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A conceptual approach to the modelling of herbage intake by hill sheep
A C O N C E P T U A L A P P R O A C H TO THE M O D E L L I N G OF HERBAGE I N T A K E BY HILL SHEEP
A. R. SIBBALD, T. J. MAXWELL & J. EADIE
Hill Farming Research Organisation, Bush Estate, Penicuik, Midlothian, EH26 OPY, Scotland, Great Britain
SUMMARY
A modelling approach is examined as a method of int,estigating alternatit'e management strategies jor improl,ed systems of hill sheep production. In order to take account of the wide range in the quality of hill herbage and the ability oJ'the hill sheep to select preferred components, herbage has been conceptually classified in terms of i t s digestibility; the digestibility classes are then grazed selectit,ely by sheep. The model deals with herbage growth and deterioration, diet selection and the maintenance and liveweight change of wether sheep. Results produced by the model, in which wethers grazed Agrostis-Festuca at two stocking rates, are discussed.
INTRODUCTION
An analysis of the biological and economic characteristics of hill sheep farming in Scotland has been made and a synthesis of an improved system of hill sheep production has been described (Eadie, 1971; Eadie & Maxwell, 1975). The resources for large scale 'on farm' systems experiments required to test the synthesis are such as to make it possible to examine responses to only a small number of inputs and alternative management strategies. They do not provide an adequate means of investigating the many alternative management and input possibilities which require to be studied at the systems level. A mathematical or modelling approach to systems analysis and simulation is perhaps the only potential means by which a solution to these problems may be achieved. An adequate model of the grazed pasture/grazing animal interface is of fundamental importance in animal production systems based on grazed pasture as the principal source of nutrients. 119 Agricultural Systems (4) (1979) Printed ill Great Britain
~" Applied Science Publishers Ltd, England, 1979
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A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
H I L L SHEEP SYSTEMS
The basic pastoral resources of hill sheep farming in the UK are, in the main, those classified in the agricultural statistics as rough grazings. These are indigenous pastures often at elevations in excess of 250 m above sea level. These indigenous pastures inhabit a wide range of soil and climatic environments. Individual grazings include a wide variety of vegetation types, each with its own mixture of pasture species. Traditional hill sheep production is based on set stocked, year long, free grazing systems. The sheep obtain almost all of their nutrient requirements from grazed pasture, even in winter. Stocking rates are based on the capacity of the pasture to support stock over the winter. As a consequence, hill pastures tend to be greatly under-utilised during the spring and summer and the resulting accumulation of dead and dying herbage material is carried forward into the next winter. The cycle of under-grazing leads to pastures with a large component of dead, poor quality herbage. THE M O D E L
The model has been developed to take account of both the wide range in quality of hill herbage at any point in time and the ability of hill sheep to select herbage, although this does not preclude the application of the concepts of the model to a sown upland or lowland pasture. Herbage is represented as quantities of dry matter contained within a range of discrete organic matter digestibility classes so that a grazing selection procedure sensitive to a digestibility distribution can be used. The representation of herbage as quantities (kg DM/ha) in discrete quality (organic matter digestibility) classes is wholly conceptual although it is possible to describe the component parts of a pasture in terms of digestibility ranges (Vine, 1977). Currently each quality class covers a range of two digestibility units. The overall range of dry matter digestibility represented in the model (for an Agrostis Festuca pasture) is 34-~80,'~. The changes that take place in the distribution of the quantity and quality of herbage are a function of the rate of herbage growth, the rate at which the quality of herbage declines (this has been termed the "deterioration rate') and the amount removed by the grazing animal. HERBAGE GROWTH
Growth is defined as the addition of new material to the pasture rather than as the more commonly used net accumulation rate which also assumes a loss from pasture.
121
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
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This definition is used because herbage deterioration is considered as a separate component of the model and because ultimately it may be essential to be able to take account of the effect on herbage growth of both the method and intensity of grazing. Herbage growth (Fig. I) is currently described by a modified net accumulation curve (g/DM/ha/week) for an Agrostis-Festuca pasture (R. H. Armstrong, unpublished data). New growth is assumed to have a digestibility of 80~o throughout the year.
HERBAGE DETERIORATION
There is little published information on the rate of change of digestibility of herbage in a form that would be applicable to the concepts of the model. Terry & Tilley (1964) have produced data on the decline of digestibility in grasses on a daily basis but data in this form do not indicate the quantitative movement of material down the digestibility range. In the absence of such data it was decided to represent the change in herbage digestibility by a deterioration rate, i.e. the proportion of material by weight in a digestibility class that moves into the next lower class in a day, Within any standing crop specific parts become less digestible with time (Terry & Tilley, 1964) and a rate of quality reduction can be measured. It is therefore reasonable to assume that deterioration rates as defined may be calculated for discrete classes of herbage quality. In autumn and winter there is an accumulation of dead material (in Agrostis-Festuca pasture). Eadie & Black (1968) showed that in winter an Agrostis--Festuca pasture was composed of equal parts of dead and green material; the in t'itro DM digestibility of the dead material lay between 35 and 40 ~o while that of the green material lay between 60 and 65 ~o. This accumulation of dead material suggests that the deterioration rate of low quality herbage in autumn and winter would be low and the gradual disappearance of dead material during the summer
122
A. R. SIBBALD, T. J. MAXWELL, J. EADIE
suggests that with higher temperatures the deterioration rate of low quality material increases. Terry and Tilley's work indicates that ~he lowest rates of decline of digestibility were at the higher initial digestibility levels; this is also confirmed by more recent examination of the decline in digestibility of the component parts of a perennial ryegrass pasture (Vine, 1977). However, early experience with the model suggests that the only way in which to obtain the proportions of dead and green herbage with their appropriate digestibility ranges, as measured by Eadie & Black (1968), is to assume that highly digestible material (78-80 "~idigestibility) during the winter, spring and autumn deteriorates at high rates. On reaching a digestibility of 70 °4; the winter, spring and autumn rates of deterioration have been adjusted to agree more closely with those suggested by the evidence of Terry & Tilley (1964) and of Vine (1977). Based on these assumptions a family of relationships between
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deterioration rate and digestibility class for the different periods of an annual cycle has been devised (Fig. 2). The higher rates of deterioration at about 45 ~o digestibility in Fig. 2 represent the transition of material from green to dead, though it is appreciated that this value is likely to vary with species composition of the pasture. Material deteriorating from the lowest digestibility class is assumed to be unavailable to the grazing animal and falls out of the system.
