Application of the Wood model to analyse lactation curves of organic dairy sheep farming

2014 ◽  
Vol 54 (10) ◽  
pp. 1609 ◽  
Author(s):  
Juan Carlos Ángeles Hernández ◽  
Octavio Castelán Ortega ◽  
Benito Albarrán Portillo ◽  
Hugo H. Montaldo ◽  
Manuel González Ronquillo
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Evaluation Criteria ◽  
Coefficient Of Determination ◽  
Dairy Sheep ◽  
Organic System ◽  
Dairy Ewes ◽  
Lactation Curve ◽  
Total Milk ◽  
Wood Model

The aim of the present study was to evaluate the performance of the Wood model to describe the characteristics of lactation curves of dairy ewes under organic management in Mexico. In total, 4861 weekly test-day milk yield records from 194 lactations of crossbred dairy ewes were analysed to assess the performance of an empirical model to fit their lactation curve. We used the mathematical model proposed by Wood. The evaluation criteria were the correlation coefficient (r) between the values of total milk yield observed and estimated, the coefficient of determination (R2), and the mean square prediction error (MSPE). In addition, the peak yield (PYest) and time at peak yield (PTest) were calculated. The Wood model showed adequate goodness of fit (r = 0.95, R2 = 0.92 and MSPE = 0.024). The Wood model detected that 52.06% of lactation curves had a continuously decreasing shape (atypical curve), probably as a consequence of the characteristic management of the organic system, mainly due to the genotype used and the nutritional management. Residuals were greater for atypical curves than for typical ones, indicating differences in the ability of the Wood model to fit the two types of shapes. In typical curves, the Wood model showed adequate estimates of total milk yield and time at peak yield. The peak yield was underestimated both in typical and atypical curves. The Wood model in atypical curves underestimated the time at peak yield and milk yields in late lactation. The Wood model showed a reasonable fit of lactation curve in dairy sheep in organic systems but presented deficiencies of fit in atypical curves; therefore, estimates should be interpreted carefully.

Introducing a sinusoidal equation to describe lactation curves for cumulative milk yield and composition in Holstein cows

2020 ◽  
Vol 87 (2) ◽  
pp. 220-225
Author(s):  
Navid Ghavi Hossein-Zadeh ◽  
Hassan Darmani Kuhi ◽  
James France ◽  
Secundino López
Keyword(s):  
Linear Model ◽  
Milk Yield ◽  
Milk Fat ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Production Traits ◽  
Lactation Curve

AbstractThe aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

scholarly journals Comparison of the parameters of the lactation curve between normal and difficult calvings in Iranian Holstein cows

2019 ◽  
Vol 17 (1) ◽  
pp. e0401
Author(s):  
Navid Ghavi Hossein-Zadeh
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Lactation Curve ◽  
Non Linear ◽  
Best Fit

To evaluate effect of dystocia on the lactation curve characteristics for milk yield and composition in Holstein cows, six non-linear models (Brody, Wood, Sikka, Nelder, Dijkstra and Rook) were fitted on 5,917,677 test day records for milk yield (MY), fat (FP) and protein (PP) percentages, fat to protein ratio (FPR) and somatic cell score (SCS) of 643,625 first lactation Holstein cows with normal calving or dystocia from 3146 herds which were collected by the Animal Breeding Center of Iran. The models were tested for goodness of fit using adjusted coefficient of determination, root means square error, Akaike’s information criterion and Bayesian information criterion. Rook model provided the best fit of the lactation curve for MY and SCS in normal and difficult calvers and dairy cows with dystocia for FP. Dijkstra model provided the best fit of the lactation curve for PP and FPR in normal and difficult calvers and dairy cows with normal calving for FP. Dairy cows with dystocia had generally lower 100-d, 200-d and 305-d cumulative milk yield compared with normal calvers. Time to the peak milk yield was observed later for difficult calvers (89 days in milk vs. 79 days in milk) with lower peak milk yield (31.45 kg vs. 31.88 kg) compared with normal calvers. Evaluation of the different non-linear models indicated that dystocia had important negative effects on milk yield and lactation curve characteristics in dairy cows and it should be reduced as much as possible in dairy herds.

