Simulation of an intensified lambing system incorporating two flocks and the rapid remating of ewes

SIMULATION OF AN INTENSIFIED LAMBING INCORPORATING TWO FLOCKS AND THE REMATING OF EWES

SYSTEM RAPID

P. A. GEISLER, A. C. PAINE

The Grassland Research Institute, Hurley, Maidenhead, Berks., SL6 5LR, Great Britain & P. E. GEYTENBEEK

The University of Adelaide, Waite Agricultural Research Institute, Glen Osmond, South Australia. Australia 5064 SUMMARY

A computer model Jot the population o f a frequent lambing system has been constructed. The model has 2 ewe)qocks, the mating cycle o f one flock being 4 months out oJphase with that o/the other. Each flock lambs 3 times in 2 years. Ewes diagnosed as non-pregnant in one flock are transJerred to the other in time for the next mating. Total numbers o f lambs Jrom each lambing and Jor each year are predicted. From long term data on lamb prices, a value is assigned to lambs and the relative value of each lamb crop is calculated. Both the number and value oJ lambs depend on the time oJ year at which the first flock is initially mated. Simulation runs made at 13 diJJerent starting times throughout the year indicate, however, that the total output Jrom the system is remarkably steady over a 4 year period. INTRODUCTION

Ewe flocks normally lamb once each year. In order to increase lamb output and efficiency, workers in a number of countries (Copenhaver & Carter, 1968; Basson el al., 1969; Land & McClelland, 1971 ; Tchamitchian & Ricordeau, 1974; Robinson et al., 1975) have demonstrated that lambing frequency can be increased. In a study conducted at the Mortlock Experiment Station in South Australia over a 4 year period, Geytenbeek (1973) has shown that the Dorset × Merino ewe can be bred successfully under field conditions at intervals of 8 months. This study provided statistics on the number of ewes in oestrus at different months of the year, lambing percentages and ewe and lamb mortality rates. A current project is recording the reproductive performance of a dual flock of similar ewes. The dual flock consists of" two groups each mated at 8-monthly intervals with one group beingjoined every 4 months. Four months after joining, an ultrasonic pregnancy detection device is used 109

Agricultural Systems (2) (1977)--.~ Applied Science Publishers Ltd, England, 1977 Printed in Great Britain

I l0

P.A. GEISLER, A. C. PAINE, P. E. GEYTENBEEK

to identify the non-pregnant ewes. These are immediately transferred to the other group, thus reducing the delay normally associatcd with the remating of dry ewes. In practice the pregnancy test could be performed earlier than this, but on the 8-month cycle considered here this is not necessary. The experimental design and the results of the experiment will be reported elsewhere. The work described below is a first attempt at a computer simulation of the proposed rapid remating system using statistics gathered in the earlier field studies. The objective of the model is to investigate possible effects on total output of starting the system at different times of the year. To assess the worth of different starting times, the total number of lambs marketed and their relative gross value have been calculated for each of the 13 starting times. MODEL DESIGN

A conceptual diagram of the flows in the model is shown in Fig. I with the time scale attached. The model covers a 4 year period for each flock and with the time lag between the 2 flocks this means that the program runs over 4 years 4 months, with each flock lambing 6 times. Although not shown in Fig. l, a projected date of death for each ewe is generated with a random number generator at the start of the program and from time to time ewes are removed from the model as their date of death is passed. There is no replacement policy for the ewes in the computer model since there is none in the field experiment which it is simulating, though such a policy could readily be incorporated into the model if desired. For simplicity in the model it is assumed that all matings for each flock take place on a single day, that the gestation period is fixed, that the lambs all grow at the same rate and the lambs of each crop are all sold on the same day. These are clearly not realistic assumptions but they allow for the construction of a simple model, which it is hoped shows up the essential features of the system. In particular, one can investigate the number of ewes that will be transferred from flock to flock and the effect of varying the starting time on flock productivity. The program was written in the simulation language G P D S (Xerox, 1972), which is designed for discrete simulation problems. A listing of the program can be obtained from the authors. The language allows one to assign and readily keep track of a number of parameters in which information can be stored fbr each ewe. The parameters used in this model are: pl = 0 if non-pregnant l if pregnant p2 = N u m b e r of matings up to the present time p3 = Number of lambings up to the present time p4 = Most recent litter size p5 = Day of death for ewe p6 = Current lamb crop number of the model

