ABSTRACT Six non-linear mathematical models were evaluated (Wood, modified Wood, Quadratic, Sikka, Singh-Gopal and Cobby) to determine their ability to fit to describe the lactation curve in mares. The modeling was carried out from 197 records of milk production from mares between 2 and 190 days of lactation. The models were fitted using non-linear regression algorithms and were evaluated through the following comparison criteria: MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error), RMSE (Root Mean Squared Error), AIC (Akaike information criterion), BIC (Bayesian information criterion) and residual analysis. The Wood, Singh-Gopal, modified Wood and Sikka models predicted that maximum milk production varies between 10 and 13 kg/day, which occurs between 30 and 42 days postpartum. According to the criteria evaluated, the Wood and Singh-Gopal models presented the best fit and were suitable for modeling lactation curves in equids.

RESUMEN Seis modelos matemáticos no lineales fueron evaluados (Wood, Wood modificado, Cuadrático, Sikka, Singh-Gopal y Cobby) para determinar su capacidad de ajuste para describir la curva de lactancia en yeguas. La modelación se realizó a partir de 197 registros de producción de leche de yeguas entre los 2 y 190 días de lactancia. Los modelos fueron ajustados empleando algoritmos de regresión no lineal y se evaluaron a través de los siguientes criterios de comparación: MAE (Error absoluto medio), MAPE (Error porcentual absoluto medio), RMSE (Raíz del error cuadrático medio), AIC (Criterio de información de Akaike), BIC (Criterio de información bayesiano) y análisis de residuales. Los modelos Wood, Singh-Gopal, Wood modificado y Sikka predijeron que la máxima producción de leche varía entre 10 y 13 kg/día, la cual ocurre entre los 30 y 42 días posparto. De acuerdo con los criterios evaluados, los modelos Wood y Singh-Gopal presentaron el mejor ajuste y se mostraron adecuados para modelar las curvas de lactancia en équidos.

Abstract The objective of this work was to evaluate the influence of environmental factors on the lactation curve parameters and milk yield of Holstein cows. Data on lactations conducted from 2010 to 2019 in the state of Paraná, Brazil, obtained from the official dairy control service, were used. The parameters of the lactation curves were estimated using the Wood model and NLIN procedure of the SAS software. The influence of the environmental factors lactation order and calving region and season on the parameters of the lactation curves and on milk yield was evaluated using the MIXED procedure of SAS. First-lactation cows reached peak lactation later and showed a more persistent lactation. Milk yield increased with lactation order. The highest lactation peaks occurred in lactations started in winter and in fall, at 305 days. Cows raised in the center-east region of the state of Paraná had the highest milk yield at the peak and at 305 days of lactation. Lactation order and calving region and season influence the shape of the lactation curve of Holstein cows, with an increase in milk yield when lactation cycles begin in winter-spring. 201 Brazil service used software Firstlactation First fall 30 centereast center east winterspring. winterspring spring. spring winter-spring 20 3 2

Resumo O objetivo deste trabalho foi avaliar a influência de fatores ambientais nos parâmetros da curva de lactação e na produção de leite de vacas da raça Holandesa. Foram utilizados dados de lactações realizadas de 2010 a 2019 no estado do Paraná, Brasil, obtidos do serviço oficial de controle leiteiro. Os parâmetros das curvas de lactação foram estimados com uso do modelo de Wood e do procedimento NLIN do programa SAS. A influência dos fatores ambientais ordem de lactação e região e época de parto nos parâmetros das curvas de lactação e na produção de leite foi avaliada com uso do procedimento MIXED do SAS. Vacas de primeira lactação atingiram o pico de lactação mais tarde e apresentaram lactação mais persistente. A produção de leite aumentou com a ordem de lactação. Os maiores picos ocorreram nas lactações iniciadas no inverno e no outono, aos 305 dias. Vacas criadas na região Centro-Oriental do estado do Paraná apresentaram a maior produção de leite no pico e aos 305 dias de lactação. A ordem de lactação e a região e a estação de parto influenciam o formato da curva de lactação em vacas holandesas, com aumento na produção de leite quando os ciclos de lactação começam no inverno-primavera. Holandesa 201 Brasil leiteiro SAS persistente outono 30 CentroOriental Centro Oriental holandesas invernoprimavera. invernoprimavera primavera. primavera inverno-primavera 20 3 2

