Livestock Production Science 62 1999 1–13 www.elsevier.com locate livprodsci
On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production
a , b
c
N.C. Friggens , G.C. Emmans , R.F. Veerkamp
a
Department of Animal Health and Welfare , Danish Institute of Agricultural Sciences, Research Centre Foulum, P.O. Box 50,
DK- 8830 Tjele, Denmark
b
Animal Biology Division , Scottish Agricultural College, West Mains Road, Edinburgh EH9 3JG, United Kingdom
c
Department of Animal Breeding and Genetics , ID-DLO, P.O. Box 65, 8200 AB Lelystad, The Netherlands
Received 26 October 1998; received in revised form 9 April 1999; accepted 20 April 1999
Abstract
The objective of this study was to quantify how the pattern of milk production relative to time from calving is affected by parity in cows fed high quality rations. For this purpose two models; those of Emmans and Fisher 1986 and Dijkstra et al.
1997, were considered. Comparison with Wood’s 1967 function was made to evaluate their fitting ability. Daily records of milk yield from 40 cows fed a grass silage based, high concentrate total mixed ration were used. The cows had ad libitum
access to food, they were milked twice daily. Each of the cows had milk yield records from calving to 240 days post calving in parities 1, 2 and 3. The model of Dijkstra et al. 1997 was found, on inspection, to be an alternative parameterization of
the Emmans and Fisher model 1986. In the analyses, the Emmans and Fisher form was used: Yield 5 aU exp [2cdays from calving] where U 5 exp h 2 exp G 2 b[days from calving]j. The Emmans and Fisher model 1986 performed
marginally better than the Wood’s function 1967 in terms of percentage of variance accounted for and residual standard error. There was no significant effect of parity on G or b, which are the main parameters describing the evolution of
lactation to peak. However, there was a highly significant effect P , 0.001 of parity on coefficients a, the scalar, and c, the decay coefficient. The coefficient values in parity 1 and 2 were found to be a constant proportion of the values in parity 3.
Parity effects can therefore be described by simple ratios, offering the possibility of simplifying the inputs needed in models to describe potential milk production.
1999 Elsevier Science B.V. All rights reserved.
Keywords : Dairy cows; Lactation; Parity; Model; Milk yield
1. Introduction dairy cows, that is the performance the cow would
achieve if it were not limited by diet or environment, The ability to predict the potential performance of
and thus calculate the energy required to support potential, is important for two reasons. If potential
can be predicted, both relative to days in milk and
Corresponding author. Tel.: 145-8999-1555; fax: 145-8999-
across parities, then rations can be designed that
1500. E-mail address
: n.friggensagrsci.dk N.C. Friggens
capitalise on the genetic ability of the cow. Further,
0301-6226 99 – see front matter
1999 Elsevier Science B.V. All rights reserved. P I I : S 0 3 0 1 - 6 2 2 6 9 9 0 0 1 1 0 - 4
2 N
.C. Friggens et al. Livestock Production Science 62 1999 1 –13
in models that aim to predict the partition of The model of Neal and Thornley 1983 uses five
nutrients between body reserves and milk product- input values to define initial state, and has 14
ion, the potential performance provides the biologi- parameters. The model of Dijkstra et al. 1997 is a
cal basis from which to develop rules for nutrient description of the rates of profileration and death of
partitioning in all feeding situations. The largest mammary cells in simpler, and more general, terms
component of potential, in terms of energy require- than the model of Neal and Thornley 1983 and can
ments, is milk production. be applied to describe the lactation curve using four
It is clear that milk production varies with time, parameters. The model of Emmans and Fisher
´ both within and between lactations Remond et al.,
1986 also uses four parameters. In this model the 1997, though the major focus of studies to char-
growth phase is described by a Gompertz function acterise the temporal patterns of milk production has
Gompertz, 1825; Winsor, 1932 and the declining been on the variation within lactations. There are a
phase by a partial gamma decay first used for substantial number of existing lactation curve models
lactation curves by Brody et al. 1923 and included of varying complexity Nelder, 1966; Wood, 1967;
in the well established model of Wood 1967. The Cobby and Le Du, 1978; Goodall and Sprevak, 1985;
same form was used by France et al. 1985 to Grossman and Koops, 1988; Morant and Gnanasak-
describe faecal marker excretion patterns. thy, 1989 and a number of studies which have
Both the Emmans and Fisher model and the model examined the performance of different models in
of Dijkstra et al. 1997 have two clear advantages terms of their ability to fit milk yield data Rowlands
over the simpler, three-parameter, Wood’s function ´
et al., 1982; Rook et al., 1993; Perochon et al., 1996 1967. The disadvantages of the Wood’s function
b
or give accurate predictions of future yield from part arise from the use of a power function, t , to describe
records Wilmink, 1987; Jones, 1997. However, for the growth phase of lactation. When t 5 0, the
the purpose of predicting potential a high degree of function predicts zero yield. The data used by Wood
flexibility of curve shape and ability to fit environ- 1967 were weekly records which may have made
mentally or nutritionally induced distortions of the the zero intercept seem likely. However, it is clear
underlying curve are not valuable attributes. The key from daily records that cows can have appreciable
attributes of a useful model to describe potential are milk yields at calving as would be expected from the
that it is biologically interpretable and provides the finding that the secretory potential of the mammary
simplest sufficient description of the potential yield gland is well developed at parturition Knight and
b
curve. Both of these attributes are important when it Wilde,
1993. Further,
t does
not have
an comes to subsequently developing modifiers to the
assymptote and so continues to have an effect, potential curve. Development of models to incorpo-
implying continued growth of the gland, throughout rate, in a logical and general manner, effects such as
lactation. Under normal conditions there is no evi- those of parity, pregnancy, limiting nutrition and
dence for this Knight and Wilde, 1993, and from environment depends upon a clear association be-
the point of view of interpreting the model, the decay tween model parameters and the underlying bio-
phase is not simply described but is the consequence
b
logical phenomena Dijkstra et al. 1997. The pro- of two parameters. By replacing the t term with an
cess of extending such a model to accommodate asymptotic function which can have a positive
parity effects provided the impetus for this study. intercept, both the Emmans and Fisher model 1986
The set of lactation curve models which explicitly and the model of Dijkstra et al. 1997 overcome
aim to reflect the underlying biology is a small one these two problems albeit at the cost of an extra
Neal and Thornley, 1983; Emmans and Fisher, parameter.
1986; Dijkstra et al., 1997 though it can be argued Although they are derived from very different sets
that any model which comprises explicit growth and of theoretical assumptions, the models of Emmans
decay phases is biologically interpretable Wood, and Fisher 1986 and Dijksta et al. 1997 would
1977. All of these models, either implicitly Dijk- both appear to satisfy the fundamental criteria for use
stra et al., 1997 or explicitly Neal and Thornley, as biologically interpretable models to describe
1983; Emmans and Fisher, 1986 relate to potential potential milk production. However, neither of these
production. models, which appear to use different functional
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
