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A dynamic model for the simulation of cattle herd production systems: Part 1—General description and the effects of simulation techniques on model results
,tgricultural Systems 12 (1983) 101-111
A Dynamic Model for the Simulation of Cattle Herd Production Systems: Part 1 General Description and the Effects of Simulation Techniques on Model Results*
Hava E. Kahnt & C. R. W. Spedding Department of Agriculture and Horticulture, University of Reading, Earley Gate, Reading, Great Britain
SUMMARY A computerised model to describe andpredict cattle productionjor any herd size and time period and jor a wide range oJ environments, was developedjrom a model published by Sanders & Cartwright (1979a,b). The dynamics of the model are based on the flow oj energy J~'om vegetatit'e sources to animal products in a single-animal or cow-caljunit, so that the model is appropriate et'en./or smallholder herds. A separate flow oj numbers records the dynamically changing herd size and slruclure. Reproduction and mortality are linked to the nutritional and physiological status of each indit,idual. Their occurrence is triggered stochastically to presert'e the integer quality of the herd. In all other respects the model is deterministic. The simulated herd can be oj any number, breed, sex and age composition. Breeds are distinguished by mature size, growth rate and milk production: they can be single, dual and/or triple purpose (dairy and/or beef and/or draught). Feeding management can be grazing, stalljeeding or a combination of the two. Routines are included which can simulate different types of management decisions and their repercussions. * Contribution No.654-E, 1983 series, from the Agricultural Research Organization, Volcani Center, Bet Dagan, Israel. t Present address: State of Israel Ministry of Agriculture, Agricultural Research Organization, The Volcani Center, PO Box 6, Bet Dagan 50-250, Israel. 101 Agricultural Systems 0308-521X/83/$03.00 © Applied Science Publishers Ltd, England, 1983. Printed in Great Britain
102
Hava E. Kahn, C. R. W. Spedding Functions tot the quantification of the model were selected according to preset guidelines, generally .[bllowing an investigation of conflicting hypotheses. There are eight different output options (tabular and graphical), representing various levels of model resolution.
INTRODUCTION The contribution of computerised simulation models to the analysis of existing and projected livestock systems has become recognised as increasingly important in recent years, in particular that of the TAMU model reported by Sanders (1977). TAMU is a beef cattle production model developed for environments assumed to represent central Texas conditions. Subsequently, the model was adapted for use under several widely differing sets of environmental and management conditions in the USA, South and Central America and Africa (ILCA, 1978; Sanders & Cartwright, 1979a). The present paper describes a new model, constructed by Kahn (1982). It is an adaptation of the TAMU model, designed to make it valid for the very small herds typical of developing countries. It incorporates many of the principles underlying the TAMU model, i.e.: (1) The dynamics of the system are represented by a flow of energy, translated at various points into tangible units (kilograms of liveweight, litres of milk, kilograms of feed, hours of ploughing) to give a meaningful external account of the system. (2) Cattle performance is dependent on specified feed resources and genetic production potentials. (3) Genetic production potentials are specified by mature weight, growth rate and milk yield. (4) The ratio of current weight to potential (optimal) weight, referred to as the 'condition of the animal' (in the TAMU model) or 'weight index' (in the present model), governs actual performance (milk production, reproduction, mortality) relative to genetic potential. (5) The voluntary intake (VI) of DM is governed by feed quality and physiological requirements. (6) The model program is written in Fortran IV, making it compatible with most computer installations.
Model for simulation of cattle production: Part 1
103
However, in many respects, the present model differs from its precursor, both in structure and content, as follows: (1) Animal performance is calculated on an individual basis, in contrast to the fractionised herd-class structure of the TAMU model. (2) The randomly occurring discrete events--conception, mortality and calf sex--are treated stochastically. (3) Integration time-steps for cows can be set at any value between 1 and 30 days, and those for calves as a predetermined fraction of the cow time-step, compared with the fixed 30-day time-step of TAMU. (4) Routines have been included to simulate a variety of additional management options: (a)
(b) (c)
Supplementation with one/two feeds of different quality and its interaction with the voluntary intake of a third feed (e.g. pasture). The employment of adult cattle (male and female) as draught animals. Culling and rearing in response to externally determined parameters and internally calculated variables.
