Multiple-trait, random regression, and compound symmetry models for analyzing multi-environment trials in maize breeding.

Comparison of random regression and repeatability models to predict breeding values from test-day records of Norwegian goats

Various random regression models have been advocated for the fitting of covariance structures. It was suggested that a spline model would fit better to weight data than a random regression model that utilizes orthogonal polynomials. The objective of this study was to investigate which kind of random regression model fits best to weight data of pigs. Two random regression models that described weight of individual pigs, one using orthogonal polynomials, and the other using splines, were compared. A comparison with a multivariate model, Akaike's information criterion, and the Bayesian-Schwarz information criterion were used to select the best model. Genetic, permanent environmental, and total variances increased with age. Heritabilities for the multivariate model ranged from 0.14 to 0.19, and for both random regression models the heritabilities were fluctuating around 0.17. Both genetic and phenotypic correlations decreased when the interval between measurements increased. The spline model needed fewer parameters than the multivariate and polynomial models. Akaike's information criterion was least for the spline model and greatest for the multivariate model. The Bayesian-Schwarz information criterion was least for the polynomial model and greatest for the multivariate model. Residuals of all models were normally distributed. Based on these results, it is concluded that random regression models provide the best fit to pig weight data.

The main objective of the present study was to detect the most appropriate random regression model for estimating the genetic parameters of weekly egg production. Two strains of Japanese quails including wild and white quails and pure and cross mating methods were considered. The egg collection started at the seventh week of age and lasted for 7weeks. A random regression model using Legendre polynomial was used to analyze the weekly egg records. The model with Legendre polynomial of order 1 for the additive genetic and order 3 for permanent environmental effect was chosen as the appropriate model, based on Bayesian information criterion (BIC) and Akaike information criterion (AIC). The heritability estimates for weekly egg production were low (ranging from 0.06 to 0.09). Furthermore, the ratios of permanent environmental variance to the phenotypic variance were almost moderate, varying from 0.18 to 0.44. Genetic and phenotypic correlations between weekly egg records ranged from 0.65 to 0.93 and from 0.27 to 0.67, respectively. These results indicated that the selection based on the early egg numbers could effectively improve egg production in later periods. Furthermore, the efficiency of egg production can be enhanced with a combination of breeding programs and management strategies.

Kernel row number (KRN) is a pivotal determinant for yield in maize breeding programs. However, the genetic basis underlying KRN remains largely elusive. To identify candidate genes regulating KRN, a population of 318 BC4F4 chromosomal segment substitution lines (CSSLs) was developed via backcrossing, with Baimaya (BMY) as the donor parent and B73 as the recurrent parent. Furthermore, a high-density genetic linkage map containing 2859 high-quality single-nucleotide polymorphism (SNP) markers was constructed for quantitative trait locus (QTL) mapping of KRN. Notably, 19 QTLs controlling KRN were detected across three environments and in the Best Linear Unbiased Prediction (BLUP) values; among these, a major-effect QTL (qKRN4.09-1) was consistently identified across all three environments and BLUP. Then, the integration of linkage mapping and transcriptome analysis of 5 mm immature ears from near-isogenic lines (NILs) uncovered a candidate gene, Zm00001eb205550. This gene exhibited significant downregulation in qKRN4.09-1BMY, and two missense variants were detected between qKRN4.09-1BMY and qKRN4.09-1B73. Zm00001eb205550 exhibited preferential expression in developing ears. Moreover, the pyramiding of favorable alleles from the five stable QTLs significantly increased KRN in maize. These findings advance our genetic understanding of maize ear development and provide valuable genetic targets for improving KRN in maize breeding.

Estimates of genetic parameters for scrotal circumference using random regression models in Nelore cattle

