Exploring the Use of Random Regression Models with Legendre Polynomials to Analyze Measures of Volume of Ejaculate in Holstein Bulls

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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Modelling lactation curves of dairy goats by fitting random regression models using Legendre polynomials or B-splines

Canadian Journal of Animal Science ◽

10.1139/cjas-2017-0019 ◽

2017 ◽

Cited By ~ 1

Author(s):

Luiz Fernando Brito ◽

Felipe Gomes da Silva ◽

Hinayah Rojas de Oliveira ◽

Nadson Souza ◽

Giovani Caetano ◽

...

Keyword(s):

Legendre Polynomials ◽

Regression Models ◽

Random Regression ◽

Dairy Goats ◽

B Splines

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

Journal of Animal Breeding and Genetics ◽

10.1111/j.1439-0388.2010.00853.x ◽

2010 ◽

Vol 127 (4) ◽

pp. 289-299 ◽

Cited By ~ 17

Author(s):

F. Baldi ◽

L.G. Albuquerque ◽

M.M. Alencar

Keyword(s):

Legendre Polynomials ◽

Regression Models ◽

Genetic Parameters ◽

Random Regression ◽

Adult Age

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Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

animal ◽

10.1017/s1751731117001951 ◽

2018 ◽

Vol 12 (4) ◽

pp. 667-674 ◽

Cited By ~ 3

Author(s):

L.F.M. Mota ◽

P.G.M.A. Martins ◽

T.O. Littiere ◽

L.R.A. Abreu ◽

M.A. Silva ◽

...

Keyword(s):

Legendre Polynomials ◽

Regression Models ◽

Selection Response ◽

Genetic Evaluation ◽

Random Regression ◽

Spline Functions ◽

B Spline ◽

Meat Type

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Reliability of breeding values between random regression and 305-day lactation models

Pesquisa Agropecuária Brasileira ◽

10.1590/s0100-204x2016001100007 ◽

2016 ◽

Vol 51 (11) ◽

pp. 1848-1856

Author(s):

Alessandro Haiduck Padilha ◽

◽

Jaime Araujo Cobuci ◽

Darlene dos Santos Daltro ◽

José Braccini Neto

Keyword(s):

Legendre Polynomials ◽

Regression Models ◽

Protein Yield ◽

Random Regression ◽

Holstein Cattle ◽

Average Increase ◽

Data Set ◽

Breeding Values ◽

Estimated Breeding Values ◽

Genetic Evaluations

Abstract The objective of this work was to verify the gain in reliability of estimated breeding values (EBVs), when random regression models are applied instead of conventional 305-day lactation models, using fat and protein yield records of Brazilian Holstein cattle for future genetic evaluations. Data set contained 262,426 test-day fat and protein yield records, and 30,228 fat and protein lactation records at 305 days from first lactation. Single trait random regression models using Legendre polynomials and single trait lactation models were applied. Heritability for 305-day yield from lactation models was 0.24 (fat) and 0.17 (protein), and from random regression models was 0.20 (fat) and 0.21 (protein). Spearman correlations of EBVs, between lactation models and random regression models, for 305-day yield, ranged from 0.86 to 0.97 and 0.86 to 0.98 (bulls), and from 0.80 to 0.89 and 0.81 to 0.86 (cows), for fat and protein, respectively. Average increase in reliability of EBVs for 305-day yield of bulls ranged from 2 to 16% (fat) and from 4 to 26% (protein), and average reliability of cows ranged from 24 to 38% (fat and protein), which is higher than in the lactation models. Random regression models using Legendre polynomials will improve genetic evaluations of Brazilian Holstein cattle due to the reliability increase of EBVs, in comparison with 305-day lactation models.

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Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Journal of Dairy Science ◽

10.3168/jds.2011-5051 ◽

2013 ◽

Vol 96 (1) ◽

pp. 565-574 ◽

Cited By ~ 22

Author(s):

R.J. Pereira ◽

A.B. Bignardi ◽

L. El Faro ◽

R.S. Verneque ◽

A.E. Vercesi Filho ◽

...

Keyword(s):

Milk Yield ◽

Legendre Polynomials ◽

Regression Models ◽

Bos Indicus ◽

Random Regression ◽

Linear Splines

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Components of (co)variance of the days open in Siboney dairy cows

Arquivo Brasileiro de Medicina Veterinária e Zootecnia ◽

10.1590/s0102-09352010000100019 ◽

2010 ◽

Vol 62 (1) ◽

pp. 136-143 ◽

Cited By ~ 2

Author(s):

D. González-Peña ◽

J.L. Espinoza-Villavicencio ◽

D. Guerra ◽

A. Palacios ◽

J.C. Évora ◽

...

Keyword(s):

Dairy Cows ◽

Legendre Polynomials ◽

Regression Models ◽

Genetic Correlations ◽

Random Regression ◽

Residual Variance ◽

Parity Number ◽

Days Open ◽

Univariate Model

The records of 63,406 calvings of Siboney dairy cows (5/8 Holstein 3/8 Cuban Zebu) were used to estimate the components of covariance of the days open (DO). Five models were used: of repeatability; univariate; bivariate; of random regression with Legendre polynomials and the parity number as predicting variable; and a model of random regression with Legendre polynomials and heterogeneity of the residual variance. The heritability obtained with the univariate model was 0.09 in the first calving and decreased to 0.05 in the fifth. A higher estimate of heritability (0.12) was obtained with the repeatability model. When the model of random regression with heterogeneity of the residual variance was used, the heritability was higher than the values estimated with the previous models. The genetic correlations among the DO in different calvings, estimated with the models of random regression with and without heterogeneity of the residual variance, were close to 1.0. It is concluded that the estimates of heritability increased with the use of the random regression models. The genetic correlations among the DO of different calvings indicated that in the first three, the DO are regulated for the most part by the same genes.

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