The efficiency of genome-wide selection for genetic improvement of net merit

Optimising desired gain indices to maximise selection response

Introduction

In plant breeding, we often aim to improve multiple traits at once. However, without knowing the economic value of each trait, it is hard to decide which traits to focus on. This is where "desired gain selection indices" come in handy, which can yield optimal gains in each trait based on the breeder's prioritisation of desired improvements when economic weights are not available. However, they lack the ability to maximise the selection response and determine the correlation between the index and net genetic merit.

Methods

Here, we report the development of an iterative desired gain selection index method that optimises the sampling of the desired gain values to achieve a targeted or a user-specified selection response for multiple traits. This targeted selection response can be constrained or unconstrained for either a subset or all the studied traits.

Results

We tested the method using genomic estimated breeding values (GEBVs) for seven traits in a bread wheat (Triticum aestivum) reference breeding population comprising 3,331 lines and achieved prediction accuracies ranging between 0.29 and 0.47 across the seven traits. The indices were validated using 3,005 double haploid lines that were derived from crosses between parents selected from the reference population. We tested three user-specified response scenarios: a constrained equal weight (INDEX1), a constrained yield dominant weight (INDEX2), and an unconstrained weight (INDEX3). Our method achieved an equivalent response to the user-specified selection response when constraining a set of traits, and this response was much better than the response of the traditional desired gain selection indices method without iteration. Interestingly, when using unconstrained weight, our iterative method maximised the selection response and shifted the average GEBVs of the selection candidates towards the desired direction.

Discussion

Our results show that the method is an optimal choice not only when economic weights are unavailable, but also when constraining the selection response is an unfavourable option.

The statistical theory of linear selection indices from phenotypic to genomic selection

A linear selection index (LSI) can be a linear combination of phenotypic values, marker scores, and genomic estimated breeding values (GEBVs); phenotypic values and marker scores; or phenotypic values and GEBVs jointly. The main objective of the LSI is to predict the net genetic merit (H), which is a linear combination of unobservable individual traits' breeding values, weighted by the trait economic values; thus, the target of LSI is not a parameter but rather the unobserved random H values. The LSI can be single-stage or multi-stage, where the latter are methods for selecting one or more individual traits available at different times or stages of development in both plants and animals. Likewise, LSIs can be either constrained or unconstrained. A constrained LSI imposes predetermined genetic gain on expected genetic gain per trait and includes the unconstrained LSI as particular cases. The main LSI parameters are the selection response, the expected genetic gain per trait, and its correlation with H. When the population mean is zero, the selection response and expected genetic gain per trait are, respectively, the conditional mean of H and the genotypic values, given the LSI values. The application of LSI theory is rapidly diversifying; however, because LSIs are based on the best linear predictor and on the canonical correlation theory, the LSI theory can be explained in a simple form. We provided a review of the statistical theory of the LSI from phenotypic to genomic selection showing their relationships, advantages, and limitations, which should allow breeders to use the LSI theory confidently in breeding programs.

Genomics and breeding innovations for enhancing genetic gain for climate resilience and nutrition traits

KEY MESSAGE

Integrating genomics technologies and breeding methods to tweak core parameters of the breeder's equation could accelerate delivery of climate-resilient and nutrient rich crops for future food security. Accelerating genetic gain in crop improvement programs with respect to climate resilience and nutrition traits, and the realization of the improved gain in farmers' fields require integration of several approaches. This article focuses on innovative approaches to address core components of the breeder's equation. A prerequisite to enhancing genetic variance (σ2g) is the identification or creation of favorable alleles/haplotypes and their deployment for improving key traits. Novel alleles for new and existing target traits need to be accessed and added to the breeding population while maintaining genetic diversity. Selection intensity (i) in the breeding program can be improved by testing a larger population size, enabled by the statistical designs with minimal replications and high-throughput phenotyping. Selection priorities and criteria to select appropriate portion of the population too assume an important role. The most important component of breeder's equation is heritability (h2). Heritability estimates depend on several factors including the size and the type of population and the statistical methods. The present article starts with a brief discussion on the potential ways to enhance σ2g in the population. We highlight statistical methods and experimental designs that could improve trait heritability estimation. We also offer a perspective on reducing the breeding cycle time (t), which could be achieved through the selection of appropriate parents, optimizing the breeding scheme, rapid fixation of target alleles, and combining speed breeding with breeding programs to optimize trials for release. Finally, we summarize knowledge from multiple disciplines for enhancing genetic gains for climate resilience and nutritional traits.

