ORW presentation on lactation curve

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WELCOME TO ORW PRESENTATION ON

COMPARATIVE STUDY OF LACTATION CURVES IN CATTLE
BUFFALO IN AN ORGANISED FARM
Shashank KshandakarM-5405Division of LES IT
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19th Livestock census 2012, Ministry of
Agriculture
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Contribution of Agriculture Allied Practices In
GDP
1950-51

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2012-2013
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Per capita milk availability
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Growth Rate In Milk Production
Year Decadal Growth Rate ()
1950-51 to 1960-61 1.64
1960-61 to 1973-74 1.15
1973-74 to 1980-81 4.51
1980-81 to 1990-91 5.48
1990-91 to 2000-01 4.31
2000-01 to 2009-10 3.77
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Model

• Represent the behaviour of a system
  
• 
  
  (France and Thornley, 1984)
• Linear Model.
• Non linear Model.
• Intrinsically linear.
• Intrinsically Nonlinear.

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Lactation curve

• Derivatives of maximum daily yield and the
  persistency.
• 
  (Davydov 1933)
• Graphical representation of the ratio between
  milk production and lactation time starting at
  calving.
  (Bodero et
  al.,1988)
• Importance of lactation curve
• Estimation purpose.
• Farm management.

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Objective of study

• To compare various lactation curve models in
  cattle and buffalo under diseased and
  non-diseased conditions.
• To study the effect of disease and other
  associated factors on lactation curve in cattle
  and buffalo.

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Review of Literature

• Percentage decline method.
• Ratio method.
• Regression method.
• Modelling the shape of lactation curve.
• Factors affecting lactation curve

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Review of Literature

• Percentage decline method .
• Sturtevant (1886) concluded that There is
  approximately 9 average reduction in milk
  production per month
• Carlyle and Woll (1903) ) concluded that There
  is 8 (approx) average reduction in milk
  production per month
• Beach (1904) estimated that the average reduction
  in milk production in first five month is 6.5
  and about 13 reduction in milk production from
  eight to tenth month after calving.
• Arreola et al.(2004) concluded that general
  declining rate of milk production is about 7 per
  month after the peak yield.

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• Ratio Method
• Sanders (1930) divided lactation curve into
  two components first the rate to which the yield
  raises to peak yield, second the rate at which it
  falls from the peak yield and stated that maximum
  yield and persistency are two important component
  of lactation.
• Shape of curve
• Regression coefficient method
• Regression coefficient techniques studied by
  Madden (1959).
• Regression coefficient techniques was used to
  estimate 305-day yield from test day yield.
  (Vleck et al.1961 Appleman et al.1969).
• Khan et al.(1999) stated that Regression
  coefficient method are generally more efficient
  as compared to ratio-method

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Modelling the shape of lactation curve

• Madalena et al.(1979) fitted lactation data of HF
  HF X Gir stated that the simple exponential
  model is better fit than simple linear regression
  model.
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• Malhotra et al. (1980) studied lactation curve
  model of Karan Swiss cattle shows that Quadratic
  cum log model (1982) was best fitted with respect
  to Quadratic, Inverse polynomial Gamma
  lactation curve models.
• Batra (1986) studied environmental and genetic
  effects on the coefficients of the lactation
  curves derived by modified gamma and inverse
  polynomial functions by using WTDMY of 2066
  first, 1407 second, and 755 third lactation pure
  and crossbred cows and concluded that the inverse
  polynomial function provided a better fit than
  the modified gamma function based on comparison
  of R2 values

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• Singh and Bhat (1987) concluded that Multiphasic
  logistic model was best fitted with respect to
  gamma, Parabolic, Exponential functions for
  estimating lactation curve based on WTDMY data of
  Haryana cow
• Sherchand et al. (1995) studied different
  lactation curve models using DTDMY of 120
  Holstein cows and concluded that the Diphasic
  logistic function was best fitted for all
  lactations and for the first 30 day, Modified
  gamma function Inverse polynomial Quadratic
  log function were best fitted to first, second
  and third lactation respectively.
• Olori et al. (1999) collected WTDMY records of
  488 1st lactation HF cow for comparative study on
  5 standard lactation curve models (Incomplete
  gamma, Inverse polynomial, Polynomial regression,
  Exponential and Mixed log).on the basis of study
  Incomplete gamma, Inverse polynomial, Mixed log
  lactation curve model under predicted milk yield
  around peak production and over predicted
  immediately after peak production. polynomial
  regression lactation curve model is best fit
  (R299.6) whereas Incomplete gamma lactation
  curve model is least fit (R294.4).

