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A model of the effect of nutrition on litter size and weight in the pregnant ewe
A MODEL OF THE EFFECT OF N U T R I T I O N ON LITTER SIZE A N D WEIGHT IN THE P R E G N A N T EWE
J. E. NEWTON & P. R. EDELSTEN
Grassland Research Institute, Hurley, Great Britain
SUMMAR Y
A model has been developed to predict litter size, lamb birthweight, perinatal lamb mortality and ewe weight change during the second part of pregnancy from different nutritional regimes. The model, which can contain 200 ewes, has been tested against ]~eld data from experimental flocks of Masham, Finn x Scottish Halfbred and Welsh Mountain ewes. The prediction of litter size from weight at mating is reasonable as is the prediction of mean lamb birthweight for a range of litter sizes. The model currently overestimates the weight of Finn x S. Halfbred singles, and underestimates ewe weight increase in late pregnancy and the mortality of lambs from some litter sizes. The problem of predictive accuracy is discussed and weighed against the task of collecting a great deal of data. The problem with a predictive reproductive model is that reproductive performance is a breed characteristic whereas nutritional demand can be predicted from size and physiological state.
INTRODUCTION
The purpose of building this model was to examine two effects of nutrition on the reproductive process in sheep. The first was the effect of a range of ewe weights at mating, within a flock, on the subsequent litter size distribution. The second was the effect of different levels of nutrition during the last eight weeks of pregnancy on growth rate, birthweight and survival. This is a simple model and a great many processes have been missed out, largely because of insufficient knowledge or irrelevance to the purpose of the model. For instance, there is nothing in the model concerning the effect of the ewe being mated at different stages of the breeding season, or about the effect of type of mating (natural or AI) on fertilisation rate, or about the effect of nutrition on embryonic 185 Agricultural Systems (1) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain
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J. E. N E W T O N A N D P. R. EDELSTEN
mortality in the first 30 days of pregnancy. In our opinion, knowledge is lacking about the effect of ewe bodyweight and condition, related to any British breed, on ovulation rate at different stages of the breeding season. Nor is it possible to ascribe the high level of embryonic mortality in the first 30 days of pregnancy to under- or over-feeding or to relate it to the number of embryos present in the uterus. The model deals with a flock of ewes and will predict the number of live lambs born per ewe for up to 200 individual ewes. Litter size is set at mating in relation to ewe weight. The foetuses grow in relation to the ewe's plane of nutrition during pregnancy. At the same time, changes in ewe weight and body condition are produced. Finally, date of lambing, lamb birthweight and survival rate, and ewe weight directly after lambing are predicted for each ewe. This provides input data for the model of ewes and lambs grazing at pasture (Edelsten & Newton, 1975).
D E S C R I P T I O N OF R E L A T I O N S H I P S IN TIlE M O D E L
A flow diagram of the model is shown in Figs. 1 and 2. The model can be divided into two parts--the population side and the food intake and energetics.
The population side 1. Ewe weight at mating: A mean weight and standard deviation for the flock is put in as an initial value; this can be varied for breed. A random number generator then selects a weight for each ewe. It is assumed that, although each ewe will have a different weight at mating, it is in the same body condition. This body condition is set as the ratio of the amount of 'fat' to the amount of 'bones' plus 'fat'. The amount of 'fat' and 'bones' can then be calculated for each ewe. Conceptually the weight of the 'bones' is that weight below which the ewe immediately dies, the rest of the animal tissue is termed 'fat'. Thus, in a flock of ewes of mean weight 65 kg__.5, and of mean body condition 0.38, a ewe of 70 kg liveweight would be composed of 'bones' weighing 43.4 kg and 'fat' weighing 26.6 kg. A second ewe of 60 kg, also of body condition 0.38, would have 'bones' of 37.2 kg and 'fat' of 22.8 kg. The difference in weight of 'bones' is regarded as natural variation within a breed population, of size of frame and weight of essential organs. 2. Number of barren ewes: This is put into the program as an initial value which can be varied for breed. The probability of a ewe being barren is independent of weight, 3. Day of mating: It is assumed that 80 ~o of the flock are mated during the first 17 days from ram inclusion, 15 ~ during the second 17 days and the remaining 5 ~o in the third oestrous cycle. The day of ram inclusion can be varied, as can the speed
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EFFECT OF N U T R I T I O N O N LITTER SIZE A N D W E I G H T
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EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
189
at which the ewes are successfully mated. There is a random number generator which selects the day of mating for each ewe. 4. Number o f foetuses present at 90 days: The number of foetuses per ewe is affected by the breed of ewe and the weight of the ewe at mating. Thus a Masham ewe is likely to have a higher proportion of triplets than a Welsh Mountain ewe and different tables are used. The probability of various litter sizes by ewe weight for the Masham ewe is shown in Table 1. TABLE 1 CORRELATION OF LITTER SIZE WITH EWE WEIGHT (MASHAM EWE)
Weight of ewe (kg)
1
54 78
0.2 0"07
Probability of litter size 2 3 0.68 0"59
0.12 0"32
4 0 0
(Data from N. E. Young & J. E. Newton, Unpublished) There is linear interpolation within the table such that the chance of a ewe of 54 kg having a single lamb is 20 % and of a ewe of 78 kg having a single lamb is 7 %. The chance of a 66 kg ewe having a single is intermediate, i.e. 13.5%. There is no chance of a Masham ewe having quads. The foetuses appear as a weight at 90 days from time of mating. The weight of a foetus at 90 days is 0.67 kg (A. J. F. Russel, pers. comm.), irrespective of litter size. The weight of foetal fluid is assumed to be the weight of the foetuses x 0.4 (Meat and Livestock Commission, 1973). Although there are data for earlier weights for foetuses (e.g. Joubert, 1956) it was felt that the energy cost of the foetus, compared with that of the ewe, was so slight up to 90 days that it would be sufficient for the foetus to 'appear' at this stage. Furthermore, as stated in the Introduction, the modelling of the first 30 days from fertilisation would require information on the effect of nutrition and embryo number on embryo mortality, and this is lacking. 5. Rate of foetal survival: The only cause of foetal death between 90 days and lambing in the model is starvation. If ewe condition sinks to a level of 0.2, where the ewe is only just above its 'bones' weight and close to death, then the contents of the uterus die. 6. Day of lambing: Day of lambing for each ewe is 145 days from day of mating for ewes carrying triplets and quads, 146 for twins and 147 for ewes with singles, plus or minus a standard deviation factor, which is set by a random number generator. 7. Number of lambs born: The number of lambs born is generated from the
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J. E. N E W T O N A N D P . R . EDELSTEN
number of foetuses present at 90 days minus those that die of starvation between day 90 and parturition. This number is then divided into lambs born dead or alive. The probability of a lamb being born dead is related to birthweight and not to litter size, although a quad lamb is likely to have a lighter birthweight in practice and thus a lower probability of being born alive. The form of the data for Mashams is shown in Table 2, with the chances of death increasing at the lighter and heavier TABLE 2 LAMB DEATH
Lamb weight (kg)
Probability of being born dead
0"0 2"5 5"0 7"5 I0"0
0"1 0-05 0.05 0"5
1 "0
ends of the range of birth weights. Again there is linear interpolation between values in the table.