Factors affecting the lactation curves of intensively managed sheep based on a clustering approach

2013 ◽  
Vol 80 (4) ◽  
pp. 439-447 ◽  
Author(s):  
Laura Elvira ◽  
Fernando Hernandez ◽  
Pedro Cuesta ◽  
Santiago Cano ◽  
Juan-Vicente Gonzalez-Martin ◽  
...  
Keyword(s):  
Milk Yield ◽  
Clustering Analysis ◽  
Dairy Sheep ◽  
Dry Period ◽  
Factors Affecting ◽  
Lactation Curve ◽  
Total Milk ◽  
Clustering Approach ◽  
Intensively Managed ◽  
Selection Of

This study investigated factors affecting milk production and lactation curves from complete lactations of Lacaune dairy sheep. Animals were part of a single flock under intensive management and were milked twice daily starting at lambing. The results of the analyses of 7788 complete lactations showed an average total milk yield of 434±183 l from lactations 234±63 d long, with an average lambing interval of 302±65 d. A Pollott additive mathematical model was used to estimate complete lactation curves. Clustering analysis identified four lactation types among Lacaune dairy sheep differing mainly in productivity i.e. milk yield per lactation (MY) and length of lactation (DIM). The so-called SL type involved short, less productive lactations (n=2137; 27·4%; MY=222±75·5 l and DIM=182±52·9 d). The SN type involved short lactations of normal productivity (n=2039; 26·2%; MY=396±73·7 l and DIM=205±33·1 d). The LP type involved long and productive lactations (n=2169; 27·9%; MY=487±70·5 l and DIM=265±40·7 d), while the LVP type included long and extremely productive lactations (n=1443; 18·5%; MY=694±114·0 l and DIM=295±54·7 d). Sheep showing the best lactation curves were usually younger than other sheep, and they had higher yield during the previous lactation, a shorter previous dry period (55±50·4 for LP and 61±55·0 d for LVP types) and longer lambing intervals. In addition, they tended to be born in September and to lamb in March, October and December. Sheep were remarkably stable in their lactation curve behaviour: the curve type observed for the first lactation was highly likely to persist in subsequent lactations (P<0·0001). These results suggest that farmers can use the shape of the first lactation curve to guide their selection of ewes for breeding and retention on the farm, thereby improving flock productivity.

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 Genetic parameters of total milk yield and factors describing the shape of lactation curve in dairy buffaloes

2011 ◽  
Vol 79 (1) ◽  
pp. 60-65 ◽  
Author(s):  
Rúsbel R Aspilcueta-Borquis ◽  
Fernando Baldi ◽  
Francisco R Araujo Neto ◽  
Lucia G Albuquerque ◽  
Milthon Muñoz-Berrocal ◽  
...  
Keyword(s):  
Animal Model ◽  
Factor Analysis ◽  
Milk Yield ◽  
Genetic Parameters ◽  
Correlated Response ◽  
Early Lactation ◽  
Latent Factors ◽  
Latent Factor ◽  
Lactation Curve ◽  
Total Milk

The objective of this study was to apply factor analysis to describe lactation curves in dairy buffaloes in order to estimate the phenotypic and genetic association between common latent factors and cumulative milk yield. A total of 31 257 monthly test-day milk yield records from buffaloes belonging to herds located in the state of São Paulo were used to estimate two common latent factors, which were then analysed in a multi-trait animal model for estimating genetic parameters. Estimates of (co)variance components for the two common latent factors and cumulated 270-d milk yield were obtained by Bayesian inference using a multiple trait animal model. Contemporary group, number of milkings per day (two levels) and age of buffalo cow at calving (linear and quadratic) as covariate were included in the model as fixed effects. The additive genetic, permanent environmental and residual effects were included as random effects. The first common latent factor (F1) was associated with persistency of lactation and the second common latent factor (F2) with the level of production in early lactation. Heritability estimates for F1 and F2 were 0·12 and 0·07, respectively. Genetic correlation estimates between F1 and F2 with cumulative milk yield were positive and moderate (0·63 and 0·52). Multivariate statistics employing factor analysis allowed the extraction of two variables (latent factors) that described the shape of the lactation curve. It is expected that the response to selection to increase lactation persistency is higher than the response obtained from selecting animals to increase lactation peak. Selection for higher total milk yield would result in a favourable correlated response to increase the level of production in early lactation and the lactation persistency.

