Lactation Curves and Prediction of Daily and Accumulated Milk Yields in

a Multibreed Dairy Herd in Thailand Using All Daily Records[1]/

 

Skorn Koonawootrittriron*, Mauricio A. Elzo2/, Sornthep Tumwasorn, and Wirot Sintala 3/

 

Department of Animal Science, Faculty of Agriculture,

Kasetsart University, Bangkok 10900, Thailand.

 

*  Correspondence: Present address 3/  Sakon Nakhon Agricultural Research and Training Center, P.O. Box 3,

Pungkone, Sakon Nakhon 47160, Thailand.  E-mail: skornk@hotmail.com

[1]/  This research was supported by the Florida Agricultural Experiment Station and a grant from

the Thailand Research Fund under the Royal Golden Jubilee Project,

and approved for publication as Journal Series No. R-08042.

2/  Department of Animal Sciences, University of Florida, Gainesville, FL 32611-0910, USA

 

Abstract

 

Daily milk records of 88 cows in a multibreed dairy herd were used to describe lactation curves and test the ability of seven models to predict daily milk yields, and accumulated 100-d and 305-d milk yields.  The seven mathematical models were a gamma function, a mixed log second-degree polynomial model, and five polynomial regression models.  Cows were of three breed groups: Holstein Friesian (HF), 1/2HF-1/2RS (Red Sindhi), and 3/4HF-1/4RS.  Lactation number was classified as first, second, third, and fourth-and-later lactations.  Calving age was defined as age less than 30 months, and equal to or greater than 30 months for the first lactation; age less than 44 months, and equal to or greater than 44 months for the second lactation; less than 60 months, and equal to or greater than 60 months for the third lactation; and all ages for the fourth-and-later lactations.  Seasons of calving were defined as winter (November to February), summer (March to June), and rainy (July to October).  Four general types of lactation curves were found: convex, slightly convex, two-peaked, and flat.  Types of lactation curves varied across breed group x lactation x calving season and breed group x lactation x calving age subclasses.  The second-degree polynomial model was the best in terms of predicted minus actual daily and 305-d milk yields, and computational requirements.  For 100-d milk yield the best model was the sixth degree polynomial model.  The application of these results is limited to HF x RS multibreed herds in the Northeastern region of Thailand.  To further help national genetic evaluation efforts, this study needs to be repeated with a data set that is representative of the national Thai dairy cattle population.

 

Key words:  dairy cattle, lactation curve, milk yield, prediction, multibreed

 

 

Introduction

 

Knowledge of lactation curves and yields in dairy cattle is important for decisions on herd management and selection.  Different mathematical models have been evaluated for their ability to describe lactation patterns of milk yield as well as the ability to predict cumulative milk yields from partial records (Schaeffer et al., 1977, Batra, 1986, Vargas et al., 2000).  A popular model that has been widely used to describe lactation curves and predicted lactation yields is the gamma function (Wood, 1967). However, a linear regression model of yields on days in lactation (linear and quadratic) and on log of 305 divided by days in lactation (linear and quadratic) was reported to be better than Wood’s gamma function for predicting lactation yields (Ali and Schaeffer, 1987).  Recently, more complicated nonlinear models (Grossman et al., 1986, 1999, Morant and Gnanasakthy, 1989) to describe lactation curves have been proposed, but they require additional mathematical techniques and may have more computational problems because of the larger number of parameters that need to be estimated and the greater amount of data is required to estimate those parameters with a reasonable degree of accuracy.

In Thailand, although Holstein Friesian is the main breed used for crossbreeding in dairy herds, most farmers simultaneously raise many types of crossbred dairy cattle in their farms.  Each one of these breed groups of cattle can potentially have lactation curves of different shapes depending on calving age and calving season.  Because interactions among these effects can be important, if these animals are to participate in a genetic evaluation, then lactation curves within breed group x lactation number x calving age subclasses and breed group x lactation number x calving season subclasses need to be compared.  In addition, it is also important to assess the ability of various mathematical models to estimate daily milk yields using all available daily records.

Thus, the objectives of this study were: 1) to compute actual lactation curves based on means of daily milk records, 2) to compare the ability of seven mathematical models including a gamma function, a regression model and five polynomial regression models to describe lactation curves of individual cows, and 3) to compare the ability of these seven models to predict cumulative 100-d and 305-d milk yields of individual cows, within breed group x lactation number x calving age and breed group x lactation number x calving season subclasses, using all daily milk yields in a multibreed dairy herd in Thailand.

