- Cerón-Rojas, J.J.

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Cerón-Rojas

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Cerón-Rojas, J.J.

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- Chapter 11. RIndSel: selection Indices with R(Springer, 2018) Alvarado Beltrán, G.; Pacheco Gil, Rosa Angela; Pérez-Elizalde, S.; Burgueño, J.; Rodríguez, F.M.; Cerón-Rojas, J.J.; Crossa, J.
Show more RIndSel is a graphical unit interface that uses selection index theory to select individual candidates as parents for the next selection cycle. The index can be a linear combination of phenotypic values, genomic estimated breeding values, or a linear combination of phenotypic values and marker scores. Based on the restriction imposed on the expected genetic gain per trait, the index can be unrestricted, null restricted, or predetermined proportional gain indices. RIndSel is compatible with any of the following versions of Windows: XP, 7, 8, and 10. Furthermore, it can be installed on 32-bit and 64-bit computers. In the context of fixed and mixed models, RIndSel estimates the phenotypic and genetic covariance using two main experimental designs: randomized complete block design and lattice or alpha lattice design. In the following, we explain how RIndSel can be used to determine individual candidates as parents for the next cycle of improvement.Show more Publication - Chapter 9. Multistage linear selection indices(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more Multistage linear selection indices select individual traits available at different times or stages and are applied mainly in animals and tree breeding, where the traits under consideration become evident at different ages. The main indices are: the unrestricted, the restricted, and the predetermined proportional gain selection index. The restricted and predetermined proportional gain indices allow null and predetermined restrictions to be imposed on the trait expected genetic gain (or multi-trait selection response) values, whereas the rest of the traits remain changed without any restriction. The three indices can use phenotypic, genomic, or both sets of information to predict the unobservable net genetic merit values of the candidates for selection and all of them maximize the selection response, the expected genetic gain for each trait, have maximum accuracy, are the best predictor of the net genetic merit, and provide the breeder with an objective rule for evaluating and selecting several traits simultaneously. The theory of the foregoing indices is based on the independent culling method and on the linear phenotypic selection index, and is described in this chapter in the phenotypic and genomic selection context. Their theoretical results are validated in a two-stage breeding selection scheme using real and simulated data.Show more Publication - Chapter 7. Linear phenotypic eigen selection index methods(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more Based on the canonical correlation, on the singular value decomposition (SVD), and on the linear phenotypic selection indices theory, we describe the eigen selection index method (ESIM), the restricted ESIM (RESIM), and the predetermined proportional gain ESIM (PPG-ESIM), which use only phenotypic information to predict the net genetic merit. The ESIM is an unrestricted linear selection index, but the RESIM and PPG-ESIM are linear selection indices that allow null and predetermined restrictions respectively to be imposed on the expected genetic gains of some traits, whereas the rest remain without any restrictions. The aims of the three indices are to predict the unobservable net genetic merit values of the candidates for selection, maximize the selection response, and the accuracy, and provide the breeder with an objective rule for evaluating and selecting several traits simultaneously. Their main characteristics are: they do not require the economic weights to be known, the first multi-trait heritability eigenvector is used as its vector of coefficients; and because of the properties associated with eigen analysis, it is possible to use the theory of similar matrices to change the direction and proportion of the expected genetic gain values without affecting the accuracy. We describe the foregoing three indices and validate their theoretical results using real and simulated data.Show more Publication - Chapter 10. Stochastic simulation of four linear phenotypic selection indices(Springer, 2018) Crossa, J.; Burgueño, J.; Toledo, F.H.; Cerón-Rojas, J.J.
Show more Stochastic simulation can contribute to a better understanding of the problem, and has already been successfully applied to evaluate other breeding scenarios. Despite all the theories developed in this book concerning different types of indices, including phenotypic data and/or data on molecular markers, no examples have been presented showing the long-term behavior of different indices. The objective of this chapter is to present some results and insights into the in silico (computer simulation) performance comparison of over 50 selection cycles of a recurrent and generic population breeding program with different selection indices, restricted and unrestricted. The selection indices included in this stochastic simulation were the linear phenotypic selection index (LPSI), the eigen selection index method (ESIM), the restrictive LPSI, and the restrictive ESIM.Show more Publication - Chapter 8. Linear molecular and genomic eigen selection index methods(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more The three main linear phenotypic eigen selection index methods are the eigen selection index method (ESIM), the restricted ESIM (RESIM) and the predetermined proportional gain ESIM (PPG-ESIM). The ESIM is an unrestricted index, but the RESIM