Method to represent the distribution of QTL additive and dominance effects associated with quantitative traits in computer simulation

The long-term effects of genomic selection: 1. Response to selection, additive genetic variance, and genetic architecture

Background

Genomic selection has revolutionized genetic improvement in animals and plants, but little is known about its long-term effects. Here, we investigated the long-term effects of genomic selection on response to selection, genetic variance, and the genetic architecture of traits using stochastic simulations. We defined the genetic architecture as the set of causal loci underlying each trait, their allele frequencies, and their statistical additive effects. We simulated a livestock population under 50 generations of phenotypic, pedigree, or genomic selection for a single trait, controlled by either only additive, additive and dominance, or additive, dominance, and epistatic effects. The simulated epistasis was based on yeast data.

Results

Short-term response was always greatest with genomic selection, while response after 50 generations was greater with phenotypic selection than with genomic selection when epistasis was present, and was always greater than with pedigree selection. This was mainly because loss of genetic variance and of segregating loci was much greater with genomic and pedigree selection than with phenotypic selection. Compared to pedigree selection, selection response was always greater with genomic selection. Pedigree and genomic selection lost a similar amount of genetic variance after 50 generations of selection, but genomic selection maintained more segregating loci, which on average had lower minor allele frequencies than with pedigree selection. Based on this result, genomic selection is expected to better maintain genetic gain after 50 generations than pedigree selection. The amount of change in the genetic architecture of traits was considerable across generations and was similar for genomic and pedigree selection, but slightly less for phenotypic selection. Presence of epistasis resulted in smaller changes in allele frequencies and less fixation of causal loci, but resulted in substantial changes in statistical additive effects across generations.

Conclusions

Our results show that genomic selection outperforms pedigree selection in terms of long-term genetic gain, but results in a similar reduction of genetic variance. The genetic architecture of traits changed considerably across generations, especially under selection and when non-additive effects were present. In conclusion, non-additive effects had a substantial impact on the accuracy of selection and long-term response to selection, especially when selection was accurate.

A look-ahead Monte Carlo simulation method for improving parental selection in trait introgression

Multiple trait introgression is the process by which multiple desirable traits are converted from a donor to a recipient cultivar through backcrossing and selfing. The goal of this procedure is to recover all the attributes of the recipient cultivar, with the addition of the specified desirable traits. A crucial step in this process is the selection of parents to form new crosses. In this study, we propose a new selection approach that estimates the genetic distribution of the progeny of backcrosses after multiple generations using information of recombination events. Our objective is to select the most promising individuals for further backcrossing or selfing. To demonstrate the effectiveness of the proposed method, a case study has been conducted using maize data where our method is compared with state-of-the-art approaches. Simulation results suggest that the proposed method, look-ahead Monte Carlo, achieves higher probability of success than existing approaches. Our proposed selection method can assist breeders to efficiently design trait introgression projects.

Predicting the purebred-crossbred genetic correlation from the genetic variance components in the parental lines

Background

The genetic correlation between purebred and crossbred performance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc when selection is based on purebred (PB) performance. The value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc and parental allele frequencies suggests that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The expressions were derived for a genetic model with additive and dominance effects (D), and additive and epistatic additive-by-additive effects (E_AA). We validated our expressions using simulations of purebred parental lines and their crosses, where the parental lines were either selected or not. Finally, using these simulations, we investigated the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc for genetic models with both dominance and epistasis or with other types of epistasis, for which expressions could not be derived.

Results

Our simulations show that when non-additive effects are present, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc decreases with increasing differences in allele frequencies between the parental lines. Genetic models that involve dominance result in lower values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc than genetic models that involve epistasis only. Using information of parental lines only, our expressions provide exact estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc for models D and E_AA, and accurate upper and lower bounds of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc for two other genetic models.

Conclusion

This work lays the foundation to enable estimation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document}rpc from information collected in PB parental lines only.

