Selection index updating

Characteristics of restricted selection indices and geometrical interpretation of restricted breeding values

Restricted selection is used to control genetic changes in one or more characters. Three main selection indices are adopted for this purpose. First, Kempthorne's index is used to maximize aggregate breeding value (BV) with changes in some traits restricted to zero; second, Harville's index is used to maximize aggregate BV with proportional changes for some traits; and third, Yamada's index is mathematically used to achieve the relative desired changes for all traits. Kempthorne's index is equivalent to Harville's index. However, the relationship between Kempthorne's and Yamada's indices has not been clarified. In addition, the characteristics of restricted selection indices and the relationship between BV and restricted BV (RBV) are also unknown. The aim of this study was to clarify the characteristics of restricted selection indices and describe the relationship between BV and RBV by using linear algebra and geometric techniques, respectively. First, I proved that Yamada's index is part of Kempthorne's index. Second, I investigated the relationship between BVs that were estimated using an ordinary selection index (EBVs) and RBVs estimated using a restricted selection index (ERBVs) and proved that the ERBVs of the restricted traits are proportional to the relative desired changes. Third, I proved that RBV is represented by a linear function of BV and geometrically represented the relationship between BV and RBV. In this study, new findings on restricted selection indices and RBV were obtained. This useful clarification of the relationship between BV and RBV will make it possible to evaluate the response to selection using not only a restricted selection index, but also a restricted BLUP in computer simulation studies.

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.

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

A combined multistage linear genomic selection index (CMLGSI) is a linear combination of phenotypic and genomic estimated breeding values useful for predicting the individual net genetic merit, which in turn is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values. The CMLGSI is a cost-saving strategy for improving multiple traits because the breeder does not need to measure all traits at each stage. The optimum (OCMLGSI) and decorrelated (DCMLGSI) indices are the main CMLGSIs. Whereas the OCMLGSI takes into consideration the index correlation values among stages, the DCMLGSI imposes the restriction that the index correlation values among stages be zero. Using real and simulated datasets, we compared the efficiency of both indices in a two-stage context. The criteria we applied to compare the efficiency of both indices were that the total selection response of each index must be lower than or equal to the single-stage combined linear genomic selection index (CLGSI) response and that the correlation of each index with the net genetic merit should be maximum. Using four different total proportions for the real dataset, the estimated total OCMLGSI and DCMLGSI responses explained 97.5% and 90%, respectively, of the estimated single-stage CLGSI selection response. In addition, at stage two, the estimated correlations of the OCMLGSI and the DCMLGSI with the net genetic merit were 0.84 and 0.63, respectively. We found similar results for the simulated datasets. Thus, we recommend using the OCMLGSI when performing multistage selection.

Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory

Some authors have evaluated the unconstrained optimum and decorrelated multistage linear phenotypic selection indices (OMLPSI and DMLPSI, respectively) theory. We extended this index theory to the constrained multistage linear phenotypic selection index context, where we denoted OMLPSI and DMLPSI as OCMLPSI and DCMLPSI, respectively. The OCMLPSI (DCMLPSI) is the most general multistage index and includes the OMLPSI (DMLPSI) as a particular case. The OCMLPSI (DCMLPSI) predicts the individual net genetic merit at different individual ages and allows imposing constraints on the genetic gains to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. The OCMLPSI takes into consideration the index correlation values among stages, whereas the DCMLPSI imposes the restriction that the index correlation values among stages be null. The criteria to evaluate OCMLPSI efficiency vs. DCMLPSI efficiency were that the total response of each index must be lower than or equal to the single-stage constrained linear phenotypic selection index response and that the expected genetic gain per trait values should be similar to the constraints imposed by the breeder. We used one real and one simulated dataset to validate the efficiency of the indices. The results indicated that OCMLPSI accuracy when predicting the selection response and expected genetic gain per trait was higher than DCMLPSI accuracy when predicting them. Thus, breeders should use the OCMLPSI when making a phenotypic selection.