Resumo O objetivo deste trabalho foi comparar os principais modelos lineares e não lineares usados para descrever curvas de lactação e avaliar a não linearidade dos modelos não lineares, para obter o modelo mais adequado para a descrição das curvas de lactação da raça Girolando. Foram utilizados dados de 165 lactações de 89 vacas 3/4 Holandesas + 1/4 Gir, tendo-se calculado a produção média a cada 20 dias até 310 dias de lactação. Foram comparados 17 modelos de curvas de lactação disponíveis na literatura. A seleção do melhor modelo foi feita com base nas medidas de curvatura de Bates & Watts, no vício de Box, no coeficiente de determinação ajustado, no critério de informação de Akaike e no desvio-padrão residual. O modelo linear de Cobuci estimou um pico de produção de 16,7 kg aos 40 dias de lactação, enquanto o modelo não linear de Wood estimou um pico de produção de 16,8 kg aos 41 dias de lactação e persistência de 6,82. As medidas de não linearidade foram as mais adequadas para selecionar o modelo não linear mais adequado para a descrição das curvas de lactação. Para descrever as curvas de lactação da raça Girolando, o modelo linear mais adequado é o de Cobuci e o não linear é o de Wood.

Abstract The objective of this work was to compare the main linear and nonlinear models used to describe lactation curves and to evaluate the nonlinearity of the nonlinear models, in order to obtain the most adequate model to describe the lactation curves of the Girolando breed. Data from 165 lactations of 89 3/4 Holstein + 1/4 Gyr cows were used, and average yield was calculated every 20 days up to 310 days of lactation. Seventeen models of lactation curves available in the literature were compared. The selection of the best model was based on the curvature measures of Bates & Watts, the bias of Box, adjusted coefficient of determination, Akaike’s information criterion, and residual standard deviation. The linear model of Cobuci estimated a yield peak of 16.7 kg at 40 days of lactation, whereas the nonlinear model of Wood estimated a yield peak of 16.8 kg at 41 days of lactation and a persistence of 6.82. Nonlinearity measures were the most appropriate for selecting the most suitable nonlinear model for the description of lactation curves. To describe the lactation curves of the Girolando breed, the most suitable linear model is that of Cobuci and the nonlinear model is that of Wood.

ABSTRACT This study aimed to evaluate the lactation curve of female Murrah buffaloes, using mixed nonlinear models (NLM), across three lactation periods (180 d, 210 d, and 240 d). A total of 5334 data on daily milk production (kg) were analyzed. The data were collected every seven days in the interval of one to 250 days of lactation, corresponding to 221 lactations and 145 females, with calvings from 2017 to 2019. The data came from a herd located in the Centro municipality, Tabasco, Mexico. Five NLM were evaluated: Wood (WOD), Wiltmink (WIL), Cobby (COB), Brody (BRO), Sikka (SIK). The best fit model was selected based on the mean prediction error, mean absolute percentage error (MAPE), prediction error variance, coefficient of determination (R2), concordance correlation coefficient (CCC), Akaike (AIC) and Bayesian (BIC) information criteria. A regression analysis was performed between the observed and predicted values. All the NLM had a R2 above 0.91. They tend to underestimate the predictions, without residual autocorrelation. The MAPE showed an average value of 23.5%. The best fit model was WOD, followed by SIK and BRO. For WIL and COB, the mixed model did not improve the fitting. The shortest lactation period showed the best fit, followed by the 210 d and 240 d periods. The relationship between observed:predicted values fluctuated from 0.65 to 1.00, with an average value of 0.94. The use of NLM transcended in the AIC and BIC. The evaluated models showed goodness of fit, with good predictability, but low values in accuracy and precision of prediction.