Genomic selection for heterobothriosis resistance concurrent with body size in the tiger pufferfish, Takifugu rubripes

Parasite resistance traits in aquaculture species often have moderate heritability, indicating the potential for genetic improvements by selective breeding. However, parasite resistance is often synonymous with an undesirable negative correlation with body size. In this study, we first tested the feasibility of genomic selection (GS) on resistance to heterobothriosis, caused by the monogenean parasite Heterobothrium okamotoi, which leads to huge economic losses in aquaculture of the tiger pufferfish Takifugu rubripes. Then, using a simulation study, we tested the possibility of simultaneous improvement of parasite resistance, assessed by parasite counts on host fish (HC), and standard length (SL). Each trait showed moderate heritability (square-root transformed HC: h2 = 0.308 ± 0.123, S.E.; SL: h2 = 0.405 ± 0.131). The predictive abilities of genomic prediction among 12 models, including genomic Best Linear Unbiased Predictor (GBLUP), Bayesian regressions, and machine learning procedures, were also moderate for both transformed HC (0.248‒0.344) and SL (0.340‒0.481). These results confirmed the feasibility of GS for this trait. Although an undesirable genetic correlation was suggested between transformed HC and SL (rg = 0.228), the simulation study suggested the desired gains index can help achieve simultaneous genetic improvements in both traits.

Efficiency of a Constrained Linear Genomic Selection Index To Predict the Net Genetic Merit in Plants

The constrained linear genomic selection index (CLGSI) is a linear combination of genomic estimated breeding values useful for predicting the net genetic merit, which in turn is a linear combination of true unobservable breeding values of the traits weighted by their respective economic values. The CLGSI is the most general genomic index and allows imposing constraints on the expected genetic gain per trait to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. In addition, it includes the unconstrained linear genomic index as a particular case. Using two real datasets and simulated data for seven selection cycles, we compared the theoretical results of the CLGSI with the theoretical results of the constrained linear phenotypic selection index (CLPSI). The criteria used to compare CLGSI vs. CLPSI efficiency were the estimated expected genetic gain per trait values, the selection response, and the interval between selection cycles. The results indicated that because the interval between selection cycles is shorter for the CLGSI than for the CLPSI, CLGSI is more efficient than CLPSI per unit of time, but its efficiency could be lower per selection cycle. Thus, CLGSI is a good option for performing genomic selection when there are genotyped candidates for selection.

Combining grain yield, protein content and protein quality by multi-trait genomic selection in bread wheat

KEY MESSAGE

Simultaneous genomic selection for grain yield, protein content and dough rheological traits enables the development of resource-use efficient varieties that combine superior yield potential with comparably high end-use quality. Selecting simultaneously for grain yield and baking quality is a major challenge in wheat breeding, and several concepts like grain protein deviations have been developed for shifting the undesirable negative correlation between both traits. The protein quality is, however, not considered in these concepts, although it is an important aspect and might facilitate the selection of genotypes that use available resources more efficiently with respect to the quantity and quality of the final end products. A population of 480 lines from an applied wheat breeding programme that was phenotyped for grain yield, protein content, protein yield and dough rheological traits was thus used to assess the potential of using integrated genomic selection indices to ease selection decisions with regard to the plethora of quality traits. Additionally, the feasibility of achieving a simultaneous genetic improvement in grain yield, protein content and protein quality was investigated to develop more resource-use efficient varieties. Dough rheological traits related to either gluten strength or viscosity were combined in two separate indices, both of which showed a substantially smaller negative trade-off with grain yield than the protein content. Genomic selection indices based on regression deviations for the two latter traits were subsequently extended by the gluten strength or viscosity indices. They revealed a large merit for identifying resource-use efficient genotypes that combine both superior yield potential with comparably high end-use quality. Hence, genomic selection opens up the opportunity for multi-trait selection in early generations, which will most likely increase the efficiency when developing new and improved varieties.