(5) Output options are geared to the different levels of resolution desired, from day-to-day accounts of individual performance to 10-year projections of herd performance. (6) The quantified biological functions used in the TAMU model were re-evaluated and, where necessary, modified or replaced, to make them appropriate for simulating even quite small changes in individual performance. (7) Various components of the model, as well as the model as a whole, were validated using recorded data obtained under different conditions. The following is a discussion of the model's treatment of individual animal performance, stochastic variables and integration time-steps (points (1) to (3) above); the other points ((4) to (7)) are discussed in the thesis of Kahn (1982) and/or in other papers (in preparation).
Hat'a E. Kahn, C. R. W. Spedding
104
I N D I V I D U A L A N I M A L P E R F O R M A N C E IN THE HERD CONTEXT The calculation unit
In the present model, as in the TAMU model, the calculation of the within-animal and the animal-environment energy exchanges is performed by generalised equations based on individual animal performance. The values of the variables in the equations depend on the physiological attributes of the animal, e.g. sex, age, gestation stage, lactation stage, liveweight, breed. In the TAMU model, the herd population is classified by the first four of the factors listed above: the calculations are performed in accordance with the variable values associated with each class and multiplied by the respective class number. These class numbers are generally not integers, since the discrete events involved are programmed to occur in a fixed proportion of the individuals of each class. Presumably, herd classification is intended to simplify and reduce the computation load. However, up to 1000 classes may be necessary to cater for the possible class-level combinations, and the addition of another factor, e.g. breed, would be almost impossible. Moreover, the constantly changing class populations make it impossible to follow the development of a particular animal or class of animal throughout the course of the model run; hence, it is not possible to calculate or depict the long-term, carry-over effects of factors such as age and weight index at first calving, calendar month of birth, etc. Also, a model simulating animal populations in non-integer values appears unduly artificial, and is an impediment to the conceptualisation of the system. In the present model the single animal or, in the case of suckler cows, the cow-calf entity, is the calculation unit. The model simulates the continuous biological transactions (energy exchanges) occurring in each unit in accordance with the individual basic and dynamically changing attributes, and records the combined and cumulative effects of the transactions at every time-step (Fig. 1). The herd performance is then described as the aggregate of the individual unit performances. In this way, each individual can assume at any time any combination of the variable values (e.g. breed, sex, age, lactation and gestation stage, liveweight) which are considered in the model calculations. Running an individual animal model for large herds could be very
Model for simulation of cattle production: Part 1
107
TABLE 2 Coefficients of Variation (CVs) ( ~ ) Showing the Between-Years and the Between-Runs Variation of Variables in a Model-Based Experiment
CoeJficients oJ variation (%)
Number of treatments Number of replicate runs Pasture consumption Recycled feed Concentrated feed Calf sales Cow sales Conception ~o Number weaned Average wean weight Average wean age Number replaced Number o f cow deaths Number of calf deaths Replacement weight
Between-years
Between lO-year run averages
Between lO-year run averages
1 1 6.9 0.5 13.5 14.5 169.0 4.4 7.1 6.7 8.9 116.5 241.5 67-0 5.4
1 5 2.8 0.9 5.2 3.9 39.0 1.5 2.7 1.6 2.0 19.2 106.9 20-5 3.4
14 5 2.4 0.3 11.45 3.5 23.5 1.0 2.9 1.1 2.1 17.5 39.2 19.8 3.8
coefficients of variation (CVs) between five replicate runs of the same treatment, and column 3 shows the pooled estimates of these CVs for the whole experiment. The variables with the highest variance were the direct cumulative sums of the stochastic variables---cow and calf deaths. However, the combined effects of variability in conception ~o, cow and calf mortality and replacement rate on total calf liveweight sold (after deducting the liveweight of replacement calves) are reduced to a CV of 3"9~o within treatment, although the between-year CV is 14.5~. Generally, within-run, between-year coefficients of variation for the salient variables representing the system were much higher than the between-run coefficients for the 10-year averages, showing the importance of observing and evaluating herd systems, real or simulated, over several years. The stochastic variables not only solve a methodological problem in system modelling--they also enable the model to simulate the instability of small herds, due to the random occurrence of births and deaths, and the uncertainty of the male:female ratio in births. However, it is not
108
Hava E. Kahn, C. R. W. Spedding
claimed that the calculated variances represent the full extent of the variability of the system; no attempt is made to simulate the unpredictable character of some of the other variables, e.g. pasture quality. The purpose of the model is to provide an objective gauge for the comparison and relative evaluation of different management policies, rather than to propose specific management policies. The generally low variances of the key variables observed should make it possible to detect differences between treatments in any subsequent statistical analyses and evaluations of policies.