Resumen Las áreas serranas del Noroeste Argentino (NOA) están pobladas por cabras Criollas del biotipo Serrano. Estudios previos muestran que estas cabras poseen un interesante potencial lechero. Dado que no se conoce cuál es la dinámica de producción a lo largo de la lactancia, es necesario continuar con el proceso de caracterización productiva, estudiando las características de la curva de la lactancia y los modelos estadísticos de ajuste que mejor la representan. El presente trabajo se realizó a partir de una base de datos de 559 lactancias provenientes del control lechero de 256 cabras Criollas Serranas del NOA. Los registros se realizaron entre los años 1998 y 2005. Se ajustaron los registros obtenidos semanalmente a lo largo de la lactación, utilizando los siguientes modelos: polinomial inversa, función gamma incompleta, Cobby y Le Du, Wiltmink, Papajcsik y Bodero, Cappio Borlino, Danhoa y Mc Nally. Para la elección del modelo que mejor ajuste mostró para las curvas de lactancia se tuvieron en cuenta los criterios de información de Akaike y Bayesiano, el error cuadrático medio de la estimación y el coeficiente de determinación ajustado (R2 ). El modelo de Cappio Borlino resultó ser el más apropiado. Esto se debe a que ha sido formulado específicamente para modelar curvas de pequeños rumiantes, siendo particularmente indicado para curvas con una declinación importante luego del pico de la lactancia.

Abstract The mountainous areas of Northwestern Argentina (NOA) are a natural habitat to mountain biotype Creole goats (Criollas Serranas). Previous studies have shown that these goats have an interesting dairy potential. Since there exists no information about milk production dynamics throughout lactation, it becomes necessary to continue characterizing milk production processes, while studying the characteristics of the lactation curve, and the mathematical models with better fits. This work is based on a database with information on 559 lactation processes, as part of the milk production monitoring of 256 Criollas Serranas goats from the NOA region. Records were obtained from 1998 to 2005. These records, which were taken weekly throughout lactation, were fitted to the following models: inverse polynomial, incomplete gamma function, Cobby and Le Du, Wiltmink, Papajcsik and Bodero, Cappio Borlino, Danhoa, and McNally. In order to choose the model that best fit the lactation curves, the Akaike and Bayesian information criteria, the root mean square error (RMSE), and the determination coefficient (R2 ) were taken into account. The Cappio Borlino model turned out to be the most appropriate. This is because it has been specifically formulated to model small ruminant curves, being particularly suitable for curves with a significant decline after lactation peak.

Abstract Milk production and quality during lactation in hair sheep is vital to lamb survival and maintenance. Despite their importance, little data is currently available on these characteristics. An experiment was done to characterize the lactation curve and milk quality in ewes of the Santa Cruz hair sheep breed. Animals were 18 multiparous ewes that had lambed within four days. Milk production was recorded every 72 h from 6 to 60 d postpartum (dpp), and milk quality was quantified once a week from a sample of the day’s total production. Milk production was 1.95 L at 6 dpp, 2.31 L at 12 dpp and 1.01 at 57 dpp. Total solids were 18% at week two and increased to 20.5 % at week eight. Milkfat was 8% at week two and increased to 9.8 % at week eight. The protein (4.86 to 5.18 %) and lactose (4.68 to 4.74 %) percentages remained relatively uniform throughout lactation. Milk production in Santa Cruz ewes is highest in the second week of lactation and then decreases steadily and gradually. Milk total solids and fat percentages increased over time, while protein and lactose percentages remained constant.

Resumen En las ovejas de pelo existe muy poca información respecto a las características de la producción y calidad de la leche a lo largo de la lactancia, pese a sus implicaciones tanto en la sobrevivencia y mantenimiento de los corderos, como en la alimentación humana. Con el propósito de caracterizar la curva de lactancia y la calidad de la leche en ovejas Santa Cruz, se utilizaron 18 ovejas multíparas que parieron en un lapso de cuatro días. La producción láctea se registró cada 72 h en el periodo comprendido de 6 a 60 días postparto (dpp), mientras que la calidad de la leche se determinó una vez por semana de una muestra de la producción total del día. La producción de leche 6 dpp fue de 1.95 L, alcanzando un máximo de 2.31 L, 12 dpp y disminuyendo hasta 1.01, a los 57 dpp. El porcentaje de sólidos totales fue 18 %, incrementando hasta 20.5 % en la octava semana. El porcentaje de grasa durante la segunda semana fue 8 % incrementándose hasta 9.8 % al final del periodo evaluado, mientras que los porcentajes de proteína y lactosa se mantuvieron relativamente uniformes durante todo el periodo experimental en niveles entre 4.86 y 5.18 % para proteína, y 4.68 a 4.74 % para lactosa. Se concluye que la producción de leche en ovejas Santa Cruz, alcanza su máximo alrededor de la segunda semana de lactancia, disminuyendo a partir de ese momento de manera constante y paulatina, incrementando los porcentajes de sólidos totales y grasa a través del tiempo, mientras que los de proteína y lactosa se mantienen constantes.

