scholarly journals Covariance function of Legendre polynomials for the modeling of Polled Nellore cattle growth in northern Brazil

2019 ◽  
Vol 40 (2) ◽  
pp. 781
Author(s):  
Diego Helcias Cavalcante ◽  
Severino Cavalcante Sousa Júnior ◽  
Luciano Pinheiro Silva ◽  
Carlos Henrique Mendes Malhado ◽  
Raimundo Martins Filho ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Growth Parameters ◽  
Random Effect ◽  
Growth Curves ◽  
Random Regression ◽  
Analytical Models ◽  
Residual Variance ◽  
Age Related ◽  
Nellore Cattle ◽  
Northern Brazil

This study aimed to compare random regression models fitted by Legendre orthogonal polynomials and determine which best fits changes in Nellore cattle growth parameters. Age polynomial functions of different orders were evaluated using a random-effect modeling associated with a genetic study of cattle growth curves. For this purpose, weight records (15,148) were performed in Polled Nellore bovines (3,115), aged between 1 and 660 days, reared in northern Brazil and born between 1995 and 2010. The fixed effects of analytical models comprised age-matched groups, heifer calving age (linear and quadratic), and fourth-order Legendre age polynomial (cubic), depicting the mean growth curve. Besides, different order functions were considered for random effects, so that (co) variance associated with genetic effects (direct and maternal) and permanent environmental effects (animal and maternal) could be modeled. Residual variance was fitted by six heterogeneous classes throughout the analyzed period. According to AIC and BIC criteria, the model 6333 allowed the fitting of changes in variance and covariance over time (genetic and environmental). Thus, this model can be used to describe age-related changes in Polled Nellore cattle reared in northern Brazil.

scholarly journals Reaction norms in weights at 365 days old in nellore bulls in northern Brazil

2015 ◽  
Vol 36 (6Supl2) ◽  
pp. 4613 ◽  
Author(s):  
Jorge Luís Ferreira ◽  
Alliny Souza de Assis ◽  
Fernando Brito Lopes ◽  
Thomas Wayne Murphy ◽  
Marcelo Corrêa da Silva ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Reaction Norm ◽  
Genotype By Environment Interaction ◽  
Random Regression ◽  
Residual Effects ◽  
Breeding Value ◽  
Environment Interaction ◽  
Nellore Cattle ◽  
Regression Techniques ◽  
Northern Brazil

<p>Genotype by environment interaction (GxE) studies are of particular interest in Brazil because of the regional diversity of environmental effects and the wide variety of management systems. The present study evaluates GxE effects on 365 d weight (365W) of Nellore cattle raised on pasture in northern Brazil. The analysis utilized random regression techniques to model the reaction norm. Fixed effects consisted of sex, contemporary group, and the covariate of age of cow at calving. The environmental gradient, defined by the concatenation of a bull and the state in which the calf was born, was modeled by second order Legendre polynomials. Direct additive genetic and residual effects were fit as random. Results showed differences in the magnitude of expression of genotype in proportion to decreasing favorability of the environment. As the environment became more unfavorable, the correlation of breeding value to different environments decreased. The correlations between the intercept and the level slope for 365W feature were of moderate magnitude, predominantly indicating the reclassification of sires in different environments. Reaction standard model was coherent from a technical and biological view point and enabled the perception of GxE in the genetic evaluation of Nellore cattle in the states of Maranhão, Pará and Tocantins.</p><p> </p>

scholarly journals Reaction norms in weights at 365 days old in nellore bulls in northern Brazil

2015 ◽  
Vol 36 (6Supl2) ◽  
pp. 4613
Author(s):  
Jorge Luís Ferreira ◽  
Alliny Souza de Assis ◽  
Fernando Brito Lopes ◽  
Thomas Wayne Murphy ◽  
Marcelo Corrêa da Silva ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Reaction Norm ◽  
Genotype By Environment Interaction ◽  
Random Regression ◽  
Residual Effects ◽  
Breeding Value ◽  
Environment Interaction ◽  
Nellore Cattle ◽  
Regression Techniques ◽  
Northern Brazil