111

SIMULATION OF INTENSIFIED LAMBING SYSTEM

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1 12

P.A. GEISLER, A. C. PAINE, P. E. GEYTENBEEK

A further feature of the language is that it maintains a simulated clock, schedules events to occur in future simulated time and causes these events to occur in the proper time-ordered sequence (Schriber, 1974).

Data used in the model The statistics used in the model are age and breed specific, being derived over the 4 year reproductive life of Dorset × Merino ewes mated to lamb for the first time at 2 years of age. The program therefore commences with 100 young unmated ewes being assigned to each of 2 flocks designated A and B. If they survive in the system, they are culled at 6-6½ years of age. Ewe mortalities In a previous field experiment involving 238 ewes, the mean annual death rate was 4 ~ . The data provide the probabilities of death shown in Table I for each year in the model. As each ewe enters the model at the start, these probabilities are used to predict the year of its death and a date in that year is assigned at random as its date of death. In the absence of more precise information, all dates of the year are assumed equally likely. The predicted date of death is stored in parameter p5 of each ewe and when that date is reached, the ewe is removed from the system. Any ewe with a date of death that occurs more than 4 years 4 months after the start will survive the running time of the model. TABLE 1 PROBABII.II'Y O F D E A 1 H AS A F U N C T I O N O F YEAR IN T H E M O D E l .

Year Year Year Year

1 2 3 4

0.0085 0.038 0-057 0-057

Oestrus pattern The percentage of ewes in oestrus at different times of the year is shown in Table 2 and represents mean values of 4 years' observations. The program linearly interpolates between the values in order to obtain the percentage of ewes expected to be in oestrus at any time. That percentage is then used to assign oestrus randomly amongst the ewes. TABLE 2 P E R C E N T A G E O F EWES E X H I B I T I N G O E S T R U S T H R O U G H O U T

Weckofyear ~oinocstrus

I

T H E YEAR

5 9 13 17 21 25 29 33 37 41 45 49 53 93 97 100 100 94 89 86 55 61 71 77 86 92

SIMULATION

1 13

OF INTENSIFIED LAMBING SYSTEM

Conception It is assumed that 90 % o f all ewes in oestrus at mating time become pregnant. A r a n d o m n u m b e r generator assigns to parameter p l for each ewe the value 1 (if pregnant) with probability 0.90 or the value 0 (non-pregnant) with probability 0.10.

Diagnosis oJ pregnancy In the model, ewes are tested for pregnancy 115 days after mating. All pregnant ewes are assumed to be diagnosed correctly and remain in the lambing flock. If a n o n - p r e g n a n t ewe is diagnosed correctly she is transferred to the alternative flock to be remated. However, since in practice 5 % o f n o n - p r e g n a n t ewes are incorrectly diagnosed as pregnant and remain in the lambing flock, this statistic is incorporated into the model.

Litter size The mean litter size o f Dorset × Merino ewes was found by Geytenbeek (1973) to be 1.22 and 1.42 at their initial and subsequent lambings respectively. To ensure this distribution of litter sizes in the model, all pregnant ewes are assigned a value o f either 1 or 2 in p a r a m e t e r p 4 (the value o f the most recent litter size)with probabilities o f 0.78 and 0-22 respectively for the first mating and 0.58 and 0.42 respectively for later matings. N o n - p r e g n a n t ewes incorrectly diagnosed as pregnant are assigned a value o f 0 in parameter p4.