ABSTRACT The aim of this research was to model the lactation curve in dairy cows with nonlinear models (MNL) and nonlinear mixed models (NLMM), in an intensive breeding dairy farm during the period 2007-2013. In total, 22 173 data referred to biweekly milk production controls were analysed, corresponding to 1302 lactations and 668 Holstein cows. The Brody, Wood, Cobby and Wilmink mathematic models were used evaluating NLM and NLMM, considering the cow as a random effect using SAS v. 9.4 statistical package. Applying information from Akaike (AIC) and Bayesian (BIC) method, NLMM was found to be the best fit for the 305-day lactation curve. Wood mixed model was the best fit for the first calving and Wilmink mixed model for the other calvings. Likewise, production peak, days to production peak, percent productive yield by thirds during the lactation period and production at 305 days according to the number of calving were determined.

RESUMEN La investigación tuvo como objetivo modelar la curva de lactación en vacas lecheras, con modelos no lineales (MNL) y modelos mixtos no lineales (MMNL), en un establo de crianza intensiva durante el periodo 2007-2013. Se analizaron 22 173 datos referidos a controles quincenales de producción de leche (kg), correspondientes a 1302 lactaciones y 668 vacas Holstein. Se utilizaron los modelos matemáticos de Brody, Wood, Cobby y Wilmink evaluando cuatro MNL y cuatro MMNL, considerando como efecto aleatorio a la vaca a través del paquete estadístico SAS v. 9.4. Aplicando la información del método de Akaike (AIC) y Bayesiano (BIC), los MMNL resultaron ser los de mejor ajuste para la curva de lactancia a 305 días. El modelo mixto de Wood fue el de mejor ajuste para el primer parto y el modelo mixto de Wilmink para los demás partos. Asimismo, se determinó el pico de producción, días al pico de producción, rendimiento productivo porcentual por tercios durante la lactación y la producción a 305 días según el número de parto.

Abstract The objective of this study was to determine the productive behavior in Saanen goats by characterizing the lactation curve and the yield according to the number of lactations and the type of delivery in a semi-intensive dairy farm in the province of Buenos Aires. The goat herd was divided into the different categories: first lactation goats (1st L, n = 89); second lactation (2nd L, n = 39), third lactation (3rd L, n = 49); fourth and fifth lactation (4 ° L and 5 ° L, n = 41) and last lactation (UL, n = 38). The type of delivery was classified as Simple (one kid, n = 120) and Multiple (two or more kids, n = 136). The milk control was carried out evaluating the milking twice a day every 42 ± 4 days (BT6 method) by means of mechanical milking with Waikato lactometers. Using a multifactorial analysis of variance, the influence of lactation number and type of delivery on full lactation (PLT) was evaluated. There was a statistically significant difference of the factors (p = 0.0074) and (p = 0.0179) respectively on the PLT. The mean analysis verified significant differences (p <0.05) between the goats of 3 ° L and those of 1 ° L, 2 ° L and UL, likewise, those of 4 ° L and 5 ° L with respect to UL (p <0.05). The type of delivery observed significant differences (p <0.05) in the PLT between the multiple and simple goats. The productive behavior of Saanen goats from a semi-intensive goat farm in the province of Buenos Aires, associated with the number of lactations and the type of parturition, showed differences in milk production.