THE INTEGRATION TIME-STEP Most of the individual animal functions are based on daily calculations, e.g. maintenance requirements per day, milk yield per day, liveweight gain per day. These are derived from controlled laboratory experiments where it is possible to observe and record daily changes. However, in multi-year herd models, the numerous daily computations of all the variables would incur heavy computational costs. Both Sanders & Cartwright (1979a,b) and Konandreas & Anderson (1982) used a 30-day time-step in their models. The present model has options for different time-steps (1-30 days); the time-step for calves can be smaller than that for the cows. Experimental runs (15 animals × 5 years), using different time-steps, from 1 day to 30, showed that there were no significant differences between the single-day and 30-day interval in the calculation of the mean multi-year herd variable values, especially in the key variable, calf liveweight sold (see Table 3). In fact, the variation appears to be considerably greater between replicates than between the time-step treatments, for the two replicates tested, possibly due to the small herd size (15 head) and short-run period (5 years). However, there were considerable discrepancies between the 1day interval and 30-day interval results for individual animal calculations (see Table 4), especially those concerning calf performance. (Note: The cow in the 1-day integration run did not conceive; consequently, she was not subjected to nutritional stresses--as were the lactating cows in the second half of the other runs--and accordingly did not lose weight.) It appears, therefore, that a 30-day time-step is sufficiently accurate in calculating herd averages projected over several years. When more
Model for simulation of cattle production." Part
I
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TABLE 4 The Effect of Different Integration Time-Steps on Salient Cow/Calf Variable Values
Time (days)
Cow weight (kg)
Milk (MJ/day)
Weight change (kg/day)
CaW weight (kg)
CaW weight gain (kg/day)
Integration time-step: Cow --- 30; Calf = 30 0 30 60 90 120 150 180 210 240 270 300 330 360
375 354 338 329 395 404 406 407 398 378 357 335 318
0 30 60 90 120 150 180 210 240 270 300 330 360
375 356 342 335 375 392 399 401 396 392 396 395 395
0 30 60 90 120 150 180 210 240 270 300 330 360
375 356 341 332 378 394 401 401 389 369 349 330 315
40-28 37-40 42.00 32.37 29.37 27.37 0,00 0.00 0.00 37.30 31.10 32.29 36.94
-0.69 -0.54 -0.30 2.19 0.30 0.08 0.03 -0.29 -0,67 -0.72 -0.73 -0,56 -0.41
79-13 104.58 119-25 145.21 175.45 198,08 0.00 0.00 0.00 28.98 69.72 83.44 94"89
0,85 0,49 0,87 1.01 0,75 0~72 0.00 0,00 0.00 1.36 0.46 0-38 0.56
Integration time-step: Cow = 1; Calf = 1 40"28 37"46 43"05 29"27 26"08 23-81 0"00 0-00 0"00 0'00 0"00 0"00 0"00
-0"69 -0.54 -0'32 2'00 0"82 0"36 0-13 0"01 -0.14 0'15 -0"04 0"02 0-16
Integration time-step: Cow = 10; C a l f = 40,28 - 0.69 37.47 - 0.54 43.00 -0.33 31.47 2.08 28.35 0.74 26.21 0.30 0.00 0-10 0,00 -0.23 0,00 - 0.56 35.82 - 0.67 30.41 - 0.70 31.88 -0.54 36,63 - 0.40
79-13 99.10 111.89 124.55 154.81 181.01 0.00 0.00 0.00 0.00 0-00 0.00 0.00
0.85 0.58 1.02 1.02 0.02 0.86 0.00 0.00 0.00 0-00 0-00 0.00 0.00
10 79.13 100.44 113.56 130.69 161-16 187.35 0.00 0.00 0.00 28.63 58,12 73.84 86.25
0.85 0.56 1.00 1,02 0.79 0.87 0-00 0.00 0.00 1.27 0.67 0.54 0.70
Model for simulation of cattle production: Part 1
111
detailed information is required, smaller time-steps, in particular for calf performance, will be more appropriate.
