N .C. Friggens et al. Livestock Production Science 62 1999 1 –13
3 Table 1
forms, has been characterised in terms of statistical
The distribution of lactations according to calving year and parity
performance. Because these models are descriptions
a
Parity Calving year
of potential, the appropriate data against which to evaluate them are; milk yields from cows fed in a
1990 1991
1992 1993
1994 1995
manner likely to result in lactation curves whose
1 8
7 13
12
shapes are characteristic of potential milk product-
2 8
7 13
12
ion. The data used in the present study provided the
3 8
7 13
12
opportunity for such an evaluation.
Total 8
15 28
32 25
12
The first objective of this study was to evaluate the
a
two models Emmans and Fisher, 1986; Dijkstra et
The calving year started on the 1st September in any given year.
al., 1997 in order to determine which should be used in addressing the main objective of this study.
The ability of these models to fit milk yield data was 1994 were not considered in the present study. The
assessed relative to Wood’s function 1967. cows were managed in three groups for feeding
The second, and main, objective of this study was according to days in lactation; less than 100 days
to quantify the effect of parity on the coefficients of early, between 100 and 200 days mid, and greater
a simple, biologically based, model of the lactation than 200 days late. The proportions in total dry
curve and, if possible, to develop simple relation- matter DM of silage, brewers’ grains and concen-
ships between parities in the lactation curve co- trate in the TMRs offered to early, mid and late
efficients thus simplifying the inputs necessary for a lactation cows were; 40:5:55, 50:5:45 and 60:5:35
general model of lactational performance. respectively. The feeding system was designed to
achieve, over a full lactation, average proportions of silage, brewers’ grains and concentrate of 50:5:45 in
total DM. The average DM content oven drying at
2. Materials and methods 808C for 24 h of the early and mid TMRs was 364
and 334 g kg fresh, respectively. The average crude 2.1. Animals, feeding and management
protein content Association of Official Analytical Chemists, 1990 of the early and mid TMRs was 178
Data were obtained from 40 Holstein–Friesian and 176 g kg DM, respectively. The average
cows, each of which had daily milk yield records for metabolisable energy content, estimated from stan-
first, second and third lactations. The cows were dard ME values for the ration ingredients, of the
housed and managed at the Scottish Agricultural early and mid TMRs was 12.2 and 11.9 MJ ME kg
College University of Edinburgh Langhill Dairy DM, respectively. The average NDF content Rober-
Research Centre, Edinburgh, Scotland longitude; 38 tson and Van Soest, 1977 of the early and mid
109 W, latitude; 558 529 N as part of a genotype by TMRs was 372 and 374 g kg DM, respectively.
environment study Veerkamp et al., 1994. Calving Further details of the composition of the TMRs used
occurred between September and January in any in the genotype by environment experiment, and of
given year. The cows were kept indoors in conven- other performance measures made, have been re-
tional cubicle housing from calving through to the ported by Veerkamp et al. 1994.
following July. The distribution of lactations accord- ing to calving year and parity is shown in Table 1.
2.2. Data processing The cows were milked twice daily and received 0.5
kg of a standard dairy concentrate in the milking The full data set for the evaluation of the effect of
parlour at each milking. parity on lactation curve coefficients comprised
All cows included in the data set were offered ad 36 221 daily milk yield records. For the purpose of
libitum a high concentrate total mixed ration TMR deriving lactation curve coefficients, the data from
composed of grass silage, brewers’ grains and con- each lactation of each animal were treated as in-
centrate. Cows offered the low concentrate diet in dependent giving 120 lactations in all. Within each
the genotype by environment study Veerkamp et al., lactation, only milk yield data from calving until 240
4 N
.C. Friggens et al. Livestock Production Science 62 1999 1 –13
days post-calving were used as it has been shown on inspection of the equation of Dijkstra et al. it
that the concurrent pregnancy in lactating dairy cows became apparent that it was an alternative form of
causes a depression in milk yield in the last 18 weeks the model proposed by Emmans and Fisher 1986,
of pregnancy Hooper, 1923; Coulon et al., 1995. as shown below:
Estimation of the lactation curve coefficients, and the let
m k 5 q
T
effect of parity on them, was thus unaffected by pregnancy and drying off. Extremely deviant points
substituting q in the Dijkstra equation gives: were excluded from the data in a two step process
dY dt 5 M ? exp q 2 q ? exp 2kt 2 lt
f g
using a spline fitting procedure with 6 degrees of freedom Genstat
E Version 5.3.2., 1994. First, the spline was fitted to the raw data for each lactation
dY dt 5 M ? exp q ? exp 2 q ? exp 2kt f
g curve and individual milk yields which deviated
? exp2 lt
from the spline by 65 standard deviations were excluded from the data. Second, the spline was fitted
dY dt 5 M ? exp q to the data set which excluded deviant values from
the first spline fitting. Individual milk yields which ? exp 2 exp ln q ? exp 2kt ? exp 2
lt h
f g
j deviated from the second spline by 65 standard
deviations were also excluded from the data. This dY dt 5 M ? exp q ? exp 2 exp ln q 2 kt
h f
g j two step process resulted in the exclusion of, on
? exp 2 lt
average, 0.98 daily milk yields per lactation, the maximum number of data points excluded in any one
This is the Emmans and Fisher 1986 form cow lactation was 6 out of 232.
where: 2.3. Lactation curve coefficients and statistical
M ? exp q 5 a, ln q 5 G , k 5 b and l 5 c
analyses Given that the equation of Dijkstra et al. 1997 is
To determine whether the Dijkstra et al. 1997 or another form of the Emmans and Fisher model
Emmans and Fisher 1986 model should be used in 1986 it could not provide an alternative model
addressing the main objective of this study, the first against which to compare the curve fit of the
objective of this study was to compare them in terms Emmans and Fisher model. For this purpose, the
of their ability to fit data. The two equations are function of Wood 1967 was used:
shown below:
b
dY dt 5 at ? exp2ct
dY dt 5 a exp 2 exp G 2 bt ? exp 2ct
f g
h f
g j
Wood, 1967 Emmans and Fisher, 1986
where: dY dt is milk yield per day, t is days from calving, and a, b and c are the coefficients of the
dY dt 5 M ? exp m 1 2 exp 2kt k 2 lt
f g
h j
T
equation of Wood 1967. The non-linear curve Dijkstra et al., 1997
fitting procedure of Genstat Genstat E Version
where dY dt is milk yield per day, t is days from 5.3.2., 1994 was used to derive coefficients for the
calving, a, G , b and c are the coefficients of the curve of daily milk yield dY dt relative to days
Emmans and Fisher 1986 model, and M , m , k
from calving t for both the Wood’s equation 1967
T
and l are the coefficients of the Dijkstra et al. 1997
and the equation of Emmans and Fisher 1986. model as stated in their Eq. 11. The coefficient
Analysis of parity effects was carried out only on called k in the above equation is that which Dijkstra
the coefficients from the Emmans and Fisher model. et al. 1997 called k , the subscript has been
The effect of parity was quantified by analysis of
2
dropped to avoid confusion with subsequent use of variance with cow and parity within cow included as
numerical subscripts in the present paper. However, a fixed effects Genstat
E Version 5.3.2., 1994. The
N .C. Friggens et al. Livestock Production Science 62 1999 1 –13
5
standard errors S.E.s of each coefficient in the additional covariate in the analysis of variance for
curve fitting procedure were used to weight the parity effects of that coefficient parity data set.
analysis of variance for that coefficient by including
2
1 S.E. as a covariate. Given the uneven distribu- tion of parities across calving years Table 1 it was
3. Results and discussion
