منحنی شیردهی

 In dairy cows, milk yield changes over the lactation period. Lactation curve modelling could be of importance from nutritional management and genetic selection point of view. The trajectory shape of the lactation curve has inclining and declining slopes which determine total amount of milk yield during the lactation. A great number of linear and nonlinear mathematical models have been so far utilized to describe the shape of the lactation curve in dairy cows. Among the models, mechanistic functions are considered to be more accurate than empirical models in terms of taking account of biological mechanisms undertaken in mammary gland to produce milk. To our knowledge, no research has been carried out to use a complex mechanistic model for describing the lactation curve of Iranian dairy cows. Based on this, the present research aimed to apply a five-parameter nonlinear mechanistic model for mathematical description of the shape of the lactation curve in Iranian first-parity dairy cows.

Animal Breeding Centre of Iran provided the data used in this research. Initial data in separate files were merged and edited by the SPSS software. Final data comprised 5596039 milk test day records from 821153 first-parity cows distributed in 579 herds of 26 provinces over the country. The cows were the progeny of 7957 sires and 530394 dams and calved between 1996 and 2020. The cows were categorized into two groups based on the age of first calving: <=25 or >25 months. Also, two groups of cows were created based on the proportion of Holstein gene inheritance: <100% (grade cows) or 100% (pure Holstein cows). A five-parameter nonlinear mechanistic model was applied to mathematically describe the shape of the lactation curve. The fitted mechanistic model had five parameters including MSmax (maximum milk secretion potential of the lactation), GR (relative proliferation rate of secretory cell number during early lactation), MSLmax (maximum secretion loss), NOD (proportion of parenchyma cell dead at parturition), and DR (relative decline rate in cell number) which their estimates were obtained for different seasons and ages of calving, as well as different genotypes (grade and pure Holstein) using NLIN procedure of the SAS software. Based on the estimated parameters of the model in each year of calving, phenotypic trends were calculated using the SPSS software.

The results indicated that Iranian first-parity dairy cows reach to peak of milk production during the third month of the lactation curve. Based on standard deviation as well as coefficient of variation (CV) of milk test day milk records, maximum variation was observed in the last month of the lactation period. The findings also indicated that cows calved in autumn had the greatest MSmax and GR while cows calved in spring and summer had the lowest magnitude for these parameters (P<0.05). The minimum magnitude of MSLmax and NOD were detected for the cows calved in summer (P<0.05). Regarding the DR parameter of the model, cows calved in spring were observed to have a minimum value. Maximum MSmax, Gr, and DR values ​​were determined for cows calving up to 25 months of age, while maximum MSLmax and NOD values ​​were observed for cows of later ages (P<0.05). Compared to pure Holstein cows, grade cows had higher MSLmax and NOD values, but other parameters were found to be greater in the pure Holstein cows (P<0.05), suggesting that the maximum milk secretion potential during lactation in pure Holstein cows is expected to be higher than that of grade cows. Annual phenotypic change trends were found to be 0.376 kg/year (R2=0.9), 0.00009869 (R2=071), -0.146 kg/year (R2=0.59), -0.011 (R2=0.85), and 0.001 (R2=0.85) for MSmax, GR, MSLmax, NOD, and DR, respectively (P<0.0001).     

This study found that the parameters of the mechanistic model fitted to the milk test day records of Iranian primiparous dairy cows are significantly influenced by the age and season of calving as well as the genotype of the cow. Cows calving in summer are expected to have more persistency. Moreover, pure Holsteins are more persistent than grade cows. Positive and negative annual trends have been detected for MSmax and MSLmax parameters, respectively, during 1996-2020 indicating a favorable increase in maximum milk secretion potential of the lactation and also a favorable decrease in maximum secretion loss over that period.

