Lactation Curve Models Research Articles

Lactation Curves of Mastitic Vrindavani Cattle: A Statistical Approach

Mastitis is one of the important animal disease which causes huge economic loss. The present study was aimed to find the best lactation curve model that describes the milk production pattern of Vrindavani cattle suffered from mastitis. In the study, test day milk yield data of 161 mastitic Vrindavani cattle (incidence of the disease occurring within the three months of parturition) was collected from Cattle and Buffalo Farm, LPM section, ICAR‑IVRI over 5 years (2009-2014). Eight lactation curve models [Inverse quadratic polynomial model (ND), Incomplete Gamma function (WD), Linear decline model (CL), Wilmink model (WL) Mixed log model (ML), Mitscherlich x Exponential (ME), Morant and Gnanasakthy model (MG) and Ali & Schaeffer lactation curve model (AS)] were fitted. The best model was selected based on different goodness of fit criteria and the Durbin-Watson test was used to examine the presence of autocorrelation present in the data set. Kolmogorov-Smirnova test and Shapiro-Wilk were used to test the normality of the residuals. Based on the various goodness of fit test it was observed that the Mixed Log (ML) model was the best fitted model to describe the lactation pattern of mastitic Vrindavani cattle.

Association between days post-conception and lactation persistency in dairy cattle

Determining the optimal insemination moment for individual cows is complex, particularly when considering the impact of pregnancy on milk production. The effect of pregnancy on the absolute milk yield has already been reported in several studies. Currently, there is limited quantitative knowledge about the association between days post conception (DPC) and lactation persistency, based on a lactation curve model, and, specifically, how persistency changes during pregnancy and relates to the days in milk at conception (DIMc). Understanding this association might provide valuable insights to determine the optimal insemination moment. This study, therefore, aimed to investigate the association between DPC and lactation persistency, with an additional focus on the influence of DIMc. Available milk production data from 2005 to 2022 were available for 23,908 cows from 87 herds located throughout the Netherlands and Belgium. Persistency was measured by a lactation curve characteristic decay, representing the time taken to halve milk production after peak yield. Decay was calculated for 8 DPC (0, 30, 60, 90, 120, 150, 180 and 210 d after DIMc) and served as the dependent variable. Independent variables included DPC, DIMc (< = 60, 61-90, 91-120, 121-150, 151-180, 181-210, > 210), parity group, DPC × parity group, DPC × DIMc and variables from 30 d before DIMc as covariates. The results showed an increase in decay, i.e., a decrease in persistency, during pregnancy for both parity groups, albeit in different ways. Specifically, from DPC 150 to DPC 210, multiparous cows showed a higher decline in persistency compared with primiparous cows. Furthermore, a later DIMc (cows conceiving later) was associated with higher persistency. Except for the early DIMc groups (DIMc < 90), DIMc does not impact the change in persistency by gestation. The findings from this study contribute to a better understanding of how DPC and DIMc during lactation influence lactation persistency, enabling more informed decision-making by farmers who wish to take persistency into account in their reproduction management.

Bayesian approach for evaluation of lactation curve in cross bred cattle based on monthly and bimonthly test day milk yield.

In field progeny testing program milk recording at monthly or bimonthly intervals and prediction of first lactation 305-day milk yield (FL305DMY) from these test day yields have been adapted as an alternative to daily milk recording. Wood's incomplete gamma function is the one of the commonly used nonlinear lactation curve model. In recent years Bayesian approach of fitting nonlinear biological models is gaining attention among researchers. In this study Wood's incomplete gamma function was fitted using Bayesian approach using monthly (MTDY) and bimonthly test day (BTDY) yields. The lactation curve parameters thus obtained were used for prediction of FL305DMY. Efficiency of prediction based on monthly and bimonthly test day milk yield were compared using error of prediction. It was found to be 5.78% and 7.59% as root mean square error (RMSE) based on MTDY and BTDY respectively.The Breeding values of 97 Karan Fries sires were estimated using BLUP-AM based on actual and predicted FL305DMY thus obtained. The RMSE was calculated as the difference between estimated breeding values based on actual and predicted yield. It was found that RMSE calculated based on MTDY showed only a marginal superiority of 0.79% over BTDY and showed high degree of correlation with actual yield. Therefore, recording at bimonthly intervals could be an economical alternative without compromising the efficiency.