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• Rankja and Pandya (2001) analyzed WTDMY records
  of 352 Gir cows maintained at Cattle Breeding
  Farm, Junagarh with seven different mathematical
  models for different lactation period and
  concluded that the Morant and Gnanasakthy model
  was the best fitted.  
• Arreola et al. (2004) considered 3 emperical
  Gaines (exponential decay), Wood (gamma
  equation), Rook (Michaelis-Menten x exponential)
  and 2 mechanistic ones Dijkstra and Pollott
  for fitting and concluded that Rook equation
  fitted the data well Dijkstra equation
  consistently gave better predictions and the
  Pollott equation over-parameterized parameter
  estimates.
• Macciotta et al. (2005) fitted Wood incomplete
  gamma, Wilminks exponential, Ali and Schaeffers
  polynomial regression, and fifth-order Legendre
  polynomials to 229,518 DTDMY records of Italian
  Simmental cows and concluded that Five-parameter
  models (Ali and Schaeffer function and the
  Legendre polynomials) were better fitted than the
  3-parameter models (Wood and Wilmink).

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• VanRaden et al. (2007) compared 7 empirical
  Wood ,Wilmink ,Rook ,monophasic , diphasic
  lactation persistency functions and Dijkstra and
  2 mechanistic models Pollott and
  new-multiphasic for their suitability for
  modelling lactations of US HF cattleand concluded
  that Pollott model and new-multiphasic models
  were better fitted
• Pandey et al. (2007) compared four lactation
  curve model on WTDMY MTDMY records of buffalo
  and Vrindavani cattle and conclude that Gamma
  function was best fitted than other three
  (Quadratic, Parabolic Exponential, Inverse
  polynomials) models.
• Cunha et al. (2010) compared seven lactation
  curves models (Brody, Wood, Cobby Le Du,
  Wilmink, Rook, Dijkstra Pollott) and concluded
  that Wilmink (1987) model better adjusted for
  cows of the first lactation Wood (1967) model
  better adjusted for cows of the third or greater
  lactations of low milk producing groups whereas
  Dijkstra (1997) model better fitted for all
  lactation numbers for the high milk producing
  group.

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• Cankaya et al. (2011) studied five different
  lactation curve models (Wood, Cobby and Le Du,
  Wilmink, Exponential and Parabolic Exponential
  model) and concluded that Wood model best fitted
  for lactation curve of Jersey cattle.
• Fathi et al., (2011) fitted four growth and two
  lactation curve function viz. (Logistic,
  gompertz, Schumacher, Morgan) and (Wood and
  Dijkestra) on MTDMT records of HF cattle and on
  the basis of modular behaviour he concluded that
  growth function are fitted better than Wood and
  Dijkestra equation
• Korkmaz et al.,(2011) studied MTDMY records of
  dairy cows and conclude that polynomial model was
  best fitted than Wood, Gaines, Parabolic,
  Hayashi and Dhanno models

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• Adediran et al. (2012) fitted 14 lactation models
  to ATDMY and concluded that log-quadratic model
  was best fitted whereas Incomplete gamma model
  least fitted models.
• Dongre and Gandhi (2012) ) studied WTDMY records
  of first lactating 643 Sahiwal cows and
  concluded that Inverse polynomial function was
  best fitted than Exponential decline function,
  Parabolic exponential function, Gamma type
  function and Mixed log function.
• Dongre et al.(2012) studied FTDMY records of
  first lactating 643 Sahiwal cows and concluded
  that Mixed log function was the best fitted
  lactation curve models.

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• Vinay et al. (2012) studied DTDMY records of
  Holstein x Zebu cows for fitting Lactation curves
  and concluded that Ali and Schaeffer model
  fitted better than the incomplete gamma function,
  Wilmink and Dijkstra model.
• Banu et al.(2012) compared five lactation curve
  models viz. Quadratic cum log model ,Gamma
  function ,Cobby Le Du model ,Polynomial
  regression function and Multiphasic logistic
  function and concluded that polynomial regression
  function was best fitted and Gamma function was
  least fitted.
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• Dohare et al. (2014) compared four standard
  lactation curve models (Wood, Morant-Gnanasakthy,
  Mitscherlich x Exponential, and Wilmink models)
  using FTDMY records of Frieswal and concluded
  that Mitscherlich cum Exponential model was best
  fitted followed by Morant-Gnanasakthy and Wilmink
  model.

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Factor affecting lactation curve

• Madalena et al. (1979) stated that cow calving in
  rainy season is 4 superior milk producer than
  cow calving in dry season and also stated that
  mature cow produce 1.3 times more milk than 1st
  lactation cow. 
• Keown et al. (1986) stated that total and peak
  yield were lowest for cow calving in the summer
  season when feeding resources are limited and the
  heat stress effect is maximum.
• Lean et al. (1989) studied 5928 lactation records
  of high milk producing cows at three California
  dairy farms and concluded that the sub fertility
  is associated with high peak lactation yields of
  cow

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• Scott et al. (1996) stated that the herd,
  lactation number and interaction effects of herd
  account 34.1 and 44.3 of variation on milk
  production among primiparous and multiparous cows
  respectively.
• Lactation curve and persistency differ between
  lactation, and the difference was significantly
  exist between early and late maturing breed.
  (Jamrozik et al. 1998 Linde et al. 2000)
• Dekkers et al. (1998) studied the economic
  importance of lactation persistency and
  concluded that the more flat shape of parameter
  c in the 1st parity indicate better utilization
  of feed and less susceptibility of cow to
  metabolic and reproductive disorder.
• Cobuci et al. (2000) studied Lactation Curve
  models in Guzera Breed cow and observed that the
  effects of cow herd, calving year and cow age at
  calving, influenced the total milk production,
  initial milk production and milk decline
  production rate characteristics.