Resumen El objetivo de este estudio fue determinar el comportamiento productivo en cabras Saanen mediante la caracterización de la curva de lactancia y el rendimiento de acuerdo al número de lactancia y al tipo de parto en un tambo semi-intensivo de la provincia de Buenos Aires. El hato caprino fue dividido en las diferentes categorías: cabras de primera lactancia (1°L, n=89); segunda lactancia (2°L, n=39), tercera lactancia (3°L, n=49); cuarta y quinta lactancia (4°L y 5°L, n=41) y última lactancia (UL, n=38). El tipo de parto fue clasificado en Simple (una cría, n=120) y Múltiple (dos o más crías, n=136). El control lechero se realizó evaluando el ordeño 2 veces por día cada 42 ± 4 días (método BT6) mediante ordeño mecánico con lactómetros Waikato. Mediante un análisis de varianza multifactorial, se evaluó la influencia del número de lactancia y tipo de parto sobre la lactancia completa (PLT). Se observó una diferencia estadísticamente significativa de los factores (p= 0,0074) y (p= 0,0179) respectivamente sobre la PLT. El análisis de media verificó diferencias significativas (p< 0,05) entre las cabras de 3°L y las de 1°L, 2°L y UL, así mismo, las de 4°L y 5°L respecto de UL (p< 0,05). El tipo de parto observó diferencias significativas (p< 0,05) en la PLT entre las cabras múltiples y simples. El comportamiento productivo de cabras Saanen de un establecimiento caprino semi-intensivo de la provincia de Buenos Aires, asociado al número de lactancia y el tipo de parto registraron diferencias en la producción láctea.

Among milk traits, fat-to-protein ratio (FPR) is considered a potential measure of a cow's energy status and is one of the selection criteria necessary to improve metabolic stability. Further genetic analyses require an appropriate model that describes the pattern of FPR changes throughout lactation. The objective of the study was to examine five mathematical functions to describe the lactation curve for FPR in the first three lactations of Polish Holstein-Friesians. The dataset contained FPR records for 5690 cows in the first lactation, 4081 cows in the second, and 2636 cows in the third lactation based on 48908, 34706, and 22097 test-day (TD) records, respectively. Using the MIXED procedure of SAS statistical analytics software, ten linear models (five with fixed effects only, and five with the additional random effect of cow) were fitted to the TD records. The goodness of fit was tested with Akaike's information criterion, residual variances and the correlation coefficient between the actual and estimated values. The model proposed by Ali and Schaeffer (1987) had the best fit to FPR in the first three parities, and the model of Wilmink (1987) provided the worst fit. The correlation coefficient between the actual and the estimated values of FPR was higher for models that included the random cow effect compared with models without this effect.

ABSTRACT The objective of this study was to estimate the breed, heterosis, and recombination effects on different components of the lactation curve of Girolando cattle. The dataset used consisted of 12,121 purebred cows of Holstein (H) and Gyr (G) breeds, and six H×G crossbred cows (Girolando). The model used presents random effects of herd and cow, regression coefficient associated with linear effect of proportion of H breed, regression coefficient associated with the linear effect of heterosis between H and G breeds, regression coefficient associated with the linear effect of recombination between H and G breeds, and random effect of residual. Dijkstra's (DJ), Nelder's (ND), Wilmink's (WL), and Wood's (WD) models were tested to fit production records of these different genetic groups. These models were then tested according to evaluation criteria of quality of fit (AIC, BIC, and RMSE), and the two best models (WD and WL) were chosen for estimation of 305-day milk yield (MY305), peak yield, time to peak, and persistency of milk yield. The breed effect was significant for all traits and components of the lactation curve. The heterosis effect was significant for all traits, and was more significant for MY305 (945.62±79.17 kg). Peak yield was the component of lactation curve that presented the most significant heterosis effect, partially explaining the heterosis effect (12 to 21%) found for MY305. The recombination effect was positive only for lactation period and time to peak of lactation in Girolando cows.

ABSTRACT Objective. Determine the prevalence of bovine ketosis based on serum concentrations (mmol/Lt) of beta-hydroxybutyrate (βHB) and estimate its association with early postpartum diseases in dairy cows. Materials and methods. An epidemiological cross-sectional study was carried out with individual information on blood levels of βHB and clinical presentation of puerperal diseases in 1149 animals; In addition, the efficiency of the test was evaluated as a predictor of postpartum disease. Subsequently, univariate analysis and a final logistic regression model were performed to explore the factors associated with hyperketonemia. The association between blood βHB, the presentation of ketosis and the occurrence of puerperal diseases was calculated by analyzing the Receiver Operating Characteristic -ROC. Results. According to βHB levels, the prevalence of ketosis was 7.9%, clinical ketosis 0.6% and subclinical ketosis 7.3%. The test was a predictor of puerperal disease (LR+ of 13.6). Body condition score ≥3.5, number of births 2 and ≥3, presentation of retained fetal membranes, milk fever and postpartum disease, are risk factors for ketosis. The analysis of the ROC curve showed that the measurement of βHB (≥1.2 mmol/Lt) in blood serves to diagnose ketosis (p<0.0001). Conclusions. The measurement of βHB blood levels allowed to determine that ketosis presentation is low, it is an alert not only for this disease but for early postpartum diseases. The results of this study confirm risk factors observed in previous studies.

