Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

The objective of this study was to evaluate four mathematical models with regards to their fit to lactation curves of Holstein cows from herds raised in the southwestern region of the state of Parana, Brazil. Initially, 42,281 milk production records from 2005 to 2011 were obtained from "Associação Paranaense de Criadores de Bovinos da Raça Holandesa (APCBRH)". Data lacking dates of drying and total milk production at 305 days of lactation were excluded, resulting in a remaining 15,142 records corresponding to 2,441 Holstein cows. Data were sorted according to the parity order (ranging from one to six), and within each parity order the animals were divided into quartiles (Q25%, Q50%, Q75% and Q100%) corresponding to 305-day lactation yield. Within each parity order, for each quartile, four mathematical models were adjusted, two of which were predominantly empirical (Brody and Wood) whereas the other two presented more mechanistic characteristics (models Dijkstra and Pollott). The quality of fit was evaluated by the corrected Akaike information criterion. The Wood model showed the best fit in almost all evaluated situations and, therefore, may be considered as the most suitable model to describe, at least empirically, the lactation curves of Holstein cows raised in Southwestern Parana

Interação genótipo × ambiente para produção de leite de bovinos da raça Holandesa entre bacias leiteiras no estado do Paraná Genotype × environment interaction for milk yield of Holstein cows among dairy production units in the state of Paraná

Foram analisados 117.082 registros de lactações encerradas para a produção de leite corrigida para os 305 dias de lactação (PL305) de 49.676 vacas da raça Holandesa, provenientes de 308 rebanhos distribuídos em sete bacias leiteiras no estado do Paraná, com o objetivo de verificar a existência de interação genótipo &#215; ambiente para a PL305 desses animais utilizando-se a inferência Bayesiana. Todos os animais foram controlados oficialmente entre janeiro de 1992 a dezembro de 2003 pelo Serviço de Controle Leiteiro Mensal da Associação Paranaense de Criadores de Bovinos da Raça Holandesa. Os componentes de co-variância e os parâmetros genéticos foram estimados por meio de análises uni e multicaracteres, de modo que, na análise multicaracter, a PL305 em cada uma das bacias foi tratada como uma característica diferente. A produção de leite corrigida para os 305 de lactação, em kg, nas bacias leiteiras de Castro, Carambeí, Witmarsum, Arapoti, Sul, Norte e Oeste foram de 8.414 ± 1.825, 8.481 ± 2.010, 7.636 ± 1.594, 7.850 ± 1.795, 8.617 ± 2.050, 7.401 ± 1.809 e 7.336 ± 2.456, respectivamente. A estimativa de herdabilidade mais alta (0,39) foi obtida para a bacia leiteira do Oeste e a mais baixa (0,23) para a de Carambeí. As correlações genéticas obtidas entre as bacias leiteiras foram baixas (0,09 a 0,57). As correlações de Pearson e de Spearman mais baixas foram obtidas para a bacia leiteira do Oeste do Paraná e variaram de 0,37 a 0,41 e de 0,37 a 0,49, respectivamente. Esses resultados comprovam a existência de interação genótipo &#215; ambiente nas bacias leiteiras do estado do Paraná.<br>It was analyzed 117,082 complete lactation records adjusted for 305 days in milk yield (MY305) of 49,676 Holsteins cows from 308 herds distributed among seven dairy production units in the state of Paraná, Brazil. The objective was to verify the genotype &#215; environment interaction to MY305 of Holsteins cows between dairy production units in the state of Paraná using the Bayesian inference. All animals were officially controlled by the Serviço de Controle Leiteiro Mensal of Associação Paranaense de Criadores de Bovinos da Raça Holandesa, between January/1992 and December/2003. The (co)variance components and genetic parameters were estimated using one and multiple-trait analysis, where MY305 of each dairy production unit was considered as a different variable. Means and standard deviations for MY305 (kg) for dairy production units of Castro, Carambeí, Witmarsum, Arapoti, Sul, Norte and Oeste, were 8,414 ± 1,825; 8,481 ± 2,010; 7,636 ± 1,594; 7,850 ± 1,795; 8,617 ± 2,050; 7,401 ± 1,809 and 7,336 ± 2,456, respectively. The highest heritability estimated was obtained for the Oeste unit (0.39) while Carambeí unit presented the lowest value (0.23). Genetic correlations were low (0.09 to 0.57) between dairy production units. Pearson and Spearman correlations were lower for the Oeste unit, when compared with other dairy production units, which ranged from 0.37 to 0.41, and from 0.37 to 0.49, respectively. These results show the presence of genotype &#215; environment interaction between dairy production units in the state of Paraná