Rules to generate the inverse additive relationship matrix (A -1 ) are defined to enable the adoption restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) in autopolyploid populations with multiple ploidy levels. Many important agronomic, horticultural, ornamental, forestry, and aquaculture species are autopolyploids. However, the adoption of restricted maximum likelihood (REML), for estimating co/variance components, and best linear unbiased prediction (BLUP), for predicting breeding values, has been hampered in autopolyploid breeding by the absence of an appropriate means of generating the inverse additive relationship matrix (A -1 ). This paper defines rules to generate the A -1 of autopolyploid populations comprised of individuals of the same or different ploidy-levels, including populations exhibiting (1) odd-numbered ploidy levels (e.g.triploids), (2) sex-based differences in the probability that gametic genes are identical by descent and (3) somatic chromosome doubling. Inbreeding, due to double reduction, in autopolyploid founders in the absence of mating among relatives is also accounted for. A previously defined approach is modified, whereby rules are initially defined to build an inverse matrix of kinship coefficients (K -1 ), which is then used to generate A -1 . An R package (polyAinv; https://github.com/mghamilton/polyAinv ) to implement these rules has been developed and examples of analyses provided. The adoption of REML and BLUP methods made possible by these new rules has the potential to provide further insights into the quantitative genetic architecture of autopolyploid and multiple-ploidy populations, improve estimates of breeding values, and increase genetic gains made through recurrent selection.

Milk yield test-day records on the first three lactations of 25,500 Holstein cows were used to estimate genetic parameters and predict breeding values for nine measures of persistency and 305-d milk yield in a random regression animal model using two criteria to define the fixed regression. Legendre polynomials of fourth and fifth orders were used to model the fixed and random regressions of lactation curves. The fixed regressions were adjusted for average milk yield on populations (single) or subpopulations (multiple) formed by cows that calved at the same age and in the same season. Akaike Information (AIC) and Bayesian Information (BIC) criteria indicated that models with multiple regression lactation curves had the best fit to test-day milk records of first lactations, while models with a single regression curve had the best fit for the second and third lactations. Heritability and genetic correlation estimates between persistency and milk yield differed significantly depending on the lactation order and the measures of persistency used. These parameters did not differ significantly depending on the criteria used for defining the fixed regressions for lactation curves. In general, the heritability estimates were higher for first (0.07 to 0.43), followed by the second (0.08 to 0.21) and third (0.04 to 0.10) lactation. The rank of sires resulting from the processes of genetic evaluation for milk yield or persistency using random regression models differed according to the criteria used for determining the fixed regression of lactation curve.

Multiple-trait and random regression models have multiplied the number of equations needed for the estimation of variance components. To avoid inversion or decomposition of a large coefficient matrix, we propose estimation of variance components by Monte Carlo expectation maximization restricted maximum likelihood (MC EM REML) for multiple-trait linear mixed models. Implementation is based on full-model sampling for calculating the prediction error variances required for EM REML. Performance of the analytical and the MC EM REML algorithm was compared using a simulated and a field data set. For field data, results from both algorithms corresponded well even with one MC sample within an MC EM REML round. The magnitude of the standard errors of estimated prediction error variances depended on the formula used to calculate them and on the MC sample size within an MC EM REML round. Sampling variation in MC EM REML did not impair the convergence behaviour of the solutions compared with analytical EM REML analysis. A convergence criterion that takes into account the sampling variation was developed to monitor convergence for the MC EM REML algorithm. For the field data set, MC EM REML proved far superior to analytical EM REML both in computing time and in memory need.

Modeling of cultivar × trial effects for multi‐environment trials (METs) within a mixed model framework is now common practice in many plant breeding programs. The factor analytic (FA) model is a parsimonious form used to approximate the fully unstructured form of the genetic variance–covariance matrix in the model for MET data. In this study, we demonstrate that the FA model is generally the model of best fit across a range of data sets taken from early generation trials in a breeding program. In addition, we demonstrate the superiority of the FA model in achieving the most common aim of METs, namely the selection of superior genotypes. Selection is achieved using best linear unbiased predictions (BLUPs) of cultivar effects at each environment, considered either individually or as a weighted average across environments. In practice, empirical BLUPs (E‐BLUPs) of cultivar effects must be used instead of BLUPs since variance parameters in the model must be estimated rather than assumed known. While the optimal properties of minimum mean squared error of prediction (MSEP) and maximum correlation between true and predicted effects possessed by BLUPs do not hold for E‐BLUPs, a simulation study shows that E‐BLUPs perform well in terms of MSEP.

