Optimizing the allocation of resources for genomic selection in one breeding cycle

Key message

We developed a universally applicable planning tool for optimizing the allocation of resources for one cycle of genomic selection in a biparental population. The framework combines selection theory with constraint numerical optimization and considers genotype? ×? environment interactions.

Abstract

Genomic selection (GS) is increasingly implemented in plant breeding programs to increase selection gain but little is known how to optimally allocate the resources under a given budget. We investigated this problem with model calculations by combining quantitative genetic selection theory with constraint numerical optimization. We assumed one selection cycle where both the training and prediction sets comprised double haploid (DH) lines from the same biparental population. Grain yield for testcrosses of maize DH lines was used as a model trait but all parameters can be adjusted in a freely available software implementation. An extension of the expected selection accuracy given by Daetwyler et al. (2008) was developed to correctly balance between the number of environments for phenotyping the training set and its population size in the presence of genotype?×?environment interactions. Under small budget, genotyping costs mainly determine whether GS is superior over phenotypic selection. With increasing budget, flexibility in resource allocation increases greatly but selection gain leveled off quickly requiring balancing the number of populations with the budget spent for each population. The use of an index combining phenotypic and GS predicted values in the training set was especially beneficial under limited resources and large genotype × environment interactions. Once a sufficiently high selection accuracy is achieved in the prediction set, further selection gain can be achieved most efficiently by massively expanding its size. Thus, with increasing budget, reducing the costs for producing a DH line becomes increasingly crucial for successfully exploiting the benefits of GS.     

High-density linkage mapping of yield components and epistatic interactions in maize with doubled haploid lines from four crosses

Grain yield (GY) is a genetically complex and physiologically multiplicative trait which can be decomposed into the components kernel number (KN) and 100-kernel weight (HKW). Genetic analysis of these less complex yield component traits may give insights into the genetic architecture and predictive ability of complex traits. Here, we investigated how the incorporation of component traits and epistasis in quantitative trait locus (QTL) mapping approaches influences the accuracy of GY prediction. High-density genetic maps with 7,000–10,000 polymorphic single nucleotide polymorphisms were constructed for four biparental populations. The populations comprised between 99 and 227 doubled haploid maize lines which were phenotyped in field trials in two environments. Heritability was highest for HKW (88–89 %), intermediate for KN (72–80 %), and lowest for GY (64–83 %). Mapped QTL explained in total 21–55 %, 22–67 %, and 24–75 % of the genotypic variance for GY, KN, and HKW, respectively. Support intervals of QTL were short, indicating that QTL were located with high precision. Co-located QTLs with same parental origin of favorable alleles were detected within populations for different traits and between populations for the same traits. Using GY predictions based on the detected QTL, prediction accuracies (r) determined by cross validation ranged from 0.18 to 0.52. Epistatic models did not outperform the corresponding additive models. In conclusion, models based on QTL positions of component traits support the identification of favorable alleles for multiplicative traits and provide a basis to select superior inbred lines by marker-assisted breeding.     

Extent and genome-wide distribution of linkage disequilibrium in commercial maize germplasm

Association mapping is based on linkage disequilibrium (LD) resulting from historical recombinations and helps understanding the genetic basis of complex traits. Many factors affect LD and, therefore, it must be determined empirically in the germplasm under investigation to examine the prospects of successful genome-wide association mapping. The objectives of our study were to (1) examine the extent of LD with simple sequence repeat (SSR) and single nucleotide polymorphism (SNP) markers in 1,537 commercial maize inbred lines belonging to four heterotic pools, (2) compare the LD patterns determined by these two marker types, (3) evaluate the number of SNP markers needed to perform genome-wide association analyses, and (4) investigate temporal trends of LD. Mean values of the squared correlation coefficient ( $ \bar{R} $ ) were almost identical for unlinked, linked, and adjacent SSR marker pairs. In contrast, $ \bar{R} $ values were lowest for the unlinked SNP loci and highest for the SNPs within amplicons. LD decay varied across the different heterotic pools and the individual chromosomes. The SSR markers employed in the present study are not adequate for association analysis, because of insufficient marker density for the germplasm evaluated. Based on the decay of LD in the various heterotic pools, we would need between 4,000 and 65,000 SNP markers to detect with a reasonable power associations with rather large quantitative trait loci (QTL). A much higher marker density is required to identify QTL with smaller effects. However, not only the total number of markers but also their distribution among and along the chromosomes are primordial for undertaking powerful association analyses.     

Genomic prediction of dichotomous traits with Bayesian logistic models

Bayesian methods are a popular choice for genomic prediction of genotypic values. The methodology is well established for traits with approximately Gaussian phenotypic distribution. However, numerous important traits are of dichotomous nature and the phenotypic counts observed follow a Binomial distribution. The standard Gaussian generalized linear models (GLM) are not statistically valid for this type of data. Therefore, we implemented Binomial GLM with logit link function for the BayesB and Bayesian GBLUP genomic prediction methods. We compared these models with their standard Gaussian counterparts using two experimental data sets from plant breeding, one on female fertility in wheat and one on haploid induction in maize, as well as a simulated data set. With the aid of the simulated data referring to a bi-parental population of doubled haploid lines, we further investigated the influence of training set size (N), number of independent Bernoulli trials for trait evaluation (n _i ) and genetic architecture of the trait on genomic prediction accuracies and abilities in general and on the relative performance of our models. For BayesB, we in addition implemented finite mixture Binomial GLM to account for overdispersion. We found that prediction accuracies increased with increasing N and n _i . For the simulated and experimental data sets, we found Binomial GLM to be superior to Gaussian models for small n _i , but that for large n _i Gaussian models might be used as ad hoc approximations. We further show with simulated and real data sets that accounting for overdispersion in Binomial data can markedly increase the prediction accuracy.     

