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Is it possible to accurately estimate lactation curve parameters in extensive beef production systems?

  • M. Iewdiukow
    Affiliations
    Instituto Nacional de Investigación Agropecuaria (INIA), Programa Producción de Carne y Lana, Estación Experimental INIA Treinta y Tres, Ruta 8 km 281, 33000, Treinta y Tres, Uruguay
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  • O.M. Lema
    Affiliations
    Instituto Nacional de Investigación Agropecuaria (INIA), Programa Producción de Carne y Lana, Estación Experimental INIA Treinta y Tres, Ruta 8 km 281, 33000, Treinta y Tres, Uruguay
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  • J.I. Velazco
    Affiliations
    Instituto Nacional de Investigación Agropecuaria (INIA), Programa Producción de Carne y Lana, Estación Experimental INIA Treinta y Tres, Ruta 8 km 281, 33000, Treinta y Tres, Uruguay
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  • G. Quintans
    Affiliations
    Instituto Nacional de Investigación Agropecuaria (INIA), Programa Producción de Carne y Lana, Estación Experimental INIA Treinta y Tres, Ruta 8 km 281, 33000, Treinta y Tres, Uruguay
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      ABSTRACT

      Objective

      The objective was to characterize the lactation curve applying 3 different models using multiparous grazing beef cows.

      Materials and Methods

      Milk production data from 99 British crossbred multiparous cows grazing native pastures were analyzed. Lactation was assessed 15 d postpartum and then monthly until weaning (180 d postpartum) using a milking machine after an oxytocin injection. Total milk production and lactation curve were characterized using Wood (WD) and Wilmink (WIL) models, and both were compared with spline functions. Comparison was made applying adjusted coefficient of determination (R2adj) and MSE.

      Results and Discussion

      Cubic splines with 5 equally spaced knots (CS5) presented the best adjustment (lowest Akaike information criterion and Bayesian information criterion). The R2adj values were 0.55, 0.54, and 0.53 (the greater the better) and MSE values were 2.54, 2.59, and 2.47 (the lower the better) for WD, WIL, and CS5, respectively. Estimated milk production for the lactation period was 1,277, 1,255, and 1,195 kg for WD, WIL, and CS5, respectively. Milk peak was predicted to happen at 32, 25, and 36 d postpartum, with a production of 8.74, 8.21, and 8.40 kg for WD, WIL, and CS5, respectively. No differences were evident in the lactation curves (95% CI).

      Implications and Applications

      The proposed method and frequency used to assess grazing beef cattle milk production accurately estimate the lactation curve. The Wood model, used worldwide, was a precise estimator of the lactation curve, which in our case was verified applying splines. These results provide key information to calculate grazing beef cow requirements.

      Key words

      INTRODUCTION

      Livestock production systems are characterized by a high dependence on climatic conditions. Consequently, there is a high variation in forage allowance between and within years because native pastures are the main source of nutrition. They present a marked seasonality with maximum forage production in spring and summer and minimum in winter (
      • Carvalho P.D.F.
      • Fischer V.
      • Dos Santos D.T.
      • Ribeiro A.M.L.
      • De Quadros F.L.F.
      • Castilhos Z.M.S.
      • Poli C.H.E.C.
      • Monteiro A.L.G.
      • Nabinger C.
      • Genro T.C.M.
      • Jacques A.V.A.
      Produção animal no bioma campos sulinos (Southern campos bioma animal production)..
      ), which coincides with the final stage of gestation and the onset of the calving period.
      Extensive systems demand high energy requirements for maintenance and production (
      • Montaño-Bermudez M.
      • Nielsen M.K.
      • Deutscher G.H.
      Energy requirements for maintenance of crossbred beef cattle with different genetic potential for milk..
      ). The efficiency of cow-calf systems is defined by the ability to transform pasture nutrients into kilograms of weaned calves (
      • Jenkins T.G.
      • Ferrell C.L.
      Lactation characteristics of nine breeds of cattle fed various quantities of dietary energy..
      ). Moreover, milk is the main source of nutrients for calves, and it is highly correlated with the weaning weight of calves (
      • Totusek R.
      • Arnett D.W.
      • Holland G.L.
      • Whiteman J.V.
      Relation of estimation method, sampling interval and milk composition to milk yield of beef cows and calf gain..
      ); thus, it is important to better understand milk production during the lactation period in these conditions.
      Many models have been proposed to characterize milk production and the lactation curve in dairy cattle, such as the model proposed by
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      or
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      . Both have also been used to describe lactation curves in beef cattle (
      • Albertini T.Z.
      • Medeiros S.R.
      • Torres Júnior R.A.A.
      • Zocchi S.S.
      • Oltjen J.W.
      • Strathe A.B.
      • Lanna D.P.D.
      A methodological approach to estimate the lactation curve and net energy and protein requirements of beef cows using nonlinear mixed-effects modeling..
      ;
      • Espasandin A.C.
      • Gutierrez V.
      • Casal A.
      • Graña A.
      • Bentancur O.
      • Carriquiry M.
      Modeling lactation curve in primiparous beef cattle..
      ). These models have a low number of parameters and are accessible to use and apply. The Wood and Wilmink models are the most used models to describe the lactation curve among different production systems, both in dairy and beef cows.
      Other functions such as splines are used to estimate milk production, which have the advantage of providing extra flexibility in the shape of fitted lactation curves (
      • White I.M.S.
      • Thompson R.
      • Brotherstone S.
      Genetic and environmental smoothing of lactation curves with cubic splines..
      ) and improved accuracy when few samples are available (
      • Macciotta N.P.P.
      • Vicario D.
      • Cappio-Borlino A.
      Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models..
      ). Assessing daily milk production in beef cows is difficult, but 6 samples per lactation were enough to obtain a high determination coefficient using the milking machine method (
      • Albertini T.Z.
      • Medeiros S.R.
      • Torres Júnior R.A.A.
      • Zocchi S.S.
      • Oltjen J.W.
      • Strathe A.B.
      • Lanna D.P.D.
      A methodological approach to estimate the lactation curve and net energy and protein requirements of beef cows using nonlinear mixed-effects modeling..
      ).
      The aim of the present study was to characterize the lactation curve of multiparous beef cows under grazing conditions in Uruguay with splines and the parametric models published by
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      and
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      .