The nutritional-energy part of the model The nutritional part (the last 8 weeks of pregnancy) takes place indoors, when ewes are being fed in groups with bulk food (hay or silage) as a ration or ad lib and a ration of concentrates. It is assumed that, for the first 90 days from when the first ewe was mated, the ewes maintain their mating weight. 1. Concentrate ration: This can be set by the manager and typically, for a 65 kg ewe with twins, rises from 200 g/head/day on Day 90 from the time of ram inclusion to 600 g/head/day on Day 141. It is assumed that the ewes are group fed and that there is considerable variation in the amount of concentrate that each ewe manages to eat (Foot & Russel, 1973; Foot et al., 1973). At I00 g/head/day there is greater variation (36 %) than at 1000 g/head/day (I 5 % variation). The position of each ewe either side of the mean for intake is set at the beginning of the program, using a random number generator. 2. Bulk food: There is also variation in the amount of hay or silage that the ewe can eat, which is independent of the amount of concentrate that she can eat. The amount of hay or silage is decided by a random number generator for each ewe at the beginning of a run of the program. 3. Potential dry matter intake: This is calculated, for each ewe of the flock, assuming the ewe to be in good body condition. This is to stop fat ewes eating more than thin ewes. Litter size is assumed to have no modifying effect on potential intake. The values we have used are shown in Table 3.
EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
191
TABLE 3 POTENTIAL DRY MATTER INTAKE
Ewe
wt (kg)
0.0 65 100
DM intakelkg/head[day 0"0 1"7 2-2
However, for each level of potential dry matter intake there is a standard deviation of 10 %. Thus a random number generator decides what the potential dry matter intake of a 65 kg ewe is, within the range 1.7 + 0"34 kg. The amount of concentrate eaten x 0.46 (the replacement factor of concentrate for silage or hay), and the amount of bulk food eaten, are then added together. If this sum is less than the potential dry matter intake then this is what the ewe eats. If this sum is greater than the potential dry matter intake for that ewe, then the ewe eats the potential dry matter intake. Any silage or hay not consumed is left over for consumption on the following day. 4. Conversion of dry matter to metabolisable energy (ME): This is done using a series of constants. ME (Meals) = DM (kgs) x 4.4 x Digestible Organic Matter of the dry matter (D value)x0.82 (losses of CH4 and urine energy = 0.18 (Agricultural Research Council, 1965). 5. Energy partition between ewe and foetus: First, metabolisable energy is used to satisfy the maintenance requirement of the ewe (0" 1 x liveweight 0.73 Meals) and the maintenance requirement of the foetus, 0.09 x foetal wt (Russel et al., 1967), then the remaining energy is used for foetal growth and ewe growth in that order. The foetus will grow at its maximum growth rate before the ewe will grow. (The ewes are assumed to be mature.) If there is not enough metabolisable energy to satisfy the maintenance requirements of the ewe and foetus then the ewe loses weight (from the 'fat' part) and liberates energy. 6. Conversion of energy to foetal weight: Secondly, energy is used for ewe growth. There was some difficulty in finding an agreed conversion factor for converting ME to foetal weight so a compromise value of 7 kcals/1 g foetal weight increase was used (Graham, 1964; Russel et aL, 1967). This incorporates the apparent inefficiencies in the process such as uterine wall thickening. The speed at which the foetus will grow from Day 90 varies with the breed of the ewe and ram and also with litter size. We have assumed that the maximum rate of growth per day for a Dorset Down x Masham single foetus is 0.0407+0.004 x foetal weight and that for a Dorset Down x Welsh Mountain foetus it is 0.029 + 0.003 x foetal weight. It is assumed that the energy value of the foetal fluid is zero.
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7. Conversion o f energy to ewe bodyweight: Thirdly, any energy left is used for ewe weight gain. The conversion efficiency of metabolisable energy to tissue in the ewe is taken to be 75% (Agricultural Research Council, 1965) and the amount of energy required to make 1 kg of tissue depends on the state of fatness of the ewe, according to Table 4. TABLE 4 CALORIFIC VALUE OF 1 KG LIVEWEIGHT
State of fatness ('Fat'#fat'+ 'bones') ratio 0"0
0-33 0-5
Calorificvalue (Mcals) 1 "0
6-6 7"7
The fatter the ewe, the greater the energy cost of putting on 1 kg of tissue. 8. Rate at which a ewe will lose weight: It has been assumed that the rate at which a ewe loses weight is governed by its body condition, in the manner shown in Table 5. TABLE 5 RATE AT WHICH A EWE WILL LOSE WEIGHT
State of fatness
Maximum weight loss
0 0'2 0"33 0'5
0'025 0"025 0"250 0.300
('Fat'/'fat' +'bones') ratio
(kg/day)
Thus the heavier and fatter a ewe, the faster it will lose weight, but it will never lose weight faster than 300 g/head/day. The amount of energy released will also depend on calorific value, which depends on ewe body condition (Table 4). It is assumed that at a certain ewe body condition (0.2) the foetus will die and that at a lower body condition still (0.05) the ewe will die. 9. Partition o f energy between foetuses: The foetus 'appears' on Day 90 from mating and its weight on that day is 0.67 kg. If there is only a single lamb then all the energy for the foetus goes to that lamb; however, if there are two, three or four lambs, it is assumed that each lamb in the uterus received a different amount. A random number generator selects, at the outset, which lamb within the litter will get most energy. This simulates the fact that lambs within the uterus grow at different speeds, due to position and number of cotyledons, etc., and thus end up at different weights.
EFFECT OF NUTRITIONON LITTERSIZE AND WEIGHT
193
VALIDATIONOF THE MODEL Having constructed and run the model, the next stage is validation. Some of the tables in the model were derived from data from Masham, Finn x Scottish Half bred and Welsh Mountain flocks during pregnancy and lambing in 1971-2 and 1972-3. Validation of the model has therefore been undertaken by comparing model output with the performance of two separate flocks of Mashams of 57 and 100 ewes each, one flock of Finn x Scottish Halfbreds (58 ewes) and two separate flocks of Welsh Mountain ewes (132 and 100 ewes each). The two Masham flocks and the F × SH flock were housed at the Institute during pregnancy and reasonably close control was achieved over nutrition during the housed period. One flock of Welsh Mountain ewes (132) was kept at the Institute and housed during late pregnancy, the other flock was mated three weeks later and roamed the Berkshire College of Agriculture (BCA) farm during late pregnancy. Level of intake for the BCA flock during this phase was not measured, even on a group basis. All that was known was the amount of concentrate food offered. The comparison between the model predictions of mean litter size for flocks of different bodyweight at mating and the field experimental results is shown in Table 6. Having put a relationship into the model in which mean litter size was assumed to increase with increased ewe bodyweight at mating, it was disconcerting TABLE 6 EFFECT OF BODY~VEIGFIT AT MATING ON REPRODUCTIVE PERFORMANCE
Breed
No. o f ewes
Bodyweight at mating (kg)
Mean litter size
Masham
200 200 200 57 100
56-4 66"4 76"4 64.05 68"49
Model Model Model Experiment Experiment
1.88 2"0 2-10 2.16 1"95
Finn x S. Half bred
200 200 200 58
57.8 68.0 78.2 64.35
Model Model Model Experiment
2.04 2.34 2.74 2' 65
Welsh Mountain
200 200 200 132 100
29'5 34.7 39'9 35"4 40.4
Model Model Model Experiment Experiment
1"06 1.19 1"26 1.18 1.17 (later mating)
to find that the two experimental flocks of actual Mashams behaved in the opposite manner. However, if the results for the two flocks are averaged, the mean litter size was 2.02 from a bodyweight of 66.9 kg, and this fits the model prediction beautifully. Other people have discovered a similar discrepancy when making a more
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detailed comparison of two different populations of the same breed (Gunn et al., 1972). It was found that source of ewe had a significant effect on both ovulation rate and embryo mortality. The experimental flock of Finn x Scottish Halfbreds had more lambs than anticipated but the performance of the larger Welsh flock (132) fitted the model prediction well. Looking at the relationships in the model, which were based on previous lambing performance, the F x SH was more responsive both to absolute weight change and to relative weight change than the Masham or the Welsh Mountain. Over the weight range involved the change in mean litter size per kilogramme bodyweight was 0.04 for the F x SH, 0.01 for the Masham and 0.025 for the Welsh Mountain. This suggests that a generalised relationship for mean litter size and ewe bodyweight, which ignores breed, will be very inaccurate. An examination of relative weight difference, which ignores breed effects, was just as inaccurate. A 15 % increase in bodyweight would increase the mean litter size of Mashams by 0.1, the F x SH by 0.4 and the Welsh Mountain by 0.07. The conflict between a simple model and predictive accuracy is taken up more fully in the Discussion. A comparison of litter size distribution is shown in Table 7. The experimental flocks consistently had fewer barren ewes than was forecast, but apart from this the relative distribution of litter size within breeds was quite reasonable. The model failed to forecast the F x SH ewe that produced quintuplets, but that is not a major error. TABLE 7 LITTER SIZE DISTRIBUTION
Breed
Liveweight of ewe at mating (kg)
No. of ewes
Proportion (%) of ewes having litter sizes of 0
1
2
3
4
5
0 0 0
0 0 0
Masharn Masham Masham
200 57 I00
Model Expt. Expt.