A Bayesian estimation of the lactation curve of a dairy cow

1985 ◽  
Vol 40 (2) ◽  
pp. 189-193 ◽  
Author(s):  
E. A. Goodall ◽  
D. Sprevak
Keyword(s):  
Kalman Filter ◽  
Bayesian Estimation ◽  
Milk Yield ◽  
Dairy Cow ◽  
Prior Information ◽  
Recursive Procedure ◽  
Early Stages ◽  
Lactation Curve ◽  
Total Milk

ABSTRACTA recursive procedure for the estimation of the lactation curve of a dairy cow, which allows the inclusion of prior information on the curve and which takes account of the correlation between successive observations, is described. The method is based on the Kalman filter. It was found to give accurate estimates of the total milk yield at early stages of lactation.

scholarly journals Modelling of the lactation curve of grazing Mongolian mare

2020 ◽  
Vol 29 (1) ◽  
pp. 64-71
Author(s):  
Sandagdorj Badrakh ◽  
Baigalmaa Tserenpil ◽  
Burenjargal Sedkhuu ◽  
Nyam-Osor Purevdorj
Keyword(s):  
Mathematical Models ◽  
Milk Yield ◽  
Lactation Period ◽  
Linear Quadratic ◽  
Quartic Curve ◽  
Lactation Curve ◽  
Total Milk ◽  
Curve Model ◽  
Composition Curve ◽  
Best Fit

Current research was performed to determine the yield and composition of milk during entire lactation period, which lasts June to February of following year and describe fit of lactation curve using different mathematical models. Total 8 mares, aged from 5 to 12 years were used in the study. The total milk yield, calculated by Fleischmann's method, as well as the models were various and shape of curves for Linear, Quadratic, Cubic, and Quartic equations, and Wood's curve were different. The determination index (R2) of the milk yield and composition curve models ranged from 0.474-0.987, and R2 of Quartic curve model for milk yield (0.987) was the highest. Study result showed that the above models were able to describe the lactation curve of the milk yield and composition, and the Quartic model best fit to data collected from Mongolian mare and allowed a suitable description of the shape and dynamics of curve. Бэлчээрийн маллагаатай Монгол гүүний лактацын муруйн загварчлал Монгол гүүний саалийн нийт хугацаанд буюу VI сараас дараа жилийн III сар хүртэл саамны гарц, найрлагын хэмжээг үндэслэн математик загваруудаар лактацын муруй байгуулах, монгол гүүний лактацын муруйд хамгийн нийцэл сайтай загварыг сонгон тодорхойлох зорилгоор энэхүү ажлыг хийж гүйцэтгэлээ. Судалгаанд 5-12 насны 8 гүүг ашиглав. Сүүний нийт гарц, найрлагын хэмжээг Вүүд (Wood’s)-ын загвар болон шугаман, шугаман бус регрессын тэгшитгэлээр загварчлахад лактацын муруйн загварууд харилцан адилгүй байв. Саамны гарц, найрлагын муруйн загваруудын детерминацийн индекс (R2) нь 0.474-0.987-ийн хооронд хэлбэлзэж, биквадрат загварын хувьд хамгийн нийцэл өндөр буюу 0.987 байв. Судалгааны үр дүнд дээрх аргуудаар саамны гарц, найрлагын лактацын муруйг загварчлах боломжтой нь харагдаж байсан ба эдгээрээс биквадрат тэгшитгэлийн загвар нь  бэлчээрийн маллагаатай монгол гүүний саамны өгөгдөлтэй хамгийн сайн нийцэж, лактацын муруйн хэлбэр, хөдлөлзүйн хувьд тохирч байв.   Түлхүүр үг: саамны гарц, саамны найрлага, лактацын муруй  

scholarly journals Lactation curves and persistency of White Fulani and Sokoto Gudali lactating cows

2020 ◽  
Vol 44 (4) ◽  
pp. 29-37
Author(s):  
O. E. Odegbile ◽  
I. I. Adedibu ◽  
C. Alphonsus
Keyword(s):  
Milk Yield ◽  
Preliminary Analysis ◽  
Post Partum ◽  
Prediction Equation ◽  
Coefficient Of Determination ◽  
Lactation Period ◽  
Lactating Cows ◽  
Lactation Curve ◽  
Breeding Programmes ◽  
White Fulani