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
123
COMPUTATION OF INTAKE
Intake (g DM/kg°VS/day) is assumed to be linearly related to the digestibility of the ingested material (Jarrige et al., 1974) and the relationship shown in Fig. 3 is based on the data of Blaxter et al. (1961). Since there is an interdependence between quantity and quality of intake, an iterative procedure has been used to ensure that the quality value used to determine
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quantity closely matches the quality of intake finally calculated. A diagram of the iterative procedure is shown in Fig. 4. J. Z. Foot and A. J. F. Russel (unpublished data) and Osbourn (1970) have shown that intake is reduced consequent upon a sheep reaching a certain level of body fat and condition. Since body condition and body fat are related to the body weight of mature ewes (Russel et al., 1969), intake in the model is limited by the relationship shown in Fig. 5. Intake is also restricted by the total quantity of pasture per unit area (Arnold & Dudzinski, 1967a,b). The relationship (Fig. 6) is assumed to be a function of the limited bite size imposed by low amounts of pasture and the fact that the sheep has an extendible but ultimately limited grazing day; the two effects combine to reduce the total potential daily intake (Hodgson, 1977; Hodgson & Milne, 1978). The resulting calculated herbage intake, adjusted for the size and number of grazing animals, is harvested assuming that the grazing animal is selective. DIET SELECTION
The selection procedure allocates 'composite' bites to the range of digestibility classes available in the pasture. A composite bite is the aggregate of a number of
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J. MAXWELL, J. EADIE
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Diagrammatic representation of the iterative procedure relating intake quantity and quality.
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individual bites and is used to reduce the computing time that the use of individual bites would require. The composite bite is set at a level at which an acceptable degree of sensitivity in the model is retained. The number of composite bites is presently set at 100 per week for all grazing animals, each composite bite being 0.01 of the total weekly intake. A random allocation over the distribution would result in a mean digestibility of ingested material identical to that of the herbage present.
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Relationship between the percentage of the potential intake and the a m o u n t of herbage per unit area.
The selection procedure used in the model, however, is able to bias the allocation of bites towards the higher digestibility classes, the degree of bias being related to current grazing pressure expressed as the ratio of the total current calculated dry matter intake and the total dry matter of herbage present. Grazing pressure is used to derive a selection index (Fig. 7). The selection index is directly related to the slope of the assumed linear relationship between the digestibility classes within the distribution range and the preference of the sheep for taking bites ('selection bias') from each of the classes within this range (Fig. 8).
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If herbage selection is assumed to be random, then the allocation of bites to a digestibility class within a distribution (based on a random number generator) would be in exact proportion to the amount of herbage in that class. In Fig. 8, the most highly selective relationship shown would allocate sixteen times more bites to the most highly digestible class (80'Yo) than would have been allocated randomly. The relationships shown in Figs. 7 and 8 are conceptual.
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and tend to occupy a lower level in the sward. The conceptual relationship shown in Fig. 9 determines the maximum percentage of material, in each digestibility class, that may be removed by grazing. The horizontal distribution of digestibility classes within the pasture is represented by the ratio of quantity of herbage dry matter in a class and the total herbage'idry matter available. Digestibility classes which contain a large proportion of the total herbage are assumed to be more likely to be grazed than those which represent a small proportion of the total herbage which are assumed to be less likely to be grazed. The maximum amount removed by grazing from each digestibility class is therefore reduced according to another conceptual relationship, shown in Fig. 10. The combined effect of these relationships tends to make sheep graze a pasture layer by layer, a feature of grazing noted by Arnold (1960).
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A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
The iterative grazing procedure ends when the digestibility of the dry matter intake agrees with the digestibility value used to determine intake after selection has taken place. The digestible organic matter ( D O M ) intake is then calculated assuming that there is 92 011 organic matter in the dry matter.
ANIMAL COMPONENT
The animals used in the model are mature wethers; a starting mean body weight and the number per hectare are supplied to the model as initial data. Their maintenance requirement (34 g D O M / k g ° ~ 5 / d a y - - J . Eadie, unpublished data) is compared with the D O M intake determined by the intake/selection procedures. The rates of body weight change are related to the extent to which intake is in excess of, or below, that required for maintenance. In calculating the loss in body weight for intakes below maintenance, we have assumed the energy content of loss in body weight from this class of animal to be between 25 and 30 kJ/g and, since this is derived mainly from fat, we further assume that it will be utilised for maintenance with an efficiency of between 70 and 80 oj;. Given that the energy content per gramme of D O M is 15.58 kJ (Roy et al., 1977), one gramme of body weight loss will be equivalent to 1.4 g D O M intake below total maintenance requirement. When intakes are between maintanance (M) and 1,5 M, a gain of I g is calculated for every 2.5 g D O M intake in excess of maintenance and above 1.5 M, I g of gain for every 3.25 g of excess D O M intake (derived from Agricultural Research Council, 1965).
