• Title/Summary/Keyword: Wilmink Function

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Non-linear modelling to describe lactation curve in Gir crossbred cows

  • Bangar, Yogesh C.;Verma, Med Ram
    • Journal of Animal Science and Technology
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    • v.59 no.2
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    • pp.3.1-3.7
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    • 2017
  • Background: The modelling of lactation curve provides guidelines in formulating farm managerial practices in dairy cows. The aim of the present study was to determine the suitable non-linear model which most accurately fitted to lactation curves of five lactations in 134 Gir crossbred cows reared in Research-CumDevelopment Project (RCDP) on Cattle farm, MPKV (Maharashtra). Four models viz. gamma-type function, quadratic model, mixed log function and Wilmink model were fitted to each lactation separately and then compared on the basis of goodness of fit measures viz. adjusted $R^2$, root mean square error (RMSE), Akaike's Informaion Criteria (AIC) and Bayesian Information Criteria (BIC). Results: In general, highest milk yield was observed in fourth lactation whereas it was lowest in first lactation. Among the models investigated, mixed log function and gamma-type function provided best fit of the lactation curve of first and remaining lactations, respectively. Quadratic model gave least fit to lactation curve in almost all lactations. Peak yield was observed as highest and lowest in fourth and first lactation, respectively. Further, first lactation showed highest persistency but relatively higher time to achieve peak yield than other lactations. Conclusion: Lactation curve modelling using gamma-type function may be helpful to setting the management strategies at farm level, however, modelling must be optimized regularly before implementing them to enhance productivity in Gir crossbred cows.

Genetic Persistency of First Lactation Milk Yield Estimated Using Random Regression Model for Indian Murrah Buffaloes

  • Geetha, E.;Chakravarty, A.K.;Vinaya Kumar, K.
    • Asian-Australasian Journal of Animal Sciences
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    • v.19 no.12
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    • pp.1696-1701
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    • 2006
  • A random regression model was applied for the first time for the analysis of test day records and to study the genetic persistency of first lactation milk yield of Indian Murrah buffaloes. Wilmink's Function was chosen to describe the shape of lactation curves. Heritabilities of test day milk yield varied from 0.33 to 0.58 in different test days. The highest heritability was found in the initial test day ($5^{th}$ day) milk yield. Genetic correlations among test day milk yields were higher in the initial test day milk yield and decreased when the test day interval was increased. The magnitude of genetic correlations between test day and 305 day milk yield varied from 0.25 to 0.99. The genetic persistencies of first lactation milk yield were estimated based on daily breeding values using two methods. $P_1$ is the genetic persistency estimated as a summation of the deviation of estimated daily breeding value on days to attain peak yield from each day after days to attain peak yield to different lactation days. $P_2$ is the genetic persistency estimated as the additional genetic yield (gained or lost) from days to attain peak yield to estimated breeding value on different lactation days relative to an average buffalo having the same yield on days to attain peak yield. The mean genetic persistency on 90, 120, 180, 240, 278 and 305 days in milk was estimated as -4.23, -21.67, -101.67, -229.57, -330.06 and -388.64, respectively by $P_1$, whereas by $P_2$ on same days in milk were estimated as -3.96 (-0.32 kg), -23.94 (-0.87 kg), -112.81 (-1.96 kg), -245.83 (-2.81 kg), -350.04 (-3.28 kg) and -407.58 (-3.40 kg) respectively. Higher magnitude of rank correlations indicated that the ranking of buffaloes based on their genetic persistency in both methods were similar for evaluation of genetic persistency of buffaloes. Based on the estimated range of genetic persistency three types of genetic persistency were identified. Genetic correlations among genetic persistency in different days in milk and between genetic persistencies on the same day in milk were very high. The genetic correlations between genetic persistency for different days in milk and estimated breeding value for 305 DIM was increased from 90 DIM to 180 DIM, and highest around 240 DIM which indicates a minimum of 240 days as an optimum first lactation length might be required for genetic evaluation of Indian Murrah buffaloes.

