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Selecting and mating parents in conventional phenotypic and genomic selection are crucial. Plant breeding programs aim to improve the economic value of crops, considering multiple traits simultaneously. When traits are negatively correlated and/or when there are missing records in some traits, selection becomes more complex. To address this problem, we propose a multitrait selection approach using the Multitrait Parental Selection (MPS) R package-an efficient tool for genetic improvement, precision breeding, and conservation genetics. The package employs Bayesian optimization algorithms and three loss functions (Kullback-Leibler, Energy Score, and Multivariate Asymmetric Loss) to identify parental candidates with desirable traits. The software's functionality includes three main functions-EvalMPS, FastMPS, and ApproxMPS-catering to different data availability scenarios. Through the presented application examples, the MPS R package proves effective in multitrait genomic selection, enabling breeders to make informed decisions and achieve strong performance across multiple traits., (© 2024 International Maize and Wheat Organization (CIMMYT). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Background: As a result of the technological progress, the use of sensors for crop survey has substantially increased, generating valuable information for modelling agricultural data. Plant spectroscopy jointly with statistical modeling can potentially help to assess certain chemical components of interest present in plants, which may be laborious and expensive to obtain by direct measurements. In this research, the phosphorus content in wheat grain is modeled using reflectance information measured by a hyperspectral sensor at different wavelengths. A Bayesian procedure for selecting variables was used to identify the set of the most important spectral bands. Additionally, three different models were evaluated: the first model assumes that the observations are independent, the other two models assume that the observations are spatially correlated: one of the proposed models, assumes spatial dependence using a Conditionally Autoregressive Model (CAR), and the other through an exponential correlogram. The goodness of fit of the models was evaluated by means of the Deviance Information Criterion, and the predictive power is evaluated using cross validation., Results: We have found that CAR was the model that best fits and predicts the data. Additionally, the selection variable procedure in the CAR model reveals which wavelengths in the range of 500-690 nm are the most important. Comparing the vegetative indices with the CAR model, it was observed that the average correlation of the CAR model exceeded that of the vegetative indices by 23.26%, - 1.2% and 22.78% for the year 2010, 2011 and 2012 respectively; therefore, the use of the proposed methodology outperformed the vegetative indices in prediction., Conclusions: The proposal to predict the phosphorus content in wheat grain using Bayesian approach, reflect with the results as a good alternative., (© 2023. The Author(s).)

Genomic selection (GS) is a technology used for genetic improvement, and it has many advantages over phenotype-based selection. There are several statistical models that adequately approach the statistical challenges in GS, such as in linear mixed models (LMMs). An active area of research is the development of software for fitting LMMs mainly used to make genome-based predictions. The lme4 is the standard package for fitting linear and generalized LMMs in the R-package, but its use for genetic analysis is limited because it does not allow the correlation between individuals or groups of individuals to be defined. This article describes the new lme4GS package for R, which is focused on fitting LMMs with covariance structures defined by the user, bandwidth selection, and genomic prediction. The new package is focused on genomic prediction of the models used in GS and can fit LMMs using different variance-covariance matrices. Several examples of GS models are presented using this package as well as the analysis using real data., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Caamal-Pat, Pérez-Rodríguez, Crossa, Velasco-Cruz, Pérez-Elizalde and Vázquez-Peña.)

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population's genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10 th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle., (Copyright © 2018 de Jesus et al.)

Genomic selection (GS) has become a tool for selecting candidates in plant and animal breeding programs. In the case of quantitative traits, it is common to assume that the distribution of the response variable can be approximated by a normal distribution. However, it is known that the selection process leads to skewed distributions. There is vast statistical literature on skewed distributions, but the skew normal distribution is of particular interest in this research. This distribution includes a third parameter that drives the skewness, so that it generalizes the normal distribution. We propose an extension of the Bayesian whole-genome regression to skew normal distribution data in the context of GS applications, where usually the number of predictors vastly exceeds the sample size. However, it can also be applied when the number of predictors is smaller than the sample size. We used a stochastic representation of a skew normal random variable, which allows the implementation of standard Markov Chain Monte Carlo (MCMC) techniques to efficiently fit the proposed model. The predictive ability and goodness of fit of the proposed model were evaluated using simulated and real data, and the results were compared to those obtained by the Bayesian Ridge Regression model. Results indicate that the proposed model has a better fit and is as good as the conventional Bayesian Ridge Regression model for prediction, based on the DIC criterion and cross-validation, respectively. A computing program coded in the R statistical package and C programming language to fit the proposed model is available as supplementary material., (Copyright © 2018 Pérez-Rodríguez et al.)

