Demonstration and verification of a milking order in dairy sheep and its extent and consistency

Demonstration and verification of a milking order in dairy sheep and its extent and consistency

Applied Animal Behaviour Science 64 Ž1999. 111–124 Demonstration and verification of a milking order in dairy sheep and its extent and consistency An...

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Applied Animal Behaviour Science 64 Ž1999. 111–124

Demonstration and verification of a milking order in dairy sheep and its extent and consistency Anja Wasilewski

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FB BiologierZoologie, Philipps-UniÕersitat ¨ Marburg, Karl-Õ.-Frisch-Str., 35032 Marburg, Germany Accepted 16 March 1999

Abstract The objective of this study was to investigate whether dairy sheep, like cows, organise themselves into a well-defined sequence at entry into the milking parlour and to quantify the extent Ži.e., proportion of flock members with a favourite position in the sequence. and consistency of the order over different periods of time Žcorrespondence between two consecutive days and over periods of up to 13 weeks.. A 51-head flock, comprising mainly British Milksheep, were studied under commercial husbandry conditions for 13 weeks and the sequence of entry into the milking parlour Žtype side-by-side, batch size 6. recorded, resulting in 18 readings of morning and 90 of afternoon milkings, respectively. The number of times an animal had occupied each position was plotted against the positions. The comparison of these frequency distributions of the 48 sheep studied for this purpose revealed that 75% of flock members grouped their choices around a favourite position in the milking sequence, resulting in a " predictable milking order. The distribution patterns of the remaining 25% were less focused, but none of them scattered their choices evenly across the complete range of 48 possible places, demonstrating that, even among these, entry into the parlour was not at random. To test for short- and long-term consistency, analyses were carried out for morning and afternoon milking, over different periods of time, and over different groups of sheep, owing to the fact that the ewes joined the dairy flock successively. Correlations between the sequences of two consecutive days revealed, with r 2-values of up to 96%, very high degrees of consistency, all of which were significant at p - 0.001. No significant differences in consistency between the groups could be detected. Correspondence tended to be greater between morning than between afternoon milkings Ža.m.: r 2 s 73%, p.m.: r 2 s 65% on average, 0.05 - p - 0.1., which was probably due to different external conditions Že.g., practically no waiting time in collecting pen, no break, no audience, longer interval since previous milking.. When testing for long-term consistency using concordance calculations, however, any significant correspondence disappeared ŽW F 0.2298, p ) 0.05., leading to the conclusion that the milking

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0168-1591r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 5 9 1 Ž 9 9 . 0 0 0 3 2 - 5

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order has to be regarded as a dynamic rather than a static phenomenon, being consistent only for periods of less than a week. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Sheep milking; Social organisation

1. Introduction Dairy sheep farming in North-West Europe and the US is at present experiencing changes towards more intensive farming systems comparable to those undergone by dairy cow husbandry during the last 30 years, leading to a strong demand for more efficient husbandry methods. In commercial farming practice, economising is often achieved at the expense of animal welfare, inevitably reducing individual productivity ŽEvans, 1977; Rathore, 1982.. More detailed knowledge of the behavioural characteristics of farm animals enables the development of husbandry routines that meet the animals’ requirements to the greatest possible extent. This benefits the animals’ well-being and the farmer’s profit likewise by allowing the animals to realise their full individual potentials, therefore maximising individual and, ultimately, overall herd productivity Že.g., Quick, 1982; Fraser and Broom, 1990.. Secondly, many everyday handling routines can be made more efficient by considering and utilising specific behavioural features of the animals involved Že.g., Grandin, 1980; Kilgour and Dalton, 1984; Fraser and Broom, 1990.. Social behaviour characteristics are particularly important in this context. A prominent feature of the social system of dairy cattle is a consistent order of entry into the milking parlour Že.g., Guhl and Atkeson, 1959; Kilgour and Scott, 1959; Willems and Lampo, 1964; Dietrich et al., 1965; Dickson et al., 1967; Hidar et al., 1973; Reinhardt, 1973; Gadbury, 1975; Rathore, 1982.. Possible applications of detailed knowledge of the milking order in farming practice could arise from at least three aspects. First, it has been suggested by authors like Gadbury Ž1975. and Rathore Ž1982. that the order of voluntary entrance could have implications on the speed of throughput of cows, although they give no explanation of the link between the two. However, the following assumption seems justified: Batch handling time is determined by the slowest milker in the group and an unnecessary delay would be avoided if cows of similar milking-out speed only comprised a batch. Secondly, an uncharacteristically late entry into the parlour can often be related to health problems Žcf. Reinhardt, 1973. and can therefore be used as an indicator, prompting further examination. Finally, Hopster et al. Ž1998. demonstrated that a large percentage of cows in two-sided parlours Ži.e., tandem and herringbone. express high degrees of consistency in the choice of parlour side. They have suggested this might indicate that parlour side could constitute a significant factor for a dairy cow’s feeling comfortable during milking. Consequently, external or social restraints, preventing it from entering on its habitual side, might result in stress responses during milking comparable to those found when cows were milked in an unfamiliar environment ŽBruckmaier et al., 1993.. Similarly, milking position, too, might be an important factor to a dairy animal and not being able to obtain that position might result in stress and a potential decrease in milk yield.