      MATERIALS AND METHODS

      Location

      Data used in the analysis of milk production of beef cows was from different experiments carried out at the National Institute of Agricultural Research (33°26′9363″S, 54°49′4932″W), Uruguay, between 2006 and 2016.
      The grasslands were composed of 80 to 85% perennial summer grasses, with Paspalum notatum and Axonopus affinis being the most important (

      Ayala, W., E. Carriquiry, and M. Carámbula. 1993. Caracterización y estrategias de utilización de pasturas naturales en la región Este (Characterization and stratagies of native pastures utilization in the East region of Uruguay). Pages 1–28 in Campo Natural: Estrategia Invernal. Manejo y Suplementación. INIA Serie de Actividades de Difusión 49. INIA Treinta y Tres, Treinta y Tres, Uruguay.

      ). The average annual production was estimated at 3,425 kg of DM/ha, with a digestibility of OM of 53, 56.5, and 57.5% and a CP percentage of 11, 9, and 8% for winter, spring, and summer, respectively (

      Bermúdez, R., and W. Ayala. 2005. Producción de forraje de un campo natural de la zona de lomadas del Este (Rangelands production in East hills of Uruguay). Pages 33–39 in Seminario de Actualización Técnica en Manejo de Campo Natural. Resultados Experimentales. INIA Serie Técnica 151. INIA Montevideo, Montevideo, Uruguay.

      ). Average annual rainfall and temperature in the area were 1,350 ± 233 mm and 17 ± 0.72°C, respectively.

      Database

      Ninety-nine British crossbred multiparous (4 to 10 yr old) cows over 7 yr were analyzed. Data corresponded to an original Hereford × Angus crossbred herd that was consistently served with Angus; therefore, the breed of cow was described as a proportion of Angus. Cows calved in spring (from mid-September to the end of October), and they were managed on native pastures with similar forage allowance (8–10 kg of DM/kg of live weight). No treatments were applied to the animals.
      Cows were weighed at calving and monthly until weaning (180 d postpartum; autumn), and their BCS assessed visually was recorded at the same time on a 1- to 8-point scale (1 = thin, 8 = fat) as reported by
      • Vizcarra J.A.
      • Ibañez W.
      • Orcasberro R.
      Repetibilidad y reproductibilidad de dos escalas para estimar la condición corporal de vacas Hereford (Repeatability and reproducibility of two scales to estimate the body condition of Hereford cows)..
      . Calves were weighed at birth and monthly until weaning. Table 1 shows the estimated mean of cow body live weight and BCS by different periods: parturition (d 0) and 1 to 60, 61 to 120, and 121 to 180 d postpartum. Calf birth and weaning body live weight (corrected to 180 d) averaged 36.3 ± 0.22 and 180.5 ± 2.58 kg, respectively (mean ± SE).
      Table 1Average body live weight (BLW, kg) and BCS of multiparous cows (mean ± SE) by postpartum period
      ItemDays postpartum
      01–6061–120121–180
      Cow BLW419 ± 1.8441 ± 3.6447 ± 3.1449 ± 3.2
      Cow BCS4.06 ± 0.024.07 ± 0.054.2 ± 0.044.2 ± 0.04
      Milk production was assessed between 15 and 30 d postpartum and monthly until weaning (i.e., d 30, 60, 90, 120, 150, and 180). Milk production was estimated using a milking machine after an oxytocin injection; the protocol used was proposed by
      • Quintans G.
      • Banchero G.
      • Carriquiry M.
      • López-Mazz C.
      • Baldi F.
      Effect of body condition and suckling restriction with and without presence of the calf on cow and calf performance..
      . Briefly, cows were separated from calves, and each cow was injected intramuscularly with 10 to 20 IU of oxytocin (Hipofamina, Laboratorio Dispert SA, Montevideo, Uruguay) to facilitate milk letdown. Cows were milked approximately 2 min after the injection. At least 8 h later cows were milked again using the same protocol. Calves remained separated from cows in another paddock during these hours. A milking machine (Ruakura, Ruakura, New Zealand) was used in each milking, and it was removed after milk flow had ceased. Milk was weighed and recorded to calculate 24-h milk production, assuming linearity. In addition, milk samples of 47 cows were analyzed for fat, protein, and lactose.

