Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle*

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.

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Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

Pesquisa Agropecuária Brasileira ◽

10.1590/s0100-204x2014000500007 ◽

2014 ◽

Vol 49 (5) ◽

pp. 372-383 ◽

Cited By ~ 4

Author(s):

Maria Gabriela Campolina Diniz Peixoto ◽

Daniel Jordan de Abreu Santos ◽

Rusbel Raul Aspilcueta Borquis ◽

Frank Ângelo Tomita Bruneli ◽

João Cláudio do Carmo Panetto ◽

...

Keyword(s):

Milk Production ◽

Legendre Polynomial ◽

Legendre Polynomials ◽

Regression Models ◽

Environmental Effect ◽

Genetic Parameters ◽

Genetic Effect ◽

Random Regression ◽

Additive Genetic Effect ◽

Fifth Order

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.

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Estimation of Genetic Parameters for Daily Gains of Bulls with Multi-Trait and Random Regression Models

Archives Animal Breeding ◽

10.5194/aab-50-37-2007 ◽

2007 ◽

Vol 50 (1) ◽

pp. 37-46

Author(s):

H. Krejčová ◽

N. Mielenz ◽

J. Přibyl ◽

L. Schüler

Keyword(s):

Animal Model ◽

Animal Models ◽

Genetic Analysis ◽

Legendre Polynomials ◽

Regression Models ◽

Genetic Parameters ◽

Random Regression ◽

Dual Purpose ◽

Trait Model ◽

Estimation Of Genetic Parameters

Abstract. The average daily gains of 6,420 Czech Pied bulls (dual-purpose, Simmental type) from 7 breeding stations were analyzed using single-trait animal models, a multi-trait animal model and random regression models. The effects of station, year and season were taken into account by creating herd-year-season classes (HYS) with the season being defined as a 3-month class starting with December. Legendre polynomials of the 1st to the 4th degree were used to describe the daily gains within the HYS classes as well as to model bull-specific gain curves. The comparison of the h2-values estimated with single-trait models and those gained with a multi-trait model returned only insignificant differences. The comparison of genetic parameters based on the multi-trait model to those from different random regression models shows that polynomials of at least the 2nd degree are to be used for the genetic analysis of daily gains.

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Genetic parameters for production traits in primiparous Holstein cows estimated by random regression models

Revista Brasileira de Zootecnia ◽

10.1590/s1516-35982011000100012 ◽

2011 ◽

Vol 40 (1) ◽

pp. 85-94 ◽

Cited By ~ 6

Author(s):

Igor de Oliveira Biassus ◽

Jaime Araújo Cobuci ◽

Claudio Napolis Costa ◽

Paulo Roberto Nogara Rorato ◽

José Braccini Neto ◽

...

Keyword(s):

Milk Fat ◽

Legendre Polynomials ◽

Regression Models ◽

Genetic Parameters ◽

Genetic Correlations ◽

Random Regression ◽

Holstein Cows ◽

Lactation Period ◽

Production Traits ◽

Residual Variances

The objective of this study was to estimate genetic parameters for milk, fat and protein yields of Holstein cows using 56,508; 35,091 and 8,326 test-day milk records from 7,015, 4,476 and 1,114 cows, calves of 359, 246 and 90 bulls, respectively. The additive genetic and permanent environmental effects were estimated using REML. Random regression models with Legendre polynomials from order 3 to 6 were used. Residual variances were considered homogeneous over the lactation period. The estimates of variance components showed similar trends, with an increase of the polynomial order for each trait. The heritability estimates ranged from 0.14 to 0.31; 0.03 to 0.21 and 0.09 to 0.33 for milk, fat and protein yield, respectively. Genetic correlations among milk, fat and protein yields ranged from 0.02 to 1.00; 0.34 to 1.00 and 0.42 to 1.00, respectively. Models with higher order Legendre polynomials are the best suited to adjust test-day data for the three production traits studied.

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