66.40 64.05 68.49
8 0 5
17.5 57 9 67 19 62
17.5 24 14
Finn x S. Halfbred Finn x S. Halfbred
200 58
Model Expt.
68.00 64.35
8 3
18.5 32 12 27
33 43
8'5 13
0 2
Welsh Mountain Welsh Mountain
200 132
Model Expt.
34.70 35.40
10 7
0 0
0 0
0 0
72.5 17.5 76.5 16.5
The effect of nutrition during pregnancy on lamb birthweight is shown in Table 8. The most striking comparison between the model results and the experimental results was the overestimate of the birthweight of the single lambs in the model for the Masham and the F x SH ewes. This is brought out in the ratio between singles and twins and twins and triplets. The situation was reversed for the Welsh, with the model underestimating the weight of Welsh singles.
TABLE 8 THE EFFECT OF 'STANDARD' NUTRITION D U R I N G THE LAST 8 WEEKS OF PREGNANCY ON LAMB BIRTHWEIGHT ( _+ STANDARD DEVIATION)
Breed
Lamb birthweights (kg) 2 3
1
Masham--model Masham---expt. Masham---expt.
6.33 -+0.43 5.38_+0.70 5.73_+0.81
5.02 _+0.71 4.50+0.83 4.77 +_-0.82
3"84+__0"73 3"80 _+0"75 4'04-+0"85
Finn x S. Halfbred--model Finn x S. Halfbred---expt.
6-354-0.44 4.10 + 0.61
4.96-+0.76 3.64-+ 1.01
3"75+0"60 3.21 _+0"73
Welsh Mountain--model Welsh Mountain---expt. Welsh Mountain----expt. BCA
3.32 + 0.14 3.78 _+0.4 3.75_+0.71
3.06 _+0-29 2-75 _+0.47 2.57+0.57
Ewe wt. before lambing (kg)
4
66'4 64'05 68'5 2"92_+0"62 2"654-__0.54
68"0 64.35 34"7 37'4 45 "4
RATIO OF THE W E I G H T OF LAMB BIRTHWEIGHTS FROM DIFFERENT LITTER SIZES
1:2 1.26 1.20 1.20
2:3 1.31 1.I 8 1.18
3:4
Masham--model Masham--cxpt. Masham--expt. Finn x S. Half bred--model Finn x S. Halfbred--expt.
1.28 1.13
1.32 1-13
1.28 1.21
Welsh Mountain--model Welsh Mountain--expt. Welsh Mountain---expt.
1-08 1.37 1.46 TABLE 9(a) EWE W E I G H T CHANGE D U R I N G PREGNANCY ( K G )
Number of ewes
Mating wt. (6/11) (1)
Wt. at 96 days preg. (Day 31) (2)
Wt. at 124 days preg. (Day 49) (3)
Post parturient weight (4)
35 5 19
63.6 62.2_+6.5 68.4+7.3
64.4 71.2_+5.0 72.5
67.6 77.6+6.6 75.8
65.8_+6.9 73.4+4.2 70.7_+9.2
Masham with2 Model Masham with 2 Expt. 1 Masham with2 Expt. 2
114 38 62
67.0 63-1 _+5.4 70.5+5-8
68.1 74.1 +6.2 74-2
71.9 78.8_+6.7 78.8
64"4+6.5 71.7_+6.5 70.0_+6.5
Masham with 3 Model Masham with3 Expt. 1 Masham with 3 Expt. 2
35 14 14
68.6 67.3_+5.4 72.6_+ 5"6
69.8 79.0_+6.9 79.2
74.5 85.3-+7-0 85"4
64'2-+ 6.3 73.7+7.4 70.3 + 8.4
Masham with0 Masham with0
16 5
67.4 73.4-+7.1
Breed Masham with I Model (M) Masham with 1 Expt. 1 (El) Masham with 1 Expt. 2 (E2)
Model Expt.
81.7-+8.6 83.0_+9.5
RATIO OF EWE WEIGHTS AT DIFFERENT STAGES I N PREGNANCY
Ratio 2:1 3:2 4:2 4:1 Barren 4:1
Masham with 1 M E1 E2 1.01 1,14 1.06
Masham with 2 M El E2 1.02 1.17 1.05
Masham with 3 M El E2 1.02 1.17 1.09
1.05
1.08
1-05
1.06
1.06
1.06
1.07
1.08
1.08
1.02 1.03
1.03 0,97 1 - 1 8 1-03
0.94 0.96
0.97 1.14
0.94 0.99
0.92 0-94
0.93 1.09
0.89 0.97
M 1.21
E 1.13
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J. E. NEWTON AND P. R. EDELSTEN
It was assumed in the model that, because the ewes were similar in bodyweight the F x SH ewes would grow their lambs at the same rate as Mashams. In practice the F x SH ewes had lighter lambs than the Mashams, particularly the singles. The weight changes during pregnancy for the three breeds are shown in Tables 9(a), (b) and (c). Considering the Masham first, there was evidence that experimental flock 1 (El) was rather light at mating and this is brought out by comparing the ratio 2:1 and 4: 1, for E1 and E2, where weight at mating (column (1)) has been TABLE 9(b) EWE WEIGHT CHANGE DURING PREGNANCY (KG)
Breed
Number of ewes
Mating wt. (1)
Wt. at 96 days preg. (2)
Wt. at 124 days preg. (3)
Post parturient weight (4)
F × SH with 1 F x S H with 1
Model (M) Expt. (E)
37 7
65.3 66.1+_9.2
66-0 69.2 77.3+__10.7 82.4±11.3
67.3 4- 6.2 80.9+-10.8
FxSHwith2 F x SH with 2
Model Expt.
64 16
67.2 63.6+6.4
68.3 76.8+7.7
71.9 83.5±8.5
64.6 + 5.7 78.14-9-1
F x S H with 3 F x SH with 3
Model Expt.
66 26
69.4 62.9+6.6
70.8 75-84-7.5
75.1 82.8_+8.3
64.4 ± 6.1 73.64-7.6
FxSH with4 F×SH with4
Model Expt.
17 8
73.5 67.5_+7.2
74.9 81"44-8.0
79.7 87.9±9.3
67.94-3.1 77.34-9-6
Ratio 2:1 3:2 4:2 4:1
F x SH M 1.01 1-05 1.02 1-03
RATIO OF EWE WEIGHTS AS DIFFERENT STAGES IN PREGNANCY
with 1 E 1.17 1.06 1.05 1.22
F × SH M 1.02 1.05 0.94 0.96
with 2 E 1.21 1.09 1.02 1.23
F x SH M 1.02 1.06 0.91 0.93
with 3 E 1.20 1.09 0.97 1.17
F x SH M 1.02 1-06 0.90 0.92
with 4 E 1.20 1.08 0.95 1.14
TABLE 9(c) EWE WEIGHT CHANGE DURING PREGNANCY(KG)
Breed Welsh with 1 Welsh with 1
Model (M) Expt. (E)
Welshwith 2 Welsh with 2
Model Expt.