      Statistical Analysis

      An ANOVA was performed to determine the fixed effects to be included in the model. As a result, year of the experiment, cow breed proportion, and sex of calves were included as fixed effects. Cow effect was included as a random effect and BCS at calving as a covariate.
      The average lactation curve was estimated accounting for individual data from the fortnightly and monthly samplings. Lactation curve was first characterized using linear, quadratic, and cubic splines with different numbers of knots (2 to 6). Splines are special functions defined in parts by polynomials derived from the use of a thin, flexible strip called a “spline” to draw smooth curves through a set of points (
      • Guo Q.
      • White R.E.
      Cubic spline regression for the open-circuit potential curves of a lithium-ion battery..
      ). The spline functions are continuous at the breakpoints (called knots) between one segment and the next (
      • White I.M.S.
      • Thompson R.
      • Brotherstone S.
      Genetic and environmental smoothing of lactation curves with cubic splines..
      ).
      These functions were adjusted using the PROC GLIMMIX procedure of SAS (version 9.4, SAS Institute Inc., Cary, NC), and the goodness of fit used to compare the adjustment of those functions was the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). The function with the smallest AIC and BIC was the one selected to characterize the milk lactation curve.
      In addition, the lactation curve was modeled with 2 widely used models published by
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      , WD) and
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      , WIL). The same fixed and random effects were used in this analysis. The WD [1] and WIL [2] models are as follows:
      y=atbexpc×t,
      [1]


      y=a+bexp0.05×t+ct,
      [2]


      where y is daily milk production (kg); t is day of lactation; and a, b, and c are parameters that define milk production at the beginning of lactation, rate of increase to the lactation peak, and rate of decline after the peak, respectively. The value of the exponent −0.05 × t of the WIL equation determines the occurrence of milk peak day. The WD and WIL models were adjusted using the PROC NLMIXED procedure of SAS (version 9.4 SAS Institute Inc.).
      The Wood and Wilmink models and splines functions were compared using the adjusted coefficient of determination (R2adj) and the MSE. The most suitable is the one with the highest R2adj and the lowest MSE. Additionally, a 95% CI was constructed for each day of lactation to compare the estimated daily production for each of the curves.