Lamb mortality L a m b s are assumed to die only in the first few days alter birth. The percentage o f lambs that die in terms o f the week o f their birth is shown in Table 3. F o r example, if the lambs are born in week 37 o f a particular year, then 24 ~ of them are expected to die. TABLE 3 LAMB MORTALITY THROUGH THE YEAR

Week of birth % of lambs that die

1

5

9

13

17

21

25

29

33

37

41

45

49

25

22

20

18"

18

18

22

26*

25

24

24

24

25*

* Experimentally observed values; the other entries in the table are 'best guesses', bearing in mind the environmental factors. Linear interpolation is used for times between those listed in the table.

Lamb prices Values were calculated for the mean m o n t h l y selling price o f a lamb o f standard weight and grade over an 18-year period ( 1953-1971) at the Gepps Cross abbatoir in South Australia. M o n t h l y values were then expressed as a percentage o f the mean annual value. The final price schedule used in the model is shown in Table 4. It is

114

P . A . GEISLER, A. C. PAINE, P. E. GEYTENBEEK

TABLE 4 PRICE O F L A M B S T H R O U G H T H E YEAR E X P R E S S E D AS A P R O P O R T I O N O F T H E M E A N A N N U A L V A L U E

Week of sale Selling price of lambs

1 0.92

5

9

13

17

21

25

1 - 0 2 1 . 0 5 1-10 1 . 1 5 1.21 1.20

29

33

37

1.15

1.00 0.90

41

45

49

0.82

0.78

0.82

a s s u m e d t h a t all l a m b s b o r n a t a n y t i m e o f t h e y e a r r e a c h t h e r e q u i r e d w e i g h t a n d g r a d e a t a n a g e o f 120 d a y s . Output The model was operated to simulate the system over a 4 year period and assess the effect o n o u t p u t o f s e l e c t i n g a n y 1 o f 13 p o s s i b l e s t a r t i n g t i m e s . T y p i c a l o u t p u t f r o m

t h e m o d e l is s h o w n in T a b l e s 5 a n d 6 f o r s t a r t i n g t i m e s in w e e k 17 a n d w e e k 4 9 TABLE 5 T Y P I C A L O U T P U T W H E N F I R S T M A T I N G IS IN W E E K 17

Flock

Crop No.

A

1

B

2

A

3

No. of No. oJ ewes ewes mated lambing

100 Ill 135

89 65 108

No. of zero litters

No. of singles

No. of pairs of twins

0 4 2

68 46 61

21 15 45

Total No. No. of oJ lambs lambs at born 120 days

110 76 151

Year 1 totals B A B

4 5 6

91 118 130

80 63 101

2 1 0

46 34 54

32 28 47

I10 90 148

Year 2 totals A B A

7 8 9

91 112 118

75 68 93

1 2 1

39 36 48

35 30 44

109 96 136

Year 3 totals B A B

10 11 12

Year 4 totals Totals for 12 crops Averages (per year)

90 103 119

79 58 96

0 1 1

48 31 54

31 26 41

110 83 136

Relative lamb value

83 58 123

80 69 108

264

257

83 68 121

80 81 106

272

267

82 73 II1

79 87 97

266

263

83 63 111

80 75 97

257

252

1059

1039

264.75

259-75

r e s p e c t i v e l y , w h e r e w e e k 1 c o m m e n c e s o n J a n u a r y 1st. T h e s e t a b l e s s h o w t h e f l u c t u a t i o n s in t h e sizes o f f l o c k s A a n d B t h a t t a k e p l a c e as ewes a r e t r a n s f e r r e d b a c k and forth, together with information on the lambing statistics. Ewes have been