 

 

Materials and Methods

 

Animals, Management, and Records

Analyses were performed on data provided by the Sakon Nakhon Agricultural Research and Training Center (SARTC) and collected in an experimental multibreed dairy herd in northeast Thailand between November 1, 1997 and December 31, 1999.  Animals consisted of purebred Holstein Friesian (HF) and crossbred Holstein Friesian x Red Sindhi (HF-RS), which were under the cattle breeding project of Rajamangala Institute of Technology (RIT).

A total of 28,452 daily milk lactation records (days 5 to 305) from 106 lactations of 88 straightbred HF and crossbred HF x RS cows were used here (Table 1).  There were three breed groups of cows: HF, 1/2HF-1/2RS, and 3/4HF-1/4RS.  Lactation records were from first, second, third, and fourth-and-later lactations.

Calving seasons were classified as winter (November to February), summer (March to June), and rainy (July to October).  Because of the overlapping of calving ages and lactation numbers, calving age x lactation number subclasses were defined.  The resulting seven calving age x lactation subclasses were: 1) calving age less than 30 months x lactation 1, 2) calving age equal to or greater than 30 months x lactation 1, 3) calving age less than 44 months x lactation 2, 4) calving age equal to or greater than 44 months x lactation 2, 5) calving age less than 60 months x lactation 3, 6) calving age equal to or greater than 60 months for the third lactation, and 7) calving age greater than 60 months x lactation 4 and greater.

Animals of all breed compositions were raised under the same nutritional and management conditions.  All cows were milked twice a day, once in the morning (0400 hrs.) and once in afternoon (1400 hrs.).  Irrigated Napier (Penisetum pupureum) and Guinea (Panicum maximum) grasses were fresh cut and carried to feed all animals.  However, the quantity and quality of these green chops was variable and changed from season to season depending on the weather in a particular year.  During the dry season, milking cows were maintained on Ruzi (Brachiaria ruziziensis) pastures after the morning milking.  Mineral blocks were provided as supplement ad libitum.  Animals were fed 8 kg of a concentrate made at the research station using local grains, crop-residues, modified-rice straw, molasses, vitamins, and minerals.

All animals in the herd were treated against internal (IVOMECâ, ABENDAZOLEâ) and external parasites (BARICATEâ) every six months.  Breeding age and younger heifers were vaccinated against viral (e.g. Foot and Mouth Disease, Hemorrhagic Disease) and bacterial (e.g. Hemophilus sp, Leptospirosis sp) diseases annually beginning at six months of age.  The parasite control and vaccination program used in the HF-RS multibreed herd followed the guidelines given by the Department of Livestock Development of Thailand (SARTC, 1999).

Cows were mated throughout the year to maintain a minimum level of total amount of milk produced per day.  Qualified personnel observed signs of estrous behavior daily. Animals were inseminated up to three times.  Cows were palpated by a veterinarian 60 d after the last insemination.  Open cows were placed with a Holstein or a Red Sindhi clean up bull according to the mating plan.  There were 2 Holstein Friesian and 2 Red Sindhi clean up bulls available every year.  Pregnant cows were dried off two months before calving.

 

Table 1. General description of the data set

 

 

HF

1/2HF-1/2RS

3/4HF-1/4RS

Total

Cows

75

8

5

88

Lactations

88

13

5

106

   First lactations

18

4

5

27

   Second lactations

43

6

-

49

   Third lactations

9

3

-

12

   Fourth and more lactations

18

-

-

18

Number of observation (daily yields)

23,986

2,972

1,494

28,452

 

Models and Data Analysis

Genetic evaluation models require the construction of contemporary groups where comparisons among predicted genetic values of animals for traits of economic importance can be made in a fair manner.  For this Thai data set, one such contemporary group is the subclass formed by cows from the same breed group x calving age group x lactation number x calving season subclass.  Unfortunately, preliminary analyses showed that it was unfeasible to use these subclasses because 56% of them were either empty or had a single lactation.  Consequently, two larger subclasses were defined: 1) breed group x lactation x calving season, and 2) breed group x lactation x calving age.  The data set yielded 20 breed group x lactation x calving season subclasses, and 13 breed group x lactation x calving age subclasses.  Analyses were conducted separately for each one of the breed group x lactation x calving season and the breed group x lactation x calving age subclasses. 

Lactation curves were constructed using means of individual cow daily milk yields (5 to 305d) within each subclass.  Means of daily milk yields within breed group x lactation x calving season and breed group x lactation x calving age subclass were plotted using Microsoft Excel 2000 (Dodge and Stinson, 1999).

