In this article, we imagine a breeding scenario with a population of individuals that have been genotyped but not phenotyped. We derived a computationally efficient statistic that uses this genetic information to measure the reliability of genomic estimated breeding values (GEBV) for a given set of individuals (test set) based on a training set of individuals. We used this reliability measure with a genetic algorithm scheme to find an optimized training set from a larger set of candidate individuals. This subset was phenotyped to create the training set that was used in a genomic selection model to estimate GEBV in the test set. Our results show that, compared to a random sample of the same size, the use of a set of individuals selected by our method improved accuracies. We implemented the proposed training selection methodology on four sets of data on Arabidopsis, wheat, rice and maize. This dynamic model building process that takes genotypes of the individuals in the test sample into account while selecting the training individuals improves the performance of genomic selection models.

Phenotyping is the current bottleneck in plant breeding, especially because next-generation sequencing has decreased genotyping cost more than 100.000 fold in the last 20 years. Therefore, the cost of phenotyping needs to be optimized within a breeding program. When designing the implementation of genomic selection scheme into the breeding cycle, breeders need to select the optimal method for (1) selecting training populations that maximize genomic prediction accuracy and (2) to reduce the cost of phenotyping while improving precision. In this article, we compared methods for selecting training populations under two scenarios: Firstly, when the objective is to select a training population set (TRS) to predict the remaining individuals from the same population (Untargeted), and secondly, when a test set (TS) is first defined and genotyped, and then the TRS is optimized specifically around the TS (Targeted). Our results show that optimization methods that include information from the test set (targeted) showed the highest accuracies, indicating that apriori information from the TS improves genomic predictions. In addition, predictive ability enhanced especially when population size was small which is a target to decrease phenotypic cost within breeding programs.

Selection in breeding programs can be done by using phenotypes (phenotypic selection), pedigree relationship (breeding value selection) or molecular markers (marker assisted selection or genomic selection). All these methods are based on truncation selection, focusing on the best performance of parents before mating. In this article we proposed an approach to breeding, named genomic mating, which focuses on mating instead of truncation selection. Genomic mating uses information in a similar fashion to genomic selection but includes information on complementation of parents to be mated. Following the efficiency frontier surface, genomic mating uses concepts of estimated breeding values, risk (usefulness) and coefficient of ancestry to optimize mating between parents. We used a genetic algorithm to find solutions to this optimization problem and the results from our simulations comparing genomic selection, phenotypic selection and the mating approach indicate that current approach for breeding complex traits is more favorable than phenotypic and genomic selection. Genomic mating is similar to genomic selection in terms of estimating marker effects, but in genomic mating the genetic information and the estimated marker effects are used to decide which mates should be crossed to obtain the next breeding population.

Genomic selection (GS) promises to accelerate genetic gain in plant breeding programs especially for crop species such as cassava that have long breeding cycles. Practically, to implement GS in cassava breeding, it is necessary to evaluate different GS models and to develop suitable models for an optimized breeding pipeline. In this paper, we compared (1) prediction accuracies from a single-trait (uT) and a multi-trait (MT) mixed model for a single-environment genetic evaluation (Scenario 1), and (2) accuracies from a compound symmetric multi-environment model (uE) parameterized as a univariate multi-kernel model to a multivariate (ME) multi-environment mixed model that accounts for genotype-by-environment interaction for multi-environment genetic evaluation (Scenario 2). For these analyses, we used 16 years of public cassava breeding data for six target cassava traits and a fivefold cross-validation scheme with 10-repeat cycles to assess model prediction accuracies. In Scenario 1, the MT models had higher prediction accuracies than the uT models for all traits and locations analyzed, which amounted to on average a 40% improved prediction accuracy. For Scenario 2, we observed that the ME model had on average (across all locations and traits) a 12% improved prediction accuracy compared to the uE model. We recommend the use of multivariate mixed models (MT and ME) for cassava genetic evaluation. These models may be useful for other plant species.

In plant and animal breeding studies a distinction is made between the genetic value (additive plus epistatic genetic effects) and the breeding value (additive genetic effects) of an individual since it is expected that some of the epistatic genetic effects will be lost due to recombination. In this article, we argue that the breeder can take advantage of the epistatic marker effects in regions of low recombination. The models introduced here aim to estimate local epistatic line heritability by using genetic map information and combining local additive and epistatic effects. To this end, we have used semiparametric mixed models with multiple local genomic relationship matrices with hierarchical designs. Elastic-net postprocessing was used to introduce sparsity. Our models produce good predictive performance along with useful explanatory information.