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Multi-parent populations (MPPs) are attractive for genetic and breeding studies because they combine genetic diversity with an easy-to-control population structure. Most methods for mapping QTLs in MPPs focus on the detection of QTLs in single environments. Little attention has been given to mapping QTLs in multienvironment trials (METs) and to detecting and modeling QTL-by-environment interactions (QEIs). We present mixed model approaches for the detection and modeling of consistent versus environment-dependent QTLs, i.e., QTL-by-environment interaction (QEI). QTL effects are assumed to be normally distributed with variances expressing consistency or dependence on environments and families. The entries of the corresponding design matrices are functions of identity-by-descent (IBD) probabilities between parents and offspring and follow from the parental origin of offspring DNA. A polygenic effect is added to the models to account for background genetic variation. We illustrate the wide applicability of our method by analyzing several public MPP datasets with observations from METs. The examples include diallel, nested association mapping (NAM), and multi-parent advanced inter-cross (MAGIC) populations. The results of our approach compare favorably with those of previous studies that used tailored methods.

Abstract Terminal drought is one of the major constraints to crop production in chickpea (Cicer arietinum L.). In order to map drought tolerance related traits at high resolution, we sequenced multi‐parent advanced generation intercross (MAGIC) population using whole genome resequencing approach and phenotyped it under drought stress environments for two consecutive years (2013–14 and 2014–15). A total of 52.02 billion clean reads containing 4.67 TB clean data were generated on the 1136 MAGIC lines and eight parental lines. Alignment of clean data on to the reference genome enabled identification of a total, 932,172 of SNPs, 35,973 insertions, and 35,726 deletions among the parental lines. A high‐density genetic map was constructed using 57,180 SNPs spanning a map distance of 1606.69 cM. Using compressed mixed linear model, genome‐wide association study (GWAS) enabled us to identify 737 markers significantly associated with days to 50% flowering, days to maturity, plant height, 100 seed weight, biomass, and harvest index. In addition to the GWAS approach, an identity‐by‐descent (IBD)‐based mixed model approach was used to map quantitative trait loci (QTLs). The IBD‐based mixed model approach detected major QTLs that were comparable to those from the GWAS analysis as well as some exclusive QTLs with smaller effects. The candidate genes like FRIGIDA and CaTIFY4b can be used for enhancing drought tolerance in chickpea. The genomic resources, genetic map, marker‐trait associations, and QTLs identified in the study are valuable resources for the chickpea community for developing climate resilient chickpeas.

AbstractHybrid potato breeding has become a novel alternative to conventional potato breeding allowing breeders to overcome intractable barriers (e.g. tetrasomic inheritance, masked deleterious alleles, obligate clonal propagation) with the benefit of seed-based propagule, flexible population design, and the potential of hybrid vigor. Until now, however, no formal inquiry has adequately examined the relevant genetic components for complex traits in hybrid potato populations. In this present study, we use a 2-step multivariate modeling approach to estimate the variance components to assess the magnitude of the general and specific combining abilities in diploid hybrid potato. Specific combining ability effects were identified for all yield components studied here warranting evidence of nonadditive genetic effects in hybrid potato yield. However, the estimated general combining ability effects were on average 2 times larger than their respective specific combining ability quantile across all yield phenotypes. Tuber number general combining abilities and specific combining abilities were found to be highly correlated with total yield’s genetic components. Tuber volume was shown to have the largest proportion of additive and nonadditive genetic variation suggesting under-selection of this phenotype in this population. The prominence of additive effects found for all traits presents evidence that the mid-parent value alone is useful for hybrid potato evaluation. Heterotic vigor stands to be useful in bolstering simpler traits but this will be dependent on target phenotypes and market requirements. This study represents the first diallel analysis of its kind in diploid potato using material derived from a commercial hybrid breeding program.

Use of genomic prediction (GP) in tetraploid is becoming more common. Therefore, we think it is the right time for a comparison of GP models for tetraploid potato. GP models were compared that contrasted shrinkage with variable selection, parametric vs. non-parametric models and different ways of accounting for non-additive genetic effects. As a complement to GP, association studies were carried out in an attempt to understand the differences in prediction accuracy. We compared our GP models on a data set consisting of 147 cultivars, representing worldwide diversity, with over 39 k GBS markers and measurements on four tuber traits collected in six trials at three locations during 2 years. GP accuracies ranged from 0.32 for tuber count to 0.77 for dry matter content. For all traits, differences between GP models that utilised shrinkage penalties and those that performed variable selection were negligible. This was surprising for dry matter, as only a few additive markers explained over 50% of phenotypic variation. Accuracy for tuber count increased from 0.35 to 0.41, when dominance was included in the model. This result is supported by Genome Wide Association Study (GWAS) that found additive and dominance effects accounted for 37% of phenotypic variation, while significant additive effects alone accounted for 14%. For tuber weight, the Reproducing Kernel Hilbert Space (RKHS) model gave a larger improvement in prediction accuracy than explicitly modelling epistatic effects. This is an indication that capturing the between locus epistatic effects of tuber weight can be done more effectively using the semi-parametric RKHS model. Our results show good opportunities for GP in 4x potato.

The study of gene flow in pedigrees is of strong interest for the development of quantitative trait loci (QTL) mapping methods in multiparental populations. We developed a Markovian framework for modeling ancestral origins along two homologous chromosomes within individuals in fixed pedigrees. A highly beneficial property of our method is that the size of state space depends linearly or quadratically on the number of pedigree founders, whereas this increases exponentially with pedigree size in alternative methods. To calculate the parameter values of the Markov process, we describe two novel recursive algorithms that differ with respect to the pedigree founders being assumed to be exchangeable or not. Our algorithms apply equally to autosomes and sex chromosomes, another desirable feature of our approach. We tested the accuracy of the algorithms by a million simulations on a pedigree. We demonstrated two applications of the recursive algorithms in multiparental populations: design a breeding scheme for maximizing the overall density of recombination breakpoints and thus the QTL mapping resolution, and incorporate pedigree information into hidden Markov models in ancestral inference from genotypic data; the conditional probabilities and the recombination breakpoint data resulting from ancestral inference can facilitate follow-up QTL mapping. The results show that the generality of the recursive algorithms can greatly increase the application range of genetic analysis such as ancestral inference in multiparental populations.