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Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

A. B. Bignardi^*, L. El Faro, V. L. Cardoso, P. F. Machado and L. G. Albuquerque^*,,1

^* Department of Animal Science, São Paulo State University (FCAV/UNESP), 14884-900, Jaboticabal, SP, Brazil
Agência Paulista de Tecnologia dos Agronegócios - APTA, Pólo Regional Centro Leste, 14075-310, Ribeirão Preto, SP, Brazil
Department of Animal Science, University of São Paulo, 13418-900, Piracicaba, SP, Brazil
Conselho Nacional de Desenvolvimento Científico e Tecnologico (CNPq) and Instituto Nacional de Ciência e Tecnologia - Ciência Animal (INCT- CA), Jaboticabal, SP, Brazil

¹ Corresponding author: lgalb{at}fcav.unesp.br

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Key Words: covariance function • genetic parameter • parametric correlation structure