PASSAGE OF TIME
At present the time period used is one week and the model runs for a complete calendar year. The new calculated values for pasture digestibility distribution and mean animal body weight are passed to the next time period in the model for a new set of calculations. The choice of the time period was made for two main reasons: first, because of the nature of the available data on which the relationships in the model are based and, secondly, because the purpose for which this model is ultimately intended (i.e. for use in testing inputs to whole systems of hill sheep production) does not justify a shorter time period. The conceptual approach adopted in the model may be employed using shorter time intervals where it is justified. The model can be used to simulate events over a number of consecutive years and this feature allows the stability of the output of the model to be investigated. A stable state is assumed to exist when, after a consecutive number of annual runs, the output characteristics remain unchanged. Thus the ultimate results of a particular change in grazing management, for example, can be tested. As yet, however, stochastic
M O D E L L I N G OF H E R B A G E I N T A K E BY H I L L SHEEP
129
elements have not been introduced into th.e relationships upon which the model is based. The model also contains an option to graze the pasture for a number of periods during the calendar year to test on/off grazing system responses.
MODEL OUTPUT
The model optionally prints out, week by week: (1) (2) (3) (4)
Total pasture (DM/ha) and mean pasture digestibility ( ~ ) before and after grazing. Stocking rate during current week (head/ha). Total quantity (kg/DM) and mean digestibility (~o) of ingested material. Mean wether body weight (kg) and total maintenance requirement (kg DOM/week).
Also printed optionally are graphs of pasture dry matter distribution across digestibility classes for selected weeks. The model prints a graph, plotted week by week, of total herbage (kg DM/ha), its mean digestibility ('~,), the mean digestibility ('~,) of ingested herbage and the mean body weight (kg) of the wethers.
MODEL PERFORMANCE
Using a growth curve with growth (Fig. 1) commencing in mid-March and ceasing in mid-October, with a year-round stocking rate of 1.6 sheep per hectare, the output of the model in terms of the quality of the ingested pasture (Fig. 11) fits the data obtained by Eadie (1967) stocked at 1.5 sheep per hectare, other than at the start of the year. Eadie's study, however, relates to sheep on a grassy hill pasture of heterogeneous species composition. Hunter (1962), working with a pasture of similar species composition, showed that the Agrostis-Festuca and bracken sward (which was predominantly an Agrostis-Festuca sward under a bracken canopy) were predominantly grazed throughout the annual cycle, although, because of their relative scarcity during winter, other species such as Molinia and Nardus were grazed during the winter. This may explain the discrepancy between the quality of ingested herbage calculated by the model and the values obtained by Eadie (1967), particularly during the late winter period at the start of the year. As an example of how the model can be used, differences in ingested herbage quality and liveweight change that arise when sheep are grazed at two stocking rates
130
A. R. SIBBALD, T. J. MAXWELL, J. EADIE
of 1.6 and 6.0 sheep per hectare are compared using a growth curve producing 3800 kg DM/annum• Sheep at the higher stocking rate are unable to select as high a quality diet at the beginning of the year; although there is little difference in the quality of the herbage on offer (Fig. 11), the limited amount of material available to them (Fig. 12) results in a higher proportion of poorer quality material being ingested (Fig. 11) and a DOM
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intake per head 14 % lower. Consequently, sheep at the higher stocking rate tend to lose more weight during the first months of the cycle (Fig. 13). As growth of pasture begins, sheep at the higher stocking rate are able to select a higher proportion of the new material. The new material ingested by sheep at the lower stocking rate, however, is diluted by the greater amount of low quality material still in the pasture. By early April the overall digestibility of the herbage available to the high stocking rate sheep is between 10 and 15 units higher and they are able to ingest a diet which is some 8 units of digestibility higher• As a consequence, the D O M intakes per head become similar and the weights of both groups of sheep begin to increase at similar rates.
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A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
By May/June the difference in the quality of the herbage is much less (2.5 units of digestibility) and differences in the quality of ingested herbage and consequently D O M intakes per head -are small. This situation persists throughout July and August and the sheep gain body weight at a similar rate, reaching a maximum in the autumn, the high stocking rate wethers being 3.5 kg less in weight at that point. During September when there is an increase in herbage growth rate (Fig. 1) the animals at the higher stocking rate are able to make more use of the new, highly digestible herbage because less herbage has been left to deteriorate and consequently dilute the quality of intake during this period. The result is that during September and October the wethers at the higher stocking rate are able to select a diet of higher quality with DOM intakes per head 3 ",i higher than the lower stocking rate animals and they continue to gain weight at a faster rate: the weight gains of the lower stocking rate animals decline. Consequently, by mid-November~ there is only a 2.5 kg weight difference between the two stocking rates. During late November and December when there is no growth of pasture and the amount of herbage on the higher stocked pasture declines more rapidly, these sheep ingest a greater proportion of poorer quality material with DOM intakes per head falling slightly below that of the lower stocking rate sheep. Their weight loss during November and December is similar to that of the low stocked sheep, the weight difference of 2.5 kg in the autumn being maintained until the end of December. The change in weight, during an annual cycle, of the sheep at a high stocking rate is 2.5 kg less than that of the sheep at a low stocking rate, but per hectare at least 200 kg more body weight is carried and 11 kg more body weight gain produced. These results apply to wether sheep: when account is taken of the nutritional requirements of pregnancy and lactation the liveweight changes of ewes are likely to be much more sensitive to stocking rate. Before the model can be used more comprehensively to examine the effect of stocking rate and alternative grazing management strategies on animal performance, it will be necessary to add the components of pregnancy and lactation. The model does, however, support the generally accepted conclusion that the low quality of herbage intake that sheep are able to select during the winter is the overriding factor which determines the annual stocking rate that can be sustained in traditional set-stocked hill sheep production systems. Although the model has as yet some real limitations--particularly the lack of response of pasture growth to different stocking rates--and requires further development, it has provided a framework within which some of the important biological mechanisms and processes involved in the utilisation of hill pastures may be critically examined. The problem of measuring and modelling the growth of hill pastures and their responses to different grazing regimes, and the lack of understanding as to how a sheep selects its diet in the process of grazing, are highlighted. The way in which the components of herbage are distributed in space
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
133
and the nature of herbage deterioration in hill pastures also require further investigation.
