K.T. Wagenaar and E. Kontrohr
ILCA's initial modelling efforts were based on the use of existing models. The beef cattle production model of Texas A&M University (TAMU) was applied to commercial ranching and traditional cattle systems in Botswana by ILCA, TAMU and the Animal Production Research Unit (ILCA/APRU, 1978).
This work highlighted the need for a model with stochastic feature, particularly for the primary production component. An operational model was developed in which animals in the simulated hens are treated as individuals (Konandreas and Anderson, 1982) and was applied in Botswana (Konandreas et al, 1983). A users' guide to the model is in press.
Recent analysis of data from long-term animal productivity studies in Mali and Kenya provided new material for further appraisal of the ILCA model, particularly with respect to the representations of biological processes. When this data was used, the predicted patterns of productivity were significantly different from those actually observed. This prompted a closer examination of the steps by which the model operated, the basic system parameters that are provided as data and the algorithms that are used to predict animal productivity.
This paper reports on the problems encountered during the appraisal and changes to some of the subroutines of the model are proposed that should improve the simulation of the performance of range cattle in extensive pastoral production systems.
Like the TAMU model, the ILCA model simulates the response of beef cattle to specific primary production conditions. The model deals only with the animal; the primary production system is not modelled. Thus, plant production is exogenous to the model and there is no feedback of the effects of its exploitation on primary production systems.
This limitation, which has been the subject of vigorous debate in Agricultural Systems (Whelan et al, 1984 versus Cartwright and Doren, 1984), is legitimate but restricts the use of the model.
Animal productivity is simulated for individual animals on the basis of forage intake, which is calculated from the following equation derived from the work of Conrad et al (1964):
I = f (P) . W 0 73/ (1–d)
where I = forage intake (kg/day)
W = liveweight (kg)
d = digestibility of forage consumed (fraction)
f (p) = the rate of passage through the digestive tract (kg/kg metabolic weight/day) which is, in general, a function of the animal's physiological status.
The animal's age, weight and physiological status are used to determine the use of the energy supplied by the feed, plus energy from catabolism of body tissues if necessary.
Statistical descriptions of the quantity (t/ha) and quality (digestibility and crude protein) of the forage on offer, based on field observations, plus the distance walked (km/day), which is used to check whether there is a limitation on grazing time, are the driving forces of the model. They are each vectors with 12 values, corresponding to the months of the year, and are provided to the model as data. There is a discrepancy between the input of digestibility of feed on offer and its use in the model as if it were digestible feed consumed. In a draft paper, Konandreas (unpublished) tried to develop a simple model of the grazing selectivity of animals with emphasis on transhumant cattle in Mali. In this he subdivided the available biomass into quality classes. In the original TAMU model the digestibility of the forage consumed was required as input data (Sanders and Cartwright, 1979). The forage subroutine of the ILCA model requires threshold values for DM availability per hectare and distance walked, below which intake is reduced. These are used to quantify two multipliers, MQ and MD (Figures 1 and 2).
Figure 1. Multiplicative effect (MQ) of quantity of acceptable1 forage on offer (Q) on voluntary intake
Figure 2. Multiplicative effect MD of daily distance walked (D) on voluntary intake
These multipliers adjust the ad libitum intake of the individual animal if the thresholds are passed. Other multipliers adjust the voluntary intake of the animals:
m(d,t) corrects for digestibility of the fodder above 65% and below 40%; m(t) corrects for the age of the animal, less than 2 months and more than 8 years old;
m(t) corrects for the age of the animal, less than 2 months and more than 8 years old;
m(x,t) corrects for the greater appetite of young males; and
m(p,t) corrects for the physiological status of an animal (pregnant, lactating, etc.) .
Thus, equation 1.1 can be restated as:
I = a.Wt0.73.m(d,t) .MQ,MD, m(t) .m(x,t) .m(p,t)/(1–d) (1.2)
where a is the intake coefficient for the reference class of animals (7-year-old dry female, less than 7-months pregnant) and equals the rate of passage through the digestive tract.
In any production system there is a calendar month (in the most probable year type) during which the liveweight of the reference class of animals is in equilibrium, i.e. the animals are neither gaining nor losing weight. This implies that during this month the daily dry-matter intake is just sufficient to maintain the body weight of the reference animal at the level of activity for that month. The a factor is calculated from equation 1.2 at this equilibrium, for which the reference month(s) has to be specified. An adjustment is made when the reference digestibility of the feed falls outside the range of 40–65%. The a factor is also corrected for sex, age and physiological status for each category of animal.
Two major problems were encountered when the model was applied to transhumant cattle in Mali. Firstly, stocking rate is not taken into account in the model. Whether the quantity of forage available per hectare is grazed by one animal or 200 is not considered1, because there is no feedback between secondary and primary production processes in the model.
1Under controlled (fenced) conditions the stocking rate can be simulated by a smaller or larger decrease in DM availability from one month to the next.