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• Tekerli et al. (2000) concluded that 1st
  lactation cow produce lower milk yield but they
  are more persistence in milk production with
  respect to older parity animals.
• Rekik et al. (2003) concluded that the ascending
  phase of lactation is not affected by parity and
  calving season while decreasing phase of
  lactation curve affected by parity and calving
  season.
• Madani et al.(2008 ) concluded that cows calving
  in summer produced 23 and 24 lower milk per
  lactation than cows calving in winter and spring
  season respectively.
• Cole et al.(2009) proposed that cows with high
  lactation persistency produce less milk than
  expected at the beginning and produce more than
  expected at the end.
• Grainger et al. (2011) concluded that diet
  energy uptake also extended the lactation curve.

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• Lalrintluanga et al. (2003) concluded that
  Mastitis incidence was higher during the
  early stage of the third lactation (36.60)
  whereas single quarter infection (63.44) and the
  left hind quarters (30.25) were more frequently
  affected.
• Meena et al. (2006) stated that infectious
  (Diarrhea, HS, FMD, Pox, PPR etc) and parasitic
  diseases accounted more than 60 morbidity and
  mortality in livestock's.
• Prasad et al .(2004) observed that average
  mortality in Sahiwal, Tharparkar, Karan Swiss,
  Karan Fries cattle is 14.35, 7.21, 17.12 and
  13.36 respectively.
• Singh and Prasad (2008), reported that four
  diseases (FMD,HS,BQ Anthrax ) accounted about
  56.6 and 84.4 to total incidence and deaths
  due to all diseases in cattle.

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• Lucey et al. (1986) concluded that there were
  significant differences in milk yield between one
  week before and one week after clinical diagnosis
  of disease ketosis (5l kg/d), hypomagnesaemia
  (41 kg/d), and lameness (11 kg/d) and total
  loss in milk yield associated with ketosis was
  6070 kg.
• Mitev et al. (2011) studied that 10.2 animal
  suffered from lameness during the first month of
  lactation and lameness decreased peak lactation
  milk yields by about 2 kg whereas lameness along
  with ketosis lowered peak lactation milk yield by
  6.15 kg.
• Hostens et al. (2012) concluded that milk
  production increased at faster rate and also
  declined at slower rate as compared to cows that
  encountered one or more metabolic problems Milk
  fever, retained placenta, ketosis, and mastitis
  mainly affected the lactation curve as compared
  to another disease.
• Wilson et al. (2014) studied effect of clinical
  mastitis using mixed linear models and estimated
  that production loss from clinical mastitis
  during the whole lactation was 598 kg.

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Research methodology
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Source, Collection and classification of Data

• Cattle and Buffalo Farm (LPM Section, IVRI)
• Animal number
• Species and Breed
• Disease
• Date of birth
• Date of calving
• Parity of Animal
• Weekly milk yield from 1st to 44th weeks
• WTDMY
• FTDMY
• MTDMY

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Standard lactation curve models

• Parabolic exponential model  (Sikka et.al.,
  1950) Yt a exp(bt-ct2)
• Gamma function (Wood et al.,1967)
• Ytatbe-ct
• Exponential model (Wilmink et al.,1987)
  
  Yt a be-kt ct

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• Ali Schaeffer lactation curve model (1987)
• Yt a bdcd2 d ?i e ?i2 ft
  
• Dijkstra model (1997)
• Yt a exp b(1-e-ct)/c-dt
• Mitscherlich x Exponential (Rook et al.,1993)
• Yt a(1-be-dt)e-ct
• Mixed log model (Guo et al.,1995)
• Yt abt-1/2cln(t)

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• Yt The production at time t
• a scale factor or milk yield at the
  beginning of lactation
• b The rate of change from initial
  production to maximum yield
• c The rate of change from maximum
  yield to the end of lactation
• k factor associated to the time of
  peak yield
• d is a parameter related to maximum
  milk yield
• dt/305
  ?i exp(305/t)

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• Iteration procedure
• Gauss-Newton method
• Levenberg-Marquardts method
• Examination of residuals
• Normality - Shapiro-Wilk test
• Autocorrelation - Durbin-Watson test

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. Criteria for goodness of fit of
lactation curve

• Coefficient of determination (R2)
• Adjusted coefficient of determination (R2adj)
• Mean Squared Error (MSE)
• Mean Absolute Error (MAE)
• Mean squared prediction error
• Akaikes Information Criteria (AIC)
• Bayesian information criterion (BIC)
• 
  

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The effect of disease and other factors such as
breed, parity, season on lactation curve will be
analysed by appropriate general linear models
General linear model ANOVA/Regression/ANCOVA
Generalised linear logit/probit Binomial Exponenti
al Poisson gamma model
Mixed Repeated measure Change over
trails Sub-sampling Clustered data
Generalised linear mixed model Non normal data
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