SIMULATION OF INTENSIFIEDLAMBINGSYSTEM

I l5

r e m o v e d f r o m the flocks on their date o f death. Relative lamb value is the p r o d u c t o f the n u m b e r o f lambs sold and the relative price at which they were sold. Figure 2 shows the fluctuations that can take place in the total n u m b e r o f lambs sold over the 4 year period as the time o f first m a t i n g is changed. Th e 2 runs plotted used different sequences o f r a n d o m numbers. Figure 3 shows similar fluctuations in the relative value o f lambs, using d a t a f r o m the same 2 runs. This is typical o u t p u t in the sense that, as the p r o g r a m e m p l o y s several r a n d o m n u m b e r g e n e r a t o r s to simulate the stochastic elements, it will necessarily p r o d u c e different results each time that it is run with a c h a n g e d sequence o f r a n d o m numbers. TABLE 6 T Y P I C A L O U T P U T W H E N F I R S T MA I-ING IS IN W E E K 49

~7oek

Crop No.

A

1

B

2

A

3

No. of No. of ewes ewe~ mated lambblg

100 120 88

80 112 44

No. oJ zero #tters

No. oJ smg~s

No. of pairs of twins

0 2 4

59 88 24

21 22 16

7otal No. No. o]" of lambs lambs at born 120 days

101 132 56

Year 1 totals B A B

4 5 6

155 78 125

120 68 65

2 0 1

66 39 36

52 29 28

170 97 92

Year 2 totals A B A

7 8 9

128 95 100

92 86 51

2 0 2

45 48 28

45 38 21

135 124 70

Year 3 totals B A B

10 11 12

Year 4 totals Total for 12 crops Averages (for year)

132 76 112

105 65 58

1 0 1

60 31 37

44 34 20

148 99 77

Re~tive lamb va~e

82 99 42

77 91 48

223

216

139 73 69

132 67 79

281

278

ll0 93 52

104 85 59

255

248

121 74 57

114 68 65

252

247

1011

989

252.75

247-25

T h e m e a n s are n o t significantly different between these two runs. In the m a j o r i t y o f runs m ad e, the lowest o u t p u t was o b t a i n e d when the first m a t i n g occurred in the 49th week. T h e o t h e r values are r e m a r k a b l y c o n s t a n t a l t h o u g h the detailed o u t p u t for l a m b cr o p s c o n t r i b u t i n g to each 4-year total varies c o n s i d e r a b l y as the starting time is changed. A second type o f o u t p u t shows the percentage o f ewes in each l am b i n g frequency over a wide range o f starting times for all ewes in the m o d el that survived the full 4 year run. A n e x a m p l e is given in T a b l e 7.

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P. A. GEISLER, A. C. PAINE, P. E. GEYTENBEEK TABLE 7 THE EFFECT OF STARTING TIME ON THE PERCENTAGE OF EWES IN A RANGE OF LAMBING FREQUENCIES OVER A FOUR-YEAR PERIOD ( R u n 1)

Starting time (week)

Number of lambings* 3

4

5

6

1 5 9 13 17 21 25 29 33 37 41 45 49

1.2 0-6 0-6 1.2 2.4 1.8 0-6 0.6 1.2 1-8 2.4 0.0 1.2

18.0 13.2 8.4 16.2 12.6 16.2 12.6 13.2 19.2 13.2 9.0 7.8 21.6

48.5 46.7 55.7 46.7 47.3 44.3 50.9 51-5 52.7 54-5 50-3 55.1 54.5

32.3 39-5 35.3 35.9 37.7 37.7 35.9 34.7 26.9 30-5 38-3 37-1 22-8

* In the m a j o r i t y o f runs no ewes were observed to have less t h a n 3 l a m b i n g s .

