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

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی‌ارشد، بخش علوم دام، دانشکده کشاورزی، دانشگاه بیرجند

2 استاد، بخش علوم دام، دانشکده کشاورزی، دانشگاه بیرجند

3 دانشیار، مؤسسه تحقیقات علوم دامی کشور، سازمان تحقیقات، آموزش و ترویج کشاورزی

4 استادیار، بخش علوم دام، دانشکده کشاورزی، دانشگاه بیرجند

چکیده

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 رأس گاو در 579 گله در 26 استان کشور مورد استفاده قرار گرفتند. گاوهای مزبور، فرزندان 7957 رأس گاو نر و 530394 رأس گاو ماده بودند که طی سال­های 1375 تا 1399 زایش داشتند. مدل مکانیستیک برازش داده شده بر داده­ها دارای پنج فراسنجه MSmax (مرتبط با بیشترین پتانسیل ترشح شیر در دوران شیردهی)، GR (مرتبط با نرخ نسبی تکثیر سلول­های ترشحی در اوایل دوره­ شیردهی)، MSLmax (مرتبط با بیشترین اُفت ترشح شیر)، NOD  (مرتبط با نسبتی از سلول­های پارانشیم که در زمان زایمان مرده­اند)، و DR (مرتبط با نرخ نسبی کاهش در تعداد سلول­های ترشحی) بود که برآورد آن­ها برای فصول و سنین مختلف زایش گاوهای دارای رکورد، و همچنین بر اساس نوع ژنوتیپ گاو (در دو نوع زینه و اصیل هلشتاین) با نرم­افزار  SAS انجام شد. گاوهایی که در پاییز زایش داشتند، بیشترین MSmax و GR را نشان دادند و کمترین مقادیر فراسنجه­های مذکور به­ترتیب برای گاوهایی بود که در تابستان و بهار زایمان نموده بودند (05/0P<). گاوهایی که اولین زایش آن­ها تا 25 ماهگی بود، بیشترین مقدار فراسنجه­های MSmax ، GR و DR را داشتند، در حالی­که بیشترین مقدار فراسنجه­های MSLmax و NOD برای گاوهایی بود که دیرتر از سن مذکور زایش داشتند (05/0P<). گاوهای زینه در مقایسه با گاوهای اصیل هلشتاین، مقدار بالاتری از فراسنجه­های MSLmax و NOD را نشان دادند ولی برای سایر فراسنجه­های مدل، گاوهای اصیل هلشتاین مقدار بالاتری را دارا بودند (05/0P<). بر اساس یافته­های این پژوهش، نتیجه­گیری می­شود که در بین گاوهای زایش اول، گاوهای که در سنین پایین­تری زایمان می­نمایند، 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.  

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

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

نویسندگان [English]

  • M. Doosti Toosechalaki 1
  • S. H. Farhangfar 2
  • M. A. Abbasi 3
  • M. B. Montazer Torbati 4
1 MSc Student, Animal Science Department, Agriculture Faculty, University of Birjand, Birjand, Iran
2 Professor, Animal Science Department, Agriculture Faculty, University of Birjand, Birjand, Iran
3 Associate Professor, Animal Science Research Institute of IRAN (ASRI), Agricultural Research, Education & Extension Organization (AREEO), Karaj, Iran
4 Assistant Professor, Animal Science Department, Agriculture Faculty, University of Birjand, Birjand, Iran
چکیده [English]

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.  

کلیدواژه‌ها [English]