Number of ewes
Mating wt. (1)
Pregnant wt. (Day 112) (2)
Post-parturient weight (3)
145 100
34.7 34-9 + 3-7
35.7 37.1 ± 3.9
33.1 _ 3.7 36.4 +4.2
35 21
35.6 37.3 + 2.6
37.4 40.5 4- 3.3
31-1+2.9 36.9 4- 3.3
RATIO OF EWE WEIGHTS IN DIFFERENT STAGES IN PREGNANCY
Ratio2:1 3:1
Welsh with I M E 1-03 1-06 0.95 1.04
Welsh with 2 M E 1.05 1.08 0.87 0-99
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EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
used as the base line. There was good agreement between the model and E2 throughout pregnancy and up to parturition. There was experimental support for the hypothesis that the heavier ewes in the flock have the higher litter sizes and that it is harder for the ewes carrying larger litter sizes (e.g. triplets) to maintain their own bodyweight during late pregnancy. The experimental F x SH and Welsh ewes were also rather heavier than the model ewes by Day 96 in pregnancy, and so were the weights after lambing (Tables 9(b),
(c)). It would seem from Tables 8 and 9 that the relationships used in the model have overestimated lamb birthweights and underestimated ewe weight gains, particularly in the ewes having singles. However, the experimental F x SH ewes have behaved differently from the experimental Mashams, for the ratio of ewe weight after lambing to the birthweight of a single lamb was 19.7 for the F x SH, and only 12.3 for the Masham. The comparison between predicted and actual neonatal lamb mortality is shown in Table 10. The model has consistently underestimated lamb mortality for each TABLE 10 ~o LAMBMORTALITYAT BIRTH Litter size 1
2
3
2.9 (35) 40 (5) 0 (19)
0.9 (228) 5.3 (76) 4.8 (124)
3.8 (105) 9.5 (42) 19.0 (42)
F x SH--model F x SH----expt.
2.7 (37) 0 (7)
0.8 (128) 3.1 (32)
4.5 (198) 12.8 (78)
Welsh--model Welsh----expt. Welsh---expt.
4"1 (145) 5 (101) 12.5 (80)
2-8 (70) 2.3 (44) 9.4 (32)
Masham--model Masham---cxpt. Masham----expt.
4
14.7 (68) 12.5 (32)
( ) number of Iambs born.
breed and each litter size, except for the F x SH quadruplets. The F x SH quads were the lightest Iambs, which was why the model predicted higher mortality. It would seem from this comparison that, although lambs of very light and heavy birthweight have a greater chance of early death, the probability factor for lambs dying in the middle weight range should be increased.
DISCUSSION
The important question left over from the validation section is to decide whether the model is sufficiently accurate to be used. If this is not the case then what should
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J. E. NEWTON AND P. R. EDELSTEN
be done to improve it ? If it is sufficiently accurate, then to what use can it be put ? The answer to this question is that the model is good in parts. Taking the relationships, briefly, in order, the effect of ewe weight at mating on subsequent litter size was reasonable. However, the behaviour of the two experimental Masham flocks raised an important point, which concerns the collection of data. There are a great many breeds and crossbreeds of sheep in the United Kingdom alone. There appears to be no hypothesis that enables litter size to be predicted for sheep, from any other parameter, such as size. Big breeds of sheep do not have more lambs than small breeds, or vice versa. Lacking such a predictive parameter, there are two possible courses of action, one can either collect reproductive data from every known breed, crossbreed and strain within a breed, or else postulate, usefully, at the outset that there are three possible response curves to weight increase, corresponding to sheep of low, medium and high fertility, and accept a degree of inaccuracy in the answer. One purpose of the model, and modelling, is to reduce data collection and repetitive experimentation by forcing the modeller to advance new hypotheses or to acknowledge acceptance of existing ones. The purpose of this model is not to predict litter size for every known genetic variation of sheep, nor, on the other hand, to be only capable of use for one specific cross. It must be a compromise between widespread applicability and accuracy. The prediction of litter size distribution was reasonable, but the partition of energy between the ewe and the foetus was inaccurate for ewes with singles. Once again, experimental evidence suggested that there were breed differences. Does it matter if a Finn x S. Half bred ewe was predicted to behave like a Masham, because it was the same weight and had singles weighing 6.35 kg instead of 4.1 kg? It is known, for instance, that the Finn ewe has a shorter gestation period; what is the effect of assuming a 142 day gestation length instead of a 147 day one ? The model can be used to test this, but how much does the inaccuracy matter? (In fact when calculated in the model the birthweight of single lambs born to Finn x ewes was 6.35 and 5.14 kg with a gestation length of 147 and 142 days, respectively.) There are two contexts in which to answer the question of inaccuracy. One is that it is based on inaccurate scientific knowledge and that it must be right to increase knowledge, but questions of priority will arise. The other is that the inaccuracy matters to a practical system of keeping sheep. Will a 4.1 kg lamb grow more slowly than a 6.35 kg lamb? This will affect the date of slaughter, price received, etc. and, as a consequence, wrong advice might be given. It seems to us more advisable to try to test the effect of different levels of inaccuracy, if possible, rather than to say if the answer is within 10~ of the field situation it is acceptable. The accuracy has to be related to the factor and to the context. The relationship between lamb birthweight and pre-natal mortality requires further attention because the model currently underestimates mortality. The amount of population variation in ewe weight and lamb birthweight was in reasonable accordance with the field variation.
EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
199
I n conclusion, it w o u l d be preferable to v a l i d a t e the m o d e l a g a i n s t a n o t h e r y e a r ' s results b e f o r e d e v e l o p i n g it further to show w h a t the e c o n o m i c consequences o f n u t r i t i o n a l t r e a t m e n t s are likely to be.
ACKNOWLEDGEMENTS T h e a u t h o r s wish to t h a n k M r J. E. Betts, D r J a n e t F o o t , D r A. J. F. Russel a n d M r N. E. Y o u n g for supplying d a t a which was used in the model.
REFERENCES
AOmCtml"URAL RESEARCHCOUNCIL (1965). The nutrient requirements of farm livestock, No. 2. Ruminants. A.R.C., London. EDmSTEN, P. R. & NEWTON, J. E. (1975). A simulation model of intensive lamb production from grass. Tech. Rep. No. 17, Grassland Research Inst., Hurley. FOOT, J. Z. & RUSSEL,A. J. F. (1973). Some nutritional implications of group feeding hill sheep. Anim. Prod., 16, 285-92. FOOT, J. Z., RUSSEL,A. J. F., MAXWELL,T. J. • MORRIS, P. (1973). Variation in intake among group fed pregnant Scottish Blackface ewes given restricted amounts of food. Anita. Prod., 17, 169-78. GR~, M. McC. (1964). Energy exchanges of pregnant and lactating ewes..,lust. J. agric Res., 15, 127-41. Gun,q, R. G., DORY, J. M. & R~SSEL, A. J. F. (1972). Embryo mortality in Scottish Blackface ewes as influenced by body condition at mating and by post-mating nutrition. J. agric. Sci. Camb., 79, 17-25. JOUBERT, D. M. (1956). A study of pre-natal growth and development in the sheep. J. agric. Sci. Camb., 47, 382--428. MEATAND LIVESTOCKCOMMISSION(1973). Feeding the ewe, Sheep Improvement Service Technical Report No. 2. RUSSEL,A. J. F. (Personal comm.). RUSSEL, A. J. F., DONEY, J. M. & REID, R. L. (1967). Energy requirements of the pregnant ewe. J. agric. Sci. Camb., 68, 359-63. YOUNG, N. E. & NEWTON,J. E. Unpublished data.