      RESULTS AND DISCUSSION

      The lactation curve was characterized using linear, quadratic, and cubic splines with different numbers of knots (2 to 6). The spline function that presented the lowest value of AIC and BIC was selected to characterize the lactation curve of the multiparous cows and it was compared with the Wood and Wilmink models. The cubic spline with 5 equally spaced knots (CS5) was selected because it had the lowest AIC and BIC values (data not presented). Thus, the linear and quadratic splines were not analyzed in this study. Procedures used to assess the nonlinear models (Wood and Wilmink) are based on the maximum likelihood method, whereas the spline functions (estimated by generalized mixed models) base their estimates on the restricted maximum likelihood method. Thus, models and spline functions were compared using R2adj and MSE instead of the models’ comparison criteria most frequently used (AIC and BIC).
      The Wood model had the highest R2adj compared with cubic splines and Wilmink, but CS5 had the smallest MSE (better adjustment) compared with WD and WIL (Table 2). The 3 applied functions to characterize the lactation curve of multiparous beef cows presented good adjustment (R2adj and MSE). Cubic splines with 5 equally spaced knots had the best adjustment between all tested splines models (smaller AIC and BIC). The Wood and Wilmink parametric models described the expected shape as well as the splines, which are flexible and highly determined by the data structure. The described curve presents a typical lactation curve’s shape with an ascending phase to a maximum peak and a steadily decreasing phase thereafter (
      • Garcia S.C.
      • Holmes C.W.
      Lactation curves of autumn- and spring-calved cows in pasture-based dairy systems..
      ;
      • Chilibroste P.
      • Naya H.
      • Urioste J.I.
      Evaluación cuantitativa de curvas de lactancia de vacas holando en Uruguay. 3. Implicancias biológicas de las curvas de producción multifásica (Quantitative assessment of lactation curves in Uruguayan Holstein cows. 3. Biological implications of the multiphase lactation curves)..
      ;
      • Macciotta N.P.P.
      • Dimauro C.
      • Rassu S.P.G.
      • Steri R.
      • Pulina G.
      The mathematical description of lactation curves in dairy cattle..
      ). No significant differences in total milk production nor in the shape of the curve were evident when Wood, Wilmink, and cubic splines were compared applying a 95% CI. A slight numerical difference of 7 to 5% of the total milk production was detected (Table 3), which could be explained by the fact that the splines better fit individual variation. Total milk production was estimated as the area under the curve; thus, when using flexible functions (splines), the shape of the curve better adapts to the observed data.
      Table 2Adjusted multiple coefficient of determination (R2adj) and MSE of the 3 estimated methods
      MethodR2adjMSE
      Cubic spline with 5 knots0.532.47
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      model
      0.552.54
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      model
      0.542.59
      Table 3Estimated production variables for the cubic splines with 5 knots (CS5) function and the
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      and
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      models at 180 d of lactation
      ItemCS5WoodWilmink
      Total milk production (L)1,1951,2771,255
      Mean production (L/d)6.647.096.97
      Milk peak day (d)363225
      Milk at peak day (L)8.408.748.21
      The estimated production variables for each model are presented in Table 3. Total milk production estimated by WD was 6.8% higher than the estimated by CS5 and 1.8% higher than those by WIL. The days to milk peak occurred around the third, fourth, and fifth week for WIL, CS5, and WD models, respectively (Figure 1). There were no differences in estimated milk production at peak day between models (P > 0.05), because the milk peak day estimated presented a range from 25 to 36 d. No significant differences were evident between models within the 95% CI. The Wilmink model showed an earlier peak occurrence compared with the other 2 evaluated models. The reason for this observation may be based on the parameter k used in this analysis (k = 0.05) that is usually applied as a constant (
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      ).
      Figure 1
      Figure 1Lactation curves of multiparous cows for 180 d of lactation estimated with 3 different methods [sold line = cubic splines with 5 equally spaced knots; dashed line = the
      • Wood P.D.P.
      Algebraic model of the lactation curve in cattle..
      model; dotted line = the
      • Wilmink J.B.M.
      Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
      model].
      All milk production peaks estimated in this study ranged between 3.5 to 5 wk with a production of 8.2 to 8.7 kg/d, consistent with those reported in the literature.
      • Hohenboken W.D.
      • Dudley A.
      • Moody D.E.
      A comparison among equations to characterize lactation curves in beef cows..
      described a milk lactation curve of beef cows with the peak at wk 4.4 postpartum with 8.4 kg/d applying the Wood model. Working in grazing conditions similar to ours and applying the Wood model,
      • Espasandin A.C.
      • Gutierrez V.
      • Casal A.
      • Graña A.
      • Bentancur O.
      • Carriquiry M.
      Modeling lactation curve in primiparous beef cattle..
      reported a peak production at wk 5 postpartum with a lower production compared with the present study (5.2 vs. 8.7 kg/d). That difference could be explained by the age of the cows (primiparous vs. multiparous). In fact, it was reported that older cows have 16 to 28% higher milk production than primiparous cows (
      • Rodrigues P.F.
      • Menezes L.M.
      • Azambuja R.C.C.
      • Suñé R.W.
      • Barbosa Silveira I.D.
      • Cardoso F.F.
      Milk yield and composition from Angus and Angus-cross beef cows raised in southern Brazil..
      ), and according to
      • Pimentel M.A.
      • Moraes J.C.F.
      • Jaume C.M.
      • Lemes J.S.
      • Brauner C.C.
      Características da lactação de vacas Hereford criadas em um sistema de produção extensivo na região da campanha do Rio Grande do Sul (Lactation performance of Hereford cows raised in a range system in the state of Rio Grande do Sul)..