Comparison of mixed-model approaches for association mapping

Association-mapping methods promise to overcome the limitations of linkage-mapping methods. The main objectives of this study were to (i) evaluate various methods for association mapping in the autogamous species wheat using an empirical data set, (ii) determine a marker-based kinship matrix using a restricted maximum-likelihood (REML) estimate of the probability of two alleles at the same locus being identical in state but not identical by descent, and (iii) compare the results of association-mapping approaches based on adjusted entry means (two-step approaches) with the results of approaches in which the phenotypic data analysis and the association analysis were performed in one step (one-step approaches). On the basis of the phenotypic and genotypic data of 303 soft winter wheat (Triticum aestivum L.) inbreds, various association-mapping methods were evaluated. Spearman's rank correlation between P-values calculated on the basis of one- and two-stage association-mapping methods ranged from 0.63 to 0.93. The mixed-model association-mapping approaches using a kinship matrix estimated by REML are more appropriate for association mapping than the recently proposed QK method with respect to (i) the adherence to the nominal alpha-level and (ii) the adjusted power for detection of quantitative trait loci. Furthermore, we showed that our data set could be analyzed by using two-step approaches of the proposed association-mapping method without substantially increasing the empirical type I error rate in comparison to the corresponding one-step approaches.     

The length of the intact donor chromosome segment around a target gene in marker-assisted backcrossing

Recurrent backcrossing is an established procedure to transfer target genes from a donor into the genetic background of a recipient genotype. By assessing the parental origin of alleles at markers flanking the target locus one can select individuals with a short intact donor chromosome segment around the target gene and thus reduce the linkage drag. We investigated the probability distribution of the length of the intact donor chromosome segment around the target gene in recurrent backcrossing with selection for heterozygosity at the target locus and homozygosity for the recurrent parent allele at flanking markers for a diploid species. Assuming no interference in crossover formation, we derived the cumulative density function, probability density function, expected value, and variance of the length of the intact chromosome segment for the following cases: (1) backcross generations prior to detection of a recombinant individual between the target gene and the flanking marker; (2) the backcross generation in which for the first time a recombinant individual is detected, which is selected for further backcrossing; and (3) subsequent backcross generations after selection of a recombinant. Examples are given of how these results can be applied to investigate the efficiency of marker-assisted backcrossing for reducing the length of the intact donor chromosome segment around the target gene under various situations relevant in breeding and genetic research.     

Saturation of two chromosome regions conferring resistance to SCMV with SSR and AFLP markers by targeted BSA

Quantitative trait loci (QTLs) and bulked segregant analyses (BSA) identified the major genes Scmv1 on chromosome 6 and Scmv2 on chromosome 3, conferring resistance against sugarcane mosaic virus (SCMV) in maize. Both chromosome regions were further enriched for SSR and AFLP markers by targeted bulked segregant analysis (tBSA) in order to identify and map only markers closely linked to either Scmv1 or Scmv2. For identification of markers closely linked to the target genes, symptomless individuals of advanced backcross generations BC5 to BC9 were employed. All AFLP markers, identified by tBSA using 400 EcoRI/ MseI primer combinations, mapped within both targeted marker intervals. Fourteen SSR and six AFLP markers mapped to the Scmv1 region. Eleven SSR and 18 AFLP markers were located in the Scmv2 region. Whereas the linear order of SSR markers and the window size for the Scmv2 region fitted well with publicly available genetic maps, map distances and window size differed substantially for the Scmv1 region on chromosome 6. A possible explanation for the observed discrepancies is the presence of two closely linked resistance genes in the Scmv1 region.     

Bias and Sampling Error of the Estimated Proportion of Genotypic Variance Explained by Quantitative Trait Loci Determined From Experimental Data in Maize Using Cross Validation and Validation With Independent Samples

Cross validation (CV) was used to analyze the effects of different environments and different genotypic samples on estimates of the proportion of genotypic variance explained by QTL (p). Testcrosses of 344 F(3) maize lines grown in four environments were evaluated for a number of agronomic traits. In each of 200 replicated CV runs, this data set was subdivided into an estimation set (ES) and various test sets (TS). ES were used to map QTL and estimate p for each run (p(ES)) and its median (p(ES)) across all runs. The bias of these estimates was assessed by comparison with the median (p(TS.ES)) obtained from TS. We also used two independent validation samples derived from the same cross for further comparison. The median p(ES) showed a large upward bias compared to p(TS.ES). Environmental sampling generally had a smaller effect on the bias of p(ES) than genotypic sampling or both factors simultaneously. In independent validation, p(TS.ES) was on average only 50% of p(ES). A wide range among p(ES) reflected a large sampling error of these estimates. QTL frequency distributions and comparison of estimated QTL effects indicated a low precision of QTL localization and an upward bias in the absolute values of estimated QTL effects from ES. CV with data from three QTL studies reported in the literature yielded similar results as those obtained with maize testcrosses. We therefore recommend CV for obtaining asymptotically unbiased estimates of p and consequently a realistic assessment of the prospects of MAS.