Phenotypic Relationship between Lactation Persistency and Change in Body Condition Score in First-lactation Holstein Cows

  • Yamazaki, Takeshi;Takeda, Hisato;Nishiura, Akiko;Sasai, Youji;Sugawara, Naoko;Togashi, Kenji
    • Asian-Australasian Journal of Animal Sciences
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    • v.24 no.5
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    • pp.610-615
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    • 2011
  • We examined the correlations between lactation curve shape, including persistency and changes in body condition score (BCS) during early-stage (0 to 30 days in milk (DIM)), nadir-stage (31 to 90 DIM), and late-stage (91 to 240 DIM) lactation in 191 first-lactation cows. Data used were first-parity BCS records, scored twice every month after calving, and daily milk yields. Individual lactation curves were depicted by the Wilmink function. Lactation persistency was defined as the difference in estimated milk yields between 240 DIM and 60 DIM. Changes in BCSs in the early and late stages were defined as linear regression coefficients. There were no significant correlations between traits for lactation curve shape and change in BCS in early-stage lactation. Peak yield and total milk yield were negatively correlated with BCSs in nadir- and late-stage lactation and with BCS change in late-stage lactation, suggesting that cows with high lactation yields had low body reserves and health status in mid- to late lactation and had delayed recovery of body reserves. Lactation persistency was positively correlated with change in BCS in late-stage lactation, suggesting that cows with high lactation persistency tended to be healthy and to recover their body reserves well in late lactation.

Estimation of Genetic Parameters for Somatic Cell Scores of Holsteins Using Multi-trait Lactation Models in Korea

  • Alam, M.;Cho, C.I.;Choi, T.J.;Park, B.;Choi, J.G.;Choy, Y.H.;Lee, S.S.;Cho, K.H.
    • Asian-Australasian Journal of Animal Sciences
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    • v.28 no.3
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    • pp.303-310
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    • 2015
  • The study was conducted to analyze the genetic parameters of somatic cell score (SCS) of Holstein cows, which is an important indicator to udder health. Test-day records of somatic cell counts (SCC) of 305-day lactation design from first to fifth lactations were collected on Holsteins in Korea during 2000 to 2012. Records of animals within 18 to 42 months, 30 to 54 months, 42 to 66 months, 54 to 78 months, and 66 to 90 months of age at the first, second, third, fourth and fifth parities were analyzed, respectively. Somatic cell scores were calculated, and adjusted for lactation production stages by Wilmink's function. Lactation averages of SCS ($LSCS_1$ through $LSCS_5$) were derived by further adjustments of each test-day SCS for five age groups in particular lactations. Two datasets were prepared through restrictions on number of sires/herd and dams/herd, progenies/sire, and number of parities/cow to reduce data size and attain better relationships among animals. All LSCS traits were treated as individual trait and, analyzed through multiple-trait sire models and single trait animal models via VCE 6.0 software package. Herd-year was fitted as a random effect. Age at calving was regressed as a fixed covariate. The mean LSCS of five lactations were between 3.507 and 4.322 that corresponded to a SCC range between 71,000 and 125,000 cells/mL; with coefficient of variation from 28.2% to 29.9%. Heritability estimates from sire models were within the range of 0.10 to 0.16 for all LSCS. Heritability was the highest at lactation 2 from both datasets (0.14/0.16) and lowest at lactation 5 (0.11/0.10) using sire model. Heritabilities from single trait animal model analyses were slightly higher than sire models. Genetic correlations between LSCS traits were strong (0.62 to 0.99). Very strong associations (0.96 to 0.99) were present between successive records of later lactations. Phenotypic correlations were relatively weaker (<0.55). All correlations became weaker at distant lactations. The estimated breeding values (EBVs) of LSCS traits were somewhat similar over the years for a particular lactation, but increased with lactation number increment. The lowest EBV in first lactation indicated that selection for SCS (mastitis resistance) might be better with later lactation records. It is expected that results obtained from these multi-trait lactation model analyses, being the first large scale SCS data analysis in Korea, would create a good starting step for application of advanced statistical tools for future genomic studies focusing on selection for mastitis resistance in Holsteins of Korea.