      , those differences occur mainly at the peak, where multiparous cows have greater production than primiparous cows. Moreover,
      • López Valiente S.
      • Maresca S.
      • Rodríguez A.M.
      • Palladino R.A.
      • Lacau-Mengido I.M.
      • Long N.M.
      • Quintans G.
      Effect of protein restriction of Angus cows during late gestation: Subsequent reproductive performance and milk yield..
      , working on grazing conditions in Argentina, reported a maximum production at wk 14 postpartum with 6.5 kg/d in Angus cows. The difference in the moment of milk peak occurrence might be explained by the estimation method applied by these authors (quadratic regression). In addition,
      • Rodrigues P.F.
      • Menezes L.M.
      • Azambuja R.C.C.
      • Suñé R.W.
      • Barbosa Silveira I.D.
      • Cardoso F.F.
      Milk yield and composition from Angus and Angus-cross beef cows raised in southern Brazil..
      , working in southern Brazilian conditions, described a peak production around the ninth week of lactation with 6.3 and 6.6 kg/d in Angus purebred and Hereford × Angus, respectively.
      Several authors applied the Wood model to estimate milk production in different breeds or crossbreeds and conditions.
      • Hohenboken W.D.
      • Dudley A.
      • Moody D.E.
      A comparison among equations to characterize lactation curves in beef cows..
      worked with Angus and Angus × Holstein cows, and
      • Maiwashe A.
      • Nengovhela N.B.
      • Nephawe K.A.
      • Sebei J.
      • Netshilema T.
      • Mashaba H.D.
      • Nesengani L.
      • Norris D.
      Estimates of lactation curve parameters for Bonsmara and Nguni cattle using the weigh-suckle-weigh technique..
      worked with Bonsmara and Nguni cows. Under similar grazing conditions to those in the present study,
      • Espasandin A.C.
      • Gutierrez V.
      • Casal A.
      • Graña A.
      • Bentancur O.
      • Carriquiry M.
      Modeling lactation curve in primiparous beef cattle..
      , working with primiparous Hereford, Angus, and their crosses, reported a good fit of the lactation curve applying the Wood model. Nevertheless, the Wood model has some limitations in accurately predicting milk production at the beginning and end of the lactation curve (
      • Congleton Jr., W.R.J.
      • Everett R.W.
      Error and bias in using the incomplete gamma function to describe lactation curves..
      ;
      • Macciotta N.P.P.
      • Dimauro C.
      • Rassu S.P.G.
      • Steri R.
      • Pulina G.
      The mathematical description of lactation curves in dairy cattle..
      ). This mainly occurs when few data are available due to the great distance between calving and the first test day (
      • Macciotta N.P.P.
      • Vicario D.
      • Cappio-Borlino A.
      Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models..
      ) or when the time between samplings is too long. According to
      • Flores E.B.
      • Kinghorn B.P.
      • van der Werf J.
      Predicting lactation yields in dairy buffaloes by interpolation and multiple trait prediction..
      , the estimation errors of these models are produced by intervals of 90 to 120 d between samplings.
      • Silvestre A.M.
      • Petim-Batista F.
      • Colaco J.
      The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes..
      also reported that both Wood and Wilmink models were affected by long intervals between samplings.
      Parametric models (Wood and Wilmink) are used to estimate lactation curves of large and homogeneous groups of animals, with high-frequency samplings are unable to accurately estimate individual curves (
      • White I.M.S.
      • Thompson R.
      • Brotherstone S.
      Genetic and environmental smoothing of lactation curves with cubic splines..
      ). Therefore, to estimate small, heterogeneous or individual lactation curves, with few observations, flexible functions with variable coefficients such as splines are recommended by
      • Silvestre A.M.
      • Petim-Batista F.
      • Colaco J.
      The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes..
      . Splines fit better to particular data sets and, according to
      • White I.M.S.
      • Thompson R.
      • Brotherstone S.
      Genetic and environmental smoothing of lactation curves with cubic splines..
      , could deal with unbalanced data, being able to estimate both genetic and environmental effects. Cubic splines were a good compromise among fitting performance, data sensitivity, smoothness, and parameterization in fitting average lactation curves (
      • Druet T.
      • Jaffrézic F.
      • Boichard D.
      • Ducrocq V.
      Modeling lactation curves and estimation of genetic parameters for first lactation test-day records of French Holstein cows..
      ;
      • Silvestre A.M.
      • Petim-Batista F.
      • Colaco J.
      The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes..
      ).
      Extensive production systems are highly dependent on climatic conditions, with a marked seasonality in forage availability. Furthermore, assessing milk production of beef cows under those conditions can be laborious. The method used to assess milk production (milking machine after oxytocin injection) and the proposed milking frequency (6 samplings per lactation on average) allowed accurate estimation of the lactation curve, for all tested methods. Results of the present study suggest that the milking method and frequency applied in the assessment of milk production should be recommended for beef cows under range conditions.
      It has been reported that maintenance requirements may vary according to the level of milk production (
      • Montaño-Bermudez M.
      • Nielsen M.K.
      • Deutscher G.H.
      Energy requirements for maintenance of crossbred beef cattle with different genetic potential for milk..
      ). To accurately estimate cow requirements at each stage, it is necessary to know the lactation curve shape. The parameters estimated by the Wood model, in the present work, were 5.887, 0.9725, and 0.03058 for a, b, and c, respectively. These parameters are also needed for the precise estimation of maintenance requirements in beef lactating cows. Milk components (fat, protein, and lactose) are also necessary to estimate lactation requirements. Milk fat, protein, and lactose were 2.16 ± 0.05, 3.13 ± 0.02, and 4.94 ± 0.01%, respectively. Milk protein and lactose percentages were consistent with those reported by the