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So far, studies on the social behaviour of dairy animals have exclusively focused on dairy cattle. With small ruminants gaining importance nowadays as commercial dairy species Žcf. goats: Knights, 1997; sheep: Walsh, 1998., the objective of this study was to investigate whether the existence of a milking order is a unique feature of dairy cattle or whether sheep, too, organise themselves into a well-defined sequence. This would indicate that a milking order, like dominance hierarchies for example, must be regarded as a more common social feature among farm animals than previously assumed. After establishing evidence of the existence of a milking order in sheep the order was then to be analysed to quantify its extent and consistency.

2. Animals, materials and methods 2.1. Animals The study was conducted on a 51-head flock of mainly British Milksheep Žexceptions were seven Milksheep-Crosses and other breeds. under commercial husbandry conditions at The Seven Sisters Sheep Centre, East Dean, East Sussex. The Sheep Centre is a working sheep farm open to the public during spring and summer, and their dairy flock comprises third profit ewes, i.e., the sheep are left to rear their lambs for the first two months of their lactation. The ewes studied were on average 4.4 years old when the project commenced, and all but eight ewes had been milked in at least one previous year. The first group of 30 sheep had been separated from their lambs and milked for two weeks before the commencement of this study. They were joined by another ten animals on the 15th recording day and a further eleven sheep 3 days later, these 21 animals being referred to as the second group. Another two days later, the three lowest yielding sheep

Fig. 1. Layout of the milking yard. N.b., the scale of the collection pen is shown in half its proportionate size, i.e., one unit represents 2 m. The observer was positioned on the roof of the dairy cabin.

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were removed from the dairy flock and the remaining 48 were milked in eight batches of six for another nine weeks until they were communally dried off. 2.2. IndiÕidual marking Due to the set-up of the parlour Žcf. Section 2.3 and Fig. 1.. the ear-tags identifying each ewe were not legible from the observer’s position. Additional markings, beginning

Fig. 2. Examples of different types of frequency distribution. The frequency with which the particular sheep was recorded in each of the 48 positions available is plotted against the position. Numbers of milkings recorded were 70 for sheep A and Z, and 69 for sheep Y and 20, respectively. Sheep A and Z Ža and b. illustrate the ‘compact’ type Žrange of positions occupied F Ž1r2. scope of positions available, peak G10., sheep Y and 20 Žc and d. represent the ‘dispersed’ type Žrange of positions occupied ) Ž1r2. scope of positions available, peak -10.. N.b., missingss no. of unidentified recordings, U outliers Žcf. Section 2.4 and Appendix A..

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Fig. 2 Žcontinued..

with the letters of the alphabet, continued by numbers 1 to 25 were applied to the sheep’s backs on either side of the spine using Ritchey Stockmarker Spray. They were issued in alphanumerical order on the first recording day. 2.3. Milking yard layout and recording of milking sequence The parlour used in this study was of the side-by-side type with one batch comprising six sheep ŽFig. 1.. During milking they were fed equal amounts of concentrate ŽGrain