Study of the effect of genotype-environment interaction on age at first calving and production traits in Nellore cattle using multi-trait reaction norms and Bayesian inference

This study investigated the effects of genotype-environment interaction on yearling weight, age at first calving and post-weaning weight gain in Nellore cattle using multi-trait reaction norm models. The environmental gradient was defined as a function of the mean yearling weight of the contemporary groups. A first-order random regression sire model with four classes of residual variance was used in the analyses and Bayesian methods were applied to estimate the (co)variance components. The heritability estimates ranged from 0.284 to 0.547, 0.222 to 0.316 and 0.256 to 0.522 for yearling weight, age at first calving and post-weaning weight gain, respectively. The lowest genetic correlations between environment groups for each trait were 0.38, 0.02 and 0.04 for yearling weight, age at first calving and post-weaning weight gain, respectively. Differences in the correlation estimates were observed between traits in the same environments, with the magnitude of the estimates tending toward zero as the environment improved. The results highlight the importance of including genotype-environment interactions in genetic evaluation programs considering the differences observed between environmental groups not only in terms of heritability, but also of genetic correlations.

Modeling of genetic gain for single traits from marker-assisted seedling selection in clonally propagated crops

Seedling selection identifies superior seedlings as candidate cultivars based on predicted genetic potential for traits of interest. Traditionally, genetic potential is determined by phenotypic evaluation. With the availability of DNA tests for some agronomically important traits, breeders have the opportunity to include DNA information in their seedling selection operations-known as marker-assisted seedling selection. A major challenge in deploying marker-assisted seedling selection in clonally propagated crops is a lack of knowledge in genetic gain achievable from alternative strategies. Existing models based on additive effects considering seed-propagated crops are not directly relevant for seedling selection of clonally propagated crops, as clonal propagation captures all genetic effects, not just additive. This study modeled genetic gain from traditional and various marker-based seedling selection strategies on a single trait basis through analytical derivation and stochastic simulation, based on a generalized seedling selection scheme of clonally propagated crops. Various trait-test scenarios with a range of broad-sense heritability and proportion of genotypic variance explained by DNA markers were simulated for two populations with different segregation patterns. Both derived and simulated results indicated that marker-based strategies tended to achieve higher genetic gain than phenotypic seedling selection for a trait where the proportion of genotypic variance explained by marker information was greater than the broad-sense heritability. Results from this study provides guidance in optimizing genetic gain from seedling selection for single traits where DNA tests providing marker information are available.

Optimising multistage dairy cattle breeding schemes including genomic selection using decorrelated or optimum selection indices

Background

The prediction of the outcomes from multistage breeding schemes is especially important for the introduction of genomic selection in dairy cattle. Decorrelated selection indices can be used for the optimisation of such breeding schemes. However, they decrease the accuracy of estimated breeding values and, therefore, the genetic gain to an unforeseeable extent and have not been applied to breeding schemes with different generation intervals and selection intensities in each selection path.

Methods

A grid search was applied in order to identify optimum breeding plans to maximise the genetic gain per year in a multistage, multipath dairy cattle breeding program. In this program, different values of the accuracy of estimated genomic breeding values and of their costs per individual were applied, whereby the total breeding costs were restricted. Both decorrelated indices and optimum selection indices were used together with fast multidimensional integration algorithms to produce results.

Results

In comparison to optimum indices, the genetic gain with decorrelated indices was up to 40% less and the proportion of individuals undergoing genomic selection was different. Additionally, the interaction between selection paths was counter-intuitive and difficult to interpret. Independent of using decorrelated or optimum selection indices, genomic selection replaced traditional progeny testing when maximising the genetic gain per year, as long as the accuracy of estimated genomic breeding values was ≥ 0.45. Overall breeding costs were mainly generated in the path "dam-sire". Selecting males was still the main source of genetic gain per year.

Conclusion

Decorrelated selection indices should not be used because of misleading results and the availability of accurate and fast algorithms for exact multidimensional integration. Genomic selection is the method of choice when maximising the genetic gain per year but genotyping females may not allow for a reduction in overall breeding costs. Furthermore, the economic justification of genotyping females remains questionable.

