title: Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.
abstract: 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.
authors.affiliation: Department of Animal Science, São Paulo State University (FCAV/UNESP), Jaboticabal, SP, Brazil.
authors.forename: A B
authors.initials: AB
authors.lastname: Bignardi
authors.forename: L
authors.initials: L
authors.lastname: El Faro
authors.forename: V L
authors.initials: VL
authors.lastname: Cardoso
authors.forename: P F
authors.initials: PF
authors.lastname: Machado
authors.forename: L G
authors.initials: LG
authors.lastname: Albuquerque
mesh_terms: D000818:Animals; D002417:Cattle / Q000235:genetics / Q000502:physiology*; D004777:Environment; D005260:Female; D007774:Lactation / Q000235:genetics*; D008892:Milk / Q000378:metabolism*; D008954:Models, Biological; D010641:Phenotype; D019655:Quantitative Trait, Heritable; D012044:Regression Analysis