and PPG-ESIM allow null and predetermined restrictions respectively to be imposed on the expected genetic gains of some traits, whereas the rest remain without any restrictions. These indices are based on the canonical correlation, on the singular value decomposition, and on the linear phenotypic selection indices theory. We extended the ESIM theory to the molecular-assisted and genomic selection context to develop a molecular ESIM (MESIM), a genomic ESIM (GESIM), and a genome-wide ESIM (GW-ESIM). Also, we extend the RESIM and PPG-ESIM theory to the restricted genomic ESIM (RGESIM), and to the predetermined proportional gain genomic ESIM (PPG-GESIM) respectively. The latter five indices use marker and phenotypic information jointly to predict the net genetic merit of the candidates for selection, but although MESIM uses only statistically significant markers linked to quantitative trait loci, the GW-ESIM uses all genome markers and phenotypic information and the GESIM, RGESIM, and PPG-GESIM use the genomic estimated breeding values and the phenotypic values to predict the net genetic merit. Using real and simulated data, we validated the theoretical results of all five indices.Show more Publication - Chapter 4. Linear marker and genome-wide selection indices(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more There are two main linear marker selection indices employed in marker-assisted selection (MAS) to predict the net genetic merit and to select individual candidates as parents for the next generation: the linear marker selection index (LMSI) and the genome-wide LMSI (GW-LMSI). Both indices maximize the selection response, the expected genetic gain per trait, and the correlation with the net genetic merit; however, applying the LMSI in plant or animal breeding requires genotyping the candidates for selection; performing a linear regression of phenotypic values on the coded values of the markers such that the selected markers are statistically linked to quantitative trait loci that explain most of the variability in the regression model; constructing the marker score, and combining the marker score with phenotypic information to predict and rank the net genetic merit of the candidates for selection. On the other hand, the GW-LMSI is a single-stage procedure that treats information at each individual marker as a separate trait. Thus, all marker information can be entered together with phenotypic information into the GW-LMSI, which is then used to predict the net genetic merit and select candidates. We describe the LMSI and GW-LMSI theory and show that both indices are direct applications of the linear phenotypic selection index theory to MAS. Using real and simulated data we validated the theory of both indices.Show more Publication - Chapter 2. The linear phenotypic selection index theory(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more The main distinction in the linear phenotypic selection index (LPSI) theory is between the net genetic merit and the LPSI. The net genetic merit is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values, whereas the LPSI is a linear combination of several observable and optimally weighted phenotypic trait values. It is assumed that the net genetic merit and the LPSI have bivariate normal distribution; thus, the regression of the net genetic merit on the LPSI is linear. The aims of the LPSI theory are to predict the net genetic merit, maximize the selection response and the expected genetic gains per trait (or multi-trait selection response), and provide the breeder with an objective rule for evaluating and selecting parents for the next selection cycle based on several traits. The selection response is the mean of the progeny of the selected parents, whereas the expected genetic gain per trait, or multi-trait selection response, is the population means of each trait under selection of the progeny of the selected parents. The LPSI allows extra merit in one trait to offset slight defects in another; thus, with its use, individuals with very high merit in one trait are saved for breeding even when they are slightly inferior in other traits. This chapter describes the LPSI theory and practice. We illustrate the theoretical results of the LPSI using real and simulated data. We end this chapter with a brief description of the quadratic selection index and its relationship with the LPSI.Show more Publication - Chapter 1. General introduction(Springer, 2018) Cerón-Rojas, J.J.; Crossa, J.
Show more We describe the main characteristics of two approaches to the linear selection indices theory. The first approach is called standard linear selection indices whereas the second of them is called eigen selection index methods. In the first approach, the economic weights are fixed and known, whereas in the second approach the economic weights are fixed but unknown. This is the main difference between both approaches and implies that the eigen selection index methods include to the standard linear selection indices because they do not require that the economic weights be known. Both types of indices predict the net genetic merit and maximize the selection response, and they give the breeder an objective criterion to select individuals as parents for the next selection cycle. In addition, in the prediction they can use phenotypic, markers, and genomic information. In both approaches, the indices can be unrestricted, null restricted or predetermined proportional gains and can be used in the context of single-stage or multistage breeding selection schemes. We describe the main characteristics of the two approaches to the linear selection indices theory and we finish this chapter describing the Lagrange multiplier method, which is the main tool to maximize the selection index responses.Show more Publication