=Paper=
{{Paper
|id=Vol-1152/paper50
|storemode=property
|title=Comparison of Models for Describing the Lactation Curves of Chios Sheep Using Daily Records Obtained from an Automatic Milking System
|pdfUrl=https://ceur-ws.org/Vol-1152/paper50.pdf
|volume=Vol-1152
|dblpUrl=https://dblp.org/rec/conf/haicta/KarangeliAKMG11
}}
==Comparison of Models for Describing the Lactation Curves of Chios Sheep Using Daily Records Obtained from an Automatic Milking System==
https://ceur-ws.org/Vol-1152/paper50.pdf
Comparison of models for describing the lactation
curves of Chios sheep using daily records obtained from
an automatic milking system
M. Karangeli1, Z. Abas2, T. Koutroumanidis3, C. Malesios4, C. Giannakopoulos5,
1
Democritus University of Thrace, Department of Agricultural Development, GR-68200
Orestiada, Greece, e-mail: mkar_2001@yahoo.com
2
Democritus University of Thrace, Department of Agricultural Development, GR-68200
Orestiada, Greece, e-mail: abas@agro.duth.gr
3
Democritus University of Thrace, Department of Agricultural Development, GR-68200
Orestiada, Greece, e-mail: tkoutrou@agro.duth.gr
4
Democritus University of Thrace, Department of Agricultural Development, GR-68200
Orestiada, Greece, e-mail: malesios@agro.duth.gr
5
Veterinarian, Volos, Greece
Abstract. The objectives of this study were: (i) to compare five models
(Wood, Cobby & Le Du, Wilmink, Cappio Borlino, Djikstra) for describing
the lactation curve of Chios sheep, (ii) to identify variation in lactation
parameters related to environmental factors (season) and animal factors
(parity). A data base on 61,705 recordings of daily milk production obtained
from an automatic milking system was used. The lactation models were
individually adjusted for each lactation. Analysis of variance was performed
for the comparison of the parameter estimates. The goodness of fit measures
used for comparisons of the models was the coefficient of determination (R2),
mean of mean square error (MMSE), Akaike information criterion (AIC),
corrected Akaike information criterion (AICc) and Bayesian information
criterion (BIC). Wood model had the lowest values for information criteria
(MMSE = 347.4681, AIC = 1,056.436, AICc = 1,056.733, BIC = 1,063.856)
and the highest value for the coefficient of determination (R2=0.79). The
highest values for information criteria were found for Djikstra’s model
(MMSE = 636.6438, AIC = 1,076.621, AICc = 1,077.117, BIC = 1,086.582)
having the same time the lowest value for the coefficient of determination
(R2=0.59). Overall, Wood (1967) model showed the best adjustment. Despite
of being more recent, the model by Djikstra (1997) mechanist based and with a
higher number of parameters showed a low convergence for the data used.
Wood model (1967) has a greater advantage of producing a good fit
measurement with only three parameters.
Keywords: lactation curve, Chios sheep, daily milk yield, environmental
effects
571
1. Introduction
The term lactation curve refers to a graphic representation of the ratios between
milk production and lactation time (Sherchand et al., 1995). Equations that describe
milk production in time provide summary information, which is useful in making
management (nutrition) and breeding (culling) decisions, in simulating dairy
enterprise and in genetic breeding programs.
The lactation curve is also important because its wide characterization of the
animal production throughout lactation allows to estimate the peak yield, the time of
peak, days in milk, the total milk yield (Ferreira & Bearzoti, 2003).
There is a lack of studies on the complete lactation of dairy sheep and this is partly
due to the fact that in most dairy sheep production systems, lambs are allowed to
suck for at least 30 days post lambing and milk recording starts only after the
weaning. However, in some dairy sheep flocks operated under intensive
management, the common practice is to milk the ewes from the start of the lactation.