The aim of this study was to determine the lactation curve traits of White Fulani (WF) and Sokoto Gudali (SG) lactating cows. Wood's gamma and Wilmink's curve parameters were employed to identify the lactation curve types and values for the parameters beginning yield (a) , coefficient of rising (b), coefficient of decreasing (c)t=timeande= is the exponential.The parameter assumed a fixed value derived from a preliminary analysis and disassociated with the time at peak yield were used to determine the shape and type of lactation curve. All Parameters in a typical lactation curves were positive, and in the event of one parameter being negative, the curve was considered to be an atypical lactation curve. Lactation records from WF (n=96)and SG (n=130) cows were recorded in the study area between year 2016-2017. Cows were hand-milked twice per day in the morning and evening from the 5 day post-partum till the end of the lactation period (260-270 days).Prediction equation of milk yield showed R values ranging from (32.00) in the SG to (35.00) in the WF. It was observed that the Wood's model curves were typical while Wilmink's model curves were atypical respectively. For typical lactation curves, a, b, c, persistency (S), time after parturition until the peak yield occurs (T ), maximum daily peak yield (Y ), and coefficient of determination (R ) were - 0.25±0.13, 1.08±0.07, 0.23±0.19, 2.34,51.00,2.62 and 97 for WF lactating cows and - 0.23 ± 0.14,1.13 ± 0.08, 0.07± 0.03, 2.33, 51.26, 2.58 and 96 for SG Lactating cows respectively. Parameters predicted by the Wood's model have the potential of being useful for breeding programmes in the SG and WF cows.  

Characterisation of the Lactation Curve in Pakistani Buffaloes

1984 ◽  
Vol 1984 ◽  
pp. 136-136
Author(s):  
K.Z. Gondal ◽  
P. Rowlinson
Keyword(s):  
Milk Yield ◽  
Indian Subcontinent ◽  
Human Consumption ◽  
Dairy Herds ◽  
Lactation Period ◽  
General Shape ◽  
Or Groups ◽  
Lactation Curve ◽  
Total Milk ◽  
Dairy Animals

The rate of milk secretion in dairy animals displays a trend throughout the lactation period. It increases to a maximum in a few weeks following parturition and decreases thereafter until the animal goes dry.This trend draws a certain curve, namely the lactation curve.The milk yield of a single lactation may be influenced by many factors but the general shape of the lactation curve defined by the locus of weekly yields remains substantially unchanged. It rises rapidly to the peak within a few weeks after calving followed by a more or less gradual decline until the end of lactation.The analysis of the lactation curve, i.e. the week to week output of milk and trend of increase and decrease in yield with advancement of lactation is important for day to day management and forward planning of dairy herds by reliable forecasting of week by week milk production, seasonal variation and the total milk yield of individual cows or groups of cows.A number of reports pertaining to dairy cattle have been published but very few studies have been concerned with buffaloes. In most of the countries, the buffaloes have been used for draught purpose but it is in the Indian subcontinent that this animal is seen at its greatest advantage as a source of animal protein, i.e. milk and meat for human consumption.

scholarly journals Modelling the lactation curve of dairy cows using the differentials of growth functions

2008 ◽  
Vol 146 (6) ◽  
pp. 633-641 ◽  
Author(s):  
M. H. FATHI NASRI ◽  
J. FRANCE ◽  
N. E. ODONGO ◽  
S. LOPEZ ◽  
A. BANNINK ◽  
...  
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Statistical Evaluation ◽  
Parameter Estimates ◽  
Growth Functions ◽  
Lactation Curve ◽  
Significant Difference ◽  
Overall Evaluation ◽  
Mathematical Equations ◽  
The Individual

SUMMARYDescriptions of entire lactations were investigated using six mathematical equations, comprising the differentials of four growth functions (logistic, Gompertz, Schumacher and Morgan) and two other equations (Wood and Dijkstra). The data contained monthly milk yield records from 70 first, 70 second and 75 third parity Iranian Holstein cows. Indicators of fit were model behaviour, statistical evaluation and biologically meaningful parameter estimates and lactation features. Analysis of variance with equation, parity and their interaction as factors and with cows as replicates was performed to compare goodness of fit of the equations. The interaction of equation and parity was not significant for any statistics, which showed that there was no tendency for one equation to fit a given parity better than other equations. Although model behaviour analysis showed better performance of growth functions than the Wood and Dijkstra equations in fitting the individual lactation curves, statistical evaluation revealed that there was no significant difference between the goodness of fit of the different equations. Evaluation of lactation features showed that the Dijkstra equation was able to estimate the initial milk yield and peak yield more accurately than the other equations. Overall evaluation of the different equations demonstrated the potential of the differentials of simple empirical growth functions used in the current study as equations for fitting monthly milk records of Holstein dairy cattle.

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