ACKNOWLEDGEMENTS The authors wish to thank Dr J. Putter and Dr N. G. Seligman, of the Agricultural Research Organization, Bet Dagan, Israel, for their helpful advice and suggestions.
REFERENCES ILCA (1978). Mathematical modelling of livestock production Systems: Application of the Texas A & M University beef cattle production model to Botswana. International Livestock Centre for Africa, Addis Ababa, Ethiopia. Kahn, Hava E. (1982). The development of a simulation model and its use in the evaluation of cattle production systems. PhD Thesis, University of Reading. Konandreas, P. A. & Anderson, F. M. (1982). Cattle herd dynamics: An integer and stochastic model for evaluating production alternatives. ILCA, Addis Ababa, Ethiopia. Sanders, J. O. (1977). Application of a beef cattle production model to the evaluation of genetic selection criteria. PhD Dissertation, Texas A & M University. Sanders, J. O. & Cartwright, T. C. (1979a). A general cattle production systems model. Part 1. Description of the model. Agricultural Systems, 4, 217-27. Sanders, J. O. & Cartwright, T. C. (1979b). A general cattle production systems model. Part 2. Procedures used for simulating animal performance. Agricultural Systems, 4, 289-309.
A Dynamic Model for the Simulation of Cattle Herd Production Systems: Part 1 General Description and the Effects of Simulation Techniques on Model Results*
Hava E. Kahnt & C. R. W. Spedding Department of Agriculture and Horticulture, University of Reading, Earley Gate, Reading, Great Britain
SUMMARY A computerised model to describe andpredict cattle productionjor any herd size and time period and jor a wide range oJ environments, was developedjrom a model published by Sanders & Cartwright (1979a,b). The dynamics of the model are based on the flow oj energy J~'om vegetatit'e sources to animal products in a single-animal or cow-caljunit, so that the model is appropriate et'en./or smallholder herds. A separate flow oj numbers records the dynamically changing herd size and slruclure. Reproduction and mortality are linked to the nutritional and physiological status of each indit,idual. Their occurrence is triggered stochastically to presert'e the integer quality of the herd. In all other respects the model is deterministic. The simulated herd can be oj any number, breed, sex and age composition. Breeds are distinguished by mature size, growth rate and milk production: they can be single, dual and/or triple purpose (dairy and/or beef and/or draught). Feeding management can be grazing, stalljeeding or a combination of the two. Routines are included which can simulate different types of management decisions and their repercussions. * Contribution No.654-E, 1983 series, from the Agricultural Research Organization, Volcani Center, Bet Dagan, Israel. t Present address: State of Israel Ministry of Agriculture, Agricultural Research Organization, The Volcani Center, PO Box 6, Bet Dagan 50-250, Israel. 101 Agricultural Systems 0308-521X/83/$03.00 © Applied Science Publishers Ltd, England, 1983. Printed in Great Britain
102
Hava E. Kahn, C. R. W. Spedding Functions tot the quantification of the model were selected according to preset guidelines, generally .[bllowing an investigation of conflicting hypotheses. There are eight different output options (tabular and graphical), representing various levels of model resolution.