ACKNOWLEDGEMENTS
The authors wish to record their thanks to their colleagues who have contributed to some of the concepts incorporated in this paper and in particular to Anne Vine, a post-graduate student with the Organisation, for her contributions.
REFERENCES AGRICULTURAL RESEARCH COUNCIL (1965). The nutrient requirements o['./hrm lit'estock No. 2: Ruminants, London, Agricultural Research Council. ARNOLD, G. W. (1960). Selective grazing by sheep of two forage species at different stages of growth. Aust. J. agrie. Res., 11, 102633. ARNOI,I), G. W. & DUDZINSKI, M. L. (1967a). Studies on the diet of the grazing animal. I1. The effect of physiological status in ewes and pasture availability on herbage intake. Aust. J. agrie. Res., 18, 349 59. A RNOt.D, G. W. & DUDZINSK1, M. L. (1967b). Studies on the diet of the grazing animal. 111. The effect of pasture species and pasture structure on the herbage intake of sheep. Aust. J. agric. Res., 18, 657 66. BLAXTER, K. L., WAINMAN,F. W. & WILSON, R. S. (1961). The regulation of food intake by sheep. Anita. Prod., 3, 51 61. EADIE, J. (1967). The nutrition ¢~[grazing hill sheep." Utilisation ~['hill pasture. Hill Farming Research Organisation. Fourth Report (1964 67), 38-45. EAI)IE, J. ( 1971 ). Hill sheep production system det'elopment. Hill Farming Research Organisation, Fifth Report (1967 70), 70 87. EAI)IE, J. & BLACK, J. S. (1968). Herbage utilisation on hill pastures. Oce. Svmp. 4, Br. GrassldSoc., 191 95. EADI~, J. & MAXWH~L, T. J. (1975). Systems research in hill sheep farming. In: Stud)' of agricultural systems (Dalton, G. E. (Ed.)), London, Applied Science Publishers, 395 413. HOI)GSON, J. (1977). Factors limiting herbage intake by the grazing animal, Proc. Int. Meeting Anita. Prod. j?om Temperate Grassland, Dublin, 7ff 5. HODGSON,J. & MILNE, J. A. (1978). The influence of weight of herbage per unit area and per animal upon the grazing behaviour of sheep. Proe. 7th Mtg, European Grassland Fed., Ghent Congress. H UNTO:R,R. F. (1962). Hill sheep and their pasture: A study of sheep-grazing in south-east Scotland. J. Ecol., 50, 651 80. JARRIGE, R., DEMARQUILLY,C. & DULPI-IY,J. P. (1974). The voluntary intake of forage. Proc. 5th Gen. Mtg, European Grassland Fed., Uppsala, 1973, Publ. Hush. 28, 98 106. OSBOURN, D. F. (1970). The eoluntary intake of Jbrage crops b), sheep. Ph.D. Thesis, University of Reading. Roy, J. B. H., BAL('H, C. C., MILLER, E. L., ORSKOV, E. R. & SMITH, R. H. (1977). Calculation of Nrequirements for ruminants from nitrogen metabolism studies. EAAP 2nd lnternationalSymposium on Protein Metabolism and Nutrition. RUSSEL, A. J. F., DONEY, J. M. & GUNN, R. G. (1969). Subjective assessment of body fat in live sheep. J. agrie. Sci., Camb., 72, 451- 4. T~:RR¥, R. A. &TILt, EY, J. M. A. (1964). The digestibility of the leaves and stems of Perennial Ryegrass, Cocksfoot, Timothy, Tall Fescue, Lucerne and Sainfoin, as measured by an in t,itro procedure. J. Brit. GrassM Soe., 19, 363 72. VINE, D. A. (1977). Det'elopment of a pasture model for grazing studies. Ph.D. Thesis, University of Edinburgh.
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APPENDIX
OPERATING ENVIRONMENT
The model is written in Fortran and run on the ICL 2980 computer at the Edinburgh Regional Computing Centre. The program was compiled under Edinburgh Fortran (FORTE) and makes use of the Numerical Algorithms Group (NAG) random number generating sub-routines GO5BBF, GO5ARF and GO5AZF for the allocation of composite bites in the selection procedure.
INITIAL D A T A
The initial data supplied to the model are as follows and may be varied from run to run: (1) (2) (3) {4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Number of digestibility classes in pasture distribution. Minimum value of pasture digestibility range. Output index (controls quantity of printed output). Number of annual cycles. Number of composite bites to be made weekly. Growth (kg DM/ha/day) of pasture per week. Digestibility (~o) of new pasture growth per week. Starting pasture DM digestibility distribution (will change if (1) above is changed). Relationship between body weight and intake (current relationship shown in Fig. 5). Relationship between total pasture available and intake quantity reduction (current relationships shown in Fig. 6). Wether maintenance value (g DOM/kg ° 75/day ) and DOMI to body weight conversion rates. Selection index relationships (see Figs. 7 and 8). Pasture vertical distribution grazing limitations (Fig. 9). Pasture horizontal distribution grazing limitations (Fig. 10). Deterioration rates number of seasonal periods and relationships for each (Fig. 2). (These will change if(l) above changes.) Number of grazing periods and for each: (a) starting and ending weeks; (b) starting body weight (optionally carried over from previous period).