RESUMEN Objetivo. Determinar la prevalencia de cetosis bovina según las concentraciones séricas (mmol/Lt) de beta-hidroxibutirato (βHB) y estimar su asociación con enfermedades del posparto temprano en vacas lecheras. Materiales y métodos. Se llevó a cabo un estudio epidemiológico de corte transversal con información individual de los niveles sanguíneos de βHB y presentación clínica de enfermedades puerperales de n=1149 animales; además se evaluó la eficiencia de la prueba como predictora de enfermedad posparto. Posteriormente, se realizó X 2 y un modelo de regresión logística final para explorar los factores asociados con hipercetonemia. La relación entre βHB sanguíneo, la presentación de cetosis y la ocurrencia de enfermedades puerperales se calculó analizando Característica Operativa del Receptor (Receiver Operating Characteristic -ROC). Resultados. Según los niveles de |3HB, la prevalencia de cetosis fue de 7.9%, cetosis clínica 0.6% y cetosis subclínica 7.3%. La prueba fue predictora de enfermedad puerperal (LR+ del 13.6). La condición corporal ≥3.5, número de partos igual a 2 y ≥3, la presentación de retención de placenta, fiebre de leche y la enfermedad posparto, son factores de riesgo de cetosis. El análisis de la curva ROC mostró que la medición de βHB (≥1.2 mmol/Lt) en sangre sirve para diagnosticar cetosis (p<0.0001). Conclusiones. La medición de niveles sanguíneos de βB permitió determinar que la presentación de cetosis es baja, es una alerta no solamente para esta enfermedad sino para las enfermedades del posparto temprano. Los resultados de este estudio confirman lo reportado en estudios previos sobre los factores de riesgo de cetosis.

ABSTRACT Conventionally, lactation curves of confined dairy cattle have been modelled using non-linear, fixed effects models (MNL). The aims of this study were (i) to assess the fit of non-linear mixed models(MMNL), usingtheWood(y = β xβ2e-β3x) and Wilmink (y = β + β e-0.009x+ β x) functions to analyse lactation curves under grazing and in the context of heteroscedasticity and correlated errors, and (ii) to evaluate the effect of parity and calving season on the curve parameters for both functions. The Wood and the Wilmink functions were fitted, using MNL and MMNL to 600 milk production records corresponding to 42 lactations from 2004 to 2012 from dairy cattle with 1, 2 or >3 calvings in the wet or dry season from the herd in the IVITA-El Mantaro Research Station (Junin, Perú). For both functions, the MMNL outperformed the MNL in terms of residual standard error reduction, increasing of the likelihood, and being able to model random effects and correlations for all the parameters of both functions. The MMNL was also able to model heteroscedasticity by means of a variance function and correlated errors by means of a spatial correlation function. There were not important differences in the fitting of the Wood or Wilmink functions in terms of the residual standard error or the Akaike or bayesian information criteria. Both, parity and calving season did not have significant effects on the curve parameters of the Wood and Wilmink functions. It is concluded that the MMNL is an excellent tool to model lactation curves both at the populationor individual-level.

