where m is a binary variable representing whether or not an event has occurred, b Ž
represents fixed effects and u represents the random effects for cows McCullagh and .
Nelder, 1989; Engel and Keen, 1994 for the analysis of binary data . Ž .
3 The time until the occurrence of different events was analysed according to a Ž
. linear mixed model LMM , where the variance was assumed to be constant and
Ž .
normally distributed Engel, 1990 : m s b x q uz
3
Ž .
where m represents the expected value of the time that has elapsed until the occurrence Ž .
of a certain event and b and u are the same as in Eq. 2 . Analysis of time until occurrence is complicated by the fact that observations ended after 60 min. This was
corrected by the method described by Taylor for so-called censored observations Ž
. Taylor, 1973 .
Ž . 4 The number of aggressive interactions induced by a certain cow within the 1-h
Ž .
observational period was analysed by a generalised linear mixed model GLMM with a logarithmic link function:
log m s b x q uz 4
Ž .
Ž .
where m is the number of aggressive interactions and b is a variable representing the effect of omitted milking or milking on the aggression of a cow. It was assumed that
Ž variance increases proportionally to the expected response value see McCullagh and
. Nelder, 1989 for loglinear models on counted data .
Ž . 5 Data from the automatic forage installation and data about milk production were
Ž . Ž
. analysed with a linear mixed model LMM
see Eq. 3 . Ž .
6 The number of changes between automatic forage feeders was analysed with a Ž
. Ž .
generalised linear mixed model GLMM see Eq. 4 .
Ž .
The analyses 1–6 included the effect of rank in the milking order, as well as the Ž
. effect of lactation number and interaction between these factors if any .
The milking order of cows during three visits to the milking parlour and also the order during return to the compartment after the second visit to the milking parlour were
Ž .
compared using a Spearman correlation coefficient Siegel and Castellan, 1988 . The place where aggressive interactions between cows occurred after milking and after
2
Ž .
omitted milking was compared by a x test Siegel and Castellan, 1988 .
3. Results
The observations on the behaviour of milked and unmilked cows started immediately after the entire group had entered the compartment after returning from the milking
Ž .
parlour. The entrance led to the lying area see Fig. 1 , from where at least half of the cows went immediately to the feeding area. In the course of 1 h, the percentage of cases
of eating or standing in the feeding area remained the same, whereas the percentage of cases of lying increased gradually, though this tendency was less marked in the
Ž .
unmilked cows Fig. 2 . The percentage of cases of standing in the cubicles was almost
Fig 2. Activities of cows during the 1-h observational period after milking or omitted milking.
always higher for the unmilked than for the milked cows. The impression from Fig. 2 is Ž
. confirmed by the analysis of time budget per hour see Table 1 . The difference was
significantly attributed to the cows that were in the first batch that came to the milking Ž
. parlour. After omitted milking, these cows stood longer in the cubicles 14.2 min of 1 h
Ž .
and lay less 5.4 min of 1 h than milked cows for whom the corresponding figures were . Ž
. 7.0 min for standing and 16.4 min for lying in cubicles
P - 0.01 . There was no significant difference between milked and unmilked cows in time spent on eating and
Ž .
standing in the eating or in the lying area taken from video . The probabilities of the occurrence of eating, drinking and lying as well as defecation
and urination and the predicted time intervals for the occurrence of these activities in milked and unmilked cows are given in Table 2. Probability of cows eating forage was
Ž .
Ž .
Ž 80 SEM s 4 after milking and 85 SEM s 7 after omitted milking difference
. Ž
. not significant . Probability of cows drinking was 73 SEM s 4 after milking and
Ž .
Ž .
71 SEM s 7 after omitted milking difference not significant . On average, the cows ate and drank before lying. Unmilked cows were more likely to urinate than
Table 1 Ž
. Predicted time budget min of 12 cows during 1 hour following their visit to the milking parlour. In 16 trials,
Ž .
Ž .
each cow had not been milked 4= or milked 12= ; standard error of means in parenthesis Order of coming to the milking parlour
Activity Milked cows
Unmilked cows Ž
. Ž
. First batch of six cows
eating forage 13.9 1.6
19.0 3.5 Ž
. Ž
. standing in eating area
17.2 1.8 15.4 3.1
Ž .
Ž .
standing in lying area 5.5 1.0
6.0 1.9
a
Ž .
Ž .
standing in cubicle 7.0 1.1 a
14.2 3.0 b Ž
. Ž
. lying
16.4 1.7 a 5.4 1.8 b
Ž .
Ž .
Second batch of six cows eating forage
12.7 1.6 14.2 2.8
Ž .
Ž .
standing in eating area 13.7 1.7
14.9 2.8 Ž
. Ž
. standing in lying area
5.6 1.0 6.1 1.8
Ž .
Ž .
standing in cubicle 10.3 1.4
9.3 2.2 Ž
. Ž
. lying
17.7 1.9 15.5 2.9
a
Ž .
Different letters in one row indicate statistically significant difference P -0.01 .
Ž .
milked cows respective probabilities 64 and 36, P - 0.002 and the time interval Ž
until urination was predicted to be shorter for unmilked cows 56 min versus 70 min for .
milked cows, P - 0.002 . Neither the probability of defecation nor the time interval to occurrence of defecation was significantly influenced by omitted milking.