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Harvester’s Wingham Sheep Feeds.. The sequence in which the ewes entered the parlour was recorded continually, the first batch representing positions 1 to 6, the second places 7 to 12, etc. The sheep entered the parlour voluntarily except for the eight first-time milkers, who had to be encouraged initially. For the first 18 days of the study, the flock were milked twice a day, then the morning Ža.m.. milking was abandoned and only the afternoon Žp.m.. milking was continued. ŽThe p.m. milking was in two sessions, the break being due to demonstrations for the public.. Hence, a total of 18 a.m. and 90 p.m. milkings were recorded. 2.4. Data processing and statistical analysis In order to determine the proportion of sheep that showed preferences for certain positions, and the strength of the preferences Ž extent of the order., for each member of the flock the number of times it had been recorded in each of the 48 possible positions was counted and plotted against the position. To correct for the partial absence of the second group during the first three recording weeks, only weeks 4 to 13 were analysed. The maximum range of positions and the occupation frequency of the peak position of each sheep’s distribution were measured and standardised: After eliminating outliers Žcf. Appendix A. the width of the distribution reflecting the range of positions occupied was measured and divided by 48, then multiplied by 100, the result indicating the percentage of positions that fell into the actually occupied range. Similarly, the height of the peak was measured, reflecting the strength of preference, divided by the number of days for which the position of the particular sheep could be determined Ž0 to 3 readings per sheep had to be omitted due to recording errors caused by illegible markings., then multiplied by 100, the result representing the percentage of days on which the animal had managed to obtain its favourite position. To quantify short-term consistency, the milking sequences of each pair of consecutive days were tested for correlation. This was done for different periods of time Žweeks 1–13, weeks 1–2, weeks 4–13; week 3 was excluded from these calculations due to the drastic changes in flock composition, cf. Section 2.1., for different sets of animals Žentire flock, group 1, group 2. and for different milking times Ža.m., p.m... In order to quantify long-term consistency, the sequences of several days were compared to one another by concordance calculations. These were conducted over different periods of time Žweeks 1–13, weeks 1–2, weeks 4–13, weeks 1 to 13 separately., for different sets of animals Žentire flock, group 1, group 2. and different milking times Ža.m., p.m... Statistical analyses were carried out using the software package SPSS for Windows, Release 6.0. All tests are two-tailed and data interval-scaled. Data were tested for normality using Komolgorov-Smirnov Test. After ensuring normality, Pearson Product Moment Correlations were applicable. For comparing more than two sets of data, Kendall Coefficients of Concordance ŽKendall’s W . were calculated. Fisher z Transformation was applied when computing mean correlation coefficients. To test for significance of these averaged correlation coefficients, these were transformed into t-values ŽBortz, 1983, p. 261.. For comparing means, t-tests for paired and independent samples, respectively, were carried out.

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3. Results 3.1. Occupation frequency distributions None of the 48 sheep utilised the whole range of possible positions or scattered their choices evenly ŽFig. 2.. All animals focused on a " well-defined section of the entire scope ŽTable 1. and grouped their choices around a " distinct favourite position; six sheep had occupied two positions with equal frequency. Two extreme types of frequency distribution patterns became evident ŽFig. 2., consecutively referred to as ‘compact’ and ‘dispersed’ type. To allocate each sheep to one of the two types, the distinguishing features, namely relative width and relative height, had to be quantified. The choice of the key values was arbitrary, but the quantification given below provided a good basis for separation: compact: Ž1. range of occupied positions narrow, i.e., relative width F 50%, Ž2. peak high, i.e., relative height G 16% Žequalling an absolute frequency of 10 when present on all occasions; cf. Sections 2.3 and 2.4: 63 recordings analysed, that is 10r63s 0.159 f 16%.; dispersed: Ž1. range of occupied positions broad, i.e., relative width ) 50%, Ž2. peak low, i.e., - 16%. In order to attribute some rare intermediate forms to one of the two types, the criterion of width was regarded as the more binding one, as it is less influenced by the exception of two equally high peaks. Applying these criteria to the 48 sheep studied, 36 s 75% were of the compact type clearly focused on a distinct favourite position, and 12 s 25% showed the dispersed pattern. 3.2. Day-to-day correlations Testing the milking sequences of each pair of consecutive days for correlation yielded moderate to very high correlation coefficients for all different combinations of factors Žcf. Section 2.4. ŽTable 2.. These findings are significant at the highest level Žwith only one exception being significant at the 5% level only. and demonstrate a substantial general degree of day-to-day consistency.

