Appropriate mathematical models for describing the complete lactation of dairy sheep

2000 ◽  
Vol 71 (2) ◽  
pp. 197-207 ◽  
Author(s):  
G. E. Pollott ◽  
E. Gootwine
Keyword(s):  
Milk Yield ◽  
Linear Functions ◽  
Dairy Sheep ◽  
Mathematical Functions ◽  
Lactation Curve ◽  
Non Linear ◽  
Birth Records ◽  
Daily Milk Yield ◽  
Parameter Function ◽  
Better Than

AbstractDespite milk being an important product from sheep, there are very few reports of milk production from the complete lactation of dairy sheep. The Improved Awassi in Israel is kept under an intensive system of management with lambs being weaned soon after birth. Records from one such flock were analysed to investigate the suitability of various mathematical functions for describing milk yield from the complete lactations of dairy sheep. This included a consideration of whether the functions could cope with short lactations, a characteristic of dairy sheep, and a limited number of test-day records per lactation.Four non-linear mathematical functions were investigated (Wood, Morant, Grossman and Pollott), two of which could also be fitted in a linear and a linear weighted form (Wood and Morant). These functions were fitted to weekly data from a ‘typical Awassi lactation curve’, represented by least squares means of daily milk yield from each week of a 40-week lactation derived from an analysis of 25605 test day records. Characteristics of the lactation were calculated from the functions, such as total milk yield, day and level of peak yield and persistency. These functions were also fitted to 1416 individual lactation records of up to 10 test-day records per lactation. The value of the functions was investigated using the residual mean square (RMS) of the fitted curve as an indicator of how well each function described the lactation. Forms of these functions with a reduced number of parameters were also investigated.The non-linear functions always fitted the data with a lower RMS than their linear equivalent and the weighted form of the linear functions always had a lower RMS than the unweighted form. Of the linear functions, Morant fitted better than Wood. Of the non-linear functions Grossman, Morant and Pollott (additive and multiplicative) fitted the data equally as well but better than Wood. The various functions predicted characteristics of the lactation curve differently; the Wood functions tended to overestimate yield in early lactation and the Morant functions underestimated peak yield.No function was better suited to short lactations than another. However the three-parameter function of Morant, Pollott multiplicative and Pollott additive were considered to be the most suitable for describing the complete lactation of dairy sheep.

scholarly journals Genetic and environmental parameters estimation for milk traits in Slovenian dairy sheep using random regression model

2013 ◽  
Vol 58 (No. 3) ◽  
pp. 125-135 ◽  
Author(s):  
A. Komprej ◽  
Š. Malovrh ◽  
G. Gorjanc ◽  
D. Kon ◽  
M. Kovač
Keyword(s):  
Regression Model ◽  
Protein Content ◽  
Milk Yield ◽  
Random Regression ◽  
Dairy Sheep ◽  
Milk Traits ◽  
Random Regression Model ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

(Co)variance components for daily milk yield, fat, and protein content in Slovenian dairy sheep were estimated with random regression model. Test-day records were collected by the ICAR A4 method. Analysis was done for 38 983 test-day records of 3068 ewes in 36 flocks. Common flock environment, additive genetic effect, permanent environment effect over lactations, and permanent environment effect within lactation were included into the random part of the model and modelled with Legendre polynomials on the standardized time scale of days in lactation. Estimation of (co)variance components was done with REML. The eigenvalues of covariance functions for random regression coefficients were calculated to quantify the sufficient order of Legendre polynomial for the (co)variance component estimation of milk traits. The existing 13 to 24% of additive genetic variability for the individual lactation curve indicated that the use of random regression model is justified for selection on the level and shape of lactation curve in dairy sheep. Four eigenvalues sufficiently explained variability during lactation in all three milk traits. Heritability estimate for daily milk yield was the highest in mid lactation (0.17) and lower in the early (0.11) and late (0.08) lactation. In fat content, the heritability was increasing throughout lactation (0.08–0.13). Values in protein content varied from the beginning toward mid lactation (0.15–0.19), while they rapidly increased at the end of lactation (0.28). Common flock environment explained the highest percentage of phenotypic variability: 27–41% in daily milk yield, 31–41% in fat content, and 41–49% in protein content. Variance ratios for the two permanent environment effects were the highest in daily milk yield (0.10–0.27), and lower in fat (0.04–0.08) and protein (0.01–0.10) contents. Additive genetic correlations during the selected test-days were high between the adjacent ones and they tended to decrease at the extremes of the lactation trajectory.

scholarly journals  Lactation curves for milk yield, fat and protein content in Slovenian dairy sheep