Modelling Lactation Curve for Genetic Evaluation of Crossbred Cattle

The present study was conducted on first lactation 4415 monthly test-day milk yield records of 466 crossbred (CB) cattle sired by 89 bulls during 2000–2018 (19 years) maintained at Directorate of Livestock Farms, GADVASU, Ludhiana, Punjab, India. The crossbred cattle with lactation length of minimum 100 days were considered for the study. The aim was to develop the best lactation curve model and to compare the breeding values of sires based on actual and predicted first lactation 305-day milk yield (FL305DMY). The data were classified and coded according to different season and age at first calving groups for first lactation 305-day milk yield. Monthly test-day milk yields of first lactation were used to develop the best lactation curve model. The Polynomial Regression Function (PRF) model was the best model amongst all the models based on both R2 and RMSE values. The breeding values of 60 HF crossbred sires with two or more daughters were estimated from the actual and predicted FL305DMY using Polynomial Regression Function by applying two sire evaluation methods viz. least squares method (LSQ) and restricted maximum likelihood method (REML). The effectiveness of LSQ and REML methods of sire evaluation was compared on the basis of Spearman’s rank correlations, coefficients of determination (R2) and coefficients of variation (CV). LSQ was found most efficient and accurate method for sire evaluation using actual and predicted first lactation 305-day milk yield in HF crossbred cattle.

Modelling of the first lactation milk yield of Frieswal cows using different mathematical functions

A study was conducted to find the most appropriate mathematical model that describes the first lactation milk yield of Frieswal cattle. Data on 42,368 individual first lactation test day yields of 1,072 Frieswal cows calved during 2005 to 2014 in Ambala and Meerut Military dairy farms were utilized for the study. The first test day milk yield was recorded on 6thday after calving while the subsequent records were collected at seven days interval and so the average 43 test day yields were taken for fitting the lactation curve models. Five different mathematical models, viz. Exponential decline function (EDF), Parabolic exponential function (PEF), Inverse polynomial function (IPF), Gamma function (GF) and Mixed log function (MLF) were fitted.The accuracy of fitting (R2 value) the models revealed that the MLF (96.14) was more appropriate followed by IPF (95.57), GF (93.85), PEF (83.68) and EDF (69.09). The RMSE estimate of MLF was lowest (0.3483) as expected while the EDF had the highest RMSE value of 0.9858.The AIC criterion was lowest for IPF (5.7175) and highest for GF (8.0212). The BIC values of five functions ranged between –83.6262 for MLF to 3.1809 for EDF. All the DW estimates were positive and ranged between 0.3656 for EDF to 0.7106 for GF indicating positive autocorrelation between the residuals. Based on the results obtained in the present study, it may be inferred that the first lactation yield was explained accurately by the mixed log function (MLF) in Frieswal cattle. As the inverse polynomial (IPF) and gamma function (GF) also had satisfactory results, these two functions can also be used for fitting the lactation curve models in Frieswal cattle. On the other hand, exponential decline function and parabolic exponential functions least explain the first lactation curve in Frieswal cattle.

Characteristics of Lactation Curve and Reproduction in Dairy Cattle

The purpose of the research was to assess changes in the lactation activity of cows and their impact on the level of reproduction, as well as to study their fluctuations with respect to genetic and environmental factors. A sample of 807 cows of various ages was formed for the study. The cows were kept on a commercial farm in Kharkiv region, Ukraine. Data from DairyPlan C21 software were used in the study. It was revealed that the parameters of the Wood lactation curve model were significantly influenced by the calving season, days open, and cow's origin; lactation persistency of cows was more influenced by environmental factors (parity, calving season, days open) than by the sire. In order to improve the level of reproduction in dairy herds, it is advisable to take into account the lactation persistency of cows, since it has negative relationship with days open (r = -0.074). To improve lactation persistency it is necessary to use for insemination of cows semen of sires with high breeding values for this trait.

