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There is a need to strengthen maize (Zea mays L.) breeding strategies based on multivariate selection to obtain high‐yielding hybrids that are more stable and resilient to contrasting environmental conditions. Here, we show how the multi‐trait stability index (MTSI) can be used to select maize hybrids for mean performance and stability of multiple traits. A set of 10 traits, including grain yield (GY), yield components, and plant‐related traits with negative and positive desired selection gains (SGs), were accessed in 90 F1 hybrids conducted in multi‐environment trials. Hybrid and hybrid × location interaction effects were significant (p ≤ .001) for all analyzed traits. The MTSI provided positive gains for all the four traits that were wanted to increase (2.52% ≤ SG ≤ 4.86; mean, 3.28%), including GY (SG, 4.86%), and negative gains for all the six traits that were wanted to decrease (–20.28% ≤ SG ≤ –0.09%; mean, –6.70%), including tassel branch number (SG, –20.28%) and plant height (SG, –1.2%). We also observed desired gains for the stability of all traits. Direct and univariate selection for GY solely was not efficient to provide desired gains for all traits. The MTSI provides a unique, robust, and easy‐to‐handle selection process that allows identifying the strengths and weaknesses of hybrids. The index was found to be a powerful tool to develop better selection strategies, optimizing the use of resources and time, thus contributing to the sustainability of maize breeding programs worldwide. Core Ideas The selection of maize hybrids in multi‐environment trials was performed using the multi‐trait stability index (MTSI). Direct and univariate selection for grain yield is not efficient. The MTSI provided desired gains for both mean performance and stability of all studied traits. The MTSI allows identifying the strengths and weaknesses of hybrids graphically.

Key messageLarge genetic improvement can be achieved by simultaneous genomic selection for grain yield and protein content when combining different breeding strategies in the form of selection indices.Genomic selection has been implemented in many national and international breeding programmes in recent years. Numerous studies have shown the potential of this new breeding tool; few have, however, taken the simultaneous selection for multiple traits into account that is though common practice in breeding programmes. The simultaneous improvement in grain yield and protein content is thereby a major challenge in wheat breeding due to a severe negative trade-off. Accordingly, the potential and limits of multi-trait selection for this particular trait complex utilizing the vast phenotypic and genomic data collected in an applied wheat breeding programme were investigated in this study. Two breeding strategies based on various genomic-selection indices were compared, which (1) aimed to select high-protein genotypes with acceptable yield potential and (2) develop high-yielding varieties, while maintaining protein content. The prediction accuracy of preliminary yield trials could be strongly improved when combining phenotypic and genomic information in a genomics-assisted selection approach, which surpassed both genomics-based and classical phenotypic selection methods both for single trait predictions and in genomic index selection across years. The employed genomic selection indices mitigated furthermore the negative trade-off between grain yield and protein content leading to a substantial selection response for protein yield, i.e. total seed nitrogen content, which suggested that it is feasible to develop varieties that combine a superior yield potential with comparably high protein content, thus utilizing available nitrogen resources more efficiently.

Improvements in feed efficiency of beef cattle have the potential to increase producer profitability and simultaneously lower the environmental footprint of beef production. Although there are many different approaches to measuring feed efficiency, residual feed intake (RFI) has increasingly become the measure of choice. Defined as the difference between an animal’s actual and predicted feed intake (based on weight and growth), RFI is conceptually independent of growth and body size. In addition, other measurable traits related to energy expenditure such as estimates of body composition can be included in the calculation of RFI to also force independence from these traits. Feed efficiency is a multifactorial and complex trait in beef cattle and inter-animal variation stems from the interaction of many biological processes influenced, in turn, by physiological status and management regimen. Thus, the purpose of this review was to summarise and interpret current published knowledge and provide insight into research areas worthy of further investigation. Indeed, where sufficient suitable reports exist, meta-analyses were conducted in order to mitigate ambiguity between studies in particular. We have identified a paucity of information on the contribution of key biological processes, including appetite regulation, post-ruminal nutrient absorption, and cellular energetics and metabolism to the efficiency of feed utilisation in cattle. In addition, insufficient information exists on the relationship between RFI status and productivity-related traits at pasture, a concept critical to the overall lifecycle of beef production systems. Overall, published data on the effect of RFI status on both terminal and maternal traits, coupled with the moderate repeatability and heritability of the trait, suggest that breeding for improved RFI, as part of a multi-trait selection index, is both possible and cumulative, with benefits evident throughout the production cycle. Although the advent of genomic selection, with associated improved prediction accuracy, will expedite the introgression of elite genetics for feed efficiency within beef cattle populations, there are challenges associated with this approach which may, in the long-term, be overcome by increased international collaborative effort but, in the short term, will not obviate the on-going requirement for accurate measurement of the primary phenotype.