Genotype by environment interaction (GxE) studies are of particular interest in Brazil because of the regional diversity of environmental effects and the wide variety of management systems. The present study evaluates GxE effects on 365 d weight (365W) of Nellore cattle raised on pasture in northern Brazil. The analysis utilized random regression techniques to model the reaction norm. Fixed effects consisted of sex, contemporary group, and the covariate of age of cow at calving. The environmental gradient, defined by the concatenation of a bull and the state in which the calf was born, was modeled by second order Legendre polynomials. Direct additive genetic and residual effects were fit as random. Results showed differences in the magnitude of expression of genotype in proportion to decreasing favorability of the environment. As the environment became more unfavorable, the correlation of breeding value to different environments decreased. The correlations between the intercept and the level slope for 365W feature were of moderate magnitude, predominantly indicating the reclassification of sires in different environments. Reaction standard model was coherent from a technical and biological view point and enabled the perception of GxE in the genetic evaluation of Nellore cattle in the states of Maranhão, Pará and Tocantins.

scholarly journals Genetic evaluation of growth traits in Nellore cattle through multi-trait and random regression models

2018 ◽  
Vol 63 (No. 6) ◽  
pp. 212-221 ◽  
Author(s):  
B.B. Teixeira ◽  
R.R. Mota ◽  
R.B. Lôbo ◽  
L.P. Silva ◽  
A.P. Souza Carneiro ◽  
...  
Keyword(s):  
Random Effects ◽  
Variance Components ◽  
Regression Models ◽  
Growth Traits ◽  
Growth Curves ◽  
Genetic Evaluation ◽  
Information Criteria ◽  
Random Regression ◽  
Nellore Cattle ◽  
Heritability Estimates

We aimed to evaluate different orders of fixed and random effects in random regression models (RRM) based on Legendre orthogonal polynomials as well as to verify the feasibility of these models to describe growth curves in Nellore cattle. The proposed RRM were also compared to multi-trait models (MTM). Variance components and genetic parameters estimates were performed via REML for all models. Twelve RRM were compared through Akaike (AIC) and Bayesian (BIC) information criteria. The model of order three for the fixed curve and four for all random effects (direct genetic, maternal genetic, permanent environment, and maternal permanent environment) fits best. Estimates of direct genetic, maternal genetic, maternal permanent environment, permanent environment, phenotypic and residual variances were similar between MTM and RRM. Heritability estimates were higher via RRM. We presented perspectives for the use of RRM for genetic evaluation of growth traits in Brazilian Nellore cattle. In general, moderate heritability estimates were obtained for the majority of studied traits when using RRM. Additionally, the precision of these estimates was higher when using RRM instead of MTM. However, concerns about the variance components estimates in advanced ages via Legendre polynomial must be taken into account in future studies.

scholarly journals Random regression models using different functions to estimate genetic parameters for milk production in Holstein Friesians

2016 ◽  
Vol 46 (9) ◽  
pp. 1649-1655
Author(s):  
Mariana de Almeida Dornelles ◽  
Paulo Roberto Nogara Rorato ◽  
Luis Telo Lavadinho da Gama ◽  
Fernanda Cristina Breda ◽  
Carlos Bondan ◽  
...  
Keyword(s):  
Milk Production ◽  
Legendre Polynomials ◽  
Fixed Effects ◽  
Regression Models ◽  
Genetic Parameters ◽  
Random Regression ◽  
Residual Variance ◽  
Lower Estimation ◽  
The One ◽  
Residual Variances

ABSTRACT: The objective of this study was to compare the functions of Wilmink and Ali and Schaeffer with Legendre polynomials in random regression models using heterogeneous residual variances for modeling genetic parameters during the first lactation in the Holstein Friesian breed. Five thousand eight hundred and eighty biweekly records of test-day milk production were used. The models included the fixed effects of group of contemporaries and cow age at calving as covariable. Statistical criteria indicated that the WF.33_HE2, LEG.33_HE2, and LEG.55_HE4 functions best described the changes in the variances that occur throughout lactation. Heritability estimates using WF.33_HE2 and LEG.33_HE2 models were similar, ranging from 0.31 to 0.50. The LEG.55_HE4 model diverged from these models, with higher estimates at the beginning of lactation and lower estimates after the 16th fortnight. The LEG55_HE4, among the three better models indicated by the index, is the one with highest number of parameters (14 vs 34) and resulted in lower estimation of residual variance at the beginning and at the end of lactation, but overestimated heritability in the first fortnight and presented a greater difficulty to model genetic and permanent environment correlations among controls. Random regression models that used the Wilmink and Legendre polynomials functions with two residual variance classes appropriately described the genetic variation during lactation of Holstein Friesians reared in Rio Grande do Sul.

scholarly journals Analysis of Fluid Velocity inside an Agricultural Sprayer Using Generalized Linear Mixed Models

