مدل مکانیستیک

 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.

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.