To improve multi-environmental trial (MET) analysis, a compound method—which combines factor analytic (FA) model with additive main effect and multiplicative interaction (AMMI) and genotype main effect plus genotype-by-environment interaction (GGE) biplot—was conducted in this study. The diameter at breast height of 36 open-pollinated (OP) families of Pinus taeda at six sites in South China was used as a raw dataset. The best linear unbiased prediction (BLUP) data of all individual trees in each site was obtained by fitting the spatial effects with the FA method from raw data. The raw data and BLUP data were analyzed and compared by using the AMMI and GGE biplot. BLUP results showed that the six sites were heterogeneous and spatial variation could be effectively fitted by spatial analysis with the FA method. AMMI analysis identified that two datasets had highly significant effects on the site, family, and their interactions, while BLUP data had a smaller residual error, but higher variation explaining ability and more credible stability than raw data. GGE biplot results revealed that raw data and BLUP data had different results in mega-environment delineation, test-environment evaluation, and genotype evaluation. In addition, BLUP data results were more reasonable due to the stronger analytical ability of the first two principal components. Our study suggests that the compound method combing the FA method with the AMMI and GGE biplot could improve the analysis result of MET data in Pinus teada as it was more reliable than direct AMMI and GGE biplot analysis on raw data.

Os registros de produção de leite de 11.023 primeiras lactações de vacas da raça Holandesa pertencentes a 251 rebanhos distribuídos no estado de Minas Gerais foram usados para comparar os polinômios de Legendre e a função Wilmink em modelos de regressão aleatória (MRA) quanto aos seus efeitos na estimação de parâmetros genéticos e predição de valores genéticos para nove medidas de persistência na lactação e produção de leite até 305 dias. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 305(0) dia de lactação incluíram o efeito de rebanho-ano-mês do controle, os parâmetros dos polinômios de Legendre de ordens 3 a 5 ou da função de Wilmink, para modelar as curvas fixas da regressão dentro das subclasses de idade-estação de parto da vaca e os parâmetros dos polinômios de Legendre de ordens 3 a 5, para modelar os efeitos aleatórios genético-aditivo e permanente de ambiente. Os testes do critério de informação de Akaike e Bayesiano indicaram o modelo com maior número de parâmetros como o que melhor se ajustou aos dados de produção de leite. Observaram-se grandes variações nas estimativas de herdabilidade para a maioria das medidas de persistência na lactação, com uso dos modelos que envolveram ajustes dos polinômios de Legendre. As estimativas de herdabilidade variaram de 0,11 a 0,33 para produção de leite ao longo da lactação, de 0,33 a 0,36 para a produção de leite até 305 dias e de 0,00 a 0,32 para persistência na lactação. As correlações genéticas entre persistência e produção de leite até 305 dias diferiram com o modelo e a medida de persistência. A utilização da função de Wilmink, comparada aos polinômios de Legendre, proporcionou mudanças expressivas na ordem dos animais quando classificados para persistência na lactação.

The objective of this study was to estimate genetic parameters for the body weights of Turkish Holstein bulls using the random regression model. The data set consists of 1475 body weight records from 395 Holstein bulls raised in the same herd. Body weight records of bulls aged between 32 and 725 days old were collected at approximately two-month intervals from December 2013 to October 2014. In the study body weight measurements made on the same day were accepted as a group and the bulls were grouped into 10 different groups according to their age. The additive genetic and permanent environmental effects were estimated using DFREML algorithm by third order Legendre polynomials. The additive genetic variance estimates ranged from 10.73 to 4867.07, the phenotypic variance estimates ranged from 382.84 to 5514.86 and permanent environmental variance estimates ranged from 0.33 to 63.27. The heritability values were estimated between 0.03 to 0.90. The phenotypic and additive genetic correlations between body weights were positively estimated between 0.085 to 0.89 and 0.53 to 0.94, respectively. It was concluded that use of body weight at an earlier age will give advantage in breeding studies for body weight at slaughter.

Mal de Rio Cuarto (MRC) and common rust (CR), caused by Mal de Rio Cuarto virus (MRCV) and Puccinia sorghi, respectively, are endemic diseases affecting maize (Zea mays L.) production in Argentina. Exotic maize germplasm is an important source of resistance to these diseases. The aim of this work was to identify maize lines that exhibit MRC and CR resistance. A multienvironment trial was performed to phenotypically assess a diverse panel of inbred lines from the International Maize and Wheat Improvement Center (CIMMYT). The maize lines were evaluated using a disease severity index (DSI) for MRC and CR in the central area of Argentina. A multitrait mixed linear model (MLM) was used to identify the lines with the best performance for both diseases and estimate genetic parameters. No correlation of resistance between MRC and CR was found among the tested lines. Additionally, best linear unbiased predictions (BLUPs) of genotypic effects were used as response variable to perform a genome‐wide association study (GWAS). The GWAS revealed promising alleles for maize breeding, two associated with MRC and three with CR. Lines with lower DSI for MRC and CR were identified as novel materials for incorporating resistance to the local germplasm.