Methods of plant breeding in the genome era

Methods of genomic value prediction are reviewed. The majority of the methods are related to mixed model methodology, either explicitly or implicitly, by treating systematic environmental effects as fixed and quantitative trait locus (QTL) effects as random. Six different methods are reviewed, including least squares (LS), ridge regression, Bayesian shrinkage, least absolute shrinkage and selection operator (Lasso), empirical Bayes and partial least squares (PLS). The LS and PLS methods are non-Bayesian because they do not require probability distributions for the data. The PLS method is introduced as a special dimension reduction scheme to handle high-density marker information. Theory and methods of cross-validation are described. The leave-one-out cross-validation approach is recommended for model validation. A working example is used to demonstrate the utility of genome selection (GS) in barley. The data set contained 150 double haploid lines and 495 DNA markers covering the entire barley genome, with an average marker interval of 2·23 cM. Eight quantitative traits were included in the analysis. GS using the empirical Bayesian method showed high predictability of the markers for all eight traits with a mean accuracy of prediction of 0·70. With traditional marker-assisted selection (MAS), the average accuracy of prediction was 0·59, giving an average gain of GS over MAS of 0·11. This study provided strong evidence that GS using marker information alone can be an efficient tool for plant breeding.

The effect of using different culling regimens on genetic response with two-trait, two-stage selection in a nucleus broiler stock

Stochastic simulation was used to study the effect on genetic response and inbreeding of various two-stage two-trait culling strategies. Four different parameter sets were considered for the two traits, BW and egg number. Selection of replacement animals was based on animal model best linear unbiased prediction (BLUP) to obtain estimated breeding values (EBV) at the second stage. Culling at Stage 1 was based on either animal model BLUP or phenotypes, and information from culled animals was either available or not available for calculation of second stage EBV. Besides founder individuals, six discrete generations were considered. Culling based on BLUP of two traits at Stage 1 produced higher response than culling on phenotypic evaluations. It was found that culling based on phenotypic evaluation and not carrying information to the second stage reduce rates of response by 9 to 17% and produced inbreeding higher than or close to that of BLUP selection. This study clearly shows that a double penalty of less response and higher inbreeding is generally paid for not using all information. Optimum selection schemes will depend on relative costs and benefits of collecting and processing the extra information required for full BLUP selection schemes.

Efficiency of multistage marker-assisted selection in the improvement of multiple quantitative traits

The application of marker-assisted selection (MAS) to breeding programmes depends on its relative cost and the expected economic return compared to conventional phenotypic selection. The relative efficiency of MAS can be increased through a two-stage selection scheme or through marker-based, multiple-trait improvement. However, the effectiveness of these alternatives has not been quantified. In this study, we evaluate the efficiency of MAS relative to conventional phenotypic selection and marker-only selection in multistage selection for the improvement of multiple traits. We further incorporate the costs of obtaining measurements on phenotypic characters and marker loci into the objective function to evaluate the efficiency of MAS with respect to the gain per unit cost. Deterministic analyses indicate that excluding costs, multiple-trait MAS can be used to increase the aggregate breeding values in quantitative characters and is expected to be more effective than conventional selection or single-trait MAS. Two-stage MAS has a slightly reduced gain because of culling in the first stage. If the objective function is to maximize the gain per unit cost, multiple-trait MAS is inferior to phenotypic selection in most of the selection schemes investigated when the cost ratio (r) of obtaining measurements on phenotypic characters to scoring marker loci is less than unity (r < or = 1.0) and the heritability (h2) is greater than 0.3. The efficiency of MAS increases as r increases and h2 decreases. For MAS to be more effective, it is necessary to decrease further the cost associated with molecular marker assays.

Selection index updating for maximizing rate of annual genetic gain in laying hens

Four selection strategies aimed at maximizing egg production in laying hens were compared with respect to expected annual genetic gain (GA). The selection strategies were: 1) (S1P) Traditional single-stage selection based on a single-house production system using partial records for both the individual and its ancestors, 2) Single-stage selection based on a single-house production system using full records for both the individual and its ancestors (S1F), 3) Single-stage selection based on a two-house production system using partial records for the individual and full records for its ancestors (S2P), and 4) Multistage selection based on a two-house production system using partial records for the individual and all available ancestral records (M2P). Strategy M2P resulted in the shortest generation interval (0.538 yr) and was the most efficient (deltaGA4 = 3.620 eggs per year), whereas strategy S1F generated the longest generation interval (2 yr) and was the least efficient (deltaGA2 = 1.334 eggs per year). Strategies S1P and S2P resulted in generation intervals of 1 yr, and were intermediate in efficiency (deltaGA1 = 2.232 eggs per year, deltaGA3 = 2.593 eggs per year). It was concluded that a two-house production system utilizing multistage selection was the most effective selection methodology. Further, selection based on M2P is expected to improve persistency of lay, whereas selection on S1P will not.