INTRODUCTION The contribution of computerised simulation models to the analysis of existing and projected livestock systems has become recognised as increasingly important in recent years, in particular that of the TAMU model reported by Sanders (1977). TAMU is a beef cattle production model developed for environments assumed to represent central Texas conditions. Subsequently, the model was adapted for use under several widely differing sets of environmental and management conditions in the USA, South and Central America and Africa (ILCA, 1978; Sanders & Cartwright, 1979a). The present paper describes a new model, constructed by Kahn (1982). It is an adaptation of the TAMU model, designed to make it valid for the very small herds typical of developing countries. It incorporates many of the principles underlying the TAMU model, i.e.: (1) The dynamics of the system are represented by a flow of energy, translated at various points into tangible units (kilograms of liveweight, litres of milk, kilograms of feed, hours of ploughing) to give a meaningful external account of the system. (2) Cattle performance is dependent on specified feed resources and genetic production potentials. (3) Genetic production potentials are specified by mature weight, growth rate and milk yield. (4) The ratio of current weight to potential (optimal) weight, referred to as the 'condition of the animal' (in the TAMU model) or 'weight index' (in the present model), governs actual performance (milk production, reproduction, mortality) relative to genetic potential. (5) The voluntary intake (VI) of DM is governed by feed quality and physiological requirements. (6) The model program is written in Fortran IV, making it compatible with most computer installations.
Model for simulation of cattle production: Part 1
103
However, in many respects, the present model differs from its precursor, both in structure and content, as follows: (1) Animal performance is calculated on an individual basis, in contrast to the fractionised herd-class structure of the TAMU model. (2) The randomly occurring discrete events--conception, mortality and calf sex--are treated stochastically. (3) Integration time-steps for cows can be set at any value between 1 and 30 days, and those for calves as a predetermined fraction of the cow time-step, compared with the fixed 30-day time-step of TAMU. (4) Routines have been included to simulate a variety of additional management options: (a)
(b) (c)
Supplementation with one/two feeds of different quality and its interaction with the voluntary intake of a third feed (e.g. pasture). The employment of adult cattle (male and female) as draught animals. Culling and rearing in response to externally determined parameters and internally calculated variables.
(5) Output options are geared to the different levels of resolution desired, from day-to-day accounts of individual performance to 10-year projections of herd performance. (6) The quantified biological functions used in the TAMU model were re-evaluated and, where necessary, modified or replaced, to make them appropriate for simulating even quite small changes in individual performance. (7) Various components of the model, as well as the model as a whole, were validated using recorded data obtained under different conditions. The following is a discussion of the model's treatment of individual animal performance, stochastic variables and integration time-steps (points (1) to (3) above); the other points ((4) to (7)) are discussed in the thesis of Kahn (1982) and/or in other papers (in preparation).
Hat'a E. Kahn, C. R. W. Spedding
104
I N D I V I D U A L A N I M A L P E R F O R M A N C E IN THE HERD CONTEXT The calculation unit
In the present model, as in the TAMU model, the calculation of the within-animal and the animal-environment energy exchanges is performed by generalised equations based on individual animal performance. The values of the variables in the equations depend on the physiological attributes of the animal, e.g. sex, age, gestation stage, lactation stage, liveweight, breed. In the TAMU model, the herd population is classified by the first four of the factors listed above: the calculations are performed in accordance with the variable values associated with each class and multiplied by the respective class number. These class numbers are generally not integers, since the discrete events involved are programmed to occur