Trait variation and genetic diversity in a banana genomic selection training population

Banana (Musa spp.) is an important crop in the African Great Lakes region in terms of income and food security, with the highest per capita consumption worldwide. Pests, diseases and climate change hamper sustainable production of bananas. New breeding tools with increased crossbreeding efficiency are being investigated to breed for resistant, high yielding hybrids of East African Highland banana (EAHB). These include genomic selection (GS), which will benefit breeding through increased genetic gain per unit time. Understanding trait variation and the correlation among economically important traits is an essential first step in the development and selection of suitable GS models for banana. In this study, we tested the hypothesis that trait variations in bananas are not affected by cross combination, cycle, field management and their interaction with genotype. A training population created using EAHB breeding material and its progeny was phenotyped in two contrasting conditions. A high level of correlation among vegetative and yield related traits was observed. Therefore, genomic selection models could be developed for traits that are easily measured. It is likely that the predictive ability of traits that are difficult to phenotype will be similar to less difficult traits they are highly correlated with. Genotype response to cycle and field management practices varied greatly with respect to traits. Yield related traits accounted for 31-35% of principal component variation under low and high input field management conditions. Resistance to Black Sigatoka was stable across cycles but varied under different field management depending on the genotype. The best cross combination was 1201K-1xSH3217 based on selection response (R) of hybrids. Genotyping using simple sequence repeat (SSR) markers revealed that the training population was genetically diverse, reflecting a complex pedigree background, which was mostly influenced by the male parents.

A Genomic Selection Index Applied to Simulated and Real Data

A genomic selection index (GSI) is a linear combination of genomic estimated breeding values that uses genomic markers to predict the net genetic merit and select parents from a nonphenotyped testing population. Some authors have proposed a GSI; however, they have not used simulated or real data to validate the GSI theory and have not explained how to estimate the GSI selection response and the GSI expected genetic gain per selection cycle for the unobserved traits after the first selection cycle to obtain information about the genetic gains in each subsequent selection cycle. In this paper, we develop the theory of a GSI and apply it to two simulated and four real data sets with four traits. Also, we numerically compare its efficiency with that of the phenotypic selection index (PSI) by using the ratio of the GSI response over the PSI response, and the PSI and GSI expected genetic gain per selection cycle for observed and unobserved traits, respectively. In addition, we used the Technow inequality to compare GSI vs. PSI efficiency. Results from the simulated data were confirmed by the real data, indicating that GSI was more efficient than PSI per unit of time.

Potential benefits of genomic selection on genetic gain of small ruminant breeding programs

In conventional small ruminant breeding programs, only pedigree and phenotype records are used to make selection decisions but prospects of including genomic information are now under consideration. The objective of this study was to assess the potential benefits of genomic selection on the genetic gain in French sheep and goat breeding designs of today. Traditional and genomic scenarios were modeled with deterministic methods for 3 breeding programs. The models included decisional variables related to male selection candidates, progeny testing capacity, and economic weights that were optimized to maximize annual genetic gain (AGG) of i) a meat sheep breeding program that improved a meat trait of heritability (h(2)) = 0.30 and a maternal trait of h(2) = 0.09 and ii) dairy sheep and goat breeding programs that improved a milk trait of h(2) = 0.30. Values of ±0.20 of genetic correlation between meat and maternal traits were considered to study their effects on AGG. The Bulmer effect was accounted for and the results presented here are the averages of AGG after 10 generations of selection. Results showed that current traditional breeding programs provide an AGG of 0.095 genetic standard deviation (σa) for meat and 0.061 σa for maternal trait in meat breed and 0.147 σa and 0.120 σa in sheep and goat dairy breeds, respectively. By optimizing decisional variables, the AGG with traditional selection methods increased to 0.139 σa for meat and 0.096 σa for maternal traits in meat breeding programs and to 0.174 σa and 0.183 σa in dairy sheep and goat breeding programs, respectively. With a medium-sized reference population (nref) of 2,000 individuals, the best genomic scenarios gave an AGG that was 17.9% greater than with traditional selection methods with optimized values of decisional variables for combined meat and maternal traits in meat sheep, 51.7% in dairy sheep, and 26.2% in dairy goats. The superiority of genomic schemes increased with the size of the reference population and genomic selection gave the best results when nref > 1,000 individuals for dairy breeds and nref > 2,000 individuals for meat breed. Genetic correlation between meat and maternal traits had a large impact on the genetic gain of both traits. Changes in AGG due to correlation were greatest for low heritable maternal traits. As a general rule, AGG was increased both by optimizing selection designs and including genomic information.