Lambs are moved from their mothers at lambing into an artificial rearing unit. To
study the lactation curve of dairy sheep, several papers dealt specifically with the
application of Wood’s (1967) model to various sheep breeds (Torres-Hernadez and
Hohenboken, 1980, Cappio-Borlino et al, 1989, Sakul and Boylan, 1992,
Groenewald et al, 1995, 1996, Portolano et al, 1996a). The first attempts to
mathematically represent the lactation curve were made by Brody et al. (1923) and
Brody et al. (1924). However, only after the development of the model of the Wood
(1967) did the use of lactation curve models become more popular. Since then, many
researchers have attempted to develop lactation curve models from empirical
conceptions (Cobby Le Du, 1978, Wilmink, 1987, Cappio Borlino et al, 1995) or
mechanist conceptions (Djikstra et al, 1997). The major limitations of the Wood
curve are the poor fit especially around the lactation peak (Cobby Le Du, 1978) and
the large margin of error for the estimation of total milk yield. On the other hand
Wood (1967) model has the advantage of estimating three parameters a, b, c which
can easily be linked to the biology of the lactation curve. This has rendered the Wood
(1967) model the most widely used function for the description of the lactation
phenomenon. Advances in modeling, however, provided models which represent
biological processes occurring in the mammary gland. Djikstra et al. (1997)
developed a mechanistic model that describes proliferation and death of mammary
gland cells during pregnancy and lactation. The mechanistic representation provides
an understanding of factors controlling the variation in milk production throughout
lactation that cannot be attained with most empirical models. However, greater
complications arise when using a mechanistic model. For instance, non-limited
supply of nutrients to the mammary gland needs to be assumed for simplification.
The objectives of the current study were to compare five models (Wood, Cobby &
Le Du, Wilmink, Cappio Borlino, Djikstra) for describing the lactation curve of
Chios sheep and to identify effects of season and parity on the lactation curve
parameters.
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2 Materials and methods
Database
The data used in the current study consist of 61705 recordings of daily milk
production of a Chios sheep herd obtained from an automatic milking system. The
first milk recording was between 10 and 40 days after parturition, minimum and
maximum lactation lengths were 101 and 260 days. In this flock, for a period of time
lambs were weaned immediately after parturition but then due to the high mortality
rates, lambs were suckled by their mother and weaning was on average 40 days after
parturition. The data were ranked according to the lactation number, into first,
second, third or greater.
Lactation models
Five models were used in the current study to describe lactation curves. The
models are: Wood (1967), Cobby & Le Du (1978), Wilmink (1987), Cappio Borlino
(1995) and the mechanist based model by Djikstra (1997). Wood’s equation is:
y = a t be – c t (1)
Where y is milk production (gr/day) at time t of lactation (days), and a, b and c are
parameters that determine the shape and scale of the curve. The parameter a is related
to the milk yield after parturition, b is the inclining slope parameter and c is the
declining slope parameter.
The Cobby & Le Du model is:
y = a-bt – ae – c t (2)
Where y is milk production (gr/day) at time t of lactation (days), and a, b and c are
parameters that determine the shape and scale of the curve. The parameter a is related
to a milk yield, b is the inclining slope parameter and c is the declining slope
parameter.
Wilmink’s equation is:
y = a - be – k t -ct (3)
Where y is milk production (gr/day) at time t of lactation (days), and a, b and c are
parameters that determine the shape and scale of the curve. The parameter a is related
to the level of the milk production, b is the milk yield before peak and c is the
declining slope parameter, k is related to peak day of peak milk yield.
The Cappio Borlino model is:
y = a n be – c n (4)
Where y is milk production (gr/day) at time t of lactation (days), and a, b and c are
parameters that determine the shape and scale of the curve. The parameter a is related
to the milk yield after parturition, b is the inclining slope parameter and c is the
declining slope parameter.
Dkjikstra’s equation is:
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y= m*exp[(m1/k’)(1-exp(-k’*t))-l*t] (5)
Where m is the initial rate of milk production (gr/day) at parturition. The
parameters m1 and l are defined as the specific rates of secretory mammary cell
proliferation at parturition and of death respectively, k’ is a decay parameter
associated with reduction in cell proliferation capacity with time.
Statistical analysis
The models were fitted by non-linear regression to the data described above using
PROC NLIN statement of the statistical package SAS (SAS 1999). This non linear
regression method is preferred to that of log-linear transformation, because the
reduction of weighting of higher yields when using the log scale may lead to a
greater lack of fit around the peak (Cobby & Le Du, 1978). Estimates of the
parameters of each of the models were obtained for each individual lactation curve.