in a fixed proportion of the individuals of each class. Presumably, herd classification is intended to simplify and reduce the computation load. However, up to 1000 classes may be necessary to cater for the possible class-level combinations, and the addition of another factor, e.g. breed, would be almost impossible. Moreover, the constantly changing class populations make it impossible to follow the development of a particular animal or class of animal throughout the course of the model run; hence, it is not possible to calculate or depict the long-term, carry-over effects of factors such as age and weight index at first calving, calendar month of birth, etc. Also, a model simulating animal populations in non-integer values appears unduly artificial, and is an impediment to the conceptualisation of the system. In the present model the single animal or, in the case of suckler cows, the cow-calf entity, is the calculation unit. The model simulates the continuous biological transactions (energy exchanges) occurring in each unit in accordance with the individual basic and dynamically changing attributes, and records the combined and cumulative effects of the transactions at every time-step (Fig. 1). The herd performance is then described as the aggregate of the individual unit performances. In this way, each individual can assume at any time any combination of the variable values (e.g. breed, sex, age, lactation and gestation stage, liveweight) which are considered in the model calculations. Running an individual animal model for large herds could be very
Model for simulation of cattle production: Part 1
107
TABLE 2 Coefficients of Variation (CVs) ( ~ ) Showing the Between-Years and the Between-Runs Variation of Variables in a Model-Based Experiment
CoeJficients oJ variation (%)
Number of treatments Number of replicate runs Pasture consumption Recycled feed Concentrated feed Calf sales Cow sales Conception ~o Number weaned Average wean weight Average wean age Number replaced Number o f cow deaths Number of calf deaths Replacement weight
Between-years
Between lO-year run averages
Between lO-year run averages
1 1 6.9 0.5 13.5 14.5 169.0 4.4 7.1 6.7 8.9 116.5 241.5 67-0 5.4
1 5 2.8 0.9 5.2 3.9 39.0 1.5 2.7 1.6 2.0 19.2 106.9 20-5 3.4
14 5 2.4 0.3 11.45 3.5 23.5 1.0 2.9 1.1 2.1 17.5 39.2 19.8 3.8
coefficients of variation (CVs) between five replicate runs of the same treatment, and column 3 shows the pooled estimates of these CVs for the whole experiment. The variables with the highest variance were the direct cumulative sums of the stochastic variables---cow and calf deaths. However, the combined effects of variability in conception ~o, cow and calf mortality and replacement rate on total calf liveweight sold (after deducting the liveweight of replacement calves) are reduced to a CV of 3"9~o within treatment, although the between-year CV is 14.5~. Generally, within-run, between-year coefficients of variation for the salient variables representing the system were much higher than the between-run coefficients for the 10-year averages, showing the importance of observing and evaluating herd systems, real or simulated, over several years. The stochastic variables not only solve a methodological problem in system modelling--they also enable the model to simulate the instability of small herds, due to the random occurrence of births and deaths, and the uncertainty of the male:female ratio in births. However, it is not
108
Hava E. Kahn, C. R. W. Spedding
claimed that the calculated variances represent the full extent of the variability of the system; no attempt is made to simulate the unpredictable character of some of the other variables, e.g. pasture quality. The purpose of the model is to provide an objective gauge for the comparison and relative evaluation of different management policies, rather than to propose specific management policies. The generally low variances of the key variables observed should make it possible to detect differences between treatments in any subsequent statistical analyses and evaluations of policies.