Table 1 Range of characterising parameters of frequency distributions Relative width Ž%. minimum

U

maximum

12.50 Žsheep 23. 16.67 Žsheep L. 79.17 Žsheep M.

mean"s.d.

41.41"15.14

Relative height Ž%. 8.70 Žsheep 10 and 20. 61.43 Žsheep 23.U 40.00 Žsheep A. 18.34 "10.03

Relative width indicates which percentage of positions had been included into the range of positions occupied. Relative height shows for which proportion of readings the sheep had been recorded in their favourite position. N.b., sheep 23 ŽU . represents an exception in so far as it is one of the eight first-time milkers Žcf. Section 2.1. who had to be initially encouraged to enter the parlour Žcf. Section 2.3.. Its values lie outside the main range of those of more experienced dairy ewes Že.g., sheep L and A, etc...

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Overall correlation

Comparison A Ž‘times’.

p.m. entire flock, weeks 1–13

a.m. group 1, weeks 1–2

r

r2

r

Comparison B Ž‘groups’. p.m. group 1, weeks 1–2

r2

r

p.m. group 1, weeks 4–13 r2

r

r2

p.m. group 2, weeks 4–13 r

r2

minimum 0.7065UUU 49.91% 0.7335UUU 53.80% 0.7255UUU 52.64% 0.6558UUU 43.01% 0.5544U 30.74% maximum 0.9696UUU 94.01% 0.9341UUU 87.25% 0.9006UUU 81.12% 0.9817UUU 96.37% 0.9675UUU 93.61% mean"s.d. Ž z . 0.8875UUU "0.26 78.77% 0.8538UUU "0.23 72.90% 0.8041UUU "0.17 64.66% 0.9087UUU "0.31 82.57% 0.9015UUU "0.30 81.27% Five different conditions, brought about by different combinations of the factors milking time, set of animals and period of time, were considered. The correlation coefficients r were transformed into r 2-values to facilitate interpretation. Since measures of variability cannot be calculated for mean correlation coefficients, the standard deviations of the corresponding Fisher z Transforms are given instead. Levels of significance Žof the correlations.: U p- 0.05, UU p- 0.01, UUU p- 0.001. To compare the consistencies of different milking times and different groups of animals, respectively, two pairwise t-tests ŽComparisons A and B. were carried out. The results of these comparisons are given in the text, but were not included in this table.

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Table 2 Correlations between milking sequences of two consecutive days

Week 1 Week 2 Week 4 flock – group 1 0.0261 group 2 –

– 0.0090 –

0.0331 0.0457 0.2298

Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12 Week 13 Weeks 1–2 Weeks 4–13 0.0017 0.0115 0.0492

0.0087 0.0376 0.0113

0.0074 0.0196 0.0275

0.0035 0.0260 0.0572

0.0078 0.0414 0.0466

0.0070 0.0227 0.0656

0.0176 0.0137 0.0631

0.0176 0.0331 0.0153

0.0080 0.0147 0.0247

– 0.0383 –

0.0248 0.0490U 0.1346

During weeks 1 and 2, only group 1 Ž ns 28. was being milked, group 2 Ž ns 20. joined the flock successively during week 3; week 3 was consequently excluded from analysis. Levels of significance: U p- 0.05, UU p- 0.01, UUU p- 0.001. Žb. Concordances ŽKendall’s W . between morning milking sequences over different periods of time Week 1 Week 2 Weeks 1–2 flock – group 1 0.0197 group 2 –

– 0.0104 –

– 0.0203 –

The morning milking was abandoned in week 3. During weeks 1 and 2, only group 1 Ž ns 28. was being milked, group 2 Ž ns 20. joined the flock successively during week 3; week 3 was consequently excluded from analysis. Levels of significance: U p- 0.05, UU p- 0.01, UUU p- 0.001.

