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      Improvement of Predictive Ability by Uniform Coverage of the Target Genetic Space

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          Abstract

          Genome-enabled prediction provides breeders with the means to increase the number of genotypes that can be evaluated for selection. One of the major challenges in genome-enabled prediction is how to construct a training set of genotypes from a calibration set that represents the target population of genotypes, where the calibration set is composed of a training and validation set. A random sampling protocol of genotypes from the calibration set will lead to low quality coverage of the total genetic space by the training set when the calibration set contains population structure. As a consequence, predictive ability will be affected negatively, because some parts of the genotypic diversity in the target population will be under-represented in the training set, whereas other parts will be over-represented. Therefore, we propose a training set construction method that uniformly samples the genetic space spanned by the target population of genotypes, thereby increasing predictive ability. To evaluate our method, we constructed training sets alongside with the identification of corresponding genomic prediction models for four genotype panels that differed in the amount of population structure they contained (maize Flint, maize Dent, wheat, and rice). Training sets were constructed using uniform sampling, stratified-uniform sampling, stratified sampling and random sampling. We compared these methods with a method that maximizes the generalized coefficient of determination (CD). Several training set sizes were considered. We investigated four genomic prediction models: multi-locus QTL models, GBLUP models, combinations of QTL and GBLUPs, and Reproducing Kernel Hilbert Space (RKHS) models. For the maize and wheat panels, construction of the training set under uniform sampling led to a larger predictive ability than under stratified and random sampling. The results of our methods were similar to those of the CD method. For the rice panel, all training set construction methods led to similar predictive ability, a reflection of the very strong population structure in this panel.

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          Most cited references34

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          Accuracy of Predicting the Genetic Risk of Disease Using a Genome-Wide Approach

          Background The prediction of the genetic disease risk of an individual is a powerful public health tool. While predicting risk has been successful in diseases which follow simple Mendelian inheritance, it has proven challenging in complex diseases for which a large number of loci contribute to the genetic variance. The large numbers of single nucleotide polymorphisms now available provide new opportunities for predicting genetic risk of complex diseases with high accuracy. Methodology/Principal Findings We have derived simple deterministic formulae to predict the accuracy of predicted genetic risk from population or case control studies using a genome-wide approach and assuming a dichotomous disease phenotype with an underlying continuous liability. We show that the prediction equations are special cases of the more general problem of predicting the accuracy of estimates of genetic values of a continuous phenotype. Our predictive equations are responsive to all parameters that affect accuracy and they are independent of allele frequency and effect distributions. Deterministic prediction errors when tested by simulation were generally small. The common link among the expressions for accuracy is that they are best summarized as the product of the ratio of number of phenotypic records per number of risk loci and the observed heritability. Conclusions/Significance This study advances the understanding of the relative power of case control and population studies of disease. The predictions represent an upper bound of accuracy which may be achievable with improved effect estimation methods. The formulae derived will help researchers determine an appropriate sample size to attain a certain accuracy when predicting genetic risk.
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            A Large Maize (Zea mays L.) SNP Genotyping Array: Development and Germplasm Genotyping, and Genetic Mapping to Compare with the B73 Reference Genome

            SNP genotyping arrays have been useful for many applications that require a large number of molecular markers such as high-density genetic mapping, genome-wide association studies (GWAS), and genomic selection. We report the establishment of a large maize SNP array and its use for diversity analysis and high density linkage mapping. The markers, taken from more than 800,000 SNPs, were selected to be preferentially located in genes and evenly distributed across the genome. The array was tested with a set of maize germplasm including North American and European inbred lines, parent/F1 combinations, and distantly related teosinte material. A total of 49,585 markers, including 33,417 within 17,520 different genes and 16,168 outside genes, were of good quality for genotyping, with an average failure rate of 4% and rates up to 8% in specific germplasm. To demonstrate this array's use in genetic mapping and for the independent validation of the B73 sequence assembly, two intermated maize recombinant inbred line populations – IBM (B73×Mo17) and LHRF (F2×F252) – were genotyped to establish two high density linkage maps with 20,913 and 14,524 markers respectively. 172 mapped markers were absent in the current B73 assembly and their placement can be used for future improvements of the B73 reference sequence. Colinearity of the genetic and physical maps was mostly conserved with some exceptions that suggest errors in the B73 assembly. Five major regions containing non-colinearities were identified on chromosomes 2, 3, 6, 7 and 9, and are supported by both independent genetic maps. Four additional non-colinear regions were found on the LHRF map only; they may be due to a lower density of IBM markers in those regions or to true structural rearrangements between lines. Given the array's high quality, it will be a valuable resource for maize genetics and many aspects of maize breeding.
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              Genomic prediction in animals and plants: simulation of data, validation, reporting, and benchmarking.