Key messageSimultaneous 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.

Dioscorea praehensilis Benth. is a semi-wild yam species and a valuable source of resistance trait genes. To access the agronomic and tuber quality performance, eleven quantitative phenotypic traits were used to discriminate and identify promising accessions among 162 accessions of D. praehensilis collected in Ghana. Significant and high genetic variability (p < 0.001) for all eleven quantitative traits was found among the evaluated accessions. Moderate broad-sense heritability (H2) (30–60%) was observed for all the evaluated quantitative traits except the response to YMV and tuber hardness. The accessions were clustered into three groups; each cluster displayed genotypes with good potentiality for the different traits evaluated. Path coefficient analysis revealed positive contributions (p < 0.01) of the number of tubers per plant, tuber length, tuber width, stem internode length, number of internodes, and tuber flesh hardness to the total tuber weight per plant. Through the multi-trait genotype–ideotype distance index (MGIDI), 24 accessions were identified from the 162 evaluated accessions as top-ranking and could be used as progenitors for trait introgression. The results of this study provide insight for future yam breeding and improvement programs in West Africa.

Genomic selection (GS) in plant breeding aims to identify individuals with superior genetic merit while maintaining genetic diversity within populations. In plant breeding, considering multiple traits simultaneously makes optimizing selection complex, especially under genetic relatedness constraints. In this study, we propose a binary quadratic programming framework for constructing a multi-trait selection index that maximizes genetic gain while minimizing average pairwise relatedness appropriate for identifying superior candidates for advancement in the breeding pipeline. The approach combines estimated breeding values (EBVs) across multiple traits by applying trait-specific economic weights, while simultaneously accounting for coancestry through the genomic relationship matrix. By formulating the selection problem as a constrained Quadratic Programing Multi-trait Selection Index (QPMSI), our method enables the identification of a fixed number of candidate individuals that jointly optimize selection index values and control genetic relatedness. We evaluated the performance of the proposed method using five real genomic datasets and demonstrated that it provides a more effective balance between selection response and control of genetic relatedness than the Linear Programming Multi-trait Selection Index (LPMSI). In particular, the QPMSI consistently outperformed the LPMSI in terms of the MV metric (gain-to-degree of relatedness ratio), achieving improvements of at least 53.8%. This framework offers a practical and computationally efficient tool for sustainable breeding strategies in multi-trait selection contexts.

Recurrent selection is an effective breeding method for improving complex traits in wheat (Triticum aestivum L.) breeding. In this study, we propose a genitor selection strategy, employing a multi‐trait selection approach and genetic diversity analysis. To evaluate our proposed method, we conducted a lattice design trial during the winter seasons of 2020 and 2021 in Viçosa, MG, Brazil, comprising 87 lines and 13 commercial cultivars. It assessed various traits such as plant height, days to heading, wheat leaf rust, tan spot of wheat, a hundred grain mass, hectoliter weight, and grain yield, and the best linear unbiased predictor (BLUP) was obtained for each trait via restricted maximum likelihood. Next, a genotypic distance matrix, derived from principal component analysis using the BLUP values, was computed to perform hierarchical clustering via the unweighted pair group method with arithmetic mean. The selection of superior genotypes was made utilizing the multi‐trait genotype‐ideotype distance index, resulting in the identification of eight lines and two commercial cultivars as candidates. Furthermore, the genetic diversity analysis revealed distinct clusters among the selected genotypes. To assess the divergence of the chosen genitors, this study proposes a complementarity matrix using factor analysis. Our results indicate that this selection strategy effectively directed the identification of the best and divergent genitors. The complementarity matrix developed in this paper to evaluate the crossings proposal can also be used to evaluate combinations in any panel selected via a multi‐trait approach and can be easily applied and interpreted by breeders of various programs. Core Ideas Novel strategy to select divergent genitors for cycle zero of recurrent selection program is presented. Multi‐trait selection and genetic diversity analysis of tropical wheat on phenotypic data is presented. A complementarity index based on a factor analysis is presented to evaluate the proposed crossings.