Study on effect of various non-genetic factors on performance traits of Murrah buffaloes

In this study, the data was collected on production traits of Murrah buffaloes w.r.t. 1 to 4 parities for the period of 25 years maintained at Directorate Livestock Farm, Guru Angad Dev Veterinary and Animal Sciences University, Ludhiana. The effect of non-genetic factors viz; period of calving, season of calving, age at first calving and parity on daily milk yield were found to be significant and subsequently data were corrected to study the comparison of various lactation curve models to define the shape of lactation curve and to develop a suitable lactation curve model for Murrah buffaloes. The data used in the study pertained to 517293 daily milk yield records pertaining to 1524 lactations of 644 Murrah buffaloes sired by 213 bulls. The analysis was done using SAS 9.3 Least squares analysis. The period of calving showed significant (P&lt;0.01) effect on 305 MY, complete lactation milk yield (CLMY), peak yield, lactation length and service period. The season of calving showed significant (P&lt;0.01) effect on peak yield, lactation length and service period. The age at first calving showed significant (P&lt;0.05) effect on peak yield. The parity showed significant (P&lt;0.01) effect on 305 MY, complete lactation milk yield (CLMY), peak yield, lactation length and service period.

Estimation of partial lactation milk yields in Saanen goats raised in semi-intensive conditions

Objective: The objective of this study was to estimate the lactation curves of Saanen goats by using individual milk yields in the early, mid and 0-6 months periods of lactation. For this purpose, Wood’s lactation curve was used to estimate lactation yields. Material and Methods: Milk yields of Saanen goats in different periods of lactation were estimated. For this purpose, the Wood’s lactation curve model was adapted to a total of 480 milk yield measured at 14-day intervals of 40 Saanen goats. Milk yields of goats in the first three months of lactation in January-March, mid-lactation in April-June, and 0-6 months in January-June were estimated. Results: According to the harmony of Wood's model, the determination of coefficient values of the estimations of milk yields in the first, mid-lactation and 0-6 months of lactation are 0.84, 0.87 and 0.84, respectively. The root mean square errors of Wood's model are 0.91 for the first period of lactation, 0.81 for the mid-lactation period and 0.30 for the from 0 to 6 months of lactation period. Conclusions: According to the results obtained in this study, Wood's model was found sufficient to define the lactation curve in Saanen goats. However, it would be beneficial to conduct similar studies with larger herds and yield records.

Comparison of models for lactation curves of Holstein, Brown Swiss, and F1 crossbred cows under subtropical conditions.

Tropical and subtropical milk production herds in Mexico generally generate different types of milk-yield records as milk yield per month and mean production per month. Lactation curves generated by these types of records may contribute to understand milk production in the tropical regions of Mexico. The aim of this study was to compare five lactation-curve models fitted to two types of milk-yield records of Holstein, Brown Swiss, and F1 crossbred cows under subtropical conditions. The two types of records (n = 3756) used were: (1) milk yield per month (TR) and 2) mean production per months (MR). Goodness-of-fit statistics, including Akaike's information criterion (AIC) and root mean square error (RMSE), were applied to compare the models for each type of records. The Brody model provided the best goodness-of-fit when using monthly milk-yield records, while the Wilmink model provided the best goodness-of-fit for lactation milk-yield records. The RMSE and AIC values were similar between datasets. The final third of the lactation curve showed a little difference between model predictions in both datasets. The comparison of several models was useful to better describe the actual lactation curves of the herd. The Wood model may be adequate to compare information as a reference with other models for decision making process at milk production.

Milk yield, composition, and lactation curve models of Bargur cattle under farmers' production system in their native habitat.

Milk yield and composition traits (fat (%) and SNF (%)) from 1229 test day records of 205 Bargur cattle maintained under a farmers' production system were studied. This breed is known for its adaptability to the hilly tracts of Erode District in Tamil Nadu. Performance recording was done in the natural habitat through the test-day milk yield from lactating cows in the farmers' herds. Effects of non-genetic factors like season, year, parity, stage of lactation, and days from calving were studied using mixed models with animal taken as a random effect. Estimated marginal means for daily milk yield (DMY, L/day), fat (%), and SNF (%) were 2.05 ± 0.03, 4.08 ± 0.03%, and 8.19 ± 0.01%, respectively. Stage of lactation was highly significant (P < 0.01) for DMY, fat, and SNF. Season and year were significant for DMY and SNF, where higher productivity was obtained in the monsoon season, but fat remained constant in all the seasons. Parity was significant (P < 0.05) only for SNF, and year was significant for DMY (P < 0.01) and SNF (P < 0.05). Persistency was 5.9% calculated using Wood's gamma function and 63.0% calculated using the ratio of predicted yields. This was slightly lower compared to dairy breeds of cattle. Thirteen different lactation curve models were used for fitting of Bargur cattle lactation curve, and the Parabolic exponential model was the best fitting model based on model diagnostic criteria.