      NRC. 2016. Nutrient Requirements of Beef Cattle. 8th rev. ed. Natl. Acad. Press, Washington, DC. 10.17226/19014.

      in a review of several studies. In fact, the mean values were 3.38 ± 0.27 and 4.75 ± 0.91% for protein and lactose, respectively. Also,
      • López Valiente S.
      • Maresca S.
      • Rodríguez A.M.
      • Palladino R.A.
      • Lacau-Mengido I.M.
      • Long N.M.
      • Quintans G.
      Effect of protein restriction of Angus cows during late gestation: Subsequent reproductive performance and milk yield..
      , working in similar conditions to ours, reported 3.4 ± 0.11 and 4.9 ± 0.16% of protein and lactose in milk, respectively. In contrast, percentage of fat reported by the

      NRC. 2016. Nutrient Requirements of Beef Cattle. 8th rev. ed. Natl. Acad. Press, Washington, DC. 10.17226/19014.

      was higher than that in our study (4.03 ± 1.24 vs. 2.16 ± 0.05%, respectively), but the variation coefficient in the study by the NRC was also higher (31 vs. 2%, respectively). It could be hypothesized that differences in fat content were due to genetic or environmental conditions. Indeed, assessments similar to ours, such as those by
      • Astessiano A.L.
      • Perez-Clariget R.
      • Quintans G.
      • Soca P.
      • Meikle A.
      • Crooker B.A.
      • Carriquiry M.
      Metabolic and endocrine profiles and hepatic gene expression in periparturient, grazing primiparous beef cows with different body reserves..
      and
      • López Valiente S.
      • Maresca S.
      • Rodríguez A.M.
      • Palladino R.A.
      • Lacau-Mengido I.M.
      • Long N.M.
      • Quintans G.
      Effect of protein restriction of Angus cows during late gestation: Subsequent reproductive performance and milk yield..
      , found milk fat content closer to that presented in our study (2.7 and 2.8%, respectively).
      Energy is the limiting factor in grazing cow-calf systems, with NEm being around 70% of the required energy (
      • Ferrell C.L.
      • Jenkins T.G.
      Cow type and the nutritional environment: Nutritional aspects..
      ). Considering the significant proportion of the consumed energy used for maintenance, objective information that identifies animals with lower energy maintenance requirements and high productive performance is critical. This is even more important when forage availability is highly variable. The development of an EPD in maintenance energy is a relevant and challenging objective for extensive grazing situations. According to the equation proposed by

      Williams, J. L. 2007. The use of random regression to include yearling weight in mature weight analysis of the maintenance energy prediction for Red Angus cattle. MSc. Diss. Colorado State Univ., Fort Collins, CO.

      for the estimation of mature cow maintenance energy, both milk production and mature weight are needed.
      • Goldberg V.
      • Ravagnolo O.
      Description of the growth curve for Angus pasture-fed cows under extensive systems..
      reported cow mature weight under grazing conditions (similar to ours) being an outstanding contribution to extensive livestock systems. Furthermore, coefficients reported in the present study in terms of milk production and milk components for grazing cows make maintenance energy calculation possible. Consequently, all information needed to build an EPD for maintenance energy in grazing conditions is now available.

      APPLICATIONS

      Estimation of the lactation curve of grazing multiparous beef cows contributes to the accurate determination of nutritional requirements during lactation. Once requirements are determined, it will be possible to predict productive performance affected by milk production under different production circumstances. Furthermore, our results provide key information needed by breeding selection programs for the development of an EPD of maintenance requirements for grazing animals, unavailable until now.

      ACKNOWLEDGMENTS

      The authors gratefully acknowledge Ignacio Aguilar, Oscar Bentancur, and Olga Ravagnolo for their revisions and comments on this work. The authors also acknowledge funding from the Instituto Nacional de Investigación Agropecuaria, Uruguay.

      LITERATURE CITED

        • Albertini T.Z.
        • Medeiros S.R.
        • Torres Júnior R.A.A.
        • Zocchi S.S.
        • Oltjen J.W.
        • Strathe A.B.
        • Lanna D.P.D.
        A methodological approach to estimate the lactation curve and net energy and protein requirements of beef cows using nonlinear mixed-effects modeling..
        https://doi.org/10.2527/jas.2010-3540
        22665632
        J. Anim. Sci. 2012; 90: 3867-3878
        • Astessiano A.L.
        • Perez-Clariget R.
        • Quintans G.
        • Soca P.
        • Meikle A.
        • Crooker B.A.
        • Carriquiry M.
        Metabolic and endocrine profiles and hepatic gene expression in periparturient, grazing primiparous beef cows with different body reserves..
        https://doi.org/10.1016/j.livsci.2014.10.008
        Livest. Sci. 2014; 170: 63-71
      1. Ayala, W., E. Carriquiry, and M. Carámbula. 1993. Caracterización y estrategias de utilización de pasturas naturales en la región Este (Characterization and stratagies of native pastures utilization in the East region of Uruguay). Pages 1–28 in Campo Natural: Estrategia Invernal. Manejo y Suplementación. INIA Serie de Actividades de Difusión 49. INIA Treinta y Tres, Treinta y Tres, Uruguay.