Improving the performance of economic traits of domestic livestock by means of sounds breeding programs could elaborate meeting the protein demands of the human world population. The water buffalo, also called the domestic water, bears up substantial value in terms of milk and meat production. Khuzestani buffalo, the subspecies of domestic Asian water buffalo (Bubalus bubalis) has become a strategic animal species in Khuzestan province, Iran, due to its ability to adapt to adverse environmental conditions, low quality feed sources dependency and high quality products. Archaeological and ancient records show little evidence regarding the expansion of the Khuzestani buffalo. Many people in the region depend on this species for their livelihoods than on any other domestic animal. In this regards, the buffalo lactation could have crucial role in farmers' economy. In general, having knowledge of lactation curve, may shed some lights on management and farm-based operation of milk production system. The lactation curve is a graphical representation tool that reflects the effect of couple of numbers of different factors on milk production during lactation; therefore, it is useful in making better management decisions. In other words, it could summarize the pattern of milk production, biological and economic efficiency of the animal. Several models have been suggested to describe the lactation curves. In this study, in order to estimate the association between different fitted lactation curves and their comparisons on Khuzestani buffalo, six nonlinear mathematical models (Wood, Wilmink, inverse polynomial, Complex logarithm, Ali and Schaefer and Digestra) were used.

The data used in this study, consisted of 103760 test day records of milk yield of 14280 buffalu in the first parity that collected by the Agricultural Jihad Center of Khuzestan province during 1993 to 2020. The Microsoft Excel was used to edit the data. Animals with unknown birth and calving dates were removed. Those fixed effects that had significant effects on the coefficients of lactation curve (P < 5%) were included in the final model. The lactation curve parameters were estimated using the nonlinear regression procedure (NLIN) of SAS software version 9.4 on test day records. Evaluation of goodness of fit was based on the coefficient of determination (R2), root mean square error (RMSE) and Akaike information criterion (AIC). The (Co) variance components were estimated by multi-trait animal model using restricted maximum likelihood method run in WOMBAT software.

Descriptive statistics of milk production of Khuzestani buffaloes based on 103760 records from different areas shown that the average milk production was 8.048 kg, standard deviation was 3.047 and coefficient of variation was 37.87 as well. Wood's mathematical model provided the best fit of the lactation curve due to the highest value for the R2 and lower values for RMSE and AIC compared to the other models and it obtained as 0.88. The a, b and c parameter values of Wood’s model were estimated 6.91, 0.057 and 0.00083, respectively. The results showed that the wood model was able to estimate the time of peak milk yield more accurately than the other models. The peak milk yield of Khuzestani buffaloes (8.30 kg/d) appeared on average in the tenth week (day 69) after calving. The heritability of lactation curve traits for initial yield (a), upward slope of the curve (b) and downward slope of the curve (c) were obtained 0.57, 0.27 and 0.48, respectively. In this study, the persistency(s) value for typical lactations were lactation curve were estimated 7.49. The genetic correlations among lactation curve parameters ranged from -0.55 (upward slope of the curve and initial yield) to 0.138 (upward and downward slope of the curve), whereas the phenotypic correlations ranged from -0.35 (Between initial yield and the upward slope of the curve) to +0.196 (b and c). The solutions of mixed model equations revealed that Buffalo with IDs 3436, 3410, 3360, 2868, 24, and 3174 had the highest breeding value for coefficient a. In other hand, buffalo 3438, 3409, 3418, 3361, 3282, and 3169 showed the highest breeding value in the coefficient b. Finally, the buffaloes that obtained the highest hereditary value in different coefficients of lactation curve were introduced as the superior buffaloes. By knowing the best buffaloes in terms of breeding value for parameters a and b, it is possible to select buffaloes to be parent for next generation. In general, evaluating lactation curve equations using nonlinear models and multi-trait analysis is an effective step in identifying buffaloes with high genetic potential to improve and increase milk production efficiency. The results of the present study showed that among the six mathematical models studied, Wood's incomplete gamma function had more viability for fitting the lactation curve of Khuzestani buffalo. The effect of calving season was not significant on lactation parameters while year of calving had a significant effect. Negative and moderate genetic correlations between initial production parameters (a) and upward slope (b) of the lactation curve indicate that keeping on with higher initial production level will have a lower rate of increase until peak production. In the present study, multivariate analysis led to the relationship of all coefficients of the lactation curve with each other and as a result more realistic parameters were estimated for them. It is suggested that in future studies, a computer-aided economic production system be designed and the economic coefficients related to the parameters of the lactation curve be estimated for integration into the selection index. Also, in order to improve the performance of Khuzestani buffalo, it is recommended to study the genomic relationship of milk production curve parameters.