2012 ◽  
Vol 57 (No. 5) ◽  
pp. 231-239 ◽  
Author(s):  
A. Komprej ◽  
G. Gorjanc ◽  
D. Kon ◽  
M. Kovač
Keyword(s):  
Animal Model ◽  
Protein Content ◽  
Litter Size ◽  
Milk Yield ◽  
Additive Genetic Effect ◽  
Dairy Sheep ◽  
Stage Of Lactation ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

Lactation curves for daily milk yield, fat, and protein content in three dairy sheep breeds were estimated by the repeatability animal model using test-day records. A total of 38 983 records from 3068 ewes of Bovec, Improved Bovec, and Istrian Pramenka breeds, collected between the years 1994 and 2002, were analysed. The three-trait repeatability animal model included breed and lambing season as fixed. The stage of lactation within each breed was modelled by the modified Ali-Schaeffer’s lactation curve. Parity and litter size were used as covariates in quadratic and linear regression, respectively. Common flock environment, additive genetic effect, permanent environment over lactations as well as within lactation were treated as random. The average daily milk yield was 1090 g in Bovec, 1010 g in Improved Bovec, and 731 g in Istrian Pramenka breeds. Overall means for fat and protein content were 6.59 and 5.53% for Bovec, 6.22 and 5.33% for Improved Bovec, and 7.20 and 5.63% for Istrian Pramenka. Breed, lambing season, stage of lactation, parity, and litter size significantly (P < 0.001) affected all three observed milk traits, with the only exception of parity in fat and litter size in protein content. The shape of lactation curves for daily milk yield in Bovec and Improved Bovec breeds fitted well to the general lactation curve in dairy sheep. Daily milk yield was increasing in the first month of lactation and decreasing thereafter. In Istrian Pramenka, the shape of lactation curve was more or less atypical, with daily milk yield decreasing almost throughout the entire lactation. Lactation curves for fat and protein content were opposite to the lactation curves for daily milk yield in all three breeds.  

Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins

2013 ◽  
Vol 152 (2) ◽  
pp. 309-324 ◽  
Author(s):  
N. GHAVI HOSSEIN-ZADEH
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Goodness Of Fit ◽  
The Other ◽  
Linear Functions ◽  
Holstein Cows ◽  
Lactation Curve ◽  
Non Linear ◽  
Watson Statistic ◽  
Best Fit

SUMMARYIn order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin–Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second- and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second- and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first- and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second- and third- lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.

Characterization of Lactation Curve Patterns using Non-linear Models in Crossbred Dairy Cattle

2021 ◽  
Author(s):  
Tassew Mohammed Ali ◽  
Raman Narang ◽  
P.P. Dubey ◽  
Simarjeet Kaur
Keyword(s):  
Dairy Cattle ◽  
Milk Yield ◽  
Linear Models ◽  
Biological Efficiency ◽  
Lactation Curve ◽  
Non Linear ◽  
Crossbred Dairy Cattle ◽  
Daily Milk Yield ◽  
Curve Patterns ◽  
Daily Milk

Background: Lactation curve patterns are currently integrated in dairy cow’s management software. Lactation curve modeling is useful for monitoring individual yields for diet planning, determining optimum strategies for insemination and genetic evaluation. It also helps for predicting expected missing values on field records and gives concise summary of biological efficiency and persistency of dairy cows.Methods: The study was aimed to characterize the lactation curve pattern for crossbred dairy cattle using different non-linear models. During the period 1991 to 2018, daily milk yield (DMY) consisted of 281698 records of 750 crossbred dairy cows maintained at Livestock Farms. GADVASU, Ludhiana, were collected for the study. Different non-linear models viz. exponential decline function (EDF), parabolic exponential model (PEM), inverse polynomial model (IPM), gamma-type function (GTF), mixed log function (MLF) and Ali and Schaeffer model (ASF) were used for the analysis. The model(s) that best fit and describe the curve characteristics was selected on the basis of coefficient of determination (R2), coefficient of variation (CV), Akaike information criterion (AIC) and mean square error (MSE).Result: The study clearly revealed that the PRM gave highest fit to DMY data with R2, MSE, AIC and CV values of 98.10%, 0.087, -743.31 and 2.37%, respectively. The IPM had also best fitted the observed DMY data with highest R2 (98.05%), lower MSE (0.089), low AIC (-735.8972) and lower CV (2.40%) values. The fitting of observed DMY data with predicted DMY were also found to be higher in the MLF (R2= 96.46%, MSE= 0.159, AIC= -558.16 and CV= 3.21%) and GTF (R2= 95.85%, MSE= 0.190, AIC= -505.24 and CV= 3.50%), whilst the EDF and PEM Models depicted relatively low fit to the DMY data when compared with the other non-linear models. However, IPM and GTF models can be used for accurate prediction of daily milk yield in the crossbred cattle population because they were typical standard lactation curves.

