Laurence Moreau

More on the efficiency of marker-assisted selection

Abstract Computer simulations were used to study the efficiency of marker-assisted selection (MAS) based on an index combining the phenotypic value and the molecular score of individuals. The molecular score is computed from the effects attributed to markers by multiple regression of phenotype on marker genotype. The results show that in the first generation the ratio RE of the expected efficiency of MAS over the expected efficiency of purely phenotypic selection generally increases when considering: (1) larger population sizes, (2) lower heritability values of the trait, and (3) a higher type-I error risk of the regression. This is consistent with previously published results. However, at low heritabilities our results point out that response to MAS is more variable than response to phenotypic selection. Hence, when the difference of genetic gains is considered instead of their ratio, RE, the heritability values corresponding to maximal advantage of using MAS rather than phenotypic selection are still low, but higher than predicted based on RE. The study over several successive generations of the rate of fixation of QTLs shows that the higher efficiency of MAS on QTLs with large effects in early generations is balanced by a higher rate of fixation of unfavourable alleles at QTLs with small effects in later generations. This explains why MAS may become less efficient than phenotypic selection in the long term. MAS efficiency therefore depends on the genetic determinism of the trait. Finally, we investigate a modified MAS method involving an alternation of selection on markers with and without phenotypic evaluation. Our results indicate that such a selection method could at low cost, provide an important increase in the genetic gain per unit of time in practical breeding programs.

Maximizing the Reliability of Genomic Selection by Optimizing the Calibration Set of Reference Individuals: Comparison of Methods in Two Diverse Groups of Maize Inbreds ( Zea mays L.)

Genomic selection refers to the use of genotypic information for predicting breeding values of selection candidates. A prediction formula is calibrated with the genotypes and phenotypes of reference individuals constituting the calibration set. The size and the composition of this set are essential parameters affecting the prediction reliabilities. The objective of this study was to maximize reliabilities by optimizing the calibration set. Different criteria based on the diversity or on the prediction error variance (PEV) derived from the realized additive relationship matrix–best linear unbiased predictions model (RA–BLUP) were used to select the reference individuals. For the latter, we considered the mean of the PEV of the contrasts between each selection candidate and the mean of the population (PEVmean) and the mean of the expected reliabilities of the same contrasts (CDmean). These criteria were tested with phenotypic data collected on two diversity panels of maize (Zea mays L.) genotyped with a 50k SNPs array. In the two panels, samples chosen based on CDmean gave higher reliabilities than random samples for various calibration set sizes. CDmean also appeared superior to PEVmean, which can be explained by the fact that it takes into account the reduction of variance due to the relatedness between individuals. Selected samples were close to optimality for a wide range of trait heritabilities, which suggests that the strategy presented here can efficiently sample subsets in panels of inbred lines. A script to optimize reference samples based on CDmean is available on request.

Usefulness of Multiparental Populations of Maize (Zea mays L.) for Genome-Based Prediction

The efficiency of marker-assisted prediction of phenotypes has been studied intensively for different types of plant breeding populations. However, one remaining question is how to incorporate and counterbalance information from biparental and multiparental populations into model training for genome-wide prediction. To address this question, we evaluated testcross performance of 1652 doubled-haploid maize (Zea mays L.) lines that were genotyped with 56,110 single nucleotide polymorphism markers and phenotyped for five agronomic traits in four to six European environments. The lines are arranged in two diverse half-sib panels representing two major European heterotic germplasm pools. The data set contains 10 related biparental dent families and 11 related biparental flint families generated from crosses of maize lines important for European maize breeding. With this new data set we analyzed genome-based best linear unbiased prediction in different validation schemes and compositions of estimation and test sets. Further, we theoretically and empirically investigated marker linkage phases across multiparental populations. In general, predictive abilities similar to or higher than those within biparental families could be achieved by combining several half-sib families in the estimation set. For the majority of families, 375 half-sib lines in the estimation set were sufficient to reach the same predictive performance of biomass yield as an estimation set of 50 full-sib lines. In contrast, prediction across heterotic pools was not possible for most cases. Our findings are important for experimental design in genome-based prediction as they provide guidelines for the genetic structure and required sample size of data sets used for model training.

Marker-assisted selection with spatial analysis of unreplicated field trials

Abstract Many studies have shown that molecular markers can improve the efficiency of the selection of quantitative traits in plant breeding provided that large population sizes are used. As a way to limit experimental costs it appears that the use of unreplicated trials may be more valuable than the use of replicated plots in one trial. In this particular context of unreplicated large trials, spatial heterogeneity within the field may reduce the efficiency of the selection. The problem of controlling spatial heterogeneity was seldom considered in the case of marker-assisted selection (MAS). Here, we propose an integrated method to predict genetic values considering simultaneously marker information and possible spatial heterogeneity. This method was applied to a population of 300 F3 lines of maize evaluated in 11 unreplicated trials for grain yield. We show that when spatial field heterogeneity is considered through appropriate statistical models the accuracy of genetic value predictions is improved and the same genetic gain can be achieved with a reduced number of trials.