The graphical representation of daily milk yield during lactating period is lactation curve. There are many advantages of evaluation of the lactation curve in dairy cows, such as designing suitable breeding and management strategies for dairy cattle, genetic evaluation of dairy cows, and the prediction of the total milk yield of cow To explain the flow of milk production over the course of lactation in dairy cows, various mathematical models have been developed (Wilmink 1987; Wood 1967).There are many earlier studies that have successfully applied lactation curves in modeling the milk yield-DIM of Iranian Holstein. In all of these research the classic or Frequentist statistical methods have been used for parameter estimation and statistical inferences. The parameters of these models have not been estimated for Iranian dairy cows using Bayesian method. In the Bayesian approach, the parameters of the model are random variables, and inference is made on parameters using their posterior distributions (in some cases without the assumption of normality of the studied data) and need for huge data (Iqbal et al. 2019).This study was Bayesian estimation of the parameters of Wood, Milkbot, Gompertz, Dijkstra, Cobby and Le Du, Von Bertalanffy, Brody and Logistic mathematical models for the lactation curve. This was done using 30618, 30685 and 30627 days in milk (DIM) records of milk yield, fat percentage and protein percentage, respectively. These records were related to the days of 5 to 305 days of the first lactation period of Iranian Holstein cows with 3685 cows out of 350 herds. These data have been collected by National Breeding Center and improvement of animal production of Iran in registered herds of Holstein cows.

Data were initially adjusted for significant fixed effects that were herd-test-date (HTD) and age at calving. In order to be accurate and due to the high computational needs of Bayesian method, in this study, 30618, 30685 and 30627 records of milk production test day, fat percentage and protein percentage related to the first lactation period belonged to 3685 Holstein cows out of 350, respectively. For test-day records of milk yields, an outlier control assessment was conducted. 99.73 % of the observations accounted for data within the μ ± 3 standard deviations range. Records outside this range have been taken into consideration outliers (Junior et al. 2018). Bayesian inference was used to estimate the subsequent distribution of both unknown parameters of each lactation curve model, using a mixed nonlinear model to which the random lactation effect of each cow was added to account for the individual lactation curve of each cow. The parameters of lactation curves were estimated using the cow's test day records in the MCMC procedure of SAS software. To consider the individual lactation curve of each cow, the effect of each cow was used as a random effect in all nonlinear models. For sampling of the posterior distribution of parameters, the Monte Carlo Markov chain sampling algorithm was obtained by considering the burn-in period, sampling interval (thin) and number of cycles of 150,000, 100 iterations and 400,000 cycles for each, respectively. The effective sample size and Geweke detection test was used to evaluate the sampled amount and calculate the convergence indices. Comparisons of the models were made based on the Deviance Information Criterion (DIC). To determine the significance of the difference between the two models, if the difference between the two nonlinear models was less than 10, the DIC index was considered non-significant and if it was 10 or more, it was considered significant (Iqbal et al., 2019).

By examining the statistics of functions and convergence indices, Brody function for milk production and Wood function for fat percentage and protein percentage showed the most suitable model and better fit. The Convergence has been achieved according to Geweke test (Geweke 1992) statistic P-value. In the protein percentage fitting curve, Wood model was selected despite the significance of parameter a in the Geweke test (P <0.05) due to the appropriate trace plot. Effective sample size and the simulation sample size (4000) indicate convergence in all parameters. The differences between DIC values were found greater than 10 points for most of the cases, indicating high significant difference between the fitted models. In the results, the estimated parameters of the Brody function for milk production were 37.219, 0.544 and 0.084 for a, b and c, respectively. For milk fat percentage and milk protein percentage, the estimated parameters of Wood function were 4.29 and 3.53 for a, -0.08 and -0.04 for b, -0.0008 and -0.0004 for c, respectively. For the first 30 days, a modified gamma function gave the best fit for the first lactation (Sherchland et al. 1995).The Wood curve was superior to the Gompertz function in fitting the data and, hence, it was used for biological inference (Hansen et al. 2012).In another study by Bangar and Verma (2017) to compare four nonlinear models, Wood, quadratic model, mixed logarithmic model and Wilmink to fit the shape of lactation curves of milk production and its production traits in Gir crossbred cows in India, Wood model as the best model for Fitting of milk production data and production traits were introduced.

Bayesian method can be used in modeling complex nonlinear functions for lactation curves, especially with a small amount of data. Biological interpretation of these parameters makes it possible to use these estimates in a selection index to genetically modify the lactation curve. This shows that Brody and Wood functions, respectively, as the best model in predicting milk production and production traits in Iranian Holstein cows in the first lactation period.