As explained, the intake of the individual animal is adjusted if the availability of good-quality fodder drops below a certain quantity per hectare (MQ in equation 1.2). In the model, the quantity of fodder on offer is neglected in the calculation of the intake of the animal as long as the threshhold is met (MQ = 1) . This means that, via the a factor, digestibility is the sole determinant of forage intake.
In Mali feed digestibility during the dry season was high, due to regrowth of forage after burning and the stepwise accessibility of the bourgoutieres1. As a result the model predicted that the normal growth of the animals would occur during the dry season, whereas, in reality, the small quantities of forage available per hectare are a constraint to growth during the dry season. Table 1 presents data on the availability of dry matter and digestibility values for the most probable year type, and the measured and simulated body weights of adult female cattle.
Table 1. Monthly values of dry-matter availability (t/ha) and its digestibility (%) for the most probable year type as used in the Mali validation, complete with the simulated and measured average monthly body weights (kg) for adult females.
Month |
DM |
Dig |
Average LW adult females | |
|
(t/ha) |
(%) |
simulated (kg) | measured (kg) | |
January |
2.5 |
50 |
184 |
|
February |
2.5 |
50 |
171 |
|
March |
1.4 |
55 |
172 |
215 |
April |
1.0 |
62 |
193 |
|
May |
1.1 |
65 |
216 |
|
June |
1.5 |
66 |
234 |
205 |
July |
1.1 |
68 |
238 |
|
August |
0.3 |
70 |
254 |
|
September |
0.8 |
67 |
266 |
|
October |
1.0 |
46 |
225 |
|
November |
2.5 |
53 |
210 |
233 |
December |
3.5 |
52 |
196 |
|
Threshold value |
0.6 |
|||
Reference dig. |
55 |
|||
Source: Breman (unpublished data); Diallo (1978); Traore (1978)
1Wet season inundated pastures consisting of high-quality grasses such as Echinochloa stagnina, oryza longistaminata, etc, which dry out during the dry season.
Some adaptation of the model is needed for its application to extensive production systems such as in Mali. It is suggested that the input data, DM availability in t/ha, should be modified to DM availability per individual animal/day, as in the GRO subroutine of the original TAMU model (Sanders and Cartwright,. 1979). The MQ multiplier should be changed in a similar way.
The second problem is related to the a factor through which the intake of each animal is calculated. When all six multipliers are equal to unity the a factor is defined as:
a = I ref. (1–d ref)/Wt 0.73 (1.3)
where I ref. = intake of reference animals in the reference month(s)
d ref. = average digestibility in the reference month(s)
Wt = liveweight (kg)
Consequently the intake of the reference animal increases when the digestibility is greater than d ref (within the limits of 40 to 65%), resulting in an energy surplus for growth. With lower digestibilities the animal will lose weight. This formulation has important consequences, which are illustrated in Figure 3.
Figure 3. The measured weight change in adult females over the year and the fluctuation in digestibility
A user might choose June–July as the reference months while another user chooses October–November. In the first case the simulation output will tell the user that his herd died out, predicting that the animals will lose weight on all digestibilities lower than the reference 60% (Table 2). In the second case all the animals achieve a condition score of 100 corresponding to the maximum weight allowed by the model. Thus the choice of the reference months is crucial for the outcome of the simulation (Table 2). Data in Table 2 indicate that a should be about 0.045 to approach a normal outcome. Using data reported by Elliot et al (1961), Konandreas and Anderson (1982) calculated an a factor for dry cows of 0.042. It is proposed to replace the existing forage intake algorithm using the a factor by the original TAMU GRO subroutine. If the intake subroutine as it stands in the ILCA model is preferred, an alternative to the current model is to focus on the reference digestibility instead of the reference months as an input requirement.
Table 2. Results after 5 years simulation for different reference months with the same initial data set.
Ref. |
Refa digest% |
Ref |
"a" |
Herd size after |
Fertility |
Weaning |
Adult female |
Calf mortality | |
|
0–1 |
1–2 | ||||||||
10+11 |
45 |
5.25b |
0.0676 |
75 |
64 |
87 |
260 |
24 |
26 |
12+1 |
50 |
4.85 |
0.0527 |
71 |
62 |
82 |
228 |
31 |
33 |
3+4 |
53 |
5.85 |
0.0442 |
70 |
57 |
66 |
196 |
40 |
43 |
4+5 |
55 |
6.65 |
0.0400 |
60 |
54 |
46 |
175 |
36 |
55 |
6+7 |
60 |
10.05 |
0.0322 |
12 |
13 |
20 |
147 |
100 |
100 |
Base-line data entry |
67 |
53 |
70 |
210 |
34 |
40 | |||
a Digestibilities as in Figure 3.
b The "a" factor is corrected for CP less than 6%.
As specified, the model requires the minimum age in months at first parturition for heifers in best, average or poor condition. This information, together with liveweight boundary data provided elsewhere to the model, is used to calculate the moment at which a heifer becomes a breeding female (Figure 4).