QTLs and candidate genes for desiccation and abscisic acid content in maize kernels

BackgroundKernel moisture at harvest is an important trait since a low value is required to prevent unexpected early germination and ensure seed preservation. It is also well known that early germination occurs in viviparous mutants, which are impaired in abscisic acid (ABA) biosynthesis. To provide some insight into the genetic determinism of kernel desiccation in maize, quantitative trait loci (QTLs) were detected for traits related to kernel moisture and ABA content in both embryo and endosperm during kernel desiccation. In parallel, the expression and mapping of genes involved in kernel desiccation and ABA biosynthesis, were examined to detect candidate genes.ResultsThe use of an intermated recombinant inbred line population allowed for precise QTL mapping. For 29 traits examined in an unreplicated time course trial of days after pollination, a total of 78 QTLs were detected, 43 being related to kernel desiccation, 15 to kernel weight and 20 to ABA content. Multi QTL models explained 35 to 50% of the phenotypic variation for traits related to water status, indicating a large genetic control amenable to breeding. Ten of the 20 loci controlling ABA content colocated with previously detected QTLs controlling water status and ABA content in water stressed leaves. Mapping of candidate genes associated with kernel desiccation and ABA biosynthesis revealed several colocations between genes with putative functions and QTLs. Parallel investigation via RT-PCR experiments showed that the expression patterns of the ABA-responsive Rab17 and Rab28 genes as well as the late embryogenesis abundant Emb5 and aquaporin genes were related to desiccation rate and parental allele effect. Database searches led to the identification and mapping of two zeaxanthin epoxidase (ZEP) and five novel 9-cis-epoxycarotenoid dioxygenase (NCED) related genes, both gene families being involved in ABA biosynthesis. The expression of these genes appeared independent in the embryo and endosperm and not correlated with ABA content in either tissue.ConclusionsA high resolution QTL map for kernel desiccation and ABA content in embryo and endosperm showed several precise colocations between desiccation and ABA traits. Five new members of the maize NCED gene family and another maize ZEP gene were identified and mapped. Among all the identified candidates, aquaporins and members of the Responsive to ABA gene family appeared better candidates than NCEDs and ZEPs.

Linkage disequilibrium with linkage analysis of multiline crosses reveals different multiallelic QTL for hybrid performance in the flint and dent heterotic groups of maize.

Multiparental designs combined with dense genotyping of parents have been proposed as a way to increase the diversity and resolution of quantitative trait loci (QTL) mapping studies, using methods combining linkage disequilibrium information with linkage analysis (LDLA). Two new nested association mapping designs adapted to European conditions were derived from the complementary dent and flint heterotic groups of maize (Zea mays L.). Ten biparental dent families (N = 841) and 11 biparental flint families (N = 811) were genotyped with 56,110 single nucleotide polymorphism markers and evaluated as test crosses with the central line of the reciprocal design for biomass yield, plant height, and precocity. Alleles at candidate QTL were defined as (i) parental alleles, (ii) haplotypic identity by descent, and (iii) single-marker groupings. Between five and 16 QTL were detected depending on the model, trait, and genetic group considered. In the flint design, a major QTL (R2 = 27%) with pleiotropic effects was detected on chromosome 10, whereas other QTL displayed milder effects (R2 < 10%). On average, the LDLA models detected more QTL but generally explained lower percentages of variance, consistent with the fact that most QTL display complex allelic series. Only 15% of the QTL were common to the two designs. A joint analysis of the two designs detected between 15 and 21 QTL for the five traits. Of these, between 27 for silking date and 41% for tasseling date were significant in both groups. Favorable allelic effects detected in both groups open perspectives for improving biomass production.

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.

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.

Optimal selection on two quantitative trait loci with linkage

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.

Clusthaplo: a plug-in for MCQTL to enhance QTL detection using ancestral alleles in multi-cross design

AbstractKey messageWe enhance power and accuracy of QTL mapping in multiple related families, by clustering the founders of the families on their local genomic similarity.AbstractMCQTL is a linkage mapping software application that allows the joint QTL mapping of multiple related families. In its current implementation, QTLs are modeled with one or two parameters for each parent that is a founder of the multi-cross design. The higher the number of parents, the higher the number of model parameters which can impact the power and the accuracy of the mapping. We propose to make use of the availability of denser and denser genotyping information on the founders to lessen the number of MCQTL parameters and thus boost the QTL discovery. We developed clusthaplo, an R package (http://cran.r-project.org/web/packages/clusthaplo/index.html), which aims to cluster haplotypes using a genomic similarity that reflects the probability of sharing the same ancestral allele. Computed in a sliding window along the genome and followed by a clustering method, the genomic similarity allows the local clustering of the parent haplotypes. Our assumption is that the haplotypes belonging to the same class transmit the same ancestral allele. So their putative QTL allelic effects can be modeled with the same parameter, leading to a parsimonious model, that is plugged in MCQTL. Intensive simulations using three maize data sets showed the significant gain in power and in accuracy of the QTL mapping with the ancestral allele model compared to the classical MCQTL model. MCQTL_LD (clusthaplo outputs plug in MCQTL) is a versatile and powerful tool for QTL mapping in multiple related families that makes use of linkage and linkage disequilibrium (web site http://carlit.toulouse.inra.fr/MCQTL/).