The aim of this study was to compare the Wood, Dijkstra and Sineus models for fitting the lactation curve of the first abdomen of Khuzestan Buffalo. The effect of fix factor such as year, season and herd on the curve of milk parameters were studied. In this study, 73169 test day records of milk were used. Records were collected in the animal breeding center. According to the test day record and using different initial values, using SAS software and NLIN procedure were estimated the parameters of each lactation models. R2adj, AIC, MSE, RMSE and Iterations were used for comparison of models. The results of the model's comparison were showed that all three models of Wood, Dijkstra and Sinus were able to fit the buffalo curve. But the Wood model, having the lowest AIC, MSE and RMSE was goodness than the other two models. The mean of Wood parameters such as a, b and c were 2.36, 0.656 and 0.0009 were respectively. Average the peak of lactation was 84 days. The most and least lactation continuous was in summer and spring, respectively (p<0.05). All Wood parameters and lactation indexes were affected year, herd and their interaction (p<0.05). By using the lactation curve and determining the components of lactation, it is possible to plan for feeding and management of buffaloes.

Successful animal breeding strategies rely on selecting superior animals to produce progeny which are expected to have better performance compared to contemporaries at different rearing environments (Doeschl-Wilson 2007). Based on this, the main aim of a breeding scheme is to promote genetic potential of livestock for the traits of great economic importance. Milk yield varies over a course of lactation as a result of continuous physiological mechanisms of growth and death of udder cells (Val-Arreola 2004). Mathematical models used for description of the lactation curve can be empirical (shape-oriented) or mechanistic (biology-oriented) (Farhangfar 2015). Using mechanistic (biological) models it would be possible to study genetic aspects of cows' lactation curve from the biology of milk secretion in udder tissue standpoint. Vast majority of the research undertaken on the lactation curve of Iranian dairy cows have been focused on the use of empirical models. This research was carried out with the objective of evaluating genetic characteristics of the lactation curve of Iranian Holstein grade and pure-bred dairy cows using a mechanistic model. The data used in this research were provided by Animal Breeding Centre, Karaj, Iran. The data set consisted of 1,448,292 test day milk records belonging to 161,676 first parity cows (progeny of 3979 bulls) in 921 herds (in 14 provinces over the country) and calved during 1997- 2012. Minimum and maximum number of test day records were 4 and 13, respectively. Based on the percentage of Holstein gene inheritance (H), cows were divided into four groups. Pollott-Gootwine mechanistic model with two parameters of MS (maximum secretion potential of the lactation) and DR (relative decline in cell numbers) was applied to describe the shape of lactation curve. This nonlinear function was fitted to the individual lactation curves and the parameters were estimated for each cow by using nonlinear procedure of SAS software. Heritability of MS and DR traits was estimated using a fitting univariate animal model. In the model, effects of province, contemporary group of herd-year-season, calving age, type of genotype, interval of first test day from calving, fat to protein ratio, length of lactation as well as random effect of cow were included. All relationship among the animals were taken into account through including pedigree. The model was run for each trait using DMU software and restricted maximum likelihood (REML) estimate of additive genetic and residual variance components and prediction of breeding value of the animals were obtained. Genetic trend was subsequently calculated through fitting weighted regression of mean breeding value on calving year. Additive genetic and residual variance components for MS were 5.7123 and 13.7759, respectively and the corresponding figures for DR were 0.0000012 and 0.0000051, respectively. Heritabilities of MS and DR were found to be 0.293 (SE=0.008) and 0.194 (SE=0.120), respectively indicating that there is relatively good genetic variation for the traits to be used in selection programmes. Mean predicted breeding value (PBV) of the cows with records were 0.255 (Kg) and -0.000005 for MS and DR, respectively. Regarding MS, cows with 50  H  75 had minimum PBV (0.072 Kg) while cows with 87.5  H 100 had maximum PBV (0.309 Kg) and the difference was statistically significant (P<0.05). Based upon mean PBV for MS, mean PBV for the trait of 305-day milk yield in pure-bred Holstein cows (H=100) was expected to be 82.96 Kg. Pearson correlation between breeding values of the traits was -0.29 (P<0.0001) suggesting that cows of high genetic potential for MS are expected to have low breeding value for DR. Phenotypic and genetic trends for MS were 0.52 (SE=0.017) and 0.063 (SE=0.004, R2=0.95) kg per year, respectively, while the corresponding figures for DR were -0.000025 (SE=0.0000021) and -0.000007 (SE=0.00000054, R2=0.92), respectively and that all the trends were statistically significant (P<0.0001). High heritability of MS and DR suggests that appropriate genetic gain could be obtained as the selection of the cows is based upon these traits. As DR is associated with lactation persistency, it could be therefore concluded that Iranian dairy cows have become phenotypically and genetically persistent over the years of 1997-2012.