Test day yield, lactation curve and production potential of Gir cattle under hot and humid conditions of Tamil Nadu

Test day milk yield records (5130), milk production and milk composition traits from 19 lactations of Gir cows collected for two years (2019 and 2020) were used to understand the performance of Gir breed in hot and humid conditions of Tamil Nadu. Different lactation curve models were used for modelling test day records and model diagnostics like adjusted R-square, BIC and RMSE were used to obtain the model of best fit. The mean test day yield, fat per cent, SNF (%), total milk yield, peak yield, days to attain peak yield and calving interval observed were 5.78 kg, 5.05%, 7.65%, 1507 kg, 9.23 kg, 46.5 days and 447 days respectively. Ali and Shaeffer model offered the best fit for lactation curve in Gir cows. Mahadevan method and Gamma function were used to calculate the persistency of milk yield which was obtained as 1.33 and 6.348 respectively. Results of the study indicated that Gir cattle were able to adapt themselves through maintenance of reproductive traits comparable with that of the native tract but the new humid environment has caused a slight decrease in the performance of milk production traits.

Optimal value for the exponential term of Wilmink's function according to current Holstein lactation curves in Japan.

We compared values of Wilmink's exponential term to describe the lactation curves of Holstein cows in Japan. Data were a total of 100,971,798 test-day records from the first through fifth parities during 1991 through 2018. The lactation curve model used fourth-order Legendre polynomials and Wilmink's exponential term. In total, 810 analyses were executed to compare six values (-0.02, -0.03, …, -0.07) for the exponential term to select the one that yielded the smallest root mean square error. For all parities, daily milk yield and lactation persistency increased consistently and peak lactation days occurred later from year to year. For the years evaluated, the optimal exponential term was -0.05 for first and second parities, -0.04 for third parity, and -0.03 for fourth and fifth parities. The change in the exponential parameter with increasing year was related to delays in peak lactation.

Associations between feed efficiency and aspects of lactation curves in primiparous Holstein dairy cattle

Genetic selection for improved feed efficiency in dairy cattle has received renewed attention over the last decade to address the needs of a growing global population. As milk yield is a critical component of feed efficiency metrics in dairy animals, our objective was to evaluate the associations between feed efficiency in primiparous Holstein cattle and parameters of a mathematical model describing individual lactation curves. The Dijkstra lactation curve model was fit to individual lactation records from 34 Holstein heifers with previously estimated measures of feed efficiency. We found that the optimal fit of the Dijkstra model was achieved using daily milk yield records up to 21 d in milk to capture the rise to peak milk yield and using monthly dairy herd improvement records for the remainder of lactation to accurately characterize lactation persistency. In the period of lactation before peak milk yield, improved feed efficiency was associated with a faster increase in daily milk yield over a shorter period of time at the expense of increased mobilization of body reserves; this serves to reinforce the concept that dairy cattle are primarily capital breeders versus income breeders. Feed efficiency in the period following peak lactation, as measured by gross feed efficiency, return over feed costs, and net energy efficiency of lactation, was positively associated with higher peak milk yield. The findings in early lactation suggest that estimates of feed efficiency could be improved by evaluating feed efficiency relative to conception, rather than parturition and lactation, to better account for the energy stored and released from body reserves in capital breeding.

Comparative Evaluation of Lactation Curves of Crossbred Dairy Cows in Field Conditions in Tamil Nadu, India