J. E. NEWTON & P. R. EDELSTEN
Grassland Research Institute, Hurley, Great Britain
SUMMAR Y
A model has been developed to predict litter size, lamb birthweight, perinatal lamb mortality and ewe weight change during the second part of pregnancy from different nutritional regimes. The model, which can contain 200 ewes, has been tested against ]~eld data from experimental flocks of Masham, Finn x Scottish Halfbred and Welsh Mountain ewes. The prediction of litter size from weight at mating is reasonable as is the prediction of mean lamb birthweight for a range of litter sizes. The model currently overestimates the weight of Finn x S. Halfbred singles, and underestimates ewe weight increase in late pregnancy and the mortality of lambs from some litter sizes. The problem of predictive accuracy is discussed and weighed against the task of collecting a great deal of data. The problem with a predictive reproductive model is that reproductive performance is a breed characteristic whereas nutritional demand can be predicted from size and physiological state.
INTRODUCTION
The purpose of building this model was to examine two effects of nutrition on the reproductive process in sheep. The first was the effect of a range of ewe weights at mating, within a flock, on the subsequent litter size distribution. The second was the effect of different levels of nutrition during the last eight weeks of pregnancy on growth rate, birthweight and survival. This is a simple model and a great many processes have been missed out, largely because of insufficient knowledge or irrelevance to the purpose of the model. For instance, there is nothing in the model concerning the effect of the ewe being mated at different stages of the breeding season, or about the effect of type of mating (natural or AI) on fertilisation rate, or about the effect of nutrition on embryonic 185 Agricultural Systems (1) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain
186
J. E. N E W T O N A N D P. R. EDELSTEN
mortality in the first 30 days of pregnancy. In our opinion, knowledge is lacking about the effect of ewe bodyweight and condition, related to any British breed, on ovulation rate at different stages of the breeding season. Nor is it possible to ascribe the high level of embryonic mortality in the first 30 days of pregnancy to under- or over-feeding or to relate it to the number of embryos present in the uterus. The model deals with a flock of ewes and will predict the number of live lambs born per ewe for up to 200 individual ewes. Litter size is set at mating in relation to ewe weight. The foetuses grow in relation to the ewe's plane of nutrition during pregnancy. At the same time, changes in ewe weight and body condition are produced. Finally, date of lambing, lamb birthweight and survival rate, and ewe weight directly after lambing are predicted for each ewe. This provides input data for the model of ewes and lambs grazing at pasture (Edelsten & Newton, 1975).
D E S C R I P T I O N OF R E L A T I O N S H I P S IN TIlE M O D E L
A flow diagram of the model is shown in Figs. 1 and 2. The model can be divided into two parts--the population side and the food intake and energetics.
The population side 1. Ewe weight at mating: A mean weight and standard deviation for the flock is put in as an initial value; this can be varied for breed. A random number generator then selects a weight for each ewe. It is assumed that, although each ewe will have a different weight at mating, it is in the same body condition. This body condition is set as the ratio of the amount of 'fat' to the amount of 'bones' plus 'fat'. The amount of 'fat' and 'bones' can then be calculated for each ewe. Conceptually the weight of the 'bones' is that weight below which the ewe immediately dies, the rest of the animal tissue is termed 'fat'. Thus, in a flock of ewes of mean weight 65 kg__.5, and of mean body condition 0.38, a ewe of 70 kg liveweight would be composed of 'bones' weighing 43.4 kg and 'fat' weighing 26.6 kg. A second ewe of 60 kg, also of body condition 0.38, would have 'bones' of 37.2 kg and 'fat' of 22.8 kg. The difference in weight of 'bones' is regarded as natural variation within a breed population, of size of frame and weight of essential organs. 2. Number of barren ewes: This is put into the program as an initial value which can be varied for breed. The probability of a ewe being barren is independent of weight, 3. Day of mating: It is assumed that 80 ~o of the flock are mated during the first 17 days from ram inclusion, 15 ~ during the second 17 days and the remaining 5 ~o in the third oestrous cycle. The day of ram inclusion can be varied, as can the speed
187
EFFECT OF N U T R I T I O N O N LITTER SIZE A N D W E I G H T
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EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
189
at which the ewes are successfully mated. There is a random number generator which selects the day of mating for each ewe. 4. Number o f foetuses present at 90 days: The number of foetuses per ewe is affected by the breed of ewe and the weight of the ewe at mating. Thus a Masham ewe is likely to have a higher proportion of triplets than a Welsh Mountain ewe and different tables are used. The probability of various litter sizes by ewe weight for the Masham ewe is shown in Table 1. TABLE 1 CORRELATION OF LITTER SIZE WITH EWE WEIGHT (MASHAM EWE)
Weight of ewe (kg)
1
54 78
0.2 0"07
Probability of litter size 2 3 0.68 0"59
0.12 0"32
4 0 0
(Data from N. E. Young & J. E. Newton, Unpublished) There is linear interpolation within the table such that the chance of a ewe of 54 kg having a single lamb is 20 % and of a ewe of 78 kg having a single lamb is 7 %. The chance of a 66 kg ewe having a single is intermediate, i.e. 13.5%. There is no chance of a Masham ewe having quads. The foetuses appear as a weight at 90 days from time of mating. The weight of a foetus at 90 days is 0.67 kg (A. J. F. Russel, pers. comm.), irrespective of litter size. The weight of foetal fluid is assumed to be the weight of the foetuses x 0.4 (Meat and Livestock Commission, 1973). Although there are data for earlier weights for foetuses (e.g. Joubert, 1956) it was felt that the energy cost of the foetus, compared with that of the ewe, was so slight up to 90 days that it would be sufficient for the foetus to 'appear' at this stage. Furthermore, as stated in the Introduction, the modelling of the first 30 days from fertilisation would require information on the effect of nutrition and embryo number on embryo mortality, and this is lacking. 5. Rate of foetal survival: The only cause of foetal death between 90 days and lambing in the model is starvation. If ewe condition sinks to a level of 0.2, where the ewe is only just above its 'bones' weight and close to death, then the contents of the uterus die. 6. Day of lambing: Day of lambing for each ewe is 145 days from day of mating for ewes carrying triplets and quads, 146 for twins and 147 for ewes with singles, plus or minus a standard deviation factor, which is set by a random number generator. 7. Number of lambs born: The number of lambs born is generated from the
190
J. E. N E W T O N A N D P . R . EDELSTEN
number of foetuses present at 90 days minus those that die of starvation between day 90 and parturition. This number is then divided into lambs born dead or alive. The probability of a lamb being born dead is related to birthweight and not to litter size, although a quad lamb is likely to have a lighter birthweight in practice and thus a lower probability of being born alive. The form of the data for Mashams is shown in Table 2, with the chances of death increasing at the lighter and heavier TABLE 2 LAMB DEATH
Lamb weight (kg)
Probability of being born dead
0"0 2"5 5"0 7"5 I0"0
0"1 0-05 0.05 0"5
1 "0
ends of the range of birth weights. Again there is linear interpolation between values in the table.
The nutritional-energy part of the model The nutritional part (the last 8 weeks of pregnancy) takes place indoors, when ewes are being fed in groups with bulk food (hay or silage) as a ration or ad lib and a ration of concentrates. It is assumed that, for the first 90 days from when the first ewe was mated, the ewes maintain their mating weight. 1. Concentrate ration: This can be set by the manager and typically, for a 65 kg ewe with twins, rises from 200 g/head/day on Day 90 from the time of ram inclusion to 600 g/head/day on Day 141. It is assumed that the ewes are group fed and that there is considerable variation in the amount of concentrate that each ewe manages to eat (Foot & Russel, 1973; Foot et al., 1973). At I00 g/head/day there is greater variation (36 %) than at 1000 g/head/day (I 5 % variation). The position of each ewe either side of the mean for intake is set at the beginning of the program, using a random number generator. 2. Bulk food: There is also variation in the amount of hay or silage that the ewe can eat, which is independent of the amount of concentrate that she can eat. The amount of hay or silage is decided by a random number generator for each ewe at the beginning of a run of the program. 3. Potential dry matter intake: This is calculated, for each ewe of the flock, assuming the ewe to be in good body condition. This is to stop fat ewes eating more than thin ewes. Litter size is assumed to have no modifying effect on potential intake. The values we have used are shown in Table 3.
EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
191
TABLE 3 POTENTIAL DRY MATTER INTAKE
Ewe
wt (kg)
0.0 65 100
DM intakelkg/head[day 0"0 1"7 2-2
However, for each level of potential dry matter intake there is a standard deviation of 10 %. Thus a random number generator decides what the potential dry matter intake of a 65 kg ewe is, within the range 1.7 + 0"34 kg. The amount of concentrate eaten x 0.46 (the replacement factor of concentrate for silage or hay), and the amount of bulk food eaten, are then added together. If this sum is less than the potential dry matter intake then this is what the ewe eats. If this sum is greater than the potential dry matter intake for that ewe, then the ewe eats the potential dry matter intake. Any silage or hay not consumed is left over for consumption on the following day. 4. Conversion of dry matter to metabolisable energy (ME): This is done using a series of constants. ME (Meals) = DM (kgs) x 4.4 x Digestible Organic Matter of the dry matter (D value)x0.82 (losses of CH4 and urine energy = 0.18 (Agricultural Research Council, 1965). 5. Energy partition between ewe and foetus: First, metabolisable energy is used to satisfy the maintenance requirement of the ewe (0" 1 x liveweight 0.73 Meals) and the maintenance requirement of the foetus, 0.09 x foetal wt (Russel et al., 1967), then the remaining energy is used for foetal growth and ewe growth in that order. The foetus will grow at its maximum growth rate before the ewe will grow. (The ewes are assumed to be mature.) If there is not enough metabolisable energy to satisfy the maintenance requirements of the ewe and foetus then the ewe loses weight (from the 'fat' part) and liberates energy. 6. Conversion of energy to foetal weight: Secondly, energy is used for ewe growth. There was some difficulty in finding an agreed conversion factor for converting ME to foetal weight so a compromise value of 7 kcals/1 g foetal weight increase was used (Graham, 1964; Russel et aL, 1967). This incorporates the apparent inefficiencies in the process such as uterine wall thickening. The speed at which the foetus will grow from Day 90 varies with the breed of the ewe and ram and also with litter size. We have assumed that the maximum rate of growth per day for a Dorset Down x Masham single foetus is 0.0407+0.004 x foetal weight and that for a Dorset Down x Welsh Mountain foetus it is 0.029 + 0.003 x foetal weight. It is assumed that the energy value of the foetal fluid is zero.
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J. E. N E W T O N A N D P. R. EDELSTEN
7. Conversion o f energy to ewe bodyweight: Thirdly, any energy left is used for ewe weight gain. The conversion efficiency of metabolisable energy to tissue in the ewe is taken to be 75% (Agricultural Research Council, 1965) and the amount of energy required to make 1 kg of tissue depends on the state of fatness of the ewe, according to Table 4. TABLE 4 CALORIFIC VALUE OF 1 KG LIVEWEIGHT
State of fatness ('Fat'#fat'+ 'bones') ratio 0"0
0-33 0-5
Calorificvalue (Mcals) 1 "0
6-6 7"7
The fatter the ewe, the greater the energy cost of putting on 1 kg of tissue. 8. Rate at which a ewe will lose weight: It has been assumed that the rate at which a ewe loses weight is governed by its body condition, in the manner shown in Table 5. TABLE 5 RATE AT WHICH A EWE WILL LOSE WEIGHT
State of fatness
Maximum weight loss
0 0'2 0"33 0'5
0'025 0"025 0"250 0.300
('Fat'/'fat' +'bones') ratio
(kg/day)
Thus the heavier and fatter a ewe, the faster it will lose weight, but it will never lose weight faster than 300 g/head/day. The amount of energy released will also depend on calorific value, which depends on ewe body condition (Table 4). It is assumed that at a certain ewe body condition (0.2) the foetus will die and that at a lower body condition still (0.05) the ewe will die. 9. Partition o f energy between foetuses: The foetus 'appears' on Day 90 from mating and its weight on that day is 0.67 kg. If there is only a single lamb then all the energy for the foetus goes to that lamb; however, if there are two, three or four lambs, it is assumed that each lamb in the uterus received a different amount. A random number generator selects, at the outset, which lamb within the litter will get most energy. This simulates the fact that lambs within the uterus grow at different speeds, due to position and number of cotyledons, etc., and thus end up at different weights.
EFFECT OF NUTRITIONON LITTERSIZE AND WEIGHT
193
VALIDATIONOF THE MODEL Having constructed and run the model, the next stage is validation. Some of the tables in the model were derived from data from Masham, Finn x Scottish Half bred and Welsh Mountain flocks during pregnancy and lambing in 1971-2 and 1972-3. Validation of the model has therefore been undertaken by comparing model output with the performance of two separate flocks of Mashams of 57 and 100 ewes each, one flock of Finn x Scottish Halfbreds (58 ewes) and two separate flocks of Welsh Mountain ewes (132 and 100 ewes each). The two Masham flocks and the F × SH flock were housed at the Institute during pregnancy and reasonably close control was achieved over nutrition during the housed period. One flock of Welsh Mountain ewes (132) was kept at the Institute and housed during late pregnancy, the other flock was mated three weeks later and roamed the Berkshire College of Agriculture (BCA) farm during late pregnancy. Level of intake for the BCA flock during this phase was not measured, even on a group basis. All that was known was the amount of concentrate food offered. The comparison between the model predictions of mean litter size for flocks of different bodyweight at mating and the field experimental results is shown in Table 6. Having put a relationship into the model in which mean litter size was assumed to increase with increased ewe bodyweight at mating, it was disconcerting TABLE 6 EFFECT OF BODY~VEIGFIT AT MATING ON REPRODUCTIVE PERFORMANCE
Breed
No. o f ewes
Bodyweight at mating (kg)
Mean litter size
Masham
200 200 200 57 100
56-4 66"4 76"4 64.05 68"49
Model Model Model Experiment Experiment
1.88 2"0 2-10 2.16 1"95
Finn x S. Half bred
200 200 200 58
57.8 68.0 78.2 64.35
Model Model Model Experiment
2.04 2.34 2.74 2' 65
Welsh Mountain
200 200 200 132 100
29'5 34.7 39'9 35"4 40.4
Model Model Model Experiment Experiment
1"06 1.19 1"26 1.18 1.17 (later mating)
to find that the two experimental flocks of actual Mashams behaved in the opposite manner. However, if the results for the two flocks are averaged, the mean litter size was 2.02 from a bodyweight of 66.9 kg, and this fits the model prediction beautifully. Other people have discovered a similar discrepancy when making a more
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J. E. N E W T O N A N D P. R . EDELSTEN
detailed comparison of two different populations of the same breed (Gunn et al., 1972). It was found that source of ewe had a significant effect on both ovulation rate and embryo mortality. The experimental flock of Finn x Scottish Halfbreds had more lambs than anticipated but the performance of the larger Welsh flock (132) fitted the model prediction well. Looking at the relationships in the model, which were based on previous lambing performance, the F x SH was more responsive both to absolute weight change and to relative weight change than the Masham or the Welsh Mountain. Over the weight range involved the change in mean litter size per kilogramme bodyweight was 0.04 for the F x SH, 0.01 for the Masham and 0.025 for the Welsh Mountain. This suggests that a generalised relationship for mean litter size and ewe bodyweight, which ignores breed, will be very inaccurate. An examination of relative weight difference, which ignores breed effects, was just as inaccurate. A 15 % increase in bodyweight would increase the mean litter size of Mashams by 0.1, the F x SH by 0.4 and the Welsh Mountain by 0.07. The conflict between a simple model and predictive accuracy is taken up more fully in the Discussion. A comparison of litter size distribution is shown in Table 7. The experimental flocks consistently had fewer barren ewes than was forecast, but apart from this the relative distribution of litter size within breeds was quite reasonable. The model failed to forecast the F x SH ewe that produced quintuplets, but that is not a major error. TABLE 7 LITTER SIZE DISTRIBUTION
Breed
Liveweight of ewe at mating (kg)
No. of ewes
Proportion (%) of ewes having litter sizes of 0
1
2
3
4
5
0 0 0
0 0 0
Masharn Masham Masham
200 57 I00
Model Expt. Expt.