      2. Bermúdez, R., and W. Ayala. 2005. Producción de forraje de un campo natural de la zona de lomadas del Este (Rangelands production in East hills of Uruguay). Pages 33–39 in Seminario de Actualización Técnica en Manejo de Campo Natural. Resultados Experimentales. INIA Serie Técnica 151. INIA Montevideo, Montevideo, Uruguay.

        • Carvalho P.D.F.
        • Fischer V.
        • Dos Santos D.T.
        • Ribeiro A.M.L.
        • De Quadros F.L.F.
        • Castilhos Z.M.S.
        • Poli C.H.E.C.
        • Monteiro A.L.G.
        • Nabinger C.
        • Genro T.C.M.
        • Jacques A.V.A.
        Produção animal no bioma campos sulinos (Southern campos bioma animal production)..
        Brazilian J. Anim. Sci. 2006; 35: 156-202
        • Chilibroste P.
        • Naya H.
        • Urioste J.I.
        Evaluación cuantitativa de curvas de lactancia de vacas holando en Uruguay. 3. Implicancias biológicas de las curvas de producción multifásica (Quantitative assessment of lactation curves in Uruguayan Holstein cows. 3. Biological implications of the multiphase lactation curves)..
        Rev. Argent. Prod. Anim. 2002; 22: 358-359
        • Congleton Jr., W.R.J.
        • Everett R.W.
        Error and bias in using the incomplete gamma function to describe lactation curves..
        https://doi.org/10.3168/jds.S0022-0302(80)82894-3
        J. Dairy Sci. 1980; 63: 101-108
        • Druet T.
        • Jaffrézic F.
        • Boichard D.
        • Ducrocq V.
        Modeling lactation curves and estimation of genetic parameters for first lactation test-day records of French Holstein cows..
        https://doi.org/10.3168/jds.S0022-0302(03)73842-9
        12906066
        J. Dairy Sci. 2003; 86: 2480-2490
        • Espasandin A.C.
        • Gutierrez V.
        • Casal A.
        • Graña A.
        • Bentancur O.
        • Carriquiry M.
        Modeling lactation curve in primiparous beef cattle..
        https://doi.org/10.5539/jas.v8n4p116
        J. Agric. Sci. 2016; 8: 116-125
        • Ferrell C.L.
        • Jenkins T.G.
        Cow type and the nutritional environment: Nutritional aspects..
        https://doi.org/10.2527/jas1985.613725x
        4066531
        J. Anim. Sci. 1985; 61: 725-741
        • Flores E.B.
        • Kinghorn B.P.
        • van der Werf J.
        Predicting lactation yields in dairy buffaloes by interpolation and multiple trait prediction..
        https://doi.org/10.1016/j.livsci.2012.10.017
        Livest. Sci. 2013; 151: 97-107
        • Garcia S.C.
        • Holmes C.W.
        Lactation curves of autumn- and spring-calved cows in pasture-based dairy systems..
        https://doi.org/10.1016/S0301-6226(00)00237-2
        Livest. Prod. Sci. 2001; 68: 189-203
        • Goldberg V.
        • Ravagnolo O.
        Description of the growth curve for Angus pasture-fed cows under extensive systems..
        https://doi.org/10.2527/jas.2015-9208
        26440328
        J. Anim. Sci. 2015; 93: 4285-4290
        • Guo Q.
        • White R.E.
        Cubic spline regression for the open-circuit potential curves of a lithium-ion battery..
        https://doi.org/10.1149/1.1845336
        J. Electrochem. Soc. 2005; 152: A343-A350
        • Hohenboken W.D.
        • Dudley A.
        • Moody D.E.
        A comparison among equations to characterize lactation curves in beef cows..
        https://doi.org/10.1017/S0003356100037223
        Anim. Prod. 1992; 55: 23-28
        • Jenkins T.G.
        • Ferrell C.L.
        Lactation characteristics of nine breeds of cattle fed various quantities of dietary energy..
        https://doi.org/10.2527/1992.7061652x
        1634388
        J. Anim. Sci. 1992; 70: 1652-1660
        • López Valiente S.
        • Maresca S.
        • Rodríguez A.M.
        • Palladino R.A.
        • Lacau-Mengido I.M.
        • Long N.M.
        • Quintans G.
        Effect of protein restriction of Angus cows during late gestation: Subsequent reproductive performance and milk yield..
        https://doi.org/10.15232/pas.2017-01701
        Prof. Anim. Sci. 2018; 34: 261-268
        • Macciotta N.P.P.
        • Dimauro C.
        • Rassu S.P.G.
        • Steri R.
        • Pulina G.
        The mathematical description of lactation curves in dairy cattle..
        https://doi.org/10.4081/ijas.2011.e51
        Ital. J. Anim. Sci. 2011; 10: e51
        • Macciotta N.P.P.
        • Vicario D.
        • Cappio-Borlino A.
        Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models..
        https://doi.org/10.3168/jds.S0022-0302(05)72784-3
        15738251
        J. Dairy Sci. 2005; 88: 1178-1191
        • Maiwashe A.
        • Nengovhela N.B.
        • Nephawe K.A.
        • Sebei J.
        • Netshilema T.
        • Mashaba H.D.
        • Nesengani L.
        • Norris D.
        Estimates of lactation curve parameters for Bonsmara and Nguni cattle using the weigh-suckle-weigh technique..
        https://doi.org/10.4314/sajas.v43i5.2
        S. Afr. J. Anim. Sci. 2013; 43: 12-16
        • Montaño-Bermudez M.
        • Nielsen M.K.
        • Deutscher G.H.
        Energy requirements for maintenance of crossbred beef cattle with different genetic potential for milk..
        https://doi.org/10.2527/1990.6882279x
        2401650
        J. Anim. Sci. 1990; 68: 2279-2288
      3. NRC. 2016. Nutrient Requirements of Beef Cattle. 8th rev. ed. Natl. Acad. Press, Washington, DC. 10.17226/19014.