For each model were calculated the typical characteristics of the lactation curve, peak
day, peak milk yield and total milk yield. Cluster analysis was used to investigate the
nature of the lactation curves in each model. Analysis of variance was performed for
the comparisons of the parameter estimates between seasons and number of
lactations. Based on information theory, several methods have been developed for
comparing models, determining which model is more likely to be correct for
describing the used data. The mean of mean square error (MMSE) was calculated as:
MMSE=(1/N)*(MSE) (6)
Where N is the number of animals and MSE is the mean square error.
Akaike information criterion (AIC) was calculated as
AIC=Nln(RSS/N)+2K (7)
Where RSS is the residual sum of squares, N is the number of data points and k is
the number of independent parameters of the model (Burnham & Anderson, 2002,
Motulsky & Christopoulos 2003).
With data sets without a large number of data points (N) or for models containing
more parameters the corrected AICC is more accurate:
AICc=AIC+2k(k+1)/Ν(Ν+1) (8)
Bayesian information criterion (BIC; Leonard & Hsu 2001) is a model order
selection criterion and imposes a penalty on more complicated models for inclusion
of additional parameters:
BIC = N*N ln(RSS/N)+K*ln(N) (9)
A small numerical value of MMSE, AIC, AICc, BIC indicates a better fit when
comparing models.
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Table 1. Number of lactations with the smallest information criteria for each model
Cappio Cobby &
Wood Djikstra Wilmink
Borlino Le Du
Number of lactations with the
153 21 43 86 47
smallest AIC
Number of lactations with the
186 25 22 97 20
smallest BIC
Number of lactations with the
124 19 60 71 76
smallest MSE
Table 2. Information criteria for each model
Convergence
2
Model MMSE AIC AICC BIC R Percentage
(C %)
Wood 347.4681 1,056.436 1,056.733 1,063.856 0.79 82.1
Cobby 457.9985 1,076.762 1,073.041 1,084.2278 0.78 77.3
Cappio 423.5469 1,076.931 1,073.2102 1,084.386 0.76 81.01
Wilmink 530.7866 1,087.444 1,082.9083 1,097.423 0.79 63.5
Djikstra 636.6438 1,076.621 1,077.117 1,086.582 0.59 53.5
575
3000
2500
Milk Yield (gr/day)
2000
1500
1000
500
0
1
20
39
58
77
96
115
134
153
172
191
210
229
Tim e since parturition (days)
Fig.1. The plot of the average lactation curve for Cobby & Le Du Model.
3000
2500
Milk yield (gr/day)
2000
1500
1000
500
0
0 50 100 150 200 250
Tim e since parturition (days)
Fig.2. The plot of the average lactation curve for Wilmink Model.
3000
2500
Milk yield (gr/day)
2000
1500
1000
500
0
1
20
39
58
77
96
115
134
153
172
191
210
229
Time since parturition (days)
Fig.3. The plot of the average lactation curve for Djikstra Model.
576
3500
3000
Milk yield (gr/day)
2500
2000
1500
1000
500
0 24
47
70
93
116
139
162
185
208
231
254
277
1
Time since parturition (days)
Fig.4. The plot of the average lactation curves of two clusters for Cappio Borlino Model
(cluster 1 solid line, cluster 2 dashed line).
3000
2500
Milk yield (gr/day)
2000
1500
1000
500
0
106
127
148
169
190
211
232
253
274
1
22
43
64
85
Time since parturition (days)
Fig.5. The plot of the average lactation curves of two clusters for Wood Model (cluster 1 solid
line, cluster 2 dashed line).
