of the sibs except with intense selection, when its advantage was only marginal. The most effective selection scheme overall was the use of sib pairs from entire families selected on the basis of high within-family variance for the trait in question. There is little effect of selection on QTL position estimates, which are in good agreement with the simulated values. However, QTL variance estimates are biased to a greater or lesser degree, depending on the selection method.     

Use of molecular markers for estimating breeding parameters: a case study in a Pinus pinaster Ait. progeny trial

The management of a genetic improvement program is based on the knowledge of the genetic parameters and their relationships to determine the genetic gains. Knowledge of the coefficient of coancestry (θ) is a requirement for efficient progeny testing scheme and for estimating additive variance components for any quantitative trait. When using open-pollinated families, most authors assume that the seedlings are related as half-sibs, but this is not always true. Our aim was to estimate a mean value of the coancestry coefficient of the families present in a maritime pine Pinus pinaster Ait. (maritime or cluster pine) progeny trial originating from seed collected in a clonal seed orchard and to study how deviations from the standard assumption of θ = 0.125 affect heritability estimations. Five highly polymorphic microsatellite markers were scored in 125 offspring from a subsample of five families from the progeny trial. The mean value of the coancestry coefficient of the families present in this progeny trial was 0.130. Differences between the unadjusted and adjusted heritability estimates were more pronounced in wood density (0.609 and 0.586, respectively) than in diameter (0.166 and 0.154, respectively). We conclude that in the trial, the associated error in heritability estimates due to the inclusion of full-sibs, when assuming a standard coefficient of relationship among open-pollinated sibs of 0.250, was low and that this result is robust with respect to the number of families sampled, given unbiased estimates of average relationship among offspring within sib families.     

Mapping epistatic quantitative trait loci with one-dimensional genome searches

The discovery of epistatically interacting QTL is hampered by the intractability and low power to detect QTL in multidimensional genome searches. We describe a new method that maps epistatic QTL by identifying loci of high QTL by genetic background interaction. This approach allows detection of QTL involved not only in pairwise but also higher-order interaction, and does so with one-dimensional genome searches. The approach requires large populations derived from multiple related inbred-line crosses as is more typically available for plants. Using maximum likelihood, the method contrasts models in which QTL allelic values are either nested within, or fixed over, populations. We apply the method to simulated doubled-haploid populations derived from a diallel among three inbred parents and illustrate the power of the method to detect QTL of different effect size and different levels of QTL by genetic background interaction. Further, we show how the method can be used in conjunction with standard two-locus QTL detection models that use two-dimensional genome searches and find that the method may double the power to detect first-order epistasis.     

Quantitative trait loci (QTL) detection in multicross inbred designs: recovering QTL identical-by-descent status information from marker data

Mapping quantitative trait loci in plants is usually conducted using a population derived from a cross between two inbred lines. The power of such QTL detection and the parameter estimates depend largely on the choice of the two parental lines. Thus, the QTL detected in such populations represent only a small part of the genetic architecture of the trait. In addition, the effects of only two alleles are characterized, which is of limited interest to the breeder, while common pedigree breeding material remains unexploited for QTL mapping. In this study, we extend QTL mapping methodology to a generalized framework, based on a two-step IBD variance component approach, applicable to any type of breeding population obtained from inbred parents. We then investigate with simulated data mimicking conventional breeding programs the influence of different estimates of the IBD values on the power of QTL detection. The proposed method would provide an alternative to the development of specifically designed recombinant populations, by utilizing the genetic variation actually managed by plant breeders. The use of these detected QTL in assisting breeding would thus be facilitated.     

Mapping quantitative trait loci with dominant markers in four-way crosses

 A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families. Received: 16 June 1998 / Accepted: 29 September 1998     

Identification of candidate markers associated with agronomic traits in rice using discriminant analysis

Plant genetic mapping strategies routinely utilize marker genotype frequencies obtained from progeny of controlled crosses to declare presence of a quantitative trait locus (QTL) on previously constructed linkage maps. We have evaluated the potential of discriminant analysis (DA), a multivariate statistical procedure, to detect candidate markers associated with agronomic traits among inbred lines of rice (Oryza sativa L.). A total of 218 lines originating from the US and Asia were planted in field plots near Alvin, Texas, in 1996 and 1997. Agronomic data were collected for 12 economically important traits, and DNA profiles of each inbred line were produced using 60 SSR and 114 RFLP markers. Model-based methods revealed population structure among the lines. Marker alleles associated with all traits were identified by DA at high levels of correct percent classification within subpopulations and across all lines. Associated marker alleles pointed to the same and different regions on the rice genetic map when compared to previous QTL mapping experiments. Results from this study suggest that candidate markers associated with agronomic traits can be readily detected among inbred lines of rice using DA combined with other methods described in this report.N. Zhang and Y. Xu contributed equally to work and considered as first authors.Approved for publication by the Director of the Louisiana Agricultural Experiment Station as paper no. 04-14-0335.