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Table 3 Ža. Concordances ŽKendall’s W . between afternoon milking sequences over different periods of time

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The results for the entire flock over the complete length of the study period ŽTable 2, Overall correlation. show that the milking sequences of two consecutive days correlated to a high to very high extent and at the highest level of significance Ž p - 0.001.. A more differentiated examination was carried out to investigate the possible influence of milking time and set of animals, respectively. For that purpose, two comparisons ŽComparisons A and B in Table 2. were made using t-tests Žwhile all other relevant factors were controlled for.. When comparing the consistencies of a.m. and p.m. milkings ŽTable 2, Comparison A., the values for a.m. recordings are consistently higher than those of the p.m. milkings. However, this difference shows only a trend towards statistical significance Ž t-test for paired samples: 0.05 - p - 0.1.. The comparison of groups 1 and 2 ŽTable 2, Comparison B. reveals only a slight difference between their average r 2-values, that of group 1 being only marginally higher than that of group 2. This difference is not significant Ž t-test for independent samples: p ) 0.05.. 3.3. Long-term concordances The concordance calculations using Kendall’s W-test for different combinations of factors ŽSection 2.4. yielded only rather low W-values, all but one of them not even bordering on statistical significance ŽTable 3a: p.m. and Table 3b: a.m... The only significant value is the result for group 1 over the 10 weeks when the entire flock was present, being significant at the lowest level Ž p - 0.05.. 4. Discussion The fact that none of the flock members scattered their choices evenly across the entire range shows that the sheep did not enter the parlour at random. All 48 ewes restricted the range of occupied positions to a section only of the 48 positions available, grouping their choices in G 75% of cases around a favourite place, the entirety of these preferred places resulting in the flock’s milking order. Further evidence of the existence of a milking order is provided by the remarkably high degrees of correspondence between the sequences of consecutive days reaching up to 96%. These findings suggest that a milking order is not a species-specific feature of the social organisation of cattle, but seems to be a more common phenomenon among dairy animals. Three quarters of the flock members showed a choice of milking positions that was closely focused on a favourite place Ž‘compact’ distribution type.. This proportion is considerably higher than the extent documented for cows. Kilgour and Scott Ž1959. report that just the first four or five animals of a 30-head herd Žequalling approx. 13 and 17%. were consistently found in these positions. These percentages are very similar to the findings of the study of Gadbury Ž1975. of three herds, in which 15% Žtwo herds. and 18% Žone herd., respectively, of all cows showed any preferences at all. In her work, however, the preferences were not restricted to the first batch but could occur at any position throughout, which is similar to the results obtained for sheep. Taking into account that the majority of those sheep classified as the ‘dispersed’ type did not equally

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utilise the entire scope of available positions either, the proportion of ewes without any indication of a preference has to be considered even far lower than 25%, approaching nil. Hence, relatively stable positions in the milking sequence seem to be the rule in sheep and rather the exception in cows. Therefore, any investigations into the factors determining an individual’s position in the sequence would appear to be more rewarding if conducted on sheep rather than cows. Gadbury Ž1975. noticed that some cows, regardless of which batch they entered with, tried to obtain the first position within the batch. Within the sheep’s individual occupation frequency distributions no pattern emerged indicating the particular popularity of any position within the batch. This finding is in concordance with the explanation offered by A. and S. Crosby-Jones Žpers. comm.. for within-batch preferences in cows. Due to the design of herringbone parlours Žthe type used in Gadbury’s study., the first andror last stall on either side tend to be slightly bigger than the ones in the middle, so that particularly large animals prefer to be milked there. The side-by-side parlour on the sheep farm, however, offered no such advantages, explaining why position within a batch seemed to be irrelevant to the ewes. When considering day-to-day consistencies, even the wider approach of looking at the entire flock over the complete length of the recording period yielded remarkably high degrees of correspondence. In the more detailed approach, the milking sequence of one day accounted for between 30.74 and 96.37% for that of the following day. These scores are in the same range as those published for cows: Dickson et al. Ž1967. report values of 26.36% Žbetween a.m. and p.m. milking of the same day. and Rathore Ž1982. found consistencies of 59.60 to 84.27%. The trend towards morning sequences being slightly more consistent than those of the afternoon could be due to a number of aspects in which morning milking differed from afternoon milking: The a.m. milking was not interrupted and the time spent waiting in the collecting pen was substantially shorter Ža.m. approx. 5 min, p.m. around 70 min due to organisational constraints., which resulted in less time for the sheep to change their priorities and mingle. ŽWhen being kept waiting in the pen, obtaining comfortable resting places in the shade, for example, became more important than securing places close to the entry door.. In addition to this, an audience was only present in the afternoon, being a potential source of disturbance and distraction. Finally, the interval since the previous milking was almost twice as long in the morning as in the afternoon Ža.m.: 15 h, 25 min; p.m.: 8 h, 35 min., resulting in an increased motivation to be milked. This is independent of the actual incentive. The motivation may be based on, e.g., hungerrappetite for concentrate feed ŽReinhardt, 1973., udder pressure due to accumulated milk ŽRathore, 1982., psychological reward of suckling ŽReinhardt, 1973. or milk let-down ŽWhittlestone, 1974., with the food being the most likely factor Žown additional unpublished data; Prescott et al., 1988.. As preference for a particular position or at least range of positions seems to be a rather common feature in dairy sheep, it would be interesting to investigate if, and to what extent, being prevented from obtaining a place in the habitual range has any detrimental effects on the animal’s emotional state. It might result in the ewe’s feeling only a little uncomfortable as has been suggested by Hopster et al. Ž1998. for dairy cows unable to enter a tandem parlour on their favourite side. On the other hand, conse-