RESUMEN En el análisis de curvas de lactación bovina bajo estabulación se han usado, convencionalmente, modelos de efectos fijos no lineales (MNL). Los objetivos de este estudio fueron (i) evaluar el ajuste de los modelos mixtos no lineales (MMNL) utilizando las funciones de Wood (y = β xβ2e-β3x) y Wilmink (y = β + β e-0.009x+ β x) para describir curvas de lactación en condiciones de heterocedasticidad y correlación de errores y (ii) evaluar el efecto del número y época de partos sobre los parámetros de ambas funciones. Las funciones fueron ajustadas, usando MNL y MMNL, a 600 registros de producción de leche pertenecientes a 42 lactaciones, bajo pastoreo, entre 2004 y 2102. Las lactaciones correspondieron a vacas con 1, 2 o >3 partos, ocurridos en época seca o época húmeda en el establo de la Estación Experimental IVITA-El Mantaro (Junín, Perú). Para ambas funciones, los MMNL tuvieron un mejor desempeño que los MNL, reduciendo el error estándar residual, incrementando la verosimilitud y modelando los efectos de las lactaciones individuales y sus respectivas correlaciones para todos los parámetros de ambas funciones. Los MNNL también fueron capaces de modelar la heterocedasticidad con una función de varianza y la dependencia entre errores con una función de correlación espacial. No se observaron diferencias sustanciales en el ajuste entre las funciones de Wood y de Wilmink en términos del error estándar residual y de los criterios de información de Akaike y bayesiano. El número y la estación de parto tampoco tuvieron efectos significativos sobre los parámetros de las curvas de lactación de ambas funciones. Se concluye que los MMNL son una excelente herramienta para modelar curvas de lactación poblacionales e individuales.

Abstract This study evaluated the genetic (TG) and phenotypic (TF) trends for the peak yield (PP), milk yield (RL), and lactation persistency (P) traits of the Murciano-Granadina (MG) goat lactation curve obtained from 80,872 lactations of 85,404 goats (historical records from 1990-2012). The biomodelling of lactation curves allowed us to estimate the PP, RL, and P traits using the Spline model in the “R” software. The genetic values (VGs) were obtained using the univariate animal model with repeated observations, employing the MTDFREML package. The TG and TF were estimated via the least-squares regression of the average of VGs and known yield information according to the year of birth. While calculating the TG and TF, linear regression coefficients (b) were obtained, where the b values for PP, RL, and P were +0.00071, +0.00698; +0.00114, +0.01117; and +0.00002, -0.00076, respectively. The TG and TF for the PP and RL behaved similarly following an upward trend line with increasing and decreasing intervals. The TG for P showed seasonal variations while the TF followed a downward trend with more consistent points in its trajectory; supporting the idea that high yields are detrimental to the P. These results inform the breeders about the behavior of these traits and provide the basis for the incorporation of the lactation persistency as a selection criteria in the genetic program of the MG breed.

Resumen El objetivo fue evaluar las tendencias genéticas (TG) y fenotípicas (TF) para los caracteres de pico productivo (PP), rendimiento lechero (RL) y persistencia de la lactación (P) en la curva de lactación de la raza Murciano-Granadina (MG). Para ello se utilizaron 180,872 lactaciones, de 85,404 cabras (registros históricos de 1990-2012). Para la obtención de los caracteres de interés (PP, RL y P) se realizó la biomodelación de curvas de lactación mediante el modelo Spline usando el software “R”. Los valores genéticos (VG) se obtuvieron mediante modelo animal univariado con observaciones repetidas, empleándose el paquete MTDFREML. Las TG y TF se estimaron vía mínimos cuadrados en una regresión del promedio de los VG e información productiva conocida según el año de nacimiento. En el cálculo de las TG y TF se obtuvieron coeficientes de regresión lineal (b), donde los valores b para PP, RL y P fueron de +0.00071, +0.00698; +0.00114, +0.01117 y +0.00002, -0.00076; respectivamente. El trayecto de TG, TF de PP y RL se comportó de la misma manera siguiendo una línea de tendencia ascendente con presencia de intervalos de crecimiento y decrecimiento. La TG de P mostró un comportamiento estacional y la TF fue descendente con puntos más consistentes en su recorrido; reforzando la idea de que altas producciones van en detrimento de la P. Estos resultados permiten informar a los criadores del comportamiento de estos caracteres y considerar la incorporación de la persistencia de la lactación como criterio de selección en el programa genético de la raza.