2020 ◽  
Vol 10 (15) ◽  
pp. 5029
Author(s):  
Ángel Javier Aguirre ◽  
Guillermo E. Guevara-Viera ◽  
Carlos S. Torres-Inga ◽  
Raúl V. Guevara-Viera ◽  
Antonio Boné ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Goodness Of Fit ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Fluid Velocity ◽  
Random Effect ◽  
Information Criteria ◽  
Liquid Level ◽  
Residual Variance ◽  
Operational Parameters

The fluid velocity inside the tank of agricultural sprayers is an indicator of the quality of the mixture. This study aims to formulate the best generalized linear mixed model to infer the fluid velocity inside a tank under specific operational parameters of the agitation system, such as liquid level, circuit pressures, and number of active nozzles. A complex model was developed that included operational parameters as fixed effects (FE) and the section of the tank as the random effect. The goodness of fit of the model was evaluated by considering the lowest values of Akaike’s information criteria and Bayesian information criterion, and by estimating the residual variance. The gamma distribution and log-link function enhanced the goodness of fit of the best model. The Toeplitz structure was chosen as the structure of the covariance matrix. SPSS and SAS software were used to compute the model. The analysis showed that the greatest influence on the fluid velocity was exerted by the liquid level in the tank, followed by the circuit pressure and, finally, the number of active nozzles. The development presented here could serve as a guide for formulating models to evaluate the efficiency of the agitation system of agricultural sprayers.

Analyses of growth curves of Nellore cattle by multiple-trait and random regression models

2003 ◽  
Vol 81 (4) ◽  
pp. 918-926 ◽  
Author(s):  
P. R. C. Nobre ◽  
I. Misztal ◽  
S. Tsuruta ◽  
J. K. Bertrand ◽  
L. O. C. Silva ◽  
...  
Keyword(s):  
Regression Models ◽  
Growth Curves ◽  
Random Regression ◽  
Multiple Trait ◽  
Nellore Cattle

scholarly journals Estimates of (co)variance function for growth to yearling in Horro sheep of Ethiopia using random regression model

2010 ◽  
Vol 53 (6) ◽  
pp. 689-700
Author(s):  
S. Abegaz ◽  
J. B. van Wyk ◽  
J. J. Olivier
Keyword(s):  
Fixed Effects ◽  
Model Comparison ◽  
Information Criterion ◽  
Coefficient Matrix ◽  
Random Regression ◽  
Ratio Test ◽  
Residual Variance ◽  
Genetic Covariance ◽  
Heritability Estimates ◽  
One Year

Abstract. Random regression analyses of weight data from birth to 396 days were done using 22 141 weight records of 1 951 Horro lambs. Six different models formed from three different orthogonal polynomial regressions (legendre scale)orders (quadratic, cubic, quartic) of fit for both additive genetic and animals’ permanent environmental effects, with assumption of either homogeneous or heterogeneous residual variance, were compared. Fixed effects of year and type of birth, sex and age of dam were fitted along with a fourth order polynomial. Both likelihood ratio test (LRT) and Akaike's Information Criterion (AIC) were used for model comparison. Model fit improved with increased order of polynomial and assumption of heterogeneity of residual variance. Components for additive genetic and permanent environmental (co)variance increased from 0.03 and 0.09 at birth to 23.8 and 37.6 at 396 days of age, respectively. The first three eigenvalues of the coefficient matrix of the additive genetic covariance accounted for about 98 % of the sum of all the eigenvalues. Heritability estimates have shown a declining and increasing trend at different parts of the trajectory, the lowest estimate being 0.14 for weight at birth while the highest being 0.36 for weight at about 390 days of age. Higher heritability estimates in previous uni- and bi-variate models and in the current study and also strong correlation with weight at early age makes weight at one year of age the most important trait to consider in improving productivity in Horro sheep.

scholarly journals Covariance functions under B-spline polynomials to model Polled Nellore cattle growth

2021 ◽  
Vol 42 (6supl2) ◽  
pp. 3977-3990
Author(s):  
Diego Helcias Cavalcante ◽  
◽  
Carlos Syllas Monteiro Luz ◽  
Marcelo Richelly Alves de Oliveira ◽  
Wéverton José Lima Fonseca ◽  
...  
Keyword(s):  
Random Effects ◽  
Growth Curve ◽  
Fixed Effects ◽  
Random Regression ◽  
Spline Functions ◽  
Average Growth ◽  
B Spline ◽  
Covariance Functions ◽  
Model Animal ◽  
Nellore Cattle