Background: Various mathematical models have been tried by different researchers to fit the lactation curves in indigenous, exotic and crossbred cows maintained in organised farms only. Hence, this study was aimed to fit various lactation models and to identify the best fit model (s) for prediction of milk production in crossbred dairy cows in field conditions.Methods: Multistage random sampling procedure was used for selection of 100 dairy cows for the purpose of data collection. The monthly milk yield data (up to 10 months of lactation) of the selected crossbred cows reared in field conditions of Tamil Nadu State, relating to the period from 2017-20, were collected for lactation curve modelling. The milk data so collected were used to fit 14 lactation curve models in the study. The highest Coefficient of Determination (R²) value and the least Root Mean Square Error (RMSE) value were used as the criteria to select the best fit model(s).Result: The overall average total milk production was estimated to be 2223.19 kg per lactation in 10 months of lactation in the selected crossbred cows. Average daily milk yield at the first month of lactation was 9.16 kg and the highest daily milk yield of 9.56 kg was observed at the second month of lactation. At the end of the lactation, the lowest yield was 5.01 kg per day and hence the overall average daily milk yield was found to be 7.41 kg. Based on the selection criteria, the Mitscherlich X Exponential model was identified as the best fit model, followed by Ali and Schaeffer and Morant and Gnanasakthy model for prediction of milk production in crossbred dairy cows reared in field conditions and the estimated lactation curve model parameters a, b, c and d values for the best fit model were 331.71, 1519.82, 9.56 and 0.07 kg, respectively.

Modeling and evaluation of lactation curve functions in Gir cattle

The aim of the study was to model and evaluate five different non-linear lactation curve functions for their efficiency of explaining the variations in first lactation milk yield of Gir cows maintained in the farmers herds. Information on 4,334 fortnightly test day yields of 223 cows calved during the period from 2013-2017 were used for the study. Twenty fortnightly yields starting from the day 15 of lactation were used for fitting the five different non-linear mathematical models, viz. Exponential decline function (EDF), Gamma function (GF), Inverse polynomial function (IPF), Mixed log function (MLF) and Parabolic exponential function (PEF). The curve functions (a, b and c) with standard errors and different evaluation parameters, viz. adjusted R2-value, Akaike information criterion (AIC), Bayesian information criterion (BIC), Durbin watson (DW) statistic and root mean square error (RMSE) were estimated by non-linear regression analysis using PROC NLIN procedure Newton method of SAS (SAS Institute, 2010). The adjusted R2 value of the models ranged from 69.28 (exponential decline function) to 99.36% (parabolic exponential function). All the DW estimates were positive ranging from 0.1573 for exponential decline function to 0.7707 for parabolic exponential function. The RMSE (0.1453) and AIC (4.9152) estimates were also lowest for parabolic exponential function while highest for exponential decline function. Based on the results, it may be concluded that among five functions, parabolic exponential function is the best fitted lactation curve model followed by mixed log function, gamma function, inverse polynomial function while exponential decline function was the least efficient in explaining the variations in first lactation daily yield in Gir cattle.

Lactation curve model with explicit representation of perturbations as a phenotyping tool for dairy livestock precision farming

In the context of dairy farming, ruminant females often face challenges inducing perturbations that affect their performance and welfare. A key issue is how to assess the effect of perturbations and provide metrics to quantify how animals cope with their environment. Milk production dynamics are good candidates to address this issue: i) they are easily accessible, ii) overall dynamics throughout lactation process are well described and iii) perturbations are visible through milk losses. In this study, a perturbed lactation model (PLM) with explicit representation of perturbations was developed. The model combines two components: i) the unperturbed lactation model that describes a theoretical lactation curve, assumed to reflect female production potential and ii) the perturbation model that describes all the deviations from the unperturbed lactation model with four parameters: starting date, intensity and shape (collapse and recovery). To illustrate the use of the PLM as a phenotyping tool, it was fitted on a data set of 319 complete lactations from 181 individual dairy goats. A total of 2 354 perturbations were detected, with an average of 7.40 perturbations per lactation. Loss of milk production for the whole lactation due to perturbations varied between 2 and 19% of the milk production predicted by the unperturbed lactation model. The number of perturbations was not the major factor explaining the loss of milk production, suggesting that there are different types of animal response to challenges. By incorporating explicit representation of perturbations in a lactation model, it was possible to determine for each female the potential milk production, characteristics of each perturbation and milk losses induced by perturbations. Further, it was possible to compare animals and analyze individual variability. The indicators produced by the PLM are likely to be useful to move from raw data to decision support tools in dairy production.