DISCUSSION

The output of the model has been found to be remarkably stable--the starting time has very little effect on the accumulated number of lambs produced within the system over the 4-year period. Minimum levels of production are approximately 5 ~ below maximum level. This is so despite the fact that detailed results for separate lamb crops show variation with changes in starting time. Lowest outputs were recorded when the model commenced operating in week 49. This starting week gives a sequence in which every third mating occurred near week 31 when oestrus activity was at its lowest. The relative value of the lamb output also shows little variation with starting time. The model stops short of a full economic analysis of the system since lamb production in different regions is subject to a wide range of costs for labour, feeding, housing, hormone treatments and anthelmintics, while lamb prices and support policies vary markedly. Under southern Australian conditions, ewes and their lambs graze sown pastures which permit satisfactory growth rates for lambs born in autumn, winter and early spring (weeks 9-34). Lambs born at other times and in dry seasons, however, would require irrigated pasture or special supplementary feeding to achieve satisfactory market weights at 120 days of age. No attempt has been made in the model to calculate additional feed costs to promote uniform growth rates nor to calculate the net value of lambs produced in this dual flock system. The relative value of lamb crops does, however, take into account seasonal fluctuations in lamb prices which reflect normal supply and demand factors operative in this environment. The model was developed to determine the optimum starting time for a dual flock

SIMULATION OF INTENSIFIEDLAMBINGSYSTEM

1 19

intensive l a m b i n g system involving a specific crossbred ewc with an extended breeding season. It indicates that where such a system can operate u n d e r A u s t r a l i a n c o n d i t i o n s , it will m a i n t a i n a steady o u t p u t over time a n d that the system is relatively insensitive to changes in starting time. This is a very simple model a n d clearly could be m u c h improved if more detailed i n f o r m a t i o n were available o n the inputs relating to reproductive performance. These include oestrus activity, c o n c e p t i o n rates, ewe a n d lamb mortalities and litter size, which are all likely to be specific for ewe breed a n d age a n d d e p e n d e n t on season. C o n s e q u e n t l y , the model could be expected to p r o d u c e very different o u t p u t s for different starting times over a range o f e n v i r o n m e n t s . In the model a m a t i n g p r o g r a m m e was used with a ewe flock being j o i n e d at regular 4 - m o n t h l y intervals. However, modification o f the system to permit shorter or longer intervals between m a t i n g s m a y be w a r r a n t e d a n d the model is capable of indicating the effect on o u t p u t o f such changes.

ACKNOWLEDGEMENT T h a n k s are due to Jean W a l s i n g h a m for m a n y helpful discussions d u r i n g the early d e v e l o p m e n t of this model.

REFERENCES BASSON,W. D., VANNIEKERK,B. D. H., MULDER,A. M. & CLOETE,J. G. (1969). The productive and reproductive potential of three sheep breeds mated at 8-monthly intervals under intensive feeding conditions. Proc. S. AJ?. Soc. Anon. Prod., 8, 149-54. COPENHAVER, J. S. & CARTER, R. C. (1968). Very early weaning (confinement rearing of lambs) rebreeding ewes for multiple lambing. 1967-68 livcstock research report. Res. Rep. Res. Div. Va polytech. Inst., No. 126, 61-9. GEYTENBEEK, P. E. (1973). Frequency of lambing for prime lamb production in a Mediterranean environment: UA 2S. Aust. Meat Res. Comm., ,4. Rep. 7, 82. LAND, R. B. & MC~LELLAND,T. H. (1971). The performance of Finn-Dorset sheep allowed to mate four times in two years. Anon. Prod., 13, 637-41. ROmNSON,J. J., FRASER,C., MCHATT1E,I. & GILL,J. C. (1975).The long-term reproductiveperformance of Finnish Landrace x Dorset Horn cwes subjected to photostimulation and hormone therapy. Proc. Brit. Soc. Anita. Prod., 4, 115. SCHRIBER,T. J. (1974). Simulation using GPSS. New York, Wilcy. TCI-IAMITCHIAN,L. & RICORDEAU,G. (1974). Factors of variation on fertility and prolificacy in accelerated program of meat shccp reproduction. Proc. 1st World Cong. Genelics applied to Livestock Production, 3, Contributed Papers, 979-88. XEROX(1972). Xerox General Purpose Discrete Simulator (GPDS). ReJ~,rence Manual.