The milking order was not reflected in the order in which the cows entered the Ž
. compartment prior to the start of the observations r s y0.43, not significant , because
s
the cows moved around in the return alley. However, milking order was reflected in the use of the automatic forage installation. Cows that were in the first batch to enter the
milking parlour spent more time eating, changed feeding places more and ate more feed. Intake of feed was also influenced by lactation: during the 1-h observation period, cows
in the second lactation ate 4.8 kg of forage on average, whereas cows in the first
Ž .
lactation ate 3.6 kg P - 0.05 . The omitted milking did not significantly influence time
Table 2 Probability of occurrence of different activities for the 12 cows during 1 h after returning from the milking
parlour, where three cows had been subjected to omitted milking, and predicted time until their occurrence for milked and unmilked cows; standard error of mean in parenthesis
Activity Milked cows
Unmilked cows Ž
. Ž
. Probability of activity
eating forage 0.80 0.04
0.85 0.07 Ž
. Ž
. drinking
0.73 0.04 0.71 0.07
Ž .
Ž .
lying down 0.59 0.05
0.55 0.08 Ž
. Ž
. defecation
0.48 0.05 0.48 0.08
a
Ž .
Ž .
urination 0.36 0.05 a
0.64 0.08 b Ž
. Ž
. Ž
. Time until occurrence of activity min
eating forage 33.1 4.2
31.4 2.4 Ž
. Ž
. drinking
34.5 4.2 43.0 2.4
Ž .
Ž .
lying down 52.0 4.1
57.1 2.4 Ž
. Ž
. defecation
61.9 4.7 66.8 2.7
Ž .
Ž .
urination 70.2 4.0 a
55.8 2.3 b
a
Ž .
Different letters in one row indicate a statistically significant difference P -0.002 .
spent in the forage installation, the forage intake or the rate of eating forage, as analysed on the basis of data from automatic forage installation.
One hour after an omitted milking, cows gave on average 11.48 kg milk; this was Ž
. Ž .
more than what normally milked cows gave 10.81 kg, P - 0.01 Table 3 . The
following morning the opposite was true: cows subjected to omitted milking the previous afternoon gave 13.38 kg milk on average, whereas cows normally milked gave
Ž .
Ž 14.50 kg P - 0.01 . Daily milk yield calculated as afternoon plus next morning milk
. yields on days with omitted milking averaged 24.88 kg in comparison with 25.29 kg on
Ž .
days without omitted milking P - 0.05 . Cows that were most frequently in the first batch during afternoon milking had a higher daily milk yield and a higher morning milk
yield. This relation was not found for the afternoon milk yield, because of the direct effect of omitted milking.
Throughout the experiment, the same milking order was observed, as indicated by the Ž
. correlation coefficient: r s q0.69 between morning and afternoon milking P - 0.05 ;
s
Ž .
r s q0.78 between afternoon milking and the third visit 1 h later of all cows to the
s
Ž . Ž
. milking parlour for the three unmilked cows to be milked
P - 0.01 .
Table 3 Ž
. Predicted milk yield of experimental cows kgrcow and factors found to have significant influence on it;
standard error of mean in parenthesis Milk production in the afternoon
cows normally milked cows milked 1 h later
a
Ž .
Ž .
10.81 0.42 a 11.48 0.43 b
lactation number first
second Ž
. Ž
. 9.57 0.59 a
12.73 0.59 b Milk production the next morning
cows normally milked cows milked 1 h later
Ž .
Ž .
14.50 0.51 a 13.38 0.52 b
lactation number first
second Ž
. Ž
. 12.08 0.72 a
15.80 0.72 b milking order
first batch second batch
Ž .
Ž .
14.18 0.52 a 13.71 0.52 b
Daily milk production days without omitted milkings
days with omitted milking Ž
. Ž
. 25.29 0.92 c
24.88 0.93 d lactation number
first second
Ž .
Ž .
21.67 1.23 a 28.50 1.23 b
milking order first batch
second batch Ž
. Ž
. 25.34 0.93 a
24.83 0.93 b
a
Ž Different letters in one row indicate a statistically significant difference a,b at P -0.01 level; c,d at
. P -0.05 level .
The average number of aggressive interactions was 2.2 per cowrh after milking and Ž
. 2.6 per cowrh after omitted milking
difference not statistically significant . The number of aggressive interactions was not related to the milking order or to the lactation
number. The proportion of numbers of being the aggressor to the sum of being the aggressor and of being the recipient of the aggression was similar after milking and after
Ž .
omitted milking r s q0.86, P - 0.01 . Analysis of where the 468 aggressive interac-
s
Ž .
tions 337 of milked cows and 131 of cows after omitted milking took place revealed Ž
. that cows were most aggressive at the forage feeders 43.4 of cases and the water
Ž .
trough 28.0 of cases . Aggressive interactions also took place, but less, in the feeding Ž
. Ž
. Ž
area 13.5 of cases , around the salt block 7.0 of cases and in the lying area 6.6 .
Ž of cases . Pushing a cow away from her lying place happened exceptionally seven
.
2
cases, 1.5 of all . The x test revealed no difference in the distribution of the location
of the aggressive acts of milked and unmilked cows. Milk leakage from the udder was observed in 60 of cases after omitted milking. In
Ž 5 out of 12 cows milk leakage was always observed after omitted milking e.g., for four
. Ž
occasions of omitted milking , in three cows it was never observed e.g., during any of .
four occasions ; milk leakage was observed irregularly in the remaining four cows after omitted milking. No relation was found between milk leakage after omitted milking and
behaviour after omitted milking or milk yield.
4. Discussion