Evaluation of lactation models in pasture-based dairy ewes in Bosnia and Herzegovina

Milk of Kupres, Privor and Stolac dairy ewe breeds is used for the production of the fine cheese varieties. To the best of our knowledge there are no information about milk production and milk composition of these pasture-based dairy ewes. The aim was to determine the best lactation curve model in autochthonous pasture-based dairy ewes in Bosnia and Herzegovina. Milk production was recorded and milk composition sampled (milk fat and protein) during early, mid and late lactation in 129 Kupres, 141 Privor and 129 Stolac pramenka ewes. Four lactation models (Wilmink, Cubic, Ali-Shaeffer and Guo-Swalve) were compared and selected based on the lowest coefficient of determination and root mean square error. The Guo-Swalve model described all of the measured variables most successfully. Kupres pramenka dairy ewe was the highest producing breed with 139 kg of milk during 175 days of lactation (0.79 kg/d; between lactation day 50 to 225) and showed the standard lactation curve. Privor pramenka produced 118 kg of milk during 175 days of lactation (0.67 kg/d) and Stolac pramenka 101 kg of milk during 175 days of lactation (0.58 kg/d). Both showed atypical constantly decreasing shape of the lactation curve common in low producing dairy ewes. The prediction of milk yield and milk composition from the Guo-Swalve model could be used by the national breeding program for the Kupres, Privor and Stolac pramenka sheep breeds. Additional research during a more stable management conditions is recommended for Privor and Stolac pramenka.

Comparison of lactation curve models for fortnightly test day milk yield

The study of lactation curve helps to predict lactation milk production at a certain point of time and provides useful information for taking desirable decisions on preliminary sire evaluation, early culling of poor producers, breeding and feeding management and comparison of lactation records of unequal length. The test day milk yield data on 511 crossbred cattle were obtained and utilized according to fortnightly interval upto 305th day maintained at Instructional Dairy Farm, G B Pant University of Agriculture and Technology, Pantnagar (Uttarakhand). The different statistical models predicting the shape of lactation curve considered were exponential function, parabolic exponential function, inverse polynomial function and gamma type function. For fortnightly test day milk yield, the inverse polynomial function exhibited the highest coefficient of determination (R2=99.97%) followed by parabolic exponential (89.32%), gamma type (87.26%) and exponential function (35.70). Inverse polynomial function is the best fitted function for explaining the first lactation curve by utilizing the records of fortnightly test day milk yields.

Testing the efficacy of different lactation curve models for monthly test day milk yield

The test day milk yield data on 511 crossbred cattle were obtained and utilized according to monthly interval upto 305 th day maintained at Instructional Dairy Farm, of G. B. Pant University of Agriculture and Technology, Pantnagar (Uttarakhand). The different statistical models considered in this study for predicting the shape of lactation curve were Exponential Function, Parabolic Exponential Function, Inverse Polynomial Function and Gamma Type Function. Maximum coefficient of determination (R 2 ) value was observed for Inverse Polynomial function (R 2 = 99.97%) followed by Gamma function (R 2 = 88.28%), Parabolic function (R 2 = 80.95 %), and Exponential function (R 2 = 39.10%). The root mean square error (RMSE) was least for Inverse Polynomial function (0.07 kg) followed by Gamma Type function (0.10kg ), Parabolic Exponential function (0.12 kg ) and Exponential function (0.21 kg ). The absolute mean deviation (AMD) was least for Inverse Polynomial (0.16 Kg) followed by Gamma Type function (0.24 Kg), Parabolic Exponential (0.31Kg) and Exponential function (0.48) confirming the same order of superiority.

Comparison of Five Different Lactation Curve Models to Estimate Milk Yield of Friesian Holstein Cows at BBPTU HPT Baturraden

The objective of this study was to compare the accuracy of five different lactation curve models to estimate 305 days milk yields in Friesian Holstein (FH) dairy cow at BBPTU HPT Baturraden. Appropriate lactation curve could provide useful information for genetic breeding programs, herd nutritional management, decision taking on the culling cows and milk production simulation systems. The analysis was carried out on a total of 8.167 milk yield records based on test day (TD) from first to fourth lactation from 2014 to 2017. The models compared were Wood, Yadav, Ali-Schaeffer, Wilmink, and Guo and Swalve models. The results showed that the Ali-Schaeffer’s model was the best model to predict milk production. It is known from the coefficient of determination at first, second, third, and fourth lactation respectively were 0.99156, 0.99074, 0.98985, 0.96706, correlation between predicted and observed values (r) were 0.99577, 0.99536, 0.99491, 0.98339, and Se were 0.30, 0.37, 0.38, 0.63.