کاربرد یک مدل غیرخطی مکانیستیک پنج فراسنجه ای در توصیف ریاضی شکل منحنی شیردهی گاوهای زایش اول زینه و اصیل هلشتاین ایران

هدف از این پژوهش، کاربرد یک مدل غیرخطی مکانیستیک برای توصیف ریاضی منحنی شیردهی گاوهای شیری زینه و اصیل هلشتاین ایران بود که برای اولین بار، زایش داشتند. تعداد کل 5596039 رکورد روز آزمون شیر متعلق به 821153 راس گاو در 579 گله در 26 استان کشور مورد استفاده قرار گرفتند. گاوهای مزبور، فرزندان 7957 راس گاو نر و 530394 راس گاو ماده بودند که طی سال های 1375 تا 1399 زایش داشتند. مدل مکانیستیک برازش داده شده بر داده ها دارای پنج فراسنجه msmax (مرتبط با بیشترین پتانسیل ترشح شیر در دوران شیردهی)، gr (مرتبط با نرخ نسبی تکثیر سلول های ترشحی در اوایل دوره شیردهی)، mslmax (مرتبط با بیشترین اُفت ترشح شیر)، nod  (مرتبط با نسبتی از سلول های پارانشیم که در زمان زایمان مرده اند)، و dr (مرتبط با نرخ نسبی کاهش در تعداد سلول های ترشحی) بود که برآورد آن ها برای فصول و سنین مختلف زایش گاوهای دارای رکورد، و همچنین بر اساس نوع ژنوتیپ گاو (در دو نوع زینه و اصیل هلشتاین) با نرم افزار  sas انجام شد. گاوهایی که در پاییز زایش داشتند، بیشترین msmax و gr را نشان دادند و کمترین مقادیر فراسنجه های مذکور به ترتیب برای گاوهایی بود که در تابستان و بهار زایمان نموده بودند (0.05p<). گاوهایی که اولین زایش آن ها تا 25 ماهگی بود، بیشترین مقدار فراسنجه های msmax ، gr و dr را داشتند، در حالی که بیشترین مقدار فراسنجه های mslmax و nod برای گاوهایی بود که دیرتر از سن مذکور زایش داشتند (0.05p<). گاوهای زینه در مقایسه با گاوهای اصیل هلشتاین، مقدار بالاتری از فراسنجه های mslmax و nod را نشان دادند ولی برای سایر فراسنجه های مدل، گاوهای اصیل هلشتاین مقدار بالاتری را دارا بودند (0.05p<). بر اساس یافته های این پژوهش، نتیجه گیری می شود که در بین گاوهای زایش اول، گاوهای که در سنین پایین تری زایمان می نمایند، نسبت به سنین بالاتر در زایش، تداوم شیردهی بهتری را دارند، ضمن آن که گاوهای اصیل هلشتاین در مقایسه با گاوهای زینه، عملکرد بهتری را در رابطه با تداوم شیردهی از خود نشان دادند.

application of a five-parameter nonlinear mechanistic model to mathematically describe the shape of the lactation curve in iranian grade and purebred holstein primiparous dairy cows

introduction:  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.materials and methods: 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.results and discussion: 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).     conclusions: 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.