The Impact of Non-additive Effects on the Genetic Correlation Between Populations

Average effects of alleles can show considerable differences between populations. The magnitude of these differences can be measured by the additive genetic correlation between populations ([Formula: see text]). This [Formula: see text] can be lower than one due to the presence of non-additive genetic effects together with differences in allele frequencies between populations. However, the relationship between the nature of non-additive effects, differences in allele frequencies, and the value of [Formula: see text] remains unclear, and was therefore the focus of this study. We simulated genotype data of two populations that have diverged under drift only, or under drift and selection, and we simulated traits where the genetic model and magnitude of non-additive effects were varied. Results showed that larger differences in allele frequencies and larger non-additive effects resulted in lower values of [Formula: see text] In addition, we found that with epistasis, [Formula: see text] decreases with an increase of the number of interactions per locus. For both dominance and epistasis, we found that, when non-additive effects became extremely large, [Formula: see text] had a lower bound that was determined by the type of inter-allelic interaction, and the difference in allele frequencies between populations. Given that dominance variance is usually small, our results show that it is unlikely that true [Formula: see text] values lower than 0.80 are due to dominance effects alone. With realistic levels of epistasis, [Formula: see text] dropped as low as 0.45. These results may contribute to the understanding of differences in genetic expression of complex traits between populations, and may help in explaining the inefficiency of genomic trait prediction across populations.

Seed protein content and its relationships with agronomic traits in pigeonpea is controlled by both main and epistatic effects QTLs

The genetic architecture of seed protein content (SPC) and its relationships to agronomic traits in pigeonpea is poorly understood. Accordingly, five F₂ populations segregating for SPC and four agronomic traits (seed weight (SW), seed yield (SY), growth habit (GH) and days to first flowering (DFF)) were phenotyped and genotyped using genotyping-by-sequencing approach. Five high-density population-specific genetic maps were constructed with an average inter-marker distance of 1.6 to 3.5 cM, and subsequently, integrated into a consensus map with average marker spacing of 1.6 cM. Based on analysis of phenotyping data and genotyping data, 192 main effect QTLs (M-QTLs) with phenotypic variation explained (PVE) of 0.7 to 91.3% were detected for the five traits across the five populations. Major effect (PVE ≥ 10%) M-QTLs included 14 M-QTLs for SPC, 16 M-QTLs for SW, 17 M-QTLs for SY, 19 M-QTLs for GH and 24 M-QTLs for DFF. Also, 573 epistatic QTLs (E-QTLs) were detected with PVE ranging from 6.3 to 99.4% across traits and populations. Colocalization of M-QTLs and E-QTLs explained the genetic basis of the significant (P < 0.05) correlations of SPC with SW, SY, DFF and GH. The nature of genetic architecture of SPC and its relationship with agronomic traits suggest that genomics-assisted breeding targeting genome-wide variations would be effective for the simultaneous improvement of SPC and other important traits.

Optimized breeding strategies for multiple trait integration: III. Parameters for success in version testing

Multiple trait integration (MTI) is the process by which a target hybrid (or variety) is converted to add value-added traits to the comprehensive performance package represented by that genotype. The goal is to recover all the attributes of the target hybrid, with the addition of the specified value-added traits. In maize, this process utilizes the backcross breeding method to incorporate transgenic events (or genes) of interest. Thus, MTI involves four main steps: single event introgression, event pyramiding, trait fixation, and version testing to ensure recovery of equivalent performance with at least one version of the converted hybrid. Based on a case study involving conversion of a target hybrid for 15 transgenic events (the female inbred parent was converted for 8 events, and the male inbred parent was converted for 7 events), we explored parameters in version testing to facilitate a high likelihood of recovering at least one version of the hybrid conversion with yield performance equivalency within 3 % of unconverted target hybrid. Using computer simulation, we explored the impact of two factors on the success rate of the MTI outcome: (1) the amount of residual NRP (non-recurrent parent) germplasm remaining in the converted hybrid and (2) the number of versions of each parental line conversion created. A range of residual NRP germplasm from 120 to 180 cM (which represents 95.0-96.6 % germplasm recovery of the target hybrid in maize) and up to 5 versions of each parental conversion were considered, with all possible hybrid combinations of each version of female and male RP (recurrent parent) conversion evaluated for yield. With 5 versions of each RP conversion and testing of 25 hybrid versions, a >95 % rate of success was realized when the amount of residual NRP germplasm in the hybrid conversion was ≤180 cM. When hybrid conversions contained ≤120-cM residual NRP germplasm, only 4 versions of one of the parental conversions were needed (rather than 5), requiring 20 versions of the hybrid conversion to be yield tested. These results have implications in the strategic design of an overall conversion program and for the upstream MTI process, especially in setting thresholds for the amount of NRP germplasm remaining in RP conversions. Furthermore, these results validate findings of (Peng et al. in Mol Breed 33:189-104, 2014a. doi:10.1007/s11032-013-9936-7, in Mole Breed 33:105-115, 2014b. doi:10.1007/s11032-013-9937-6) which outline effective breeding strategies to optimize earlier steps in MTI (preceding version testing).