This study was performed in order to estimate the relation between some environmental factors and somatic cell count (SCC). This relation was verified by testing the frequency of analyzed samples in classes according to the SCC as follows: very high, high, medium and low. 23,534 milk samples corresponding to 2.198 lactations of Murrah breed animals were used. The buffaloes were between 2 and 15 years old and were daughters of 187 males. The samples were taken during a period of 7 years. In general, the results showed that SCC was low, medium, high and very high for 96.34%, 2.3%, 0.96% and 0.4% for the samples, respectively. Low and medium SCC had the highest frequencies, pointing out that in buffaloes there is a tendency of lower SCC when compared to bovines. There were differences between the average SCC according to the order and season of parturition. There were also significant differences between the average SCC of some control samples (P<0.05). In relation to order of parturition there were observed differences between SCC frequencies, but as a general statement it was observed that as order of parturition was higher the rate of lower SCC decreased and the frequency of medium, high and very high SCC increased. The results indicated that the effects of farm, year and order of parturition should be considered when comparing animals.

Summary Background: the milk yield records measured along lactation provide an example of repeated measures; the random regression models are an appealing approach to model repeated measures and to estimate genetic parameters. Objective: to estimate the genetic parameters by modeling the additive genetic and the residual variance for test-day milk yield in first calving buffaloes. Methods: 3,986 test-day data from 1,246 first lactations of crossbred buffalo daughters of 23 sires and 391 dams between 1997 and 2008 from five farms were used. The model included the genetic and permanent environment additive as the random effect and the contemporary group (year, month of test-day) and age at calving as covariable (linear) fixed effects. The fixed (third order) and random (third to ninth order) regressions were obtained by Legendre polynomials. The residual variances were modeled with a homogeneous structure and various heterogeneous classes. The variance components were estimated using the WOMBAT statistical program (Meyer, 2006). Results: according to the likelihood ratio test, the best model included four variance classes, considering Legendre polynomials of the fourth order for permanent environment and additive genetic effects. The heritabilities estimates were low, varying from 0.0 to 0.14. The estimates of genetic correlations were high and positive among PDC1 and PDC8, except for PCD9, which was negative. This indicates that for any of the selection criteria adopted, the indirect genetic gain is expected for all lactation curves, except for PCD9. Conclusion: heterogeneity of residual variances should be considered in models whose goal is to examine the alterations of variances according to day of lactation. Key words: biomodeling, genetic correlations, Legendre polynomials, random regression models.Resumen Antecedentes: los registros de producción de leche medidos a lo largo de la lactancia son un ejemplo de medidas repetidas, los modelos de regresión aleatoria presentan un enfoque atractivo para modelar medidas repetidas y para estimar parámetros genéticos. Objetivo: estimar parámetros genéticos a través de la modelación de la varianza genética y residual para producción de leche en el día de control en búfalas de primer parto. Métodos: fueron analizados 3986 controles de producción de leche en la primera lactancia de 1246 búfalas, hijas de 391 hembras y 23 toros, durante los años 1997 hasta 2008 en 5 fincas.  El modelo incluyó como efectos aleatorios genético aditivo y de ambiente permanente, como efectos fijos grupo contemporáneo compuesto por mes, año de control y la covariable de la edad de la búfala al parto (lineal). Las regresiones fijas (3er orden) y aleatorias (3er a 9no orden) fueron obtenidas mediante polinomios de Legendre. Las varianzas residuales fueron modeladas con una estructura  homogénea y varias clases heterogéneas. Los componentes de varianza fueron estimados utilizando el programa WOMBAT. Resultados: de acuerdo con la prueba de la razón de verosimilitud, el mejor modelo fue con 4 clases de varianzas residuales, siendo considerado un polinomio de Legendre de cuarto orden para el efecto de ambiente permanente y genético aditivo. Las heredabilidades fueron bajas, variando desde 0,00 hasta 0,14. Las correlaciones genéticas fueron altas y positivas entre los PDC1 a PDC8, excepto en el PDC9 que fue negativo con respecto a los demás controles. Conclusiones: es necesario considerar la heterogeneidad de varianzas residuales en los modelos estudiados, con el fin de modelar los cambios en las variaciones respecto a los días en lactancia. Palabras clave: biomodelación, correlación genética, modelos de regresión aleatoria, polinomios de Legendre. Resumo Antecedentes: os registros da produção do leite medidos ao longo da lactação, apresentam um exemplo de medidas repetidas. Os modelos de regressão aleatória apresentam abordagem atraente para modelar medidas repetidas e estimar parâmetros genéticos. Objetivo: estimar parámetros genéticos mediante a modelação das variâncias genéticas e residual da produção do leite no dia do controle em búfalas de primeiro parto. Métodos: foram analisados 3986 controles de produção de leite em primeiras lactações de 1246 búfalas, filhas de 391 fêmeas e 23 touros, entre 1997 e 2008 em 5 fazendas. No modelo foram incluídos como efeitos aleatórios o genético aditivo e ambiente permanente, e como fixos o grupo contemporâneo (mês e ano de controle) e a covariável a idade da búfala ao parto (Lineal). As regressões fixas (3° ordem) e aleatórias (3° a 9° ordem) foram obtidas mediante polinômios ortogonais de Legendre. As variâncias residuais foram modeladas mediante estruturas homogêneas e diferentes classes heterogêneas. Os componentes de variância foram estimadas mediante o software WOMBAT. Resultados: de acordo com a prova da máxima verossimilhança, o melhor modelo foi com 4 classes de variâncias residuais, sendo considerado polinômios de Legendre de quarto ordem para o efeito de ambiente permanente e genético aditivo. As herdabilidades foram baixas, variando desde 0,00 até 0,14. As correlações genéticas foram altas e positivas entre o PDC1 e PDC8, a exceção do PDC9 que apresentou valores negativos com respeito aos outros controles. Conclusões: é necessário considerar heterogeneidade de variâncias nos modelos estudados, tentando modelar as mudanças nas variações respeito aos dias em lactação. Palavras chave: biomodelagem, correlação genética, modelos de regressão aleatória, polinômios de Legendre. 

Resumen El objetivo de este trabajo fue estimar factores multiplicativos de ajuste de la producción de leche a 305 días de lactación (PC305) y a edad adulta (PCEA), para rebaños de la raza Holstein colombiano. Fueron utilizadas 116.818 lactaciones de 48.707 vacas, provenientes de los archivos de la Asociación Holstein de Colombia. Los análisis estadísticos fueron realizados mediante la utilización de modelos lineales mixtos usando un modelo animal y el método de máxima verosimilitud restricta (REML). Para producción de leche a 305 días los efectos fijos considerados en el modelo fueron: grupo contemporáneo (rebaño-año), grupo genético de la vaca, mes de parto, número de partos y clases de duración de la lactación en dos grupos de edad de la vaca ( < 36 y ³ 36 meses) y la covarible edad de la vaca al parto (efecto lineal y cuadrático). Para producción de leche a edad adulta los efectos fijos considerados en el modelo fueron: grupo contemporáneo (rebaño-año), grupo genético de la vaca y clases de edad, número de partos y época de parto. Los efectos aleatorios para las dos variables fueron: efecto genético aditivo, ambiente permanente y residuo. Posteriormente fueron realizados análisis de variancia entre producciones de leche corregidas y no corregidas para determinar la efectividad de la aplicación de los factores, indicando que la aplicación de los factores de corrección si ajustaron eficientemente producciones de leche para los efectos de duración de la lactación, edad de la vaca, número de partos y época de parto. La mayor producción de leche fue alcanzada por vacas de tres o más partos con edad de 76 a 83 meses de edad y partos ocurridos entre agosto y noviembre. Palabras Clave: duración de lactación; edad adulta, producción de leche. Summary This study estimated multiplicative adjustment factors for milk yield at 305 days (PC305) of lactation and adult age (PCEA), for Colombian Holstein herds. The number of lactations used was 116,818 from 48,707 cows, originated from the databank of the Asociación Holstein de Colombia. The statistical analyses were done through the use of mixed linear models using an animal model and the restricted maximum likelihood (RML). For milk yield at 305 days the fixed effects considered in the model were: contemporary group (herd-year), genetic group of the cow, month of parity, parity number and classes of lactation duration in two cow age groups ( < 36 y ³ 36 months) and the covariable cow age at parity (linear and quadratic effects). For milk yield at adult age the fixed effects considered in the model were: contemporary group (herd-year), genetic group of the cow and age classes, number of parities and parity season. The random effects for the variables were: additive genetic effect, permanent environment and error. Subsequently analyses of variance between corrected and non-corrected milk yields were done to determine the effectiveness of factor application, indicating that the application of correction factors efficiently adjusted milk yield for the effects of lactation duration, cow age, parity number and parity season. The greatest milk yield was achieved by cows with three or more parities with age of 76 to 83 months and parities between August and November. Key Words: adult age, lactation length, milk yield.