In order to investigate the milk and its components curve of Khuzestani buffaloes a total of 9061 data of test-day milk, fat and protein yield of the first lactation period buffaloes collected during 1993-2013 were used. The buffaloes having less than 4 test-day records were removed. The lactation days was considered from the 5th to 210th days of lactation. Five different functions of Wood, Wilmink, Parabolic, Mixed Logarithmic and Reverse Polynomial were tested for fitting the lactation curve of buffaloes using the NLIN procedure of SAS 9.1 software. Comparing the studied functions, the Wood function was the best predictor of the lactation curve. The most suitable models for the fat and protein percentage, fat and protein content were Parabolic and Inverse Polynomial with the same results, Parabolic, Parabolic and Inverse Polynomial with Wood functions, respectively. Based on the suitable models, the expected daily milk yield, fat percentage, fat and protein content and protein percentage at the beginning of lactation (the 5th day of lactation) were 6.10 kg with a peak yield of 8.46 kg on the 89th day of lactation, 5.51% with a peak of 6.35% on the 210th day of lactation, 427.75 g with a peak of 513.73 g on the 153th day of lactation, 4.20% with a peak of 4.23% on the 210th day of lactation, 317.70 g with a peak of 344.43 g on the 82th day of lactation, respectively. The results showed that Khuzestani buffaloes have the same production as other breeds in the world in terms of milk production and peak yield or close to them. Considering the rural breeding situation of buffaloes in Khuzestan province, it is expected that improvement of environmental conditions such as nutrition and management provide the condition for incidence of the maximum genetic ability of the buffaloes.

The objective of this study was to investigate the effects of season and age at first calving on parameters of Wood function in fitting lactation curves (such as persistency, peak time and peak yield) of primiparous Iranian Holsteins. A total of 580,980 test day records from 953 herds recorded on 58,098 cows calved between 1990 and 2012, were analyzed. Genetic analysis was performed in a univariate animal model using DMU package. The results showed that the effects of herd, year and season of calving, age at first calving and Holstein gene percentage on lactation curve parameters were significant (P

To study the effect of calving month on occurrence probability of atypical lactation curve, a number of 751,099 test day records belonging to 85,641 first parity Holstein cows calved during 1997-2009 in 156 herds in six provinces were used. Logistic generalized linear mixed model using GLIMMIX procedure of SAS software was fit to the data. In the model, fixed effects of province, herd production level, calving year, calving month, age at first calving, sperm type, cow type, interval of first recording from calving, number of total test day records for each cow, determination coefficient of Wilmink fitted to each cow, as well as random effect of sire were included. Dependent variable was defined as a binary (0 for typical and 1 for atypical lactations) in the model. Maximum and minimum probabilities were found for the cows calving in April (0.3435) and December (0.2348), respectively so that cows calving in the former one was expected to have 70.5 % more chance of atypical lactation as compared to the cows calving in the latter one. Based upon the findings it can be concluded that the shape of the lactation curve in Iranian dairy cows is influenced by the seasonal variations.

Description of lactation curve were investigated using sine function، compare it with two functions (Dijekstra and Wood). The data contained 32233 dairy milk yield records from 93 first parity Iranian Holstein cows that had calving between Aug. 2008 and Jul. 2009. Actual milk production per day and subsequently the actual production of each animal were available in the first lactation. Lactation records of milk production per cow from 7 until the end of lactation was used for the study. The data was fitted by the Trust-Region method in MATLAB software. The models were tested for goodness of fit using sum of squares error (SSE)، root mean square error (RMSE) and coefficient of determination (R-square). Also expression for the feautures of the lactation curve were calculated by using mathematical’s formulaes. Goodness of fit and lactation features of models was subjected to analysis using the MIXED procedure of SAS (2001) that the random effect was effect of cow. The results showed that Sine function can be fitted to daily milk production records. Statistical analysis showed that significant differences exist between the goodness of models (P< 0. 01) and the best fitting was related to the Sine and Wood function. The random effect of cow was also significant (P< 0. 01) that reflects the variable response of each animal to each model. Numerically، all the estimated features of the lactation curve given by the Sine function were similar to Dijkstra and Wood functions. The results showed simple Sine function has high competence and ability to fit the daily records of milk production. Also، Sine function could describe the persistency of lactation much better than the other models. Biologically، the parameters of Sin function were acceptable and showed some part of lactation curve but all three functions couldn’t fit the first 30 days of lactation in the best way.