577
Table 3. Cluster Analysis for Cobby & Le Du model
Time of peak
a b c
Yield
Cluster Mean Mean Mean Mean
1 2,830.8497 11.6251 0.1706 31
Table 4. Cluster Analysis for Wilmink model
Time of peak
a b c k
yield
Cluster Mean Mean Mean Mean Mean
1 3,145.3152 2,670.9527 13.3077 0.0746 38
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Table 5. Cluster Analysis for Djikstra model
Time of peak
m m1 k l
yield
Cluster Mean Mean Mean Mean Mean
1 1,301.6837 0.0805 0.0506 0.0131 40
3 Results
Some lactations were well-fitted and others poorly fitted by each of the models
examined. Information criteria (MMSE, AIC, AICC, BIC) confirmed the comparison
between models. Wood model was superior in fitting the Chios sheep lactation
curves showing smaller MMSE, AIC, AICc, BIC (Table 2) based on the average
values of information criteria. For more than half of the Chios sheep lactation curves
BIC criterion values were lower than those of the rest of the models (Table 1). This
indicates that the Wood model provided a better fit than the others for over the half
of the lactation curves. It was considered not converged each lactation curve model
that completed 100 iterations without reaching the reduction of the sum-of-squares-
error (SSE) or whose parameters converged to unreal values. The percentage in each
lactation curve model was calculated. Djikstra’s model showed the worst
convergence percentage for the used data. Wood’s model had the higher convergence
percentage and then follows the Cappio Borlino model. This was expected because
Cappio Borlino’s model is a non-linear modification of Wood’s model. Problems of
convergence have been previously reported for the models by Rook et al. (1993),
(Perochon et al., 1996, Vargas et al., 2000) and Pollot (2000), Val-Arreola et al.,
(2004). The coefficient of determination (R2) also showed a higher value for the
Wood model and the Wilmink equation. This result revealed that the Wood model
provided a better fit to lactation curves. Although the model by Wilmink presented a
good coefficient of determination the values of MMSE, AIC, AIC C, BIC were high
and also showed a lower convergence percentage.
Having established that the fit of the Wood model is the best for the used data
cluster analysis was performed in order to investigate the behavior of the lactation
curves. For the models Cobby & Le Du, Wilmink, Djikstra cluster analysis detected
no differences in the behavior of the lactation curves (Table 3, Table 4, Table 5). The
results showed that in these three models the lactation curves showed similar
behavior with mean parameter values as seen in Tables 3, 4, 5. The plots of the
average lactation curves for the three above models are presented in figures 1, 2, 3.
Cluster analysis for the models Cappio Borlino and Wood detected difference in the
579
behavior of the lactation curves. The results are shown in Tables 6 and 7. The plots
of the average lactation curves of the two clusters are presented in figures 4 and 5. At
Cappio Borlino model the animals of the first cluster start with a lower initial milk
yield and reach their peak 2-3 weeks later. The animals of the second cluster start
with a higher initial milk yield reach their peak earlier and have a lower decreasing
rate c. At Wood model the animals of the first cluster have lower initial milk yield
reach their peak about three weeks later comparatively with the animals of the second
cluster which have a higher initial milk yield and reach a higher peak milk yield.
Peeters et al. (1992), Cappio Borlino et al. (1995) noted that ewes with high milk
yield at the beginning of the lactation had a significant reduction of their production
due to a genetic effect. Katsaounis and Zygogiannis (1984b) formulated that lactation
curve is significantly influenced by the genotype of the ewes. It is very possible that
the variation in the behavior of the lactation curves in the used data is due to the
differences in the genotype of the animals.
Along with the comparison of information criteria values for all models it is
necessary to examine the pattern of the residuals. Lactation data were combined to
give a mean lactation curve for all data. Plots of residuals (resulting from comparing
the fitted curves against the observed experimental values) are shown in Figures 6, 7,
8 and 9. The latter Figures clearly indicate a better fit by the Wood model than others
demonstrating smaller and more randomly distributed residuals (Figs 6, 7, 8, 9).
Analysis of variance was performed for the comparisons of the parameter
estimates, time of peak, peak milk yield and total milk yield between seasons and
number of lactations for the Wood model which is the best model to describe our
data. The data were ranked according to the lactation number, into first, second, third
or greater and according to the season of lambing into winter (season 1), spring
(season 2), summer (season 3) and autumn (season 4). Results are shown in Tables 8
and 9. The analysis of variance shows that season effects significantly the initial milk
yield a (P<0.01) of the animal. The initial milk yield a for the animals of the two
clusters has a greater value in winter. The animals of the second cluster start with a
higher initial milk yield reach their peak two to three weeks earlier and have a higher
total milk yield. Parameter b (P<0.01) is lower for the animals lambing in winter.
The decreasing rate of milk yield c (P<0.01) is lower for the animal lambing in
winter. A lower value of parameter c denotes a higher persistency in lactation. The
number of lactation has significant influence in the parameters and in the typical
characteristics of the lactation curves. Parameters a (P<0.05), b (P<0.01), peak milk
yield (P<0.01), total milk yield (P<0.01) have the tendency to increase in second and
decrease in the following lactations. Parameter c (P<0.01) has the tendency to
increase with the number of lactations. The animals of the first lactation reach their
peak later comparatively with later lactations.