A. R. SIBBALD, T. J. MAXWELL & J. EADIE
Hill Farming Research Organisation, Bush Estate, Penicuik, Midlothian, EH26 OPY, Scotland, Great Britain
SUMMARY
A modelling approach is examined as a method of int,estigating alternatit'e management strategies jor improl,ed systems of hill sheep production. In order to take account of the wide range in the quality of hill herbage and the ability oJ'the hill sheep to select preferred components, herbage has been conceptually classified in terms of i t s digestibility; the digestibility classes are then grazed selectit,ely by sheep. The model deals with herbage growth and deterioration, diet selection and the maintenance and liveweight change of wether sheep. Results produced by the model, in which wethers grazed Agrostis-Festuca at two stocking rates, are discussed.
INTRODUCTION
An analysis of the biological and economic characteristics of hill sheep farming in Scotland has been made and a synthesis of an improved system of hill sheep production has been described (Eadie, 1971; Eadie & Maxwell, 1975). The resources for large scale 'on farm' systems experiments required to test the synthesis are such as to make it possible to examine responses to only a small number of inputs and alternative management strategies. They do not provide an adequate means of investigating the many alternative management and input possibilities which require to be studied at the systems level. A mathematical or modelling approach to systems analysis and simulation is perhaps the only potential means by which a solution to these problems may be achieved. An adequate model of the grazed pasture/grazing animal interface is of fundamental importance in animal production systems based on grazed pasture as the principal source of nutrients. 119 Agricultural Systems (4) (1979) Printed ill Great Britain
~" Applied Science Publishers Ltd, England, 1979
120
A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
H I L L SHEEP SYSTEMS
The basic pastoral resources of hill sheep farming in the UK are, in the main, those classified in the agricultural statistics as rough grazings. These are indigenous pastures often at elevations in excess of 250 m above sea level. These indigenous pastures inhabit a wide range of soil and climatic environments. Individual grazings include a wide variety of vegetation types, each with its own mixture of pasture species. Traditional hill sheep production is based on set stocked, year long, free grazing systems. The sheep obtain almost all of their nutrient requirements from grazed pasture, even in winter. Stocking rates are based on the capacity of the pasture to support stock over the winter. As a consequence, hill pastures tend to be greatly under-utilised during the spring and summer and the resulting accumulation of dead and dying herbage material is carried forward into the next winter. The cycle of under-grazing leads to pastures with a large component of dead, poor quality herbage. THE M O D E L
The model has been developed to take account of both the wide range in quality of hill herbage at any point in time and the ability of hill sheep to select herbage, although this does not preclude the application of the concepts of the model to a sown upland or lowland pasture. Herbage is represented as quantities of dry matter contained within a range of discrete organic matter digestibility classes so that a grazing selection procedure sensitive to a digestibility distribution can be used. The representation of herbage as quantities (kg DM/ha) in discrete quality (organic matter digestibility) classes is wholly conceptual although it is possible to describe the component parts of a pasture in terms of digestibility ranges (Vine, 1977). Currently each quality class covers a range of two digestibility units. The overall range of dry matter digestibility represented in the model (for an Agrostis Festuca pasture) is 34-~80,'~. The changes that take place in the distribution of the quantity and quality of herbage are a function of the rate of herbage growth, the rate at which the quality of herbage declines (this has been termed the "deterioration rate') and the amount removed by the grazing animal. HERBAGE GROWTH
Growth is defined as the addition of new material to the pasture rather than as the more commonly used net accumulation rate which also assumes a loss from pasture.
121
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
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This definition is used because herbage deterioration is considered as a separate component of the model and because ultimately it may be essential to be able to take account of the effect on herbage growth of both the method and intensity of grazing. Herbage growth (Fig. I) is currently described by a modified net accumulation curve (g/DM/ha/week) for an Agrostis-Festuca pasture (R. H. Armstrong, unpublished data). New growth is assumed to have a digestibility of 80~o throughout the year.
HERBAGE DETERIORATION
There is little published information on the rate of change of digestibility of herbage in a form that would be applicable to the concepts of the model. Terry & Tilley (1964) have produced data on the decline of digestibility in grasses on a daily basis but data in this form do not indicate the quantitative movement of material down the digestibility range. In the absence of such data it was decided to represent the change in herbage digestibility by a deterioration rate, i.e. the proportion of material by weight in a digestibility class that moves into the next lower class in a day, Within any standing crop specific parts become less digestible with time (Terry & Tilley, 1964) and a rate of quality reduction can be measured. It is therefore reasonable to assume that deterioration rates as defined may be calculated for discrete classes of herbage quality. In autumn and winter there is an accumulation of dead material (in Agrostis-Festuca pasture). Eadie & Black (1968) showed that in winter an Agrostis--Festuca pasture was composed of equal parts of dead and green material; the in t'itro DM digestibility of the dead material lay between 35 and 40 ~o while that of the green material lay between 60 and 65 ~o. This accumulation of dead material suggests that the deterioration rate of low quality herbage in autumn and winter would be low and the gradual disappearance of dead material during the summer
122
A. R. SIBBALD, T. J. MAXWELL, J. EADIE
suggests that with higher temperatures the deterioration rate of low quality material increases. Terry and Tilley's work indicates that ~he lowest rates of decline of digestibility were at the higher initial digestibility levels; this is also confirmed by more recent examination of the decline in digestibility of the component parts of a perennial ryegrass pasture (Vine, 1977). However, early experience with the model suggests that the only way in which to obtain the proportions of dead and green herbage with their appropriate digestibility ranges, as measured by Eadie & Black (1968), is to assume that highly digestible material (78-80 "~idigestibility) during the winter, spring and autumn deteriorates at high rates. On reaching a digestibility of 70 °4; the winter, spring and autumn rates of deterioration have been adjusted to agree more closely with those suggested by the evidence of Terry & Tilley (1964) and of Vine (1977). Based on these assumptions a family of relationships between
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deterioration rate and digestibility class for the different periods of an annual cycle has been devised (Fig. 2). The higher rates of deterioration at about 45 ~o digestibility in Fig. 2 represent the transition of material from green to dead, though it is appreciated that this value is likely to vary with species composition of the pasture. Material deteriorating from the lowest digestibility class is assumed to be unavailable to the grazing animal and falls out of the system.