Figure 4. Age and liveweight combinations for heifer reproductive maturity
The Mali appraisal, in which excessive liveweight gains were simulated, also had most females entering the breeding herd at an age close to t1. After an animal has been identified as a potential breeding female it will have a stochastic dance to conceive in accordance with the age-specific calving rates (Rt) which are provided to the model. These are net calving rates, so abortions are excluded. With this information the model establishes the effect of age on cow fertility in the case of Mali as shown in Figure 5.
Figure 5. Effect of age on cow fertility
Together with the length of the breeding season, the expected probability of conception (
) is calculated. In the validation year-round breeding is assumed, so there is no seasonal restriction of the chance to conceive.
Subsequently, two multipliers are introduced to translate the influence of the liveweight condition (c) of the animal and of the number of months post-partum(n) on the probability .
The way these multipliers are described in the model is now believed not to be appropriate for application to Zebu cows in extensive production systems. Reasons for this conclusion are given below.
The post-partum period multiplier (mn) is assigned a constant value of 1.0 for cows more than one month post-partum.
In general, post-partum anoestrus lasts for more than one month when African Zebu cows are subject to nutritional stress (Moore, 1984) as is the case in Mali and Kenya. Under these conditions the females also suffer from. lactational stress. About 70% of the cows in the Mali sample did not conceive during lactation, which is in agreement with data from Kenya (Semenye, 1982) . Those cows which conceived while lactating were in their 7th month or later post-partum (Wagenaar et al, in press). Therefore, it is suggested that for application, in extensive systems, the post-partum. period multiplier could be modelled as in Figure 6.
Figure 6. Proposed multiplicative effect (mn,) on of the period in months post-partum
The condition multiplier (%) adjusts the probability of conception according to condition score (Figure 7).
Figure 7. Assumed multiplicative effect (mc) of liveweight condition index on the probability of conception
The increase or reduction in due to a higher or lower condition
index, respectively,is based on the assumption that
is the optimal for the breed and weight involved. It is, however, doubtful whether the 48% calving rate for Malian Zebu cows of 215 kg average weight is the maximum calving rate for this breed. An increase in weight of 83 kg is expected to have a match greater effect than the model estimate of 13% increase in calving rate. A calving rate of about
75–80% might be expected for animals in such a good condition. Cows of the same Fulani breed on the research ranch in Niono with an average body weight of 302 kg are reported to have a calving rate of about 70% (ILCA/IER, 1978, corrected for abortions).
The reproductive physiology of Zebu cows under extensive, suboptimal conditions seems much more complex than in the ILCA model. In order to test, for example, the effect of supplementation under these conditions, it is felt that the multiplicative effect (mc) of the liveweight condition index should give more room for increase in the probability of conception than the present 13%, as suggested in Figure 8. An mc of 1.45 is obviously only applicable for initially low fertility rates.
Figure 8. Proposed multiplicative effect (mc) of liveweight condition index on
Calving rate in the model is defined as:
The number of calves produced in the herd x 100 (%)
The number of breeding females in the herd
The numerator, as explained above, is directly related to the mean calving rates provided as data and the condition of the herd (via mc). Because of the model's restriction on mc this calving rate is too low under good conditions (some more calves and many more breeding females) and too high under moderate conditions.
The model is structured so that deaths can occur due directly to nutritional stress if harsh production environments are being simulated. Additionally, the model allows for normal losses caused by a complex set of factors not directly related to nutritional status.
Mortality due to starvation1 occurs when the liveweight of an animal falls below the lower liveweight limit, as shown in Figure 9, and is a function of the liveweight data and the forage data provided to the model.
Figure 9. General shape of the average liveweight evolution curve and associated boundary curves, and illustration of two simulated liveweight paths
____________________
1Starvation mortality is not printed out in the monthly output option.
The mortality rates provided to the model are used to simulate the non-nutritional losses. The average annual mortality rate (Mt) as a function of age is shown in Figure 10. These Mt values are used to calculate monthly rates, such that when compounded over 12 months they give the annual rates.
Figure 10. Average annual mortality rate (Mt) as a function of age in years
For calves less than one year old, the probability of death is calculated by month, based on the entered survival rates. These monthly rates for both adults and calves are the test values in binomial trials, where a random number between 0 and 1 is drawn for each animal from a uniform distribution. Death due to non-nutritional reasons occurs if the number drawn is less than the test value. As already mentioned at the 1983 workshop (van Keulen et al, 1984) the mortality from causes other than malnutrition is completely descriptive, so the model does not adequately simulate differential mortality losses arising as a result of changes in management.
No distinction in the input data is made between starvation and normal death. If the model is running for a system under harsh conditions, as in Mali, the mortality due to starvation is added to the stochastic mortality (input data) of which it was already a part.
The model assumes that all conceptions result in a birth 9 months later. Abortions are not considered in calf mortality to 3 months of age nor in the calving rate. In the Mali studies, however (ILCA/IER, 1978; Wagenaar et al, in press), the average percentage of abortions was found to be 10 and 6.7 