ORIGINAL ARTICLE Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle* F. Baldi 1 , L.G. Albuquerque 1 & M.M. Alencar 2 1 Animal Science Departament, FCAV, University of Sa ˜ o Paulo State. 14884 000, Jaboticabal (SP), Brazil 2 Southeast Embrapa Cattle. 13560 970, Sa ˜ o Carlos (SP), Brazil Introduction To date, genetic evaluation programmes for beef cat- tle have widely employed two-trait and multi-trait models to predict breeding values for growth traits. With these models, animals are evaluated at certain standard ages, as birth, weaning, yearling, etc. As animals are actually measured at different ages, the weights have to be adjusted for age or discarded from analyses if they are out of the accepted age range. Both procedures lower the accuracy of animal genetic evaluation (Meyer 2004). Keywords Beef cattle; covariance functions; growth curve; Legendre polynomials. Correspondence F. Baldi, Via de acesso Paulo Donato Castellane s/n, Animal Science Departament, Block 2, FCAV, University of Sa ˜ o Paulo State, 14884-000, Jaboticabal (SP), Brazil. Tel: +055 16 3209 2678; Fax: +055 16 3202 5500; E-mail: fernandobaldiuy@gmail.com Present address: Departamento de Zootecnia, Via de acesso Paulo Donato Castellane s / n. Pre ´ dio 2. CEP: 14884-900, Jaboticabal, SP, Brazil. Received: 19 May 2009; accepted: 20 December 2009 Summary The objective of this work was to estimate covariance functions for direct and maternal genetic effects, animal and maternal permanent environmental effects, and subsequently, to derive relevant genetic parameters for growth traits in Canchim cattle. Data comprised 49 011 weight records on 2435 females from birth to adult age. The model of analysis included fixed effects of contemporary groups (year and month of birth and at weighing) and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were allowed to vary and were modelled by a step function with 1, 4 or 11 classes based on ani- mal’s age. The model fitting four classes of residual variances was the best. A total of 12 random regression models from second to seventh order were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. The model with direct and maternal genetic effects, animal and maternal permanent environ- mental effects fitted by quadric, cubic, quintic and linear Legendre poly- nomials, respectively, was the most adequate to describe the covariance structure of the data. Estimates of direct and maternal heritability obtained by multi-trait (seven traits) and random regression models were very similar. Selection for higher weight at any age, especially after weaning, will produce an increase in mature cow weight. The possibility to modify the growth curve in Canchim cattle to obtain animals with rapid growth at early ages and moderate to low mature cow weight is limited. *This work was supported by Conselho Nacional de Desenvolvimento Cientı ´fico e Tecnolo ´ gico (CNPq) and Fundac ¸a ˜o de Amparo a ` Pesquisa do Estado de Sa ˜ o Paulo (FAPESP). J. Anim. Breed. Genet. ISSN 0931-2668 ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 127 (2010) 289–299 doi:10.1111/j.1439-0388.2010.00853.x