  • Dairy cows
  • Test day records
  • Mechanistic model
  • Lactation curve

مراجع

Abbasi, M. A., Pahlavan, R., Afrazandeh, M. R., Kazemi, M., Hasani Bafarani, A., Kazemi, A., & Jamali, N. (2021). Investigation of standard and atypical lactation curves of Simmental and Jersey cows in Iran. Iranian Journal of Animal Science, 52(2), 123-131. doi: 10.22059/ijas.2021.323864.653826 [In Persian]
Albarrán-Portillo, B., & Pollott, G. E. (2008). Genetic parameters derived from using a biological model of lactation on records of commercial dairy cows. Journal of Dairy Science, 91(9), 3639-3648. doi: 10.3168/jds.2007-0929
Albarrán-Portillo, B., & Pollott, G. E. (2011). Environmental factors affecting lactation curve parameters in the United Kingdom’s commercial dairy herds. Archivos de Medicina Veterinaria, 43(2), 145-153. doi: 10.4067/S0301-732X2011000200007
Angeles-Hernandez, J. C., Pollott, G., Albarran-Portillo, B., Ramírez-Perez, A. H., Lizarazo-Chaparro, A., Ortega, O. A. C., & Ronquillo, M. G. (2018). The application of a mechanistic model to analyze the factors that affect the lactation curve parameters of dairy sheep in Mexico. Small Ruminant Research, 164, 58-63. doi: 10.1016/j.smallrumres.2018.05.003
Appuhamy, J. A. D. R. N., Cassell, B. G, Dechow, C. D., & Cole, J. B. (2007). Phenotypic relationships of common health disorders in dairy cows to lactation persistency estimated from daily milk weights. Journal of Dairy Science, 90(9), 4424-4434. doi: 10.3168/jds.2007-0077
Beever, D. E., Rook, A. J., France, J., Dhanoa, M. S., & Gill, M. (1991). A review of empirical and mechanistic models of lactational performance by the dairy cow. Livestock Production Science, 29(2-3), 115-130. doi: 10.1016/0301-6226(91)90061-T
Bouallegue, M., & M’Hamdi, N. (2020). Mathematical modeling of lactation curves: a review of parametric models. In: Lactation in Farm Animals - Biology, Physiological Basis, Nutritional Requirements, and Modelization, Edited by Naceur M’Hamdi. Part of IntechOpen Book Series: Veterinary Medicine and Science, 3, 95-114. doi: 10.5772/intechopen.78900  
Capuco, A. V., Wood, D. L., Baldwin, R., Mcleod, K., & Paape, M. J. (2001). Mammary cell number, proliferation, and apoptosis during a bovine lactation: relation to milk production and effect of bST. Journal of Dairy Science, 84(10), 2177-2187. doi: 10.3168/jds.S0022-0302(01)74664-4
Chen, Y., Steeneveld, W., Nielen, M., & Hostens, M. (2023). Prediction of persistency for day 305 of lactation at the moment of the insemination decision. Frontiers in Veterinary Science, 10, 1-9. doi: 10.3389/fvets.2023.1264048
Daltro, D. S., Padilha, A. H., Gama, L. T., Silva, M. V. G. B., & Cobuci, J. A. (2021). Breed, heterosis, and recombination effects for lactation curves in Brazilian cattle. Revista Brasileira de Zootecnia, 50, 1-18. doi: 10.37496/rbz5020200085
Davis, S. R., & Collier, R. J. (1985). Mammary blood flow and regulation of substrate supply for milk synthesis. Journal of Dairy Science, 68(4), 1041-1058. doi: 10.3168/jds.S0022-0302(85)80926-7 
Dekkers, J. C. M., Ten Hag, J. H., & Weersink, A. (1998). Economic aspects of persistency of lactation in dairy cattle. Livestock Production Science, 53(3), 237–252. doi: 10.1016/S0301-6226(97)00124-3
Dijkstra, J., France, J., Dhanoa, M.S., Maas, J.A., Hanigan, M.D., Rook, A.J., & Beever, D.E. (1997). A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science, 80(10), 2340-2354. doi: 10.3168/jds.S0022-0302(97)76185-X
Dimauro, C., Atzori, A. S., & Pulina, G. (2011). Assessing and optimazing the performance of a mechanistic mathematical model of the sheep mammary gland. In: Sauvant, D., Van Milgen, J., Faverdin, P., Friggens, N. (Eds.), Modelling Nutrient Digestion and Utilisation in Farm Animals. Wageningen Acedemic Publishers, Wageningen, pp. 72–82. doi:10.3920/978-90-8686-712-7
Elahi Torshizi, M. (2016). Effects of season and age at first calving on genetic and phenotypic characteristics of lactation curve parameters in Holstein cows. Journal of Animal Science and Technology, 58(8), 1-14.doi: 10.1186/s40781-016-0089-1
Elahi Torshizi, M., & Farhangfar, H. (2020). The use of dijkstra mechanistic model for genetic analysis of the lactation curve characteristics and their relationships with age at first calving and somatic cell score of Iranian dairy cows. Acta Scientiarum Animal Sciences, 42, 1-12. doi: 10.4025/actascianimsci.v42i1.50181