Sire evaluation is one of the most important aspects of breed improvement programs which involve the estimation of breeding value of the bulls on the basis of their daughter's first lactation 305-day milk yield.Hence, the present research work was planned to estimate breeding value of Jersey crossbred sires on the basis of their daughter's first lactation 305-day milk yield, which are under Progeny testing programme, Andhra Pradesh Livestock Development Agency in Chittoor district of Andhra Pradesh.A total of 1200 progeny records belonging to 20 Jersey crossbred sires were utilized to estimate breeding values of sires for first lactation milk yield traits by using three different methods of sire evaluation viz., least squares method (LSM), best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) methods.The average breeding values for age at first calving, first lactation length, first service period and first dry period were 1045.14, 293.55, 149.40 and 113.83 days by LSM metho d and 1045.52,294.54, 145.04 and 107.50 days by BLUP method and 1043.88,295.86, 157.83 and 123.36 days by REML method for the respective traits.The error variance for REML method was lowest 18817.10day 2 for age at first calving, 377.45 day 2 for first lactation length and 2720.81day 2 for first dry period, whereas for first service period BLUP method had lower error variance of 6689.49day 2 .The highest coefficient of determination values for age at first calving (11.40%) and first dry period (37.60%) were noticed in REML method, whereas for the first lactation length (5.60%) and first service period (14.90%) highest R 2 value was observed in LSM method.The coefficient of variation values for most the first lactation milk yield traits were found to be almost similar by LSM and BLUP methods; for age at first calving (13.76%), for first service period (52.18% & 51.82%) and for first dry period (51.15% & 50.95%).The rank correlations and product moment correlations for FLMY traits estimated by three sire evaluation methods were found to be highly significant (P 0.01).Rank correlations values ranged from 0.693 (LSM with REML) to 1.000 (BLUP with REML), whereas product moment correlations values ranged from 0.772 (LSM with REML) to 1.000 (BLUP with REML).REML was found to be most effective method of sire evaluation compared to other methods for the present set of data.

In Bangladesh, sweet potato holds the fourth position as a crucial carbohydrate source, trailing rice, wheat, and potato. However, locally grown sweet potato varieties often display limited stability and yield. To tackle this challenge, diverse selection methods and statistical models were utilized to pinpoint sweet potato genotypes showcasing both stability and superior yield and quality traits. In the initial two years, multiple selection methods were employed to narrow down the collections based on preferences for yield and its contributing traits. Subsequently, a multi-environment trial (MET) was conducted in the following year to pinpoint superior and stable genotypes with desirable yield and quality characteristics. An integrated approach involving the Multi-Trait Genotype Ideotype Distance Index (MGIDI), Factor Analysis and Ideotype-Design (FAI-BLUP), and Smith-Hazel Index (SH) led to the identification of 71 superior sweet potato genotypes out of a total of 351 in the initial growing season. In the subsequent season, the MGIDI selection index was applied to the 71 genotypes, resulting in the selection of 11 top-performing genotypes. This selection process was complemented by a detailed analysis of the strengths and weaknesses of the selected genotypes. In the MET, the mixed effect model, specifically the linear mixed model (LMM), identified significant genotypic and genotype-environment interaction (GEI) variances. This points to elevated heritability and selection accuracy, ultimately boosting the model's reliability. By combining the strengths of LMM and additive main effects and multiplicative interaction (AMMI), the best linear unbiased prediction (BLUP) index identified H20 as the top-performing genotype for marketable root yield (MRY), H37 for dry weight of root (DW), H8 for beta carotene (BC) and H41 for vitamin c (VC). These genotypes surpassed the overall average in the WAAS index. For simultaneous stability and high performance, the WAASBY index selected H37 for MRY, H6 for DW, H61 for BC, and H3 for VC. Finally, genotypes H3 and H20 were selected using multi-trait stability index (MTSI), as they possessed high performance and stability. Based on the selection sense, the objective has been achieved with regards to the trait MRW, which serves as a major criterion for a superior variety of sweet potato.