Genetic improvement is crucial for ensuring food security globally. Indeed, plant breeding has contributed significantly to increasing the productivity of major crops, including rice, over the last century. Evaluating the efficiency of breeding strategies necessitates a quantification of this progress. One approach involves assessing the genetic gain achieved through breeding programs based on quantitative traits. This study aims to provide a theoretical understanding of genetic gain, summarize the major results of genetic gain studies in rice breeding, and suggest ways of improving breeding program strategies and future studies on genetic gain. To achieve this, we present the concept of genetic gain and the essential aspects of its estimation. We also provide an extensive literature review of genetic gain studies in rice (Oryza sativa L.) breeding programs to understand the advances made to date. We reviewed 29 studies conducted between 1999 and 2023, covering different regions, traits, periods, and estimation methods. The genetic gain for grain yield, in particular, showed significant variation, ranging from 1.5 to 167.6 kg/ha/year, with a mean value of 36.3 kg/ha/year. This translated into a rate of genetic gain for grain yield ranging from 0.1% to over 3.0%. The impact of multi-trait selection on grain yield was clarified by studies that reported genetic gains for other traits, such as plant height, days to flowering, and grain quality. These findings reveal that while breeding programs have achieved significant gains, further improvements are necessary to meet the growing demand for rice. We also highlight the limitations of these studies, which hinder accurate estimations of genetic gain. In conclusion, we offer suggestions for improving the estimation of genetic gain based on quantitative genetic principles and computer simulations to optimize rice breeding strategies.

Recently developed selection indexes provide solutions for plant breeding, using linear‐bilinear models that consider factors as fixed or random. This work aimed to compare the multitrait selection indexes based on factor analysis and ideotype‐design (FAI‐BLUP), GGE biplot, and grain yield × trait index (GYT), and proposes the use of predicted genetic values together with the GYT index (best linear unbiased prediction used in grain yield*trait index, GYT‐BLUP). In addition, this work indicates the best index to select superior soybean [Glycine max (L.) Merr.] genotypes, closer to the ideotype. Data from 35 homozygous soybean lines and four checks, were obtained from trials conducted in six locations in the southern region of Brazil in the 2014/2015 crop season. The grain yield, yield components, morphological and grain composition were evaluated. Phenotypic data were used for GGE biplot and GYT analysis, using the software GGE biplot. Genetic values were predicted with mixed models considering genotype and location as random and fixed effects, respectively. Thus, genetic values were used in GYT‐BLUP and FAI‐BLUP indexes. These methods were compared by Spearman's rank correlation. Genetic gains obtained by indexes and traits were estimated. Soybean lines L1 and L22, and cultivars C3 and C4 were selected based on their performance for multiple traits, for indexes used. Thus, we suggest to combined FAI‐BLUP and GYT‐BLUP indexes. The GYT‐BLUP has a high importance for grain yield, which was related to all other traits. FAI‐BLUP gave similar weights for all traits. So, combining different approaches can provide better answers to breeders.

A set of superior parental lines is imperative for the development of high-performing inbred lines in any biparental crossing program for crops. The main objectives of this study are to (a) develop a genomic prediction approach to identify superior parental lines for multi-trait selection, and (b) generate a software package for users to execute the proposed approach before conducting field experiments. According to different breeding goals of the target traits, a novel selection index integrating information from genomic-estimated breeding values (GEBVs) of candidate accessions was proposed to evaluate the composite performance of simulated progeny populations. Two rice ( Oryza sativa L.) genome datasets were analyzed to illustrate the potential applications of the proposed approach. One dataset applied to the parental selection for producing inbred lines with satisfactory performance in primary and secondary traits simultaneously. The other one applied to demonstrate the application of producing inbred lines with high adaptability to different environments. Overall, the results showed that incorporating GEBV and genomic diversity into a selection strategy based on the proposed selection index could assist in selecting superior parents to meet the desired breeding goals and increasing long-term genetic gain. An R package, called IPLGP, was generated to facilitate the widespread application of the approach.