THE INTEGRATION TIME-STEP Most of the individual animal functions are based on daily calculations, e.g. maintenance requirements per day, milk yield per day, liveweight gain per day. These are derived from controlled laboratory experiments where it is possible to observe and record daily changes. However, in multi-year herd models, the numerous daily computations of all the variables would incur heavy computational costs. Both Sanders & Cartwright (1979a,b) and Konandreas & Anderson (1982) used a 30-day time-step in their models. The present model has options for different time-steps (1-30 days); the time-step for calves can be smaller than that for the cows. Experimental runs (15 animals × 5 years), using different time-steps, from 1 day to 30, showed that there were no significant differences between the single-day and 30-day interval in the calculation of the mean multi-year herd variable values, especially in the key variable, calf liveweight sold (see Table 3). In fact, the variation appears to be considerably greater between replicates than between the time-step treatments, for the two replicates tested, possibly due to the small herd size (15 head) and short-run period (5 years). However, there were considerable discrepancies between the 1day interval and 30-day interval results for individual animal calculations (see Table 4), especially those concerning calf performance. (Note: The cow in the 1-day integration run did not conceive; consequently, she was not subjected to nutritional stresses--as were the lactating cows in the second half of the other runs--and accordingly did not lose weight.) It appears, therefore, that a 30-day time-step is sufficiently accurate in calculating herd averages projected over several years. When more
Model for simulation of cattle production." Part
I
ml o
~ S ~ - ~
0
;>
~o~
~
~°°~--" ~
o o~ ~ - o ~ o ~ .n
~
z z z ~
109
TABLE 4 The Effect of Different Integration Time-Steps on Salient Cow/Calf Variable Values
Time (days)
Cow weight (kg)
Milk (MJ/day)
Weight change (kg/day)
CaW weight (kg)
CaW weight gain (kg/day)
Integration time-step: Cow --- 30; Calf = 30 0 30 60 90 120 150 180 210 240 270 300 330 360
375 354 338 329 395 404 406 407 398 378 357 335 318
0 30 60 90 120 150 180 210 240 270 300 330 360
375 356 342 335 375 392 399 401 396 392 396 395 395
0 30 60 90 120 150 180 210 240 270 300 330 360
375 356 341 332 378 394 401 401 389 369 349 330 315
40-28 37-40 42.00 32.37 29.37 27.37 0,00 0.00 0.00 37.30 31.10 32.29 36.94
-0.69 -0.54 -0.30 2.19 0.30 0.08 0.03 -0.29 -0,67 -0.72 -0.73 -0,56 -0.41
79-13 104.58 119-25 145.21 175.45 198,08 0.00 0.00 0.00 28.98 69.72 83.44 94"89
0,85 0,49 0,87 1.01 0,75 0~72 0.00 0,00 0.00 1.36 0.46 0-38 0.56
Integration time-step: Cow = 1; Calf = 1 40"28 37"46 43"05 29"27 26"08 23-81 0"00 0-00 0"00 0'00 0"00 0"00 0"00
-0"69 -0.54 -0'32 2'00 0"82 0"36 0-13 0"01 -0.14 0'15 -0"04 0"02 0-16
Integration time-step: Cow = 10; C a l f = 40,28 - 0.69 37.47 - 0.54 43.00 -0.33 31.47 2.08 28.35 0.74 26.21 0.30 0.00 0-10 0,00 -0.23 0,00 - 0.56 35.82 - 0.67 30.41 - 0.70 31.88 -0.54 36,63 - 0.40
79-13 99.10 111.89 124.55 154.81 181.01 0.00 0.00 0.00 0.00 0-00 0.00 0.00
0.85 0.58 1.02 1.02 0.02 0.86 0.00 0.00 0.00 0-00 0-00 0.00 0.00
10 79.13 100.44 113.56 130.69 161-16 187.35 0.00 0.00 0.00 28.63 58,12 73.84 86.25
0.85 0.56 1.00 1,02 0.79 0.87 0-00 0.00 0.00 1.27 0.67 0.54 0.70
Model for simulation of cattle production: Part 1
111
detailed information is required, smaller time-steps, in particular for calf performance, will be more appropriate.
ACKNOWLEDGEMENTS The authors wish to thank Dr J. Putter and Dr N. G. Seligman, of the Agricultural Research Organization, Bet Dagan, Israel, for their helpful advice and suggestions.
REFERENCES ILCA (1978). Mathematical modelling of livestock production Systems: Application of the Texas A & M University beef cattle production model to Botswana. International Livestock Centre for Africa, Addis Ababa, Ethiopia. Kahn, Hava E. (1982). The development of a simulation model and its use in the evaluation of cattle production systems. PhD Thesis, University of Reading. Konandreas, P. A. & Anderson, F. M. (1982). Cattle herd dynamics: An integer and stochastic model for evaluating production alternatives. ILCA, Addis Ababa, Ethiopia. Sanders, J. O. (1977). Application of a beef cattle production model to the evaluation of genetic selection criteria. PhD Dissertation, Texas A & M University. Sanders, J. O. & Cartwright, T. C. (1979a). A general cattle production systems model. Part 1. Description of the model. Agricultural Systems, 4, 217-27. Sanders, J. O. & Cartwright, T. C. (1979b). A general cattle production systems model. Part 2. Procedures used for simulating animal performance. Agricultural Systems, 4, 289-309.