580
Table 6. Cluster Analysis for Cappio Borlino model
Time of peak
a b c
yield
Cluster Ν Mean Mean Mean Mean
1 162 212.4825 0.9079 0.0059 46
2 124 705.5924 0.5514 0.0123 27
Table 7. Cluster Analysis for Wood model
Time of peak
a b c
yield
Cluster Ν Mean Mean Mean Mean
1 143 469.9499 0.5713 0.0125 46
2 147 1,330.144 0.2868 0.0108 26
581
150
100
Residual (gr/day)
50
0
0 5 10 15 20 25 30 35
-50
-100
-150
-200
Tim e since parturition (w eeks)
Fig.6. The residual plot for: Wood model (•), Cobby and Le Du model (◦).
200
150
100
Residual (gr/day)
50
0
0 5 10 15 20 25 30 35
-50
-100
-150
-200
Tim e since parturition (w eeks)
Fig.7. The residual plot for: Wood model (•), Cappio Borlino model (◦).
582
200
150
100
Residual (gr/day)
50
0
-50 0 5 10 15 20 25 30 35
-100
-150
-200
-250
Tim e since parturition (w eeks)
Fig.8. The residual plot for: Wood model (•), Wilmink model (◦).
250
200
150
100
Residual (gr/day)
50
0
-50 0 5 10 15 20 25 30 35
-100
-150
-200
-250
-300
Tim e since parturition (w eeks)
Fig.9. The residual plot for: Wood model (•), Djikstra model (◦).
583
Table 8. Parameters and estimates of the Wood model (Cluster 1) for the data
Wood
(1967) a b c Pday PY TY
Cluster 1
581.71297 0.4802 0.0108 44 2,007.909 291,941.1877
Season 1
(48.2602) (0.0426) (0.0007) (2) (117.9499) (17,418.0397)
396.6664 0.611 0.0116 53 2,156.6187 318,768.4752
Season 2
(30.6201) (0.027) (0.00045) (1) (74.8368) (11,051.388)
516.0028 0.5633 0.01344 42 2,278.521 307,230.3048
Season 3
(30.0631) (0.02658) (0.00044) (1) (73.4754) (10,850.3495)
478.213 0.5895 0.0142 41 2,337.3908 309,210.5243
Season 4
(38.8608) (0.0343) (0.0005722) (2) (94.9774) (14,025.6112)
No 460.3654 0.5473 0.0107 50 2,001.1615 299,531.051
lactation 1 (30.6854) (0.0271) (0.0004) (1) (74.9963) (11,074.9456)
No 526.5262 0.5753 0.0134 43 2,396.3517 325,904.06829
lactation 2 (41.7315) (0.0369) (0.00061) (2) (101.9935) (15,061.7088)
No 492.5548 0.5604 0.0134 41 2,187.8165 294,927.7498
lactation 3 (25.2103) (0.0222) (0.00037) (1) (61.6149) (9,098.8792)
1
Values in parenthesis = standard deviation.
a, b, c, = parameters of the Wood model, PY = peak milk yield , Pday = Peak day, TY = total
milk yield
Table 9. Parameters and estimates of the Wood model (Cluster 2) for the data
Wood
(1967) a b c Pday PY TY
Cluster 2
1,474.2059 0.2303 0.0089 26 2,448.8119 340,085.1043
Season 1
(63.6863) (0.018) (0.0005) (1) (73.4418) (11,090.9179)
1,028.6415 0.3436 0.0108 31 2,429.6752 332,038.5337
Season 2
(99.4689) (0.0282) (0.00082) (2) (114.7056) (17,322.4357)
1,362.07084 0.2733 0.01162 23 2,450.0601 304,214.8992
Season 3
(72.4404) (0.0205) (0.0006) (1) (83.5369) (10,085.2688)
1,267.6736 0.2867 0.01079 26 2,460.165 319,155.1797
Season 4
(74.7357) (0.0212) (0.0006) (1) (86.1837) (13,015.1623)
No 1,375.2912 0.2106 0.009 23 2,168.12461 292,155.2798
lactation 1 (96.7763) (0.02745) (0.0008) (2) (111.6005) (16,853.5172)
No 1,434.8362 0.3324 0.0109 30 2,628.4687 353,573.3822
lactation 2 (73.6961) (0.0209) (0.00061) (1) (84.9849) (12,834.1276)
No 1,285.3165 0.3074 0.01158 26 2,544.941 325,891.6257
lactation 3 (46.7921) (0.0132) (0.00038) (1) (53.9598) (8,148.8196)