Resumen Introducción. La precipitación, temperatura, radiación y humedad relativa varían según la altura, esto provoca la presencia de microclimas que afectan la productividad de los animales. Objetivo. Asociar las condiciones climáticas presentes en el sistema productivo con la producción láctea de un hato jersey puro en dos pisos altitudinales de la provincia de Cartago, Costa Rica. Materiales y métodos. De forma retrospectiva, durante el año 2016, se evaluó la información productiva de dos sistemas ubicados a 660 y 1800 msnm. Del primero se analizaron los registros de 61 animales durante doce años (12 083 datos); mientras que en el segundo se analizaron las lactancias de 387 animales en cinco años (13 820 registros). Las observaciones incluyeron: identificación del semoviente, día de generación del registro, mes, año, producción de leche diaria, días de lactancia, número de partos, edad del animal, temperatura, precipitación, radiación solar y humedad relativa promedio. Resultados. Los días de lactancia, el número de lactancia (3a-5a), la edad del animal (3,7 a 5,8 años) y el número de partos afectaron la producción de leche diaria en ambas fincas (p<0,001). A 1800 m, cuando la precipitación fue mayor a 5 pero menor o igual a 10 mm día-1 y la humedad relativa mayor a 80 pero menor a 90 % día-1 (p<0,001), la producción de leche disminuyó. En cambio, a 660 m el efecto provino de la humedad relativa menor o igual a 70 %. La temperatura ambiental tuvo un efecto significativo sobre ambas altitudes. Conclusiones. Las condiciones de temperatura, humedad, precipitación y radiación en cada ecosistema, generaron diferencias en la productividad de los animales, relacionadas con el tipo de forraje y la sensación térmica a la que estaba expuesto el ganado, lo cual provocó estrés por calor o por frío.

Abstract Introduction. Precipitation, temperature, radiation, and relative humidity vary according to height, this causes the presence of microclimates that affect the productivity of the animals. Objective. Associate the climatic conditions present in the productive systems with dairy production of a pure Jersey herd in two altitudinal floors of the province of Cartago, Costa Rica. Materials and methods. In retrospect, during the year 2016, the productive information of two dairy farms, located at 660 and 1800 m.a.s.l. was evaluated. From the first farm, the records of 61 animals in a twelve-year period (12,083 data) were analyzed; while in the second, the lactations of 387 animals in a five-year period (13,820 records) were analyzed. Observations included: identification of the cow, day of generation of the record, month, year, daily milk production, lactation days, calving number, animal age, temperature, precipitation, solar radiation and average relative humidity. Results. The lactation days, the lactation number (3-5), the age of the animal (3.7 to 5.8 years), and the calving number affected the daily milk production on both farms (p<0.001). At 1800 m, when the precipitation was greater than 5 but less than or equal to 10 mm day-1 and the relative humidity greater than 80 but less than 90 % day-1 (p<0.001), milk production decreased. On the other hand, at 660 m the effect came from relative humidity less than or equal to 70 %. The environmental temperature had a significant effect in both altitudes. Conclusion. The conditions of temperature, humidity, precipitation, and radiation in each ecosystem, generated differences in the productivity of the animals, related to the type of forages and the thermal sensation to which the cattle was exposed, which caused heat or cold stress.

ABSTRACT Lactation records from cows of the southwestern Paraná state, Brazil, form the dataset of this study. We applied the information-theoretic approach to evaluate the ability of the nonlinear Wood, Brody, Dijkstra, and Gamma functions to fit to these data by employing a two-step technique based on nonlinear mixed-effects models and generalized linear mixed-effects models. Wood's equation was fitted with the combination of a first-order autoregressive correlation structure and a variance function to account for heteroscedasticity. This version was the best choice to mimic lactation records. Some geometric attributes of Wood's model were deduced, mainly the ascending specific rate from parturition to peak milk yield and the descending specific rate as a measure of the lactation persistence of the milk yield at peak production. Breed and parity order of the cows were assumed as fixed effects to obtain a reliable model fitting process. Regardless of breed, first-order parity cows had greater persistency than their older counterparts, and the greater the ascending rate of milk yield from the parturition to the peak, the sharper the decrease in milk yield post-peak; therefore, the rates (absolute values) of ascending and descending phases correlated positively. Nonetheless, the actual estimated values of the descending phase rates are negative. Wood's equation was flexible enough to mimic either concave- and convex-shaped lactation profiles. The correlations between both peak milk yield and random estimates for β with total milk yield per lactation were positive. However, peak milk yield might not be the only variable used for ranking cows; the total milk yield integrates all information of the lactation profile through the estimated parameters of Wood's equation.