Genomic selection for two traits in a maternal pig breeding scheme

The objective of this study was to compare different implementations of genomic selection to a conventional maternal pig breeding scheme, when selection was based partly on production traits and partly on maternal traits. A nucleus pig breeding population with size and structure similar to Norwegian Landrace was simulated where equal weight was used for maternal and production traits. To genotype the boars at the boar station and base the final selection of boars on genomic breeding values increased total genetic gain by 13% and reduced the rate of inbreeding by 40%, without significantly affecting the relative contribution of each trait to total genetic gain. To increase the size of the reference population and thereby accuracy of selection, female sibs in the selected litters can also be genotyped to increase genetic gain for maternal traits more than for production traits, thereby resulting in an increased relative contribution of maternal traits to total genetic gain. Genotyping 2,400 females each year increased the relative contribution of maternal traits to total genetic gain from 16 to 32%. Performing preselection of males by allowing genotyping of 2 males per litter and allowing for selection across and within litters before the boar test increased genetic gain by 5 to 11%, compared with genotyping the boars at the boar station, without significant effects on the relative contribution of each trait to total genetic gain. Genotyping more animals consequently increased genetic gain. Genotyping females to build a larger reference base for maternal traits gave similar genetic gain as genotyping the same amount of additional males but with a lower rate of inbreeding and a greater contribution of maternal traits to total genetic gain. In conclusion, genotyping females should be prioritized before genotyping more males than the tested boars if the breeding goal is to increase maternal traits specifically over production traits or genomic selection is used as a tool to reduce the rate of inbreeding.

Lactation persistency as a component trait of the selection index and increase in reliability by using single nucleotide polymorphism in net merit defined as the first five lactation milk yields and herd life

We first sought to clarify the effects of discounted rate, survival rate, and lactation persistency as a component trait of the selection index on net merit, defined as the first five lactation milks and herd life (HL) weighted by 1 and 0.389 (currently used in Japan), respectively, in units of genetic standard deviation. Survival rate increased the relative economic importance of later lactation traits and the first five lactation milk yields during the first 120 months from the start of the breeding scheme. In contrast, reliabilities of the estimated breeding value (EBV) in later lactation traits are lower than those of earlier lactation traits. We then sought to clarify the effects of applying single nucleotide polymorphism (SNP) on net merit to improve the reliability of EBV of later lactation traits to maximize their increased economic importance due to increase in survival rate. Net merit, selection accuracy, and HL increased by adding lactation persistency to the selection index whose component traits were only milk yields. Lactation persistency of the second and (especially) third parities contributed to increasing HL while maintaining the first five lactation milk yields compared with the selection index whose only component traits were milk yields. A selection index comprising the first three lactation milk yields and persistency accounted for 99.4% of net merit derived from a selection index whose components were identical to those for net merit. We consider that the selection index comprising the first three lactation milk yields and persistency is a practical method for increasing lifetime milk yield in the absence of data regarding HL. Applying SNP to the second- and third-lactation traits and HL increased net merit and HL by maximizing the increased economic importance of later lactation traits, reducing the effect of first-lactation milk yield on HL (genetic correlation (rG) = -0.006), and by augmenting the effects of the second- and third-lactation milk yields on HL (rG = 0.118 and 0.257, respectively).