The effects of days in milk (DIM) on the curves of milk yield and milk fat percentage in Holstein cows of Iran were studied. A total of 964,606 and 885,346 test day records were used for milk yield and milk fat percentage, respectively. The data were grouped in four classes including: 1) 240 < DIM < 301, 2) 300 < DIM < 401, 3) 400 < DIM < 501 and 4) 500 < DIM < 601 days. To fit the curves, nine non-linear models for every one of the classes were applied. The Narushin & Takma 1 function which previously has been used for fitting the production and growth characteristics of chickens was used in this study. It showed a relatively high goodness of fit in fitting milk yield and milk fat percentage curves compared to other functions. Wood, Dijkstra and Rook functions showed higher Adjusted R2 whereas the third order Legendre polynomial function showed the lowest value in all the classes. The cows had longer lactation period, showed higher persistency and yielded higher daily milk at peak and post peak stages of lactation period. The forth class of cows yielded considerably higher milk and fat (based on 305 day production) compared to other groups. On the contrary, the rate of reduction of milk yield was significantly high for cows located in the lowest lactation length class and the slope of declining stage of milk yield curve was sharper.

Test day milk records of a Holstein dairy farm collected during years 2004 to 2006 on 142 cows in the 1st lactation vs. 140 cows in the 2nd lactation were used in this research. There were real milk yields of cows available in each part of lactation in this farm making it possible to compare functions based on the new criteria (squared error of estimation). Five functions were compared to estimate production records during each month of lactation, using test day records. These functions were incompelete gama, polynomial regression, inverse polynomial, Wilmink and mixed log function. These functions were compared with third order legender polynomial function for an estimation of total lactation milk yield (305 day milk yield). The criterion for comparing these six functions was the squared error of estimation. Functions were ranked through Quad test on squared error. The first rank in the 1st lactation belonged to incomplete gama function in the 1st, 2nd, 4th, 5th, 8th, and 9th month, polynomial regression function in the 3rd, and 6th month, mixed log function in the 7th month while Wilmink function in the 10th month of lactation. The first rank in the 2nd lactation belonged to incomplete gama function in the 1st, 4th, 5th, 6th, and 9th month, mixed log function in the 7th, and 8th month, while Wilmink function in the the 3rd, and 10th month and polynomial regression function in the 2nd month of lactation. Incomplete gama function won the first rank for estimation of total milk yield (305 day milk yield) in the 1st, 2nd lactation. In the 1st lactation, difference between Incomplete gama function and polynomial regression, third order legender polynomial function and in the 2nd lactation the difference between incomplete gama function and polynomial regression functions were significant.

The objective of this study was to determine the effect of some environmental factors on the parameters and characteristics of the lactation curve in Iranian Buffalo ecotypes. The data consisted of 53222 test-day records in various stages of lactation and different parities recorded from 743 herds by Iranian Animal Breeding Center (ABC) during 1992-2005. The parameters and characteristics studied were milk production at the beginning of lactation (a); slope of the lactation curve up to the peak of milk production (b); slope after the peak of milk production(c); peak time; peak yield and persistency. Average milk yield, a, b, c, peak time; peak yield and persistency were 2340.8, 8.6, 0.6, 0.2, 3.2, 9.3, and 2.8 respectively. The effect of herd and year were significant on all parameters and characteristics of lactation curve (P<0.01). Season exerted a significant effect on milk yield, a, c, peak time and persistency (P<0.01). The effect of lactation period was significant on milk yield, a, c, peak yield (P<0.01) and b, persistency (P<0.05). Lactation period had no significant effect on peak time (P>0.05). Calving age had significant effects only on c, persistency (P<0.01) and b (P<0.05).