        • Pimentel M.A.
        • Moraes J.C.F.
        • Jaume C.M.
        • Lemes J.S.
        • Brauner C.C.
        Características da lactação de vacas Hereford criadas em um sistema de produção extensivo na região da campanha do Rio Grande do Sul (Lactation performance of Hereford cows raised in a range system in the state of Rio Grande do Sul)..
        https://doi.org/10.1590/S1516-35982006000100021
        Rev. Bras. Zootec. 2006; 35: 159-168
        • Quintans G.
        • Banchero G.
        • Carriquiry M.
        • López-Mazz C.
        • Baldi F.
        Effect of body condition and suckling restriction with and without presence of the calf on cow and calf performance..
        https://doi.org/10.1071/AN10021
        Anim. Prod. Sci. 2010; 50: 931-938
        • Rodrigues P.F.
        • Menezes L.M.
        • Azambuja R.C.C.
        • Suñé R.W.
        • Barbosa Silveira I.D.
        • Cardoso F.F.
        Milk yield and composition from Angus and Angus-cross beef cows raised in southern Brazil..
        https://doi.org/10.2527/jas.2013-7055
        24753378
        J. Anim. Sci. 2014; 92: 2668-2676
        • Silvestre A.M.
        • Petim-Batista F.
        • Colaco J.
        The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes..
        https://doi.org/10.3168/jds.S0022-0302(06)72250-0
        16606753
        J. Dairy Sci. 2006; 89: 1813-1821
        • Totusek R.
        • Arnett D.W.
        • Holland G.L.
        • Whiteman J.V.
        Relation of estimation method, sampling interval and milk composition to milk yield of beef cows and calf gain..
        https://doi.org/10.2527/jas1973.371153x
        J. Anim. Sci. 1973; 37: 153-158
        • Vizcarra J.A.
        • Ibañez W.
        • Orcasberro R.
        Repetibilidad y reproductibilidad de dos escalas para estimar la condición corporal de vacas Hereford (Repeatability and reproducibility of two scales to estimate the body condition of Hereford cows)..
        Investigaciones Agronómicas. 1986; 7: 45-47
        • White I.M.S.
        • Thompson R.
        • Brotherstone S.
        Genetic and environmental smoothing of lactation curves with cubic splines..
        https://doi.org/10.3168/jds.S0022-0302(99)75277-X
        10194684
        J. Dairy Sci. 1999; 82: 632-638
      4. Williams, J. L. 2007. The use of random regression to include yearling weight in mature weight analysis of the maintenance energy prediction for Red Angus cattle. MSc. Diss. Colorado State Univ., Fort Collins, CO.

        • Wilmink J.B.M.
        Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation..
        https://doi.org/10.1016/0301-6226(87)90003-0
        Livest. Prod. Sci. 1987; 16: 335-348
        • Wood P.D.P.
        Algebraic model of the lactation curve in cattle..
        https://doi.org/10.1038/216164a0
        Nature. 1967; 216: 164-165