Effects of crossbreeding on milk production and composition in dairy sheep under organic management

2014 ◽  
Vol 54 (10) ◽  
pp. 1641 ◽  
Author(s):  
Octavio A. Castelan Ortega ◽  
Manuel González Ronquillo
Keyword(s):  
Protein Content ◽  
Milk Yield ◽  
Fat Content ◽  
Dairy Sheep ◽  
Organic Management ◽  
Total Solids ◽  
Lactation Curve ◽  
Fat Yield ◽  
Daily Milk Yield ◽  
Daily Milk

The crossbreeding of local sheep breeds with dairy breeds is an option to improve dairy production parameters in organic sheep dairy systems. Weekly milk yield (WMY) was recorded and individual samples of milk for chemical analysis were taken during 17 weeks from 45 dairy ewes of the following three genotypes: 15 East Friesian (EF), 15 EF × Suffolk (EF × SF) and 15 EF × Pelibuey (EF × PL) under organic management. For analysis of the lactation curve the Wood gamma model was used. The effect of genotype on the WMY was analysed using repeated-measures. The comparison of the least square means among genotypes for total milk yield (TMY), daily milk yield, protein content, protein yield, fat content, fat yield, non-fat solids concentration, non-fat solids yield, total solids yield and acidity was analysed using a general linear model. The genetic group influenced only in the ascent phase of the lactation curve, with values of the Parameter b of model Wood higher in EF (P = 0.01). There were no differences (P > 0.05) between genotypes in relation to the WMY, TMY, protein content and acidity; however, the effects of week of lactation trial and the interaction of genotype and week of lactation trial on WMY were significant (P < 0.05). The values of daily milk yield, fat yield, protein yield and total solids yield were higher (P < 0.005) in EF and EF × SF than EF × PL. Fat content was higher in EF × PL. EF × SF had similar values of TMY than EF and better chemical composition, which places this genotype as an option of crossbreeding in dairy sheep systems under organic management with similar agro climatic characteristics to the present study.

scholarly journals Impact Of Genotypes And Parity On Reproductive And Productive Attributes In Dairy Cattle Of Natore District, Bangladesh

1970 ◽  
Vol 6 ◽  
pp. 91-96
Author(s):  
M Saiful Islam ◽  
Susanta Kumar Kundu
Keyword(s):  
Dairy Cattle ◽  
Dairy Cows ◽  
Milk Yield ◽  
Dairy Farms ◽  
Gestation Length ◽  
Overall Performance ◽  
Daily Milk Yield ◽  
Better Than ◽  
Daily Milk ◽  
Smallholder Dairy Farms

Impact of genotypes and parity on some vital reproductive and productive attributes in the local (L×L, n = 100) and four crossbred cows (L×F, L×SL, L×JR and L×S; n = 318) raised in randomly selected smallholder dairy farms scattered all over Natore District and adjacent areas have been assessed during a period from September 2007 to June 2010. With regard to reproductive attributes, significant differences existed among the cattle genotypes (P<0.05) except for gestation length (GL) and age at weaning (AW). The lowest age at puberty (AP) was found for L×F (21.42±0.37 months), while the highest for L×L (31.67±0.74 months). In terms of productivity, L×F cows produced the highest daily milk yield (DMY; 6.22±0.13 L), coupled with the highest total lactation yield (TLY; 2163.43±47.77 L), while L×L produced the lowest values (1.49±0.04 L and 416.40±12.3 L, respectively) for the traits. The effect of parity on both reproductive and productive attributes showed that the middle-aged dairy cows of the 3rd and 4th parities performed better than the younger (1st and 2nd parities) or the older (5th and beyond) ones. Considering the overall performance, the L×F cows could be ranked as the best genotype followed by their L×SL, L×JR, L×S and L×L counterparts in the study area. DOI: http://dx.doi.org/10.3329/jles.v6i0.9727 JLES 2011 6: 91-96

scholarly journals Comparison of different lactation curve models in Holstein cows raised on a farm in the south-eastern Anatolia region

2008 ◽  
Vol 51 (4) ◽  
pp. 329-337
Author(s):  
Ö. Koçak ◽  
B. Ekiz
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Exponential Model ◽  
Eastern Anatolia ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

Abstract. The objective of this study was to compare the goodness of fit of seven mathematical models (including the gamma function, the exponential model, the mixed log model, the inverse quadratic polynomial model and their various modifications) on daily milk yield records. The criteria used to compare models were mean R2, root mean squared errors (RMSE) and difference between actual and predicted lactation milk yields. The effect of lactation number on curve parameters was significant for models with three parameters. Third lactation cows had the highest intercept post-calving, greatest incline between calving and peak milk yield and greatest decline between peak milk yield and end of lactation. Latest peak production occurred in first lactation for all models, while third lactation cows had the earliest day of peak production. The R2 values ranged between 0.590 and 0.650 for first lactation, between 0.703 and 0.773 for second lactation and between 0.686 and 0.824 for third lactation, depending on the model fitted. The root mean squared error values of different models varied between 1.748 kg and 2.556 kg for first parity cows, between 2.133 kg and 3.284 kg for second parity cows and between 2.342 kg and 7.898 kg for third parity cows. Lactation milk yield deviations of Ali and Schaeffer, Wilmink and Guo and Swalve Models were close to zero for all lactations. Ali and Schaeffer Model had the highest R2 for all lactations and also yielded smallest RMSE and actual and predicted lactation milk yield differences. Wilmink and Guo and Swalve Models gave better fit than other three parameter models.