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quences could be more severe stress responses which will almost inevitably reduce the animal’s milk yield. If this was the case, and if time spent waiting in the collection pen could be proven to have a negative effect on the consistency of the order Žsee above., then keeping this time as short as possible could be one method of enabling a greater proportion of the flock to obtain positions in their favourite range. The negligible and insignificant differences in short-term consistencies between the groups show that joining the flock at a later stage does not prevent the sheep from establishing habitual places in the milking sequence. However, members of the second group occupied places that were on average between 8.1 Žweek 4. and 2.4 Žweek 13. positions behind those of the first group. These differences declined during the course of time, but were significant Ž p - 0.05, t-test for independent samples. in weeks 4 and 5, i.e., during the first two weeks after group 2 had joined the dairy flock. These findings Žunpublished additional data. imply that joining a flock which has already established a " stable milking hierarchy at a later stage entails initial disadvantages on the newcomers. Despite the extremely high day-to-day correspondences, no significant consistencies oÕer longer periods of time, such as weeks or months, became evident. No data on long-term consistency of the milking order in cows could be located for comparison. Only within periods of time considerably shorter than a week can an individual’s position be reliably predicted by the positions previously occupied. A certain degree of flexibility due to the animals’ focusing on a preferred range of positions, rather than exclusively on one specific place, and a certain amount of rearrangement result in a considerable number of subtle changes from one day to the next. These accumulate to more substantial alterations within less than a week and obscure consistencies over periods of time G 2–7 days. The degree of flexibility is, however, weak enough to allow a pattern to emerge when data are accumulated over substantially longer periods of time, i.e., several months. ŽThis is in concordance with the finding that the only significant long-term correspondence occurred for group 1 over the maximum time considered, i.e., weeks 4–13. Why it should be expressed by group 1 alone, however, is less apparent.. The findings for short- and long-term consistencies, taken together, imply that the milking order ought to be regarded as a dynamic rather than a static order.

5. Conclusions Conclusive evidence of the existence of a milking order in sheep has been established. Individual preferences for particular positions in the milking sequence seem to be the rule in sheep, and rather the exception in cows. The milking order, allowing for a certain amount of flexibility, should be regarded as a dynamic rather than a static order.

Acknowledgements I most gratefully acknowledge Professor Dr. Heinrich-Otto von Hagen who supervised my diploma project of which the study presented here was a part. He provided

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invaluable advice and encouragement. I am also indebted to Terry and Pam Wigmore who kindly permitted me to ‘count their sheep’ and Ralf Reinecke and Melina Rauch who ‘kept a vigilant eye’ on my statistics. Thanks are further due to Andy and Sue Crosby-Jones for ‘talking cows’ with me and finally a huge ‘Thank You!’ to Kerstin and Dave Edwards, Anne Gardiner, John Middleton and Angie and Ian Gilliat who commented on the manuscript, as did Kiwi Schuster, helped me improve my English and made me so welcome in England.

Appendix A The elimination of outliers was conducted according to the following convention. Beginning at each end of the distribution, blocks or groups of blocks of the width x that were separated from the core by gaps wider G x q 1, were successively eliminated. Groups of blocks with a cumulative width y Žsum of the widths of each block or sub-group of blocks. were treated as outliers when the cumulative width of the gaps between the elements of the group plus the gap separating the group from the core was G y q 1.

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