66.40 64.05 68.49
8 0 5
17.5 57 9 67 19 62
17.5 24 14
Finn x S. Halfbred Finn x S. Halfbred
200 58
Model Expt.
68.00 64.35
8 3
18.5 32 12 27
33 43
8'5 13
0 2
Welsh Mountain Welsh Mountain
200 132
Model Expt.
34.70 35.40
10 7
0 0
0 0
0 0
72.5 17.5 76.5 16.5
The effect of nutrition during pregnancy on lamb birthweight is shown in Table 8. The most striking comparison between the model results and the experimental results was the overestimate of the birthweight of the single lambs in the model for the Masham and the F x SH ewes. This is brought out in the ratio between singles and twins and twins and triplets. The situation was reversed for the Welsh, with the model underestimating the weight of Welsh singles.
TABLE 8 THE EFFECT OF 'STANDARD' NUTRITION D U R I N G THE LAST 8 WEEKS OF PREGNANCY ON LAMB BIRTHWEIGHT ( _+ STANDARD DEVIATION)
Breed
Lamb birthweights (kg) 2 3
1
Masham--model Masham---expt. Masham---expt.
6.33 -+0.43 5.38_+0.70 5.73_+0.81
5.02 _+0.71 4.50+0.83 4.77 +_-0.82
3"84+__0"73 3"80 _+0"75 4'04-+0"85
Finn x S. Halfbred--model Finn x S. Halfbred---expt.
6-354-0.44 4.10 + 0.61
4.96-+0.76 3.64-+ 1.01
3"75+0"60 3.21 _+0"73
Welsh Mountain--model Welsh Mountain---expt. Welsh Mountain----expt. BCA
3.32 + 0.14 3.78 _+0.4 3.75_+0.71
3.06 _+0-29 2-75 _+0.47 2.57+0.57
Ewe wt. before lambing (kg)
4
66'4 64'05 68'5 2"92_+0"62 2"654-__0.54
68"0 64.35 34"7 37'4 45 "4
RATIO OF THE W E I G H T OF LAMB BIRTHWEIGHTS FROM DIFFERENT LITTER SIZES
1:2 1.26 1.20 1.20
2:3 1.31 1.I 8 1.18
3:4
Masham--model Masham--cxpt. Masham--expt. Finn x S. Half bred--model Finn x S. Halfbred--expt.
1.28 1.13
1.32 1-13
1.28 1.21
Welsh Mountain--model Welsh Mountain--expt. Welsh Mountain---expt.
1-08 1.37 1.46 TABLE 9(a) EWE W E I G H T CHANGE D U R I N G PREGNANCY ( K G )
Number of ewes
Mating wt. (6/11) (1)
Wt. at 96 days preg. (Day 31) (2)
Wt. at 124 days preg. (Day 49) (3)
Post parturient weight (4)
35 5 19
63.6 62.2_+6.5 68.4+7.3
64.4 71.2_+5.0 72.5
67.6 77.6+6.6 75.8
65.8_+6.9 73.4+4.2 70.7_+9.2
Masham with2 Model Masham with 2 Expt. 1 Masham with2 Expt. 2
114 38 62
67.0 63-1 _+5.4 70.5+5-8
68.1 74.1 +6.2 74-2
71.9 78.8_+6.7 78.8
64"4+6.5 71.7_+6.5 70.0_+6.5
Masham with 3 Model Masham with3 Expt. 1 Masham with 3 Expt. 2
35 14 14
68.6 67.3_+5.4 72.6_+ 5"6
69.8 79.0_+6.9 79.2
74.5 85.3-+7-0 85"4
64'2-+ 6.3 73.7+7.4 70.3 + 8.4
Masham with0 Masham with0
16 5
67.4 73.4-+7.1
Breed Masham with I Model (M) Masham with 1 Expt. 1 (El) Masham with 1 Expt. 2 (E2)
Model Expt.
81.7-+8.6 83.0_+9.5
RATIO OF EWE WEIGHTS AT DIFFERENT STAGES I N PREGNANCY
Ratio 2:1 3:2 4:2 4:1 Barren 4:1
Masham with 1 M E1 E2 1.01 1,14 1.06
Masham with 2 M El E2 1.02 1.17 1.05
Masham with 3 M El E2 1.02 1.17 1.09
1.05
1.08
1-05
1.06
1.06
1.06
1.07
1.08
1.08
1.02 1.03
1.03 0,97 1 - 1 8 1-03
0.94 0.96
0.97 1.14
0.94 0.99
0.92 0-94
0.93 1.09
0.89 0.97
M 1.21
E 1.13
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J. E. NEWTON AND P. R. EDELSTEN
It was assumed in the model that, because the ewes were similar in bodyweight the F x SH ewes would grow their lambs at the same rate as Mashams. In practice the F x SH ewes had lighter lambs than the Mashams, particularly the singles. The weight changes during pregnancy for the three breeds are shown in Tables 9(a), (b) and (c). Considering the Masham first, there was evidence that experimental flock 1 (El) was rather light at mating and this is brought out by comparing the ratio 2:1 and 4: 1, for E1 and E2, where weight at mating (column (1)) has been TABLE 9(b) EWE WEIGHT CHANGE DURING PREGNANCY (KG)
Breed
Number of ewes
Mating wt. (1)
Wt. at 96 days preg. (2)
Wt. at 124 days preg. (3)
Post parturient weight (4)
F × SH with 1 F x S H with 1
Model (M) Expt. (E)
37 7
65.3 66.1+_9.2
66-0 69.2 77.3+__10.7 82.4±11.3
67.3 4- 6.2 80.9+-10.8
FxSHwith2 F x SH with 2
Model Expt.
64 16
67.2 63.6+6.4
68.3 76.8+7.7
71.9 83.5±8.5
64.6 + 5.7 78.14-9-1
F x S H with 3 F x SH with 3
Model Expt.
66 26
69.4 62.9+6.6
70.8 75-84-7.5
75.1 82.8_+8.3
64.4 ± 6.1 73.64-7.6
FxSH with4 F×SH with4
Model Expt.
17 8
73.5 67.5_+7.2
74.9 81"44-8.0
79.7 87.9±9.3
67.94-3.1 77.34-9-6
Ratio 2:1 3:2 4:2 4:1
F x SH M 1.01 1-05 1.02 1-03
RATIO OF EWE WEIGHTS AS DIFFERENT STAGES IN PREGNANCY
with 1 E 1.17 1.06 1.05 1.22
F × SH M 1.02 1.05 0.94 0.96
with 2 E 1.21 1.09 1.02 1.23
F x SH M 1.02 1.06 0.91 0.93
with 3 E 1.20 1.09 0.97 1.17
F x SH M 1.02 1-06 0.90 0.92
with 4 E 1.20 1.08 0.95 1.14
TABLE 9(c) EWE WEIGHT CHANGE DURING PREGNANCY(KG)
Breed Welsh with 1 Welsh with 1
Model (M) Expt. (E)
Welshwith 2 Welsh with 2
Model Expt.