Daily milk yields (5 to 305 d) for individual cows were predicted using each of the seven equations used to model lactation curves within each subclass.  The predictive ability of these seven equations was tested using deviations of predicted minus actual daily milk yields within lactations.  Least squares means of daily deviations of predicted minus actual daily productions were computed for each breed group x lactation x calving season and breed group x lactation x calving age subclass.  To evaluate the predictive ability of the seven models, least squares means of differences between predicted and actual daily milk yields were tested (t-test) for their difference with respect to zero, and for differences between lactation models.  The statistical model used was:

 

            dijkl = + subclassi + modelj + cowk + eijkl

where

dijkl             =    difference between predicted and actual milk production in lactation day j of cow k within subclass i and model j,

               =    overall mean,

subclassi     =    ith breed group x lactation x calving season or breed group x lactation x calving age,

modelj         =    jth prediction model,

cowk          =    kth cow,

eijkl             =    residual.

 

All effects in the model were assumed to be fixed, except for the residual term that was assumed to be independent, identically distributed with mean zero and a common variance.  Because a cow will be in each subclass type, separate computations were done for breed group x lactation x calving season and breed group x lactation x calving age subclasses. 

Individual cow actual and predicted 100-d and 305-d milk yields were compared to evaluate the performance of the seven models to predict milk yield for two traits of economic importance used in genetic evaluation of dairy cattle.  Least squares means of 100-d and 305-d differences between predicted and actual milk yields were also computed for each breed group x lactation x calving season and breed group x lactation x calving age subclass for comparison purposes. These subclass deviations were used to assess (t-tests) the ability of the seven models to predict 100-d and 305-d milk yields.  The statistical model used was:

 

dijk = + subclassi + modelj + eijk

where

dijk              =    difference between predicted and actual milk production of cow k at 100-d or at 305-d of lactation, within subclass i and model j,

               =    overall mean,

subclassi     =    ith breed group x lactation x calving season or breed group x lactation x calving age,

modelj         =    jth prediction model,

eijkl             =    residual.

 

All effects in the model were assumed to be fixed, except for the residual term that was assumed to be independent, identically distributed with mean zero and a common variance.  Separate computations were done for breed group x lactation x calving season and breed group x lactation x calving age subclasses.

Models that had smaller differences between predicted and actual milk yields within breed group x lactation x calving season and breed group x lactation x calving age subclasses were considered to have better predictive ability.

The seven mathematical models used here were as follows.

Model 1:  Wood gamma function (Wood, 1967),

                                                                                         [1]

where yt  is the milk yield on day t in each subclass, a is the initial yield of lactation, b represents the increasing slope, and c represents the decreasing slope.  Because nonlinear regression does not guarantee convergence (SAS, 1990), natural logarithms were taken on both sides of equation [1] giving           

                                                               

where  is the residual. The predicted yield on day t (yt) was computed as yt = exp (ln yt).

Model 2: mixed log second-degree polynomial model of milk yield on day in lactation and log of day in lactation (linear and quadratic), of Ali and Schaeffer (1987),

                                        [2]

where yt  is the milk yield on day t in each subclass,  = t /305, = ln(305/ t), t = days since calving or days in milk, b0, b1, b2, b3, and b4 are the regression coefficients where b0 is associated with peak yield, b3 and b4  the increasing slope of the curve and b1 and b2 are associated with the decreasing slope; and et is the residual.

Models 3, 4, 5, 6 and 7: second, third, fourth, fifth, and sixth polynomial regression models, respectively,

Model 3:                                                       [4]

Model 4:                                            [5]

Model 5:                                  [6]

Model 6:                       [7]

Model 7:            [8]

where yt  is the milk yield on day t in each subclass, t = days since calving or days in milk, b0, b1, b2, b3, b4, b5 and b6 are coefficients, and et is the residual.

Estimates of regression coefficients for models 1 through 7 were obtained using PROC REG of the SAS program (SAS, 1990).  This program was also used to compute predicted daily milk yields (5 to 305 d) for all models. 

Individual cow actual milk yields at 100-d and 305-d, predicted minus actual milk yield daily deviations, and predicted 100-d, and 305-d milk yield deviations were computed using the general SAS program (SAS, 1990).  Least squares means of milk yield deviations per subclass were obtained using LSMEANS statement of PROC GLM (SAS, 1990).