B-spline functions have been used in random regression models (RRM) to model animal weight from birth to adulthood because they are less vulnerable to common difficulties of other methods. However, its application to model growth traits of Polled Nellore cattle has been little studied. Therefore, this study aimed to evaluate polynomial functions of different orders and segment numbers to model effects associated with the Polled Nellore cattle growth curve. For this purpose, we used 15,148 weight records of 3,115 animals aged between 1 and 660 days and reared in northern Brazil and born between 1995 and 2010. Random effects were modeled using B-spline polynomials. As random effects, we considered the direct and maternal genetic additives, as well as direct and maternal permanent environments. As fixed effects were included contemporary group, cow age at calving (linear and quadratic) and fourth-order Legendre polynomials to represent average growth curve. The residue was modeled by considering seven age classes. The bestfitted model was the one that considered cubic B-spline functions with four knots for direct additive genetic effects and three knots for maternal genetic, animal permanent environment, and maternal permanent environment effects (C6555). Therefore, covariance functions under B-spline polynomials are efficient and can be used to model the growth curve of Polled Nellore cattle from birth to 660 days of age.

scholarly journals Analyses of growth curves of Nellore cattle by Bayesian method via Gibbs sampling

2003 ◽  
Vol 55 (4) ◽  
pp. 480-490 ◽  
Author(s):  
P.R.C. Nobre ◽  
P.S. Lopes ◽  
R.A. Torres ◽  
L.O.C. Silva ◽  
A.J. Regazzi ◽  
...  
Keyword(s):  
Birth Weight ◽  
Bayesian Method ◽  
Growth Curves ◽  
Random Regression ◽  
Multiple Trait ◽  
Covariance Functions ◽  
Contemporary Group ◽  
Random Regression Model ◽  
Nellore Cattle ◽  
Covariance Components

Growth curves of Nellore cattle were analyzed using body weights measured at ages ranging from 1 day (birth weight) to 733 days. Traits considered were birth weight, 10 to 110 days weight, 102 to 202 days weight, 193 to 293 days weight, 283 to 383 days weight, 376 to 476 days weight, 551 to 651 days weight, and 633 to 733 days weight. Two data samples were created: one with 79,849 records from herds that had missing traits and another with 74,601 from herds with no missing traits. Records preadjusted to a fixed age were analyzed by a multiple trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were carried out by a Bayesian method for all nine traits. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, permanent environment, additive maternal, and maternal permanent environment. Legendre cubic polynomials were used to describe random effects. MTM estimated covariance components and genetic parameters for birth weight and sequential weights and RRM for all ages. Due to the fact that covariance components based on RRM were inflated for herds with missing traits, MTM should be used and converted to covariance functions.

scholarly journals 210 Genotype by environment interaction for pre-weaning survival in commercial crossbred pigs

2019 ◽  
Vol 97 (Supplement_3) ◽  
pp. 40-41
Author(s):  
Francesco Tiezzi ◽  
Justin Fix ◽  
Clint Schwab
Keyword(s):  
Fixed Effects ◽  
Genotype By Environment Interaction ◽  
Single Step ◽  
Random Regression ◽  
Residual Variance ◽  
Phenotypic Variance ◽  
Environment Interaction ◽  
Genomic Breeding ◽  
Genotype By Environment ◽  
The Impact

Abstract Pre-weaning survival (PWS) is a trait of major importance in swine productions systems. Selection is made difficult by the low heritability of the trait(s) and genotype by environment interaction (GxE) could be present. In addition to that, given the binary nature of the trait, phenotypic variance is virtually null in contemporary group where PWS is large. The objective of this study was to assess the impact of heterogeneous phenotypic variance and GxE on PWS. We used survival to day 5 as a trait of interest, available for 574,828 crossbred piglets raised in a commercial environment. Piglets were progeny of 559 sires (450 genotyped with 60k SNP chip) and raised into 242 contemporary groups (CG). In estimating GxE, the E component was represented by fourth-order Legendre polynomials built on the CG solutions. A Single-Step random-regression sire model with heterogeneous residuals (10 classes) was used, once the CG solutions were obtained by a similar model that neglected GxE. Other (fixed) effects in the models were sow parity, litter size, litter transfer of the piglet, gender of the piglet, dam genetic line and litter (random). Results show an increase in phenotypic and residual variance as PWS decreased, which is expected given the nature of the binary trait. Genetic variance increased following the same trend, which made heritability to be constant (~2%). Genomic breeding values for most represented sires were plotted as a function of CG survival. While no variation among the sires can be found in CG with full survival, larger variance is shown as PWS decreases. Re-ranking among the sires is present as CG change. Results suggest that modeling PWS should account for the heterogeneous variance among CG. A moderate GxE in PWS at day 5 is also suggested.

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