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
123
COMPUTATION OF INTAKE
Intake (g DM/kg°VS/day) is assumed to be linearly related to the digestibility of the ingested material (Jarrige et al., 1974) and the relationship shown in Fig. 3 is based on the data of Blaxter et al. (1961). Since there is an interdependence between quantity and quality of intake, an iterative procedure has been used to ensure that the quality value used to determine
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Relationship between the dry matter intake and the digestibility of the ingested herbage of sheep.
quantity closely matches the quality of intake finally calculated. A diagram of the iterative procedure is shown in Fig. 4. J. Z. Foot and A. J. F. Russel (unpublished data) and Osbourn (1970) have shown that intake is reduced consequent upon a sheep reaching a certain level of body fat and condition. Since body condition and body fat are related to the body weight of mature ewes (Russel et al., 1969), intake in the model is limited by the relationship shown in Fig. 5. Intake is also restricted by the total quantity of pasture per unit area (Arnold & Dudzinski, 1967a,b). The relationship (Fig. 6) is assumed to be a function of the limited bite size imposed by low amounts of pasture and the fact that the sheep has an extendible but ultimately limited grazing day; the two effects combine to reduce the total potential daily intake (Hodgson, 1977; Hodgson & Milne, 1978). The resulting calculated herbage intake, adjusted for the size and number of grazing animals, is harvested assuming that the grazing animal is selective. DIET SELECTION
The selection procedure allocates 'composite' bites to the range of digestibility classes available in the pasture. A composite bite is the aggregate of a number of
124
A. R. SIBBALD,
T.
J. MAXWELL, J. EADIE
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Diagrammatic representation of the iterative procedure relating intake quantity and quality.
125
MODELLING OF HERBAGE INTAKE BY HILL SHEEP 100 ,°,°,,,,,,°|,,,°,,,,°,°,,i
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individual bites and is used to reduce the computing time that the use of individual bites would require. The composite bite is set at a level at which an acceptable degree of sensitivity in the model is retained. The number of composite bites is presently set at 100 per week for all grazing animals, each composite bite being 0.01 of the total weekly intake. A random allocation over the distribution would result in a mean digestibility of ingested material identical to that of the herbage present.
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Relationship between the percentage of the potential intake and the a m o u n t of herbage per unit area.
The selection procedure used in the model, however, is able to bias the allocation of bites towards the higher digestibility classes, the degree of bias being related to current grazing pressure expressed as the ratio of the total current calculated dry matter intake and the total dry matter of herbage present. Grazing pressure is used to derive a selection index (Fig. 7). The selection index is directly related to the slope of the assumed linear relationship between the digestibility classes within the distribution range and the preference of the sheep for taking bites ('selection bias') from each of the classes within this range (Fig. 8).
126
A. R. S1BBALD, T, J. MAXWELL, J. EADIE
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If herbage selection is assumed to be random, then the allocation of bites to a digestibility class within a distribution (based on a random number generator) would be in exact proportion to the amount of herbage in that class. In Fig. 8, the most highly selective relationship shown would allocate sixteen times more bites to the most highly digestible class (80'Yo) than would have been allocated randomly. The relationships shown in Figs. 7 and 8 are conceptual.
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127
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
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and tend to occupy a lower level in the sward. The conceptual relationship shown in Fig. 9 determines the maximum percentage of material, in each digestibility class, that may be removed by grazing. The horizontal distribution of digestibility classes within the pasture is represented by the ratio of quantity of herbage dry matter in a class and the total herbage'idry matter available. Digestibility classes which contain a large proportion of the total herbage are assumed to be more likely to be grazed than those which represent a small proportion of the total herbage which are assumed to be less likely to be grazed. The maximum amount removed by grazing from each digestibility class is therefore reduced according to another conceptual relationship, shown in Fig. 10. The combined effect of these relationships tends to make sheep graze a pasture layer by layer, a feature of grazing noted by Arnold (1960).
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128
A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
The iterative grazing procedure ends when the digestibility of the dry matter intake agrees with the digestibility value used to determine intake after selection has taken place. The digestible organic matter ( D O M ) intake is then calculated assuming that there is 92 011 organic matter in the dry matter.
ANIMAL COMPONENT
The animals used in the model are mature wethers; a starting mean body weight and the number per hectare are supplied to the model as initial data. Their maintenance requirement (34 g D O M / k g ° ~ 5 / d a y - - J . Eadie, unpublished data) is compared with the D O M intake determined by the intake/selection procedures. The rates of body weight change are related to the extent to which intake is in excess of, or below, that required for maintenance. In calculating the loss in body weight for intakes below maintenance, we have assumed the energy content of loss in body weight from this class of animal to be between 25 and 30 kJ/g and, since this is derived mainly from fat, we further assume that it will be utilised for maintenance with an efficiency of between 70 and 80 oj;. Given that the energy content per gramme of D O M is 15.58 kJ (Roy et al., 1977), one gramme of body weight loss will be equivalent to 1.4 g D O M intake below total maintenance requirement. When intakes are between maintanance (M) and 1,5 M, a gain of I g is calculated for every 2.5 g D O M intake in excess of maintenance and above 1.5 M, I g of gain for every 3.25 g of excess D O M intake (derived from Agricultural Research Council, 1965).