Number of ewes
Mating wt. (1)
Pregnant wt. (Day 112) (2)
Post-parturient weight (3)
145 100
34.7 34-9 + 3-7
35.7 37.1 ± 3.9
33.1 _ 3.7 36.4 +4.2
35 21
35.6 37.3 + 2.6
37.4 40.5 4- 3.3
31-1+2.9 36.9 4- 3.3
RATIO OF EWE WEIGHTS IN DIFFERENT STAGES IN PREGNANCY
Ratio2:1 3:1
Welsh with I M E 1-03 1-06 0.95 1.04
Welsh with 2 M E 1.05 1.08 0.87 0-99
197
EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
used as the base line. There was good agreement between the model and E2 throughout pregnancy and up to parturition. There was experimental support for the hypothesis that the heavier ewes in the flock have the higher litter sizes and that it is harder for the ewes carrying larger litter sizes (e.g. triplets) to maintain their own bodyweight during late pregnancy. The experimental F x SH and Welsh ewes were also rather heavier than the model ewes by Day 96 in pregnancy, and so were the weights after lambing (Tables 9(b),
(c)). It would seem from Tables 8 and 9 that the relationships used in the model have overestimated lamb birthweights and underestimated ewe weight gains, particularly in the ewes having singles. However, the experimental F x SH ewes have behaved differently from the experimental Mashams, for the ratio of ewe weight after lambing to the birthweight of a single lamb was 19.7 for the F x SH, and only 12.3 for the Masham. The comparison between predicted and actual neonatal lamb mortality is shown in Table 10. The model has consistently underestimated lamb mortality for each TABLE 10 ~o LAMBMORTALITYAT BIRTH Litter size 1
2
3
2.9 (35) 40 (5) 0 (19)
0.9 (228) 5.3 (76) 4.8 (124)
3.8 (105) 9.5 (42) 19.0 (42)
F x SH--model F x SH----expt.
2.7 (37) 0 (7)
0.8 (128) 3.1 (32)
4.5 (198) 12.8 (78)
Welsh--model Welsh----expt. Welsh---expt.
4"1 (145) 5 (101) 12.5 (80)
2-8 (70) 2.3 (44) 9.4 (32)
Masham--model Masham---cxpt. Masham----expt.
4
14.7 (68) 12.5 (32)
( ) number of Iambs born.
breed and each litter size, except for the F x SH quadruplets. The F x SH quads were the lightest Iambs, which was why the model predicted higher mortality. It would seem from this comparison that, although lambs of very light and heavy birthweight have a greater chance of early death, the probability factor for lambs dying in the middle weight range should be increased.
DISCUSSION
The important question left over from the validation section is to decide whether the model is sufficiently accurate to be used. If this is not the case then what should
198
J. E. NEWTON AND P. R. EDELSTEN
be done to improve it ? If it is sufficiently accurate, then to what use can it be put ? The answer to this question is that the model is good in parts. Taking the relationships, briefly, in order, the effect of ewe weight at mating on subsequent litter size was reasonable. However, the behaviour of the two experimental Masham flocks raised an important point, which concerns the collection of data. There are a great many breeds and crossbreeds of sheep in the United Kingdom alone. There appears to be no hypothesis that enables litter size to be predicted for sheep, from any other parameter, such as size. Big breeds of sheep do not have more lambs than small breeds, or vice versa. Lacking such a predictive parameter, there are two possible courses of action, one can either collect reproductive data from every known breed, crossbreed and strain within a breed, or else postulate, usefully, at the outset that there are three possible response curves to weight increase, corresponding to sheep of low, medium and high fertility, and accept a degree of inaccuracy in the answer. One purpose of the model, and modelling, is to reduce data collection and repetitive experimentation by forcing the modeller to advance new hypotheses or to acknowledge acceptance of existing ones. The purpose of this model is not to predict litter size for every known genetic variation of sheep, nor, on the other hand, to be only capable of use for one specific cross. It must be a compromise between widespread applicability and accuracy. The prediction of litter size distribution was reasonable, but the partition of energy between the ewe and the foetus was inaccurate for ewes with singles. Once again, experimental evidence suggested that there were breed differences. Does it matter if a Finn x S. Half bred ewe was predicted to behave like a Masham, because it was the same weight and had singles weighing 6.35 kg instead of 4.1 kg? It is known, for instance, that the Finn ewe has a shorter gestation period; what is the effect of assuming a 142 day gestation length instead of a 147 day one ? The model can be used to test this, but how much does the inaccuracy matter? (In fact when calculated in the model the birthweight of single lambs born to Finn x ewes was 6.35 and 5.14 kg with a gestation length of 147 and 142 days, respectively.) There are two contexts in which to answer the question of inaccuracy. One is that it is based on inaccurate scientific knowledge and that it must be right to increase knowledge, but questions of priority will arise. The other is that the inaccuracy matters to a practical system of keeping sheep. Will a 4.1 kg lamb grow more slowly than a 6.35 kg lamb? This will affect the date of slaughter, price received, etc. and, as a consequence, wrong advice might be given. It seems to us more advisable to try to test the effect of different levels of inaccuracy, if possible, rather than to say if the answer is within 10~ of the field situation it is acceptable. The accuracy has to be related to the factor and to the context. The relationship between lamb birthweight and pre-natal mortality requires further attention because the model currently underestimates mortality. The amount of population variation in ewe weight and lamb birthweight was in reasonable accordance with the field variation.
EFFECT OF NUTRITION ON LITTER SIZE AND WEIGHT
199
I n conclusion, it w o u l d be preferable to v a l i d a t e the m o d e l a g a i n s t a n o t h e r y e a r ' s results b e f o r e d e v e l o p i n g it further to show w h a t the e c o n o m i c consequences o f n u t r i t i o n a l t r e a t m e n t s are likely to be.
ACKNOWLEDGEMENTS T h e a u t h o r s wish to t h a n k M r J. E. Betts, D r J a n e t F o o t , D r A. J. F. Russel a n d M r N. E. Y o u n g for supplying d a t a which was used in the model.
REFERENCES
AOmCtml"URAL RESEARCHCOUNCIL (1965). The nutrient requirements of farm livestock, No. 2. Ruminants. A.R.C., London. EDmSTEN, P. R. & NEWTON, J. E. (1975). A simulation model of intensive lamb production from grass. Tech. Rep. No. 17, Grassland Research Inst., Hurley. FOOT, J. Z. & RUSSEL,A. J. F. (1973). Some nutritional implications of group feeding hill sheep. Anim. Prod., 16, 285-92. FOOT, J. Z., RUSSEL,A. J. F., MAXWELL,T. J. • MORRIS, P. (1973). Variation in intake among group fed pregnant Scottish Blackface ewes given restricted amounts of food. Anita. Prod., 17, 169-78. GR~, M. McC. (1964). Energy exchanges of pregnant and lactating ewes..,lust. J. agric Res., 15, 127-41. Gun,q, R. G., DORY, J. M. & R~SSEL, A. J. F. (1972). Embryo mortality in Scottish Blackface ewes as influenced by body condition at mating and by post-mating nutrition. J. agric. Sci. Camb., 79, 17-25. JOUBERT, D. M. (1956). A study of pre-natal growth and development in the sheep. J. agric. Sci. Camb., 47, 382--428. MEATAND LIVESTOCKCOMMISSION(1973). Feeding the ewe, Sheep Improvement Service Technical Report No. 2. RUSSEL,A. J. F. (Personal comm.). RUSSEL, A. J. F., DONEY, J. M. & REID, R. L. (1967). Energy requirements of the pregnant ewe. J. agric. Sci. Camb., 68, 359-63. YOUNG, N. E. & NEWTON,J. E. Unpublished data.