Predicted means of daily milk yields per breed group x lactation x calving season and breed group x lactation x calving age subclass using the seven models above were drawn using Microsoft Excel 2000 (Dodge and Stinson, 1999).  These lines were compared with the corresponding lines of daily milk yields within subclasses.

 

 

Results and Discussion

 

Actual Lactation Curves

Plots of actual lactation curves showed that the shape of actual lactation curves varied across breed group x lactation x calving season and breed group x lactation x calving age subclasses.  Lactation curves were classified into four types according to the pattern of milk production from day 5 to 305.  Type 1: milk production increased continuously from the beginning of lactation, it reached a peak between 50 to 70 d of lactation, then it decreased until the end of the lactation (convex line); type 2:  milk production peaked before 30 d of lactation, then it steadily decreases to the end of lactation (slightly convex line); type 3:  milk production peaked twice, one between 30 to 70 d of lactation, and another between 180 and 210 d of lactation (double peak line); and type 4:  milk production remained fairly constant throughout the lactation (flat line).

 

Breed group subclasses.   First lactation curves of HF cows were of type 2, their milk production increased after calving to reach a small peak around 30 d of lactation, and then it decreased until the end of their lactations.  Crossbred 1/2HF-1/2RS cows had flat lactation curves (type 4), and 3/4HF-1/4RS cows had type 1 lactation curves, with a peak in milk production at about 75 d of lactation.

 

Figure 1.  Means of first lactation curves of HF, 1/2HF-1/2RS, and 3/4HF-1/4RS cows that calved at ages equal to or greater than 30 mo

 

Figure 1 shows means of first lactation curves of HF, 1/2HF-1/2RS, and 3/4HF-1/4RS cows that calved at ages equal to or greater than 30 months.  The mean peak milk yield of HF cows (14.2 kg at 37 d in milk) was lower than that of 3/4HF-1/4RS cows (17.3 kg at 65 d in milk), but higher than the one from 1/2HF1/2RS cows (13.2 kg at 5 d in milk).  The shape of the mean of lactation curves of 1/2HF1/2RS cows was flatter than those of HF and 3/4HF-1/4RS in this calving age subclass.

Tekerli et al. (2000) indicated that Holstein cows with flat lactation curves would be expected to show higher persistency and higher milk yields per lactation.  However, when comparing cows across breed groups this may not be the case.  Here (Figure 1), the pattern mean lactation curves of 1/2HF-1/2RS cows that calved at ages equal to or greater than 30 months was flatter than that of HF and 3/4HF-1/4RS cows, however, they had lower total 305-d milk yields. The means of 305-d milk yields of first lactations of HF, 1/2HF-1/2RS, and 3/4HF-1/4RS cows that calved at ages equal to or greater than 30 months were 2,723.6, 2,014.5 and 3,579.0 kg, respectively.  Milk production in these three groups was clearly related to the fraction of Holstein genes.  Higher fractions (HF, and 3/4HF-1/4RS) produced more milk than 1/2HF-1/2RS.  The 3/4HF-1/4RS group of cows produced more milk than purebred Holstein cows probably due to the inability of Holstein cows to cope with the environmental conditions (heat, humidity, internal and external parasite load) at the SARTC farm in Thailand.

The results obtained here reconfirmed those obtained in previous studies conducted at SARTC.  SARTC (1999) reported that HF raised under Northeastern conditions of Thailand needed more veterinary care than HF x RS crossbred cows because of environmental stresses and tropical diseases.  The F1 (1/2HF-1/2RS) cows were healthier, but had lower milk production than HF and 3/4HF-1/4RS.  Crossbred 3/4HF-1/4RS and higher HF fraction (up to 87.25 %HF) cows produced more milk than 1/2HF-1/2RS and HF cows (SARTC, 1999).

Later lactations in HF cows had similar patterns of lactation curves to the first lactation, except that they had higher peak yields.  On the other hand, the shape patterns of later lactation curves of 1/2HF-1/2RS cows were different from those of their first lactations. Later lactations of 1/2HF-1/2RS cows were of type 2 (slightly convex) instead of type 4 (flat). In all breed groups initial and peak milk yield increased from lactation 1 to 3.