scholarly journals On designing the average lactation curve at the ascending phase

1962 ◽  
Vol 34 (1) ◽  
pp. 162-168
Author(s):  
Aarne Mäkelä
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Lactation Period ◽  
Lactation Curve ◽  
The Mean ◽  
The Individual ◽  
Daily Milk Yield ◽  
Daily Milk

Comparisons are made between different methods to find the peak production (maximum daily milk yield) and methods to design the average lactation curve at the ascending phase in dairy cows. It was noted that in order to determine the height and location of the maximal producing capacity of a cow in a known lactation period, it is preferable to choose the peak production as a mean of three subsequent best days. It was also noted that the usual methods for drawing the average lactation curves do not give a true picture of the height and location of the peak. The author suggests a method for determining the average lactation curve at the ascending phase by using the averages of both milk productions and times involved in reaching the peak and known fractions (e.g. 1/8, 1/4, 1/2, 3/4, and 5/4) of it. In this lactation curve the peak production is the mean of the peaks of individual cows, and the time involved in reaching it is the mean of the durations of the ascending phases of the individual cows.

The relationship between nitrogen supply and the nitrogen yield of cut grass swards

1977 ◽  
Vol 88 (2) ◽  
pp. 289-292 ◽  
Author(s):  
I. R. Richards ◽  
R. D. Hobson
Keyword(s):  
Nitrogen Supply ◽  
Linear Functions ◽  
Available Nitrogen ◽  
England And Wales ◽  
Nitrogen Yield ◽  
Non Linear ◽  
Using Data ◽  
The Relationship ◽  
Potential Maximum ◽  
Better Than

SUMMARYUsing data from 140 experiments conducted at sites throughout England and Wales, a relationship between nitrogen supply and the nitrogen yield of cut grass swards was sought. One linear and three non-linear functions were fitted to the data. The non-linear functions fitted the data slightly better than did the linear and, over the range in nitrogen supply normally found, provided consistent predictions of grass nitrogen yield. The recovery of available nitrogen in the herbage was found to decline with level of nitrogen supply from a potential maximum of 79%.

scholarly journals Covariance components by a repeatability model in Slovenian dairy sheep using test-day records

2009 ◽  
Vol 54 (No. 9) ◽  
pp. 426-434 ◽  
Author(s):  
A. Komprej ◽  
G. Gorjanc ◽  
D. Kon ◽  
M. Kovač
Keyword(s):  
Protein Content ◽  
Litter Size ◽  
Milk Yield ◽  
Genetic Correlations ◽  
Dairy Sheep ◽  
Milk Traits ◽  
Environment Effect ◽  
Covariance Components ◽  
Daily Milk Yield ◽  
Daily Milk

The estimation of covariance components for daily milk yield, fat and protein content was performed in three Slovenian dairy sheep breeds (Bovec, Improved Bovec, and Istrian Pramenka). In the period 1994–2002, 38 983 test-day records of 3 068 ewes were collected according to ICAR regulations (method A4). All the available relationships between animals were considered. For that reason, information on 3 534 animals was included. Test-day records were analysed by a multiple-trait repeatability animal model. In its fixed part, the model contained breed and season of lambing as classes. Days after lambing, parity, and litter size were treated as covariates. Days after lambing were modelled with modified Ali-Schaeffer’s lactation curve, parity with quadratic, and litter size with linear regression. The random part of the model consisted of flock-test month effect, additive genetic effect, permanent environment effect over lactations, and permanent environment effect within lactation. Covariance components were estimated using the restricted maximum likelihood method (REML). The estimated heritabilities were 0.11 for daily milk yield, 0.08 for fat content, and 0.10 for protein content. A relatively high variance ratio for all milk traits was explained by the flock-test month effect (from 0.27 for daily milk yield to 0.57 for protein content), while ratios explained by both permanent environment effects were lower (up to 0.13). Additive genetic correlations between daily milk yield and fat content, and daily milk yield and protein content were negative and similar (–0.36 and –0.37). A high and positive (0.67) additive genetic correlation between fat and protein content was found. Correlations for environmental effects showed a pattern similar to additive genetic correlations. Genetic parameters estimated in Slovenian dairy sheep showed that genetic progress in milk traits could be achieved using test-day milk records.

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