1 Values in parenthesis = standard deviation.
a, b, c, = parameters of the Wood model, PY = peak milk yield , Pday = Peak day, TY = total
milk yield
4 Discussion
Over the years, Wood’s equation has been the standard model to describe the
lactation curve of animals. Wood in 1977 tried to integrate the rate parameters of this
584
empirical model with the processes of proliferation and death of mammary gland
cells. The Wood (1967) model was generally found to be of statistically better fit
than other’s equations. The animals of the second cluster have a lower value of
parameter c. This means that persistency is higher. Animals with a more persistent
lactation curve may be less stressed, have better feed utilization efficiency and less
nutrition related diseases than animals with a less persistent lactation curve. Also,
differences in persistency between animals of two clusters may exist because of
genetic selection (Shanks et al., 1981).
In most mammals there is a tendency for the amount of milk produced to increase
with successive lactations up to a certain age and thereafter to decline. This is also
observed to our data. Those who have studied the effect of age on milk yield in sheep
have demonstrated a similar pattern, for example, Bonsma (1939) and Barnicoat et al.
(1949). In dairy sheep, Montanaro (1940) found that in Sicilian sheep milk
production increased in succeeding lactations to reach a maximum in the fifth and
subsequently declined. A similar trend is observed for the peak milk yield. In
literature have been reported similar trends (Ramirez-Valverde et al., 1998; Rekik et
al., 2003; Magana-Sevilla). Casoli et al. (1989), Hatziminaoglou et al. (1990) and
Ubertalle et al. (1990) observed increasing milk yields with the progress of lactation
periods. Hatziminaogloy et al. (1990) in their study for the sheep Karagouniko
reported that lactation period influences significantly the milk yield. Ewes reach
maturity at second lactation period. Similar results have been found by Bencini and
Purvis (1990), Kremer et al. (1996), Maurogenis (1996), El Saied et al. (1996).
According to Gootwine και Goot (1996) at first lactation period is observed the
lowest milk yield. Gradiz et al. (2009) reported that milk yield is usually low in first
parity cows because the animal is not fully developed yet and they partition more
resources to maintenance and growth at the expense of milk production. The high
milk yield in later lactations could also be attributed to selection since animals with
low milk yields are normally culled as part of the herd management practices leaving
only high producers in the herd.
The influence of season of parturition has been studied very early mostly in dairy
cows. Danell (1982) reported that in countries where the grazing season is short and
cows are foddered indoors for most of the year, the highest lactation yield is given by
cows calving during the autumn and early winter (eg. Johansson & Hansson, 1940,
Syrstad, 1965). Effect of month calving can vary in different years, herds and regions
(the weather conditions may be one reason), though the general pattern seems to be
the same overall (Wunder & McGilliard, 1971, Danell, 1976). Similar reports have
been demonstrated (Durhes, M. C., and J. F. Keown. 1991, Freeman. A. E. 1973, D.
Norman, R. Meinert, M. Schutz, 1995, Tekerli et al., 2000). A same trend is shown in
our results. A highest lactation yield is given by ewes lambing during the autumn
or/and winter. It is generally known that climatic conditions influence milk yield in
different ways. One way is by changing the animal's metabolism as a result of high
temperature and indirectly determining the season of forage and feed utilization
(Collier et al., 1982; Jonsson et al., 1999). Gradiz et al. (2009) reported that there was
a tendency of cows that calved in the rainy season to have lactations with higher milk
production levels than those that calved during the dry seasons. Hatziminaoglou et al.
(1990) reported that the important climatic differences and the resulting grazing
availability between consecutive production periods are probably responsible for the
585
differences in the effect of the month of lambing and the level of feeding on milk
yields.
The model by Wood (1967) has a greater advantage of producing a good fit
measurement with only three parameters. This model has been widely used in several
types of studies, such as for new models assessments (Cobby Le Du, 1978), genetic
breeding (Ferris et al., 1985) milk production simulation systems (Rotz et al., 1999)
and nutrition (Fox et al., 2003), because of its recognized capability allied to its
simplicity. In our study it is also apparent that the Wood (1967) model still remains a
good choice with a great suppleness for describing lactation curves with different
behavior.
References
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