Genomic selection (GS) facilitates the rapid selection of superior genotypes and accelerates the breeding cycle. In this review, we discuss the history, principles, and basis of GS and genomic-enabled prediction (GP) as well as the genetics and statistical complexities of GP models, including genomic genotype×environment (G×E) interactions. We also examine the accuracy of GP models and methods for two cereal crops and two legume crops based on random cross-validation. GS applied to maize breeding has shown tangible genetic gains. Based on GP results, we speculate how GS in germplasm enhancement (i.e., prebreeding) programs could accelerate the flow of genes from gene bank accessions to elite lines. Recent advances in hyperspectral image technology could be combined with GS and pedigree-assisted breeding., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Key Message: A new genomic model that incorporates genotype × environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids. The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype × environment interaction (G × E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G × E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G × E in the prediction of untested maize hybrids increases the accuracy of genomic models.

In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-environment analyses and extended to account for G × E interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific interaction effects., (Copyright © 2016 Crop Science Society of America.)

Wildlife density estimates provide an idea of the current state of populations, and in some cases, reflect the conservation status of ecosystems, essential aspects for effective management actions. In Mexico, several regions have been identified as high priority areas for the conservation of species that have some level of risk, like the Yucatan Peninsula (YP), where the country has the largest population of jaguars. However, little is known about the current status of threatened and endangered felids, which coexist in the Northeastern portion of the Peninsula. Our objective was to estimate the wild cats' density population over time at El Eden Ecological Reserve (EEER) and its surrounding areas. Camera trap surveys over four years (2008, 2010, 2011 and 2012) were conducted, and data were obtained with the use of capture-recapture models for closed populations (CAPTURE + MMDM or 1/2 MMDM), and the spatially explicit capture-recapture model (SPACECAP). The species studied were jaguar (Panthera onca), puma (Puma concolor), ocelot (Leopardus pardalis), jaguarundi (Puma yaguaroundi) and margay (Leopardus wiedii). Capture frequency was obtained for all five species and the density for three (individuals/100km2). The density estimated with The Mean Maximum Distance Moved (MMDM), CAPTURE, ranged from 1.2 to 2.6 for jaguars, from 1.7 to 4.3 for pumas and from 1.4 to 13.8 for ocelots. The density estimates in SPACECAP ranged from 0.7 to 3.6 for jaguars, from 1.8 to 5.2 for pumas and 2.1 to 5.1 for ocelots. Spatially explicit capture recapture (SECR) methods in SPACECAP were less likely to overestimate densities, making it a useful tool in the planning and decision making process for the conservation of these species. The Northeastern portion of the Yucatan Peninsula maintains high populations of cats, the EEER and its surrounding areas are valuable sites for the conservation of this group of predators. Rev. Biol.

Genomic-enabled prediction in plant and animal breeding has become an active area of research. Many prediction models address the collinearity that arises when the number (p) of molecular markers (e.g. single-nucleotide polymorphisms) is larger than the sample size (n). Here we propose four Bayesian approaches to the problem based on commonly used data reduction methods. Specifically, we use a Gaussian linear model for an orthogonal transformation of both the observed data and the matrix of molecular markers. Because shrinkage of estimates is affected by the prior variance of transformed effects, we propose four structures of the prior variance as a way of potentially increasing the prediction accuracy of the models fitted. To evaluate our methods, maize and wheat data previously used with standard Bayesian regression models were employed for measuring prediction accuracy using the proposed models. Results indicate that, for the maize and wheat data sets, our Bayesian models yielded, on average, a prediction accuracy that is 3% greater than that of standard Bayesian regression models, with less computational effort., (Copyright © 2014 Cuevas et al.)