Random Regression Models for Test-day Milk and Fat Yields in Brazilian Gyr Cattle R.J. Pereira * , L. El Faro † , M.G.C.D. Peixoto ‡ , R.S. Verneque ‡ and L.G. Albuquerque *§ Introduction Nowadays, random regression models (RRM) applied to test-day records have been implemented by most Interbull members for genetic evaluation of dairy cattle. Some benefits attributed to the adoption of RRM are: the use of test day records per animal can be maximized with correspondent increasing in genetic evaluation accuracies (Meyer (2004)); better definition of contemporary groups and quantification of the environmental effects (Visscher and Goddard (1995)); the possibility of calculating persistency of milk yield breeding values as functions of days in milk. Additionally, RRM allow genetic evaluation of animals whose lactation is still ongoing, without projections, which enables more frequent evaluations and decreases generation interval (Swalve (2000)). Orthogonal Legendre polynomials (LP) have been frequently used for modeling the covariance structure of test- day records in dairy cattle. Orthogonal polynomials show low correlations between random regression coefficients and provide covariance matrices estimates that tend to be robust over different data sets (Schaeffer (2004)). The objective of this study was to estimate genetic covariance functions for first lactation milk and fat yields of Brazilian Gyr cows using random regression on orthogonal Legendre polynomials of days in milk. Material and methods Data were provided by Embrapa Dairy Cattle (Brazilian Agricultural Research Corporation), comprising 38,268 test-day milk yields (TDMY) and 10,769 test-day fat yields (TDFY) from 5,158 and 1,559 first lactation records of Brazilian Gyr cows. Lactations were recorded in 4,444 (milk) and 467 (fat) herds between 1990 and 2007. Cows with records were daughters of 327 (milk) and 183 (fat) sires. Test day yields from 5 to 305 days of lactation, time interval between successive tests less than 45 days and age of calving between 24 and 60 months were required. Contemporary groups (CG) were defined as herd-year-test month (HTM) and had at least three records. Test day records were grouped in 10 monthly classes (TDC) according to days in milk: 5-30, 31-60, 61-90, 91-120, 121-150, 151-180, 181-210, * Department of Animal Science, FCAV/UNESP. Via de Acesso Prof. Paulo Donato Castellane s/n. CEP 14884- 900, Jaboticabal – SP, Brazil. † Agência Paulista de Tecnologia dos Agronegócios, APTA/SAA. Avenida Bandeirantes, 2419. CEP 14030-670, Ribeirão Preto – SP, Brazil. ‡ Brazilian Agricultural Research Corporation, Embrapa Dairy Cattle. Rua Eugênio do Nascimento, 610, Bairro Dom Bosco. CEP 36038-330, Juiz de Fora – MG, Brazil. § CNPq and INCT-CA, SP, Brazil.