Farhangfar, H., & Naeemipour, H. (2007). Phenotypic study of lactation curve in Iranian Holsteins. Journal of Agricultural Science and Technology, 9(4), 279-286. doi: 20.1001.1.16807073.2007.9.4.8.9
Farhangfar, H., Nezamdoost, S., Montazar Torbati, M. B., & Asghari, M. R. (2018). Genetic analysis of Pollott-Gootwine mechanistic model parameters for lactation curve of Iranian dairy cows. Journal of Animal Science Research, 28(3), 31-46. [In Persian]
Farhangfar, S. H., Rashidi Toghroljerdi, M. S., Montazer Torbati, M. B. & Sayyad Nezhad, M. B. (2023). A study on the lactation curve characteristics of grade and Iranian purebred Holstein cows with the use of raw, fat corrected, and energy-corrected milk test day records. Animal Production Research, 12(2), 71-84. doi: 10.22124/AR.2023.22771.1718 [In Persian]
Ferris, T. A., Mao, I. L., & Anderson, C. R. (1985). Selection for lactation curve and milk yield in cattle. Journal of Dairy Science, 68(6), 1438-1448. doi: 10.3168/jds.S0022-0302(85)80981-4
Gebreyohanes, G., Tegegne, A., Diedhiou, M. L., & Hegde, B. P. (2007). Persistency of lactation and comparison of different persistency measures in indigenous and crossbred cows at Bako, Ethiopian Journal of Animal Production, 7(1), 1-11.
Gengler, N. (1996). Persistency of lactation yields: a review. Interbull Bulletin, 12, 102-106.
George, D., & Mallery, P. (2020). IBM SPSS Statistics 26 Step by Step: A Simple Guide and Reference. 16th Edition. Taylor & Francis.
Ghavi Hossein-Zadeh, N. (2014). Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins. The Journal of Agricultural Science, 152, 309-324. doi: 10.1017/S0021859613000415
Ghavi Hossein-Zadeh, N. (2017).  Application of growth models to describe the lactation curves for test-day milk production in Holstein cows. Journal of Applied Animal Research, 45(1), 145-151, doi: 10.1080/09712119.2015.1124336
Ghavi Hossein-Zadeh, N. (2019a). Application of non-linear mathematical models to describe effect of twinning on the lactation curve features in Holstein cows. Research in Veterinary Science, 122, 111-117. doi: 10.1016/j.rvsc.2018.11.017
Ghavi Hossein-Zadeh, N. (2019b). Comparison of the parameters of the lactation curve between normal and difficult calvings in Iranian Holstein cows. Spanish Journal of Agricultural Research, 17(1), e0401. doi: 10.5424/sjar/2019171-13673
Griver, Y. A. (1994). The FOXPRO 2.6 Codebook. Sybex, San Francisco Inc., USA.
Grossman, M., Kuck, A. L., & Norton, H. W. (1986). Lactation curves of purebred and crossbred dairy cattle. Journal of Dairy Science, 69(1), 195-203. doi: 10.3168/jds.S0022-0302(86)80386-1
Guevara Muñeton, L. P., Gloria, L. S., Benaouda, M., Teuntle-López, I. A., Valdés-Córdoba, X. S., Ángeles-Hernández, J. C., Aniceto, E. S., & Acero, A. P. (2023). The shape of curve lactation of crossbred dairy sheep affects the fitting of empirical and mechanistic models. Archivos Latinoamericanos de Producción Animal, 31(Supl. 1), 305-311. doi: 10.53588/alpa.310553
Harder, B., Bennewitz, J., Hinrichs, D., & Kalm, E. (2006). Genetic parameters for health traits and their relationship to different persistency traits in German Holstein dairy cattle. Journal of Dairy Science, 89(8), 3202-3212. doi: 10.3168/jds.S0022-0302(06)72595-4
Imagawa, W., Bandyopadhyay, G. K., & Nandi, S. (1990). Regulation of mammary epithelial cell growth in mice and rats. Endocrine Reviews, 11(4), 494-523. doi: 10.1210/edrv-11-4-494
Innes, D. J., Pot, L. J., Seymour, D. J., France, J., Dijkstra, J., Doelman, J., & Cant, J. P. (2024). Fitting mathematical functions to extended lactation curves and forecasting late-lactation milk yields of dairy cows. Journal of Dairy Science, 107(1), 329-345. doi: 10.3168/jds.2023-23478
Jamrozik, J., Schaeffer, L. R., & Dekkers, J. C. M. (1997). Genetic evaluation of dairy cattle using test day yields and random regression model. Journal of Dairy Science, 80(6), 1217-1226. doi: 10.3168/jds.S0022-0302(97)76050-8
Knight, C. H., & Wilde, C. J. (1987). Mammary growth during lactation: implications for increasing milk yield. Journal of Dairy Science, 70(9), 1991-2000. doi: 10.3168/jds.S0022-0302(87)80241-2