PASSAGE OF TIME
At present the time period used is one week and the model runs for a complete calendar year. The new calculated values for pasture digestibility distribution and mean animal body weight are passed to the next time period in the model for a new set of calculations. The choice of the time period was made for two main reasons: first, because of the nature of the available data on which the relationships in the model are based and, secondly, because the purpose for which this model is ultimately intended (i.e. for use in testing inputs to whole systems of hill sheep production) does not justify a shorter time period. The conceptual approach adopted in the model may be employed using shorter time intervals where it is justified. The model can be used to simulate events over a number of consecutive years and this feature allows the stability of the output of the model to be investigated. A stable state is assumed to exist when, after a consecutive number of annual runs, the output characteristics remain unchanged. Thus the ultimate results of a particular change in grazing management, for example, can be tested. As yet, however, stochastic
M O D E L L I N G OF H E R B A G E I N T A K E BY H I L L SHEEP
129
elements have not been introduced into th.e relationships upon which the model is based. The model also contains an option to graze the pasture for a number of periods during the calendar year to test on/off grazing system responses.
MODEL OUTPUT
The model optionally prints out, week by week: (1) (2) (3) (4)
Total pasture (DM/ha) and mean pasture digestibility ( ~ ) before and after grazing. Stocking rate during current week (head/ha). Total quantity (kg/DM) and mean digestibility (~o) of ingested material. Mean wether body weight (kg) and total maintenance requirement (kg DOM/week).
Also printed optionally are graphs of pasture dry matter distribution across digestibility classes for selected weeks. The model prints a graph, plotted week by week, of total herbage (kg DM/ha), its mean digestibility ('~,), the mean digestibility ('~,) of ingested herbage and the mean body weight (kg) of the wethers.
MODEL PERFORMANCE
Using a growth curve with growth (Fig. 1) commencing in mid-March and ceasing in mid-October, with a year-round stocking rate of 1.6 sheep per hectare, the output of the model in terms of the quality of the ingested pasture (Fig. 11) fits the data obtained by Eadie (1967) stocked at 1.5 sheep per hectare, other than at the start of the year. Eadie's study, however, relates to sheep on a grassy hill pasture of heterogeneous species composition. Hunter (1962), working with a pasture of similar species composition, showed that the Agrostis-Festuca and bracken sward (which was predominantly an Agrostis-Festuca sward under a bracken canopy) were predominantly grazed throughout the annual cycle, although, because of their relative scarcity during winter, other species such as Molinia and Nardus were grazed during the winter. This may explain the discrepancy between the quality of ingested herbage calculated by the model and the values obtained by Eadie (1967), particularly during the late winter period at the start of the year. As an example of how the model can be used, differences in ingested herbage quality and liveweight change that arise when sheep are grazed at two stocking rates
130
A. R. SIBBALD, T. J. MAXWELL, J. EADIE
of 1.6 and 6.0 sheep per hectare are compared using a growth curve producing 3800 kg DM/annum• Sheep at the higher stocking rate are unable to select as high a quality diet at the beginning of the year; although there is little difference in the quality of the herbage on offer (Fig. 11), the limited amount of material available to them (Fig. 12) results in a higher proportion of poorer quality material being ingested (Fig. 11) and a DOM
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intake per head 14 % lower. Consequently, sheep at the higher stocking rate tend to lose more weight during the first months of the cycle (Fig. 13). As growth of pasture begins, sheep at the higher stocking rate are able to select a higher proportion of the new material. The new material ingested by sheep at the lower stocking rate, however, is diluted by the greater amount of low quality material still in the pasture. By early April the overall digestibility of the herbage available to the high stocking rate sheep is between 10 and 15 units higher and they are able to ingest a diet which is some 8 units of digestibility higher• As a consequence, the D O M intakes per head become similar and the weights of both groups of sheep begin to increase at similar rates.
131
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
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132
A. R. S I B B A L D , T. J. M A X W E L L , J. EADIE
By May/June the difference in the quality of the herbage is much less (2.5 units of digestibility) and differences in the quality of ingested herbage and consequently D O M intakes per head -are small. This situation persists throughout July and August and the sheep gain body weight at a similar rate, reaching a maximum in the autumn, the high stocking rate wethers being 3.5 kg less in weight at that point. During September when there is an increase in herbage growth rate (Fig. 1) the animals at the higher stocking rate are able to make more use of the new, highly digestible herbage because less herbage has been left to deteriorate and consequently dilute the quality of intake during this period. The result is that during September and October the wethers at the higher stocking rate are able to select a diet of higher quality with DOM intakes per head 3 ",i higher than the lower stocking rate animals and they continue to gain weight at a faster rate: the weight gains of the lower stocking rate animals decline. Consequently, by mid-November~ there is only a 2.5 kg weight difference between the two stocking rates. During late November and December when there is no growth of pasture and the amount of herbage on the higher stocked pasture declines more rapidly, these sheep ingest a greater proportion of poorer quality material with DOM intakes per head falling slightly below that of the lower stocking rate sheep. Their weight loss during November and December is similar to that of the low stocked sheep, the weight difference of 2.5 kg in the autumn being maintained until the end of December. The change in weight, during an annual cycle, of the sheep at a high stocking rate is 2.5 kg less than that of the sheep at a low stocking rate, but per hectare at least 200 kg more body weight is carried and 11 kg more body weight gain produced. These results apply to wether sheep: when account is taken of the nutritional requirements of pregnancy and lactation the liveweight changes of ewes are likely to be much more sensitive to stocking rate. Before the model can be used more comprehensively to examine the effect of stocking rate and alternative grazing management strategies on animal performance, it will be necessary to add the components of pregnancy and lactation. The model does, however, support the generally accepted conclusion that the low quality of herbage intake that sheep are able to select during the winter is the overriding factor which determines the annual stocking rate that can be sustained in traditional set-stocked hill sheep production systems. Although the model has as yet some real limitations--particularly the lack of response of pasture growth to different stocking rates--and requires further development, it has provided a framework within which some of the important biological mechanisms and processes involved in the utilisation of hill pastures may be critically examined. The problem of measuring and modelling the growth of hill pastures and their responses to different grazing regimes, and the lack of understanding as to how a sheep selects its diet in the process of grazing, are highlighted. The way in which the components of herbage are distributed in space
MODELLING OF HERBAGE INTAKE BY HILL SHEEP
133
and the nature of herbage deterioration in hill pastures also require further investigation.