 

                       

 

Figure 2.  Means of lactation curves of various lactation numbers in HF cows that calved in summer (a), and in 1/2HF-1/2RS cows that calved in winter (b)

 

Figures 2a and 2b contain examples of the types of lactation curves found in the HF-RS herd of this study.  Figure 2a shows that the means of first lactation curves of HF cows that calved in summer had lower initial (12.5 kg) milk productions than those of second (17.1 kg), third (20.8 kg), and fourth-and-later (15.5 kg) lactations.  All these lactations were of type 2; they had a short initial increase in milk production, reached a peak yield within the first month of lactation, and then decreased at various rates depending on the lactation number until 305 d.  The mean peak yield of first, second, third, and fourth-and-later lactations cows were 14.6 kg (at 10 days in milk), 18.96 kg (at 10 days in milk), 24.2 kg (at 23 days in milk), and 16.6 kg (at 8 days in milk), respectively. 

The means of first lactation curves of 1/2HF-1/2RS cows that calved in winter (Figure 2b) were similar to those of HF cows.  They had an initial milk yield (12.2 kg) that was lower than that observed for second (12.7 kg) and third lactations (16.9 kg).  The mean peak yield in the first lactation of 1/2HF-1/2RS cows (12.5 kg at 7 days in milk) was also lower than that in the second (16.0 kg at 17 days in milk) and in the third lactation (20.4 kg at 18 days in milk).  Comparison of first and later lactations could not be done with 3/4HF-1/4RS cows because they had only first lactation records.

Mean peak yields were lower and were reached earlier in the first lactation because cows needed to devote a substantial portion of their nutritional intake to their growth and development. 

Because 1/2HF-1/2RS mature earlier than HF cows (4 years vs. 5 years; SARTC, 1999), nutritional requirements allocated to growth and development during the second lactation were probably lower for 1/2HF-1/2RS than for HF cows.  Thus, 1/2HF-1/2RS probably utilized more nutrients for milk production than HF cows, resulting in longer peak yield times for 1/2HF-1/2RS animals.  The degree of maturity of 1/2HF-1/2RS and HF cows was probably similar at the third lactation, thus mean peak yields were achieved at similar days.  Mean peak yield would decrease as cows get older and less productive (SARTC, 1999), as found here for fourth-and-later-lactation HF cows.

 

Calving age subclasses.  The patterns of shape of lactation curves of older calving ages within lactation number were similar to those of the younger calving ages within lactations.  Older cows of all breed groups had type 2 lactation curves; milk production increased after calving for a short time, reached a peak in less than a month, and then steadily decreased until 305 d.

Plots of means of first lactation curves in Figure 3 show that HF cows that calved at less than 30 months of age (12.3 kg at 51 days in milk) had peak yields slightly lower than those of cows calved at ages equal to or greater than 30 months (13.4 kg at 25 days in milk).  The difference in peak yield between younger and older cows in the first lactation (1.1 kg) was smaller than that in the second lactation (4.4 kg), and in the third lactation (5.3 kg).  In addition, younger cows had flatter lactation curves than older cows in all lactations.  In contrast, 3/4HF-1/4RS cows calving at less than 30 months of age had peak yields (17.0 kg at 75 days in milk) higher than those of cows that calved at ages equal to or greater than 30 months (16.1 kg at 65 days in milk).  Differences in daily milk production and peak yields translated in an advantage of approximately 200 kg milk for later lactations over first lactations in HF cows, and of about 100 kg in 3/4HF 1/4RS cows.  These small differences suggest that it might be advantageous to breed cows to calve at younger ages within lactations, provided adequate feed is available.  An additional advantage would be a potential longer herd life of younger calving cows.

 

                       

 

Figure 3.  Means of first lactation curves of HF (a) and 3/4HF-1/4RS (b) cows that calved at less than 30 months, and equal to or greater than 30 months of age

 

Calving season subclasses.  Cows calving in different seasons had different types of lactation curves. The HF cows that calved in winter had lactation curves of type 2 (convex lactation curve), while cows that calved in summer were of type 3 (two peaks per lactation), and cows that calved in the rainy season had lactations of type 4 (flat lactation curve).  Examples of the types of lactation curves by calving season are shown in Figure 4.  The initial yield of lactation of HF cows calved in the rainy season (7.5 kg) was lower than that of HF cows calved in winter (10.6 kg), and summer (12.5kg). The peak yield of the first lactation of HF cows that calved in the rainy season (11.5 kg) was lower than that of cows that calved in winter (14.2 kg), and summer (14.6 kg). 

 

                       

 

Figure 4.  Means of lactation curves of first lactation HF (a) and second lactation 1/2HF-1/2RS (b) cows that calved in winter, summer, and in the rainy season

 

Holstein Friesian cows that calved in the rainy season had type 4 (flat) lactation curves with lower initial production and peak yields than cows that calved in winter and summer.  The lower production of HF cows in the rainy season was likely due to the incidence of mastitis,