Koloi, S., Pathak, K., Karunakaran, M., & Mandal, A. (2018). Lactation persistency and its genetic evaluation in cattle- A Review. Research and Reviews: Journal of Dairy Science and Technology, 7(3), 1-8. doi: 10.37591/rrjodst.v7i3.1388
Madalena, F. E., Martinez, M. L., & Freitas, A. F. (1979). Lactation curves of Holstein-Friesian and Holstein-Friesian x Gir cows. Animal Production, 29(1), 101-107. doi: 10.1017/S0003356100012198
Mehraban, H., Farhangfar, H., Rahmaninia, J., & Soltani, H. A. (2009). Comparison of some functions describing the shape of the lactation curve for Holstein cows. Iranian Journal of Animal Science Research, 1(2), 47-55. doi: 10.22067/IJASR.V1I2.1974 [In Persian]
Naeemipour, H., Shariati, M. M., Zerehdaran, S., & Jabbari, M. (2018). Effects of season and age at first caving on phenotypic and genetic characteristic of lactation curve parameters in primiparous Iranian Holstein cows. Animal Science Journal, 30(117), 163-176. doi: 10.22092/ASJ.2018.116054 [In Persian]
Neal, H. D. S. C., & Thornley, J. H. M. (1983). The lactation curve in cattle: a mathematical model of the mammary gland. Journal of Agricultural Science, 101(2), 389-400. doi: 10.1017/S0021859600037710
Pollott, G. (2000). A biological approach to lactation curve analysis for milk yield. Journal of Dairy Science, 83(11), 2448-2458. doi: 10.3168/jds.sS0022-0302(00)75136-8
Pollott, G. E., & Gootwine, E. (2000). Appropriate mathematical models for describing the complete lactation of dairy sheep. Animal Science, 71(2), 197-207. doi: 10.1017/S1357729800055028
Ptak, E., & Schaeffer, L. R. (1993). Use of test day yields for genetic evaluation of dairy sires and cows. Livestock Production Science, 34(1-2), 23-34. doi: 10.1016/0301-6226(93)90033-E
Rook, A. J., France, J., & Dhanoa, M. S. (1993). On the mathematical description of lactation curves. The Journal of Agricultural Science, 121(1), 97-102. doi: 10.1017/S002185960007684X
SAS. (2013). Base SAS® 9.4 Procedures Guide Statistical Procedures. Second Edition. SAS Institute Inc., Cary, NC, USA.
Seangjun, A., Koonawootrittriron, S., & Elzo, M. A. (2009). Characterization of lactation patterns and milk yield in a multibreed dairy cattle population in the central Thailand. Kasetsart Journal - Natural Science, 43(1),74-82.
Sölkner, J., & Fuchs, W. (1987). A comparison of different measures of persistency with special respect to variation of test-day milk yields. Livestock Production Science, 16(4), 305-319. doi: 10.1016/0301-6226(87)90001-7
Svennersten-Sjaunja, K., & Olsson, K. (2005). Endocrinology of milk production. Domestic Animal Endocrinology, 29(2), 241-258. doi: 10.1016/j.domaniend.2005.03.006
Tamminga, S. (2000). Issues arising from genetic change: Ruminants. The Challenge of Genetic Change in Animal Production. W. G. Hill, S. C. Bishop, B. McGuirk, J. C. McKay, G. Simm, and A. J. Webb, ed. British Society of Animal Science, 27, 53-62. doi: 10.1017/s146398150004053x
Tekerli, M., Akinci, Z., Dogan, I., & Akcan, A. (2000). Factors affecting the shape of lactation curves of Holstein cows from the Balikesir province of Turkey. Journal of Dairy Science, 83(6), 1381-1386. doi: 10.3168/jds.S0022-0302(00)75006-5
Thornley, J. H. M., & France, J. (2007). Mathematical Models in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences. 2nd ed. Wallingford, CABI. 928p.
Vetharaniam, I., Davis, S. R., Upsdell, M., Kolver, E. S., & Pleasants, A. B. (2003). Modeling the effect of energy status on mammary gland growth and lactation. Journal of Dairy Science, 86(10), 3148-3156. doi: 10.3168/jds.S0022-0302(03)73916-2
Wildman, E. E., Jones, G. M., Wagner, P. E., Boman, R. L., Troutt, H. F., & Lesch, T. N. (1982). A dairy cow body condition scoring system and its relationship to selected production characteristics. Journal of Dairy Science, 65(3), 495-501. doi: 10.3168/jds.S0022-0302(82)82223-6
Wilmink, J. B. M. (1987). Adjustment of test-day milk, fat and protein yields for age, season and stage of lactation. Livestock Production Science, 16(4), 335-348. doi: 10.1016/0301-6226(87)90003-0
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature, 216, 164-165. doi: 10.1038/216164A0
تحقیقات تولیدات دامی
دوره 13، شماره 2
شهریور 1403
صفحه 25-41

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