              The genomic prediction of phenotypes and breeding values in animals and plants has developed rapidly into its own research field. Results of genomic prediction studies are often difficult to compare because data simulation varies, real or simulated data are not fully described, and not all relevant results are reported. In addition, some new methods have been compared only in limited genetic architectures, leading to potentially misleading conclusions. In this article we review simulation procedures, discuss validation and reporting of results, and apply benchmark procedures for a variety of genomic prediction methods in simulated and real example data. Plant and animal breeding programs are being transformed by the use of genomic data, which are becoming widely available and cost-effective to predict genetic merit. A large number of genomic prediction studies have been published using both simulated and real data. The relative novelty of this area of research has made the development of scientific conventions difficult with regard to description of the real data, simulation of genomes, validation and reporting of results, and forward in time methods. In this review article we discuss the generation of simulated genotype and phenotype data, using approaches such as the coalescent and forward in time simulation. We outline ways to validate simulated data and genomic prediction results, including cross-validation. The accuracy and bias of genomic prediction are highlighted as performance indicators that should be reported. We suggest that a measure of relatedness between the reference and validation individuals be reported, as its impact on the accuracy of genomic prediction is substantial. A large number of methods were compared in example simulated and real (pine and wheat) data sets, all of which are publicly available. In our limited simulations, most methods performed similarly in traits with a large number of quantitative trait loci (QTL), whereas in traits with fewer QTL variable selection did have some advantages. In the real data sets examined here all methods had very similar accuracies. We conclude that no single method can serve as a benchmark for genomic prediction. We recommend comparing accuracy and bias of new methods to results from genomic best linear prediction and a variable selection approach (e.g., BayesB), because, together, these methods are appropriate for a range of genetic architectures. An accompanying article in this issue provides a comprehensive review of genomic prediction methods and discusses a selection of topics related to application of genomic prediction in plants and animals.
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                Author and article information

                Journal
                G3 (Bethesda)
                Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes|Genomes|Genetics
                Genetics Society of America
                2160-1836
                22 September 2016
                November 2016
                : 6
                : 11
                : 3733-3747
                Affiliations
                [* ]C.T. de Wit Graduate School for Production Ecology and Resource Conservation (PE&RC), Wageningen, The Netherlands
                []Biometris, Wageningen University and Research, The Netherlands
                []Commonwealth Scientific and Industrial Research Organisation (CSIRO) Agriculture, Queensland Bioscience Precinct, St. Lucia, Queensland 4067, Australia
                [§ ]Department of Agriculture and Food, Western Australia, South Perth, Western Australia 6151, Australia
                Author notes
                [1 ]Corresponding author: Biometris, Wageningen University and Research Centre, P.O. Box 100, 6700 AC Wageningen, The Netherlands. E-mail: fred.vaneeuwijk@ 123456wur.nl
                Author information
                http://orcid.org/0000-0003-3827-6726
                http://orcid.org/0000-0002-8150-1397
                http://orcid.org/0000-0003-3672-2921
                Article
                GGG_035410
                10.1534/g3.116.035410
                5100872
                27672112
                2250d8aa-e548-4db0-89e7-df4ec41fb83f
                Copyright © 2016 Bustos-Korts et al.

                This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 15 April 2016
                : 19 September 2016
                Page count
                Figures: 6, Tables: 7, Equations: 8, References: 75, Pages: 15
                Categories
                Genomic Selection

                Genetics
                genomic prediction,population structure,genetic space,training set,rkhs model,genpred,shared data resources,genomic selection

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