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This review aimed to estimate covariance components for Tabapuã the growth characteristics in Brazil, using random regression models. The random regression models (MRA) make it possible to estimate coefficients of the covariance functions by the method of restricted maximum likelihood. These are suitable for longitudinal data analysis models, because of the deficiencies of conventional methods of quantitative genetic analysis, which are considered phenotypic values inherently continuous processes, as discrete processes. The covariance functions show the statistical correlation between two features of a trajectory at different points of same, ie that present in the arrangement have the same direction and magnitude. With the current concern of cutting bovinocultores regarding the growth of animals, the use of methods or techniques that provide increasingly accurate assessments of genetic parameters to be used in studying the development of animals for meat production is relevant

Esta revisão teve como objetivo avaliar a evolução da avicultura em vários aspectos, bem como sua produção e tendência ao consumo no Brasil e no mundo. O espaço ocupado pelo Brasil atualmente, foi devido à intensificação no seu processo de produção, relacionado a fatores como introdução de novas tecnologias melhoria genética, uso de instalações mais apropriadas e alimentação racional. As inúmeras inovações na área de genética, nutrição, sanidade e no processo produtivo de forma geral, possibilitaram a produção de frangos com mais peso, em menos tempo e com menor consumo de ração são alguns dos diversos fatores que contribuíram para que o setor alcançasse o patamar atual.

The purpose of this review is to show the increase in number of researches on covariance components and genetic evaluation using random regression models (RRM) for growth traits of Nellore cattle. Random regression models, also known as infinite-dimension models have been used to estimate variance components and genetic parameters for weight of beef cattle. In addition, those models are a standard alternative for genetic analyses of longitudinal data, however, the availibility of computational resources for performing genetic evaluations widely is an obstacle. Traits related to animal growth are adopted as selection criteria in beef cattle breeding programs, because the remuneration of cattle breeders is made based on the weight of carcasses. In recent years, RRM have been adopted as standard procedure in relation to the analysis of longitudinal data in animal breeding.