ACKNOWLEDGEMENTS
The authors wish to record their thanks to their colleagues who have contributed to some of the concepts incorporated in this paper and in particular to Anne Vine, a post-graduate student with the Organisation, for her contributions.
REFERENCES AGRICULTURAL RESEARCH COUNCIL (1965). The nutrient requirements o['./hrm lit'estock No. 2: Ruminants, London, Agricultural Research Council. ARNOLD, G. W. (1960). Selective grazing by sheep of two forage species at different stages of growth. Aust. J. agrie. Res., 11, 102633. ARNOI,I), G. W. & DUDZINSKI, M. L. (1967a). Studies on the diet of the grazing animal. I1. The effect of physiological status in ewes and pasture availability on herbage intake. Aust. J. agrie. Res., 18, 349 59. A RNOt.D, G. W. & DUDZINSK1, M. L. (1967b). Studies on the diet of the grazing animal. 111. The effect of pasture species and pasture structure on the herbage intake of sheep. Aust. J. agric. Res., 18, 657 66. BLAXTER, K. L., WAINMAN,F. W. & WILSON, R. S. (1961). The regulation of food intake by sheep. Anita. Prod., 3, 51 61. EADIE, J. (1967). The nutrition ¢~[grazing hill sheep." Utilisation ~['hill pasture. Hill Farming Research Organisation. Fourth Report (1964 67), 38-45. EAI)IE, J. ( 1971 ). Hill sheep production system det'elopment. Hill Farming Research Organisation, Fifth Report (1967 70), 70 87. EAI)IE, J. & BLACK, J. S. (1968). Herbage utilisation on hill pastures. Oce. Svmp. 4, Br. GrassldSoc., 191 95. EADI~, J. & MAXWH~L, T. J. (1975). Systems research in hill sheep farming. In: Stud)' of agricultural systems (Dalton, G. E. (Ed.)), London, Applied Science Publishers, 395 413. HOI)GSON, J. (1977). Factors limiting herbage intake by the grazing animal, Proc. Int. Meeting Anita. Prod. j?om Temperate Grassland, Dublin, 7ff 5. HODGSON,J. & MILNE, J. A. (1978). The influence of weight of herbage per unit area and per animal upon the grazing behaviour of sheep. Proe. 7th Mtg, European Grassland Fed., Ghent Congress. H UNTO:R,R. F. (1962). Hill sheep and their pasture: A study of sheep-grazing in south-east Scotland. J. Ecol., 50, 651 80. JARRIGE, R., DEMARQUILLY,C. & DULPI-IY,J. P. (1974). The voluntary intake of forage. Proc. 5th Gen. Mtg, European Grassland Fed., Uppsala, 1973, Publ. Hush. 28, 98 106. OSBOURN, D. F. (1970). The eoluntary intake of Jbrage crops b), sheep. Ph.D. Thesis, University of Reading. Roy, J. B. H., BAL('H, C. C., MILLER, E. L., ORSKOV, E. R. & SMITH, R. H. (1977). Calculation of Nrequirements for ruminants from nitrogen metabolism studies. EAAP 2nd lnternationalSymposium on Protein Metabolism and Nutrition. RUSSEL, A. J. F., DONEY, J. M. & GUNN, R. G. (1969). Subjective assessment of body fat in live sheep. J. agrie. Sci., Camb., 72, 451- 4. T~:RR¥, R. A. &TILt, EY, J. M. A. (1964). The digestibility of the leaves and stems of Perennial Ryegrass, Cocksfoot, Timothy, Tall Fescue, Lucerne and Sainfoin, as measured by an in t,itro procedure. J. Brit. GrassM Soe., 19, 363 72. VINE, D. A. (1977). Det'elopment of a pasture model for grazing studies. Ph.D. Thesis, University of Edinburgh.
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APPENDIX
OPERATING ENVIRONMENT
The model is written in Fortran and run on the ICL 2980 computer at the Edinburgh Regional Computing Centre. The program was compiled under Edinburgh Fortran (FORTE) and makes use of the Numerical Algorithms Group (NAG) random number generating sub-routines GO5BBF, GO5ARF and GO5AZF for the allocation of composite bites in the selection procedure.
INITIAL D A T A
The initial data supplied to the model are as follows and may be varied from run to run: (1) (2) (3) {4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Number of digestibility classes in pasture distribution. Minimum value of pasture digestibility range. Output index (controls quantity of printed output). Number of annual cycles. Number of composite bites to be made weekly. Growth (kg DM/ha/day) of pasture per week. Digestibility (~o) of new pasture growth per week. Starting pasture DM digestibility distribution (will change if (1) above is changed). Relationship between body weight and intake (current relationship shown in Fig. 5). Relationship between total pasture available and intake quantity reduction (current relationships shown in Fig. 6). Wether maintenance value (g DOM/kg ° 75/day ) and DOMI to body weight conversion rates. Selection index relationships (see Figs. 7 and 8). Pasture vertical distribution grazing limitations (Fig. 9). Pasture horizontal distribution grazing limitations (Fig. 10). Deterioration rates number of seasonal periods and relationships for each (Fig. 2). (These will change if(l) above changes.) Number of grazing periods and for each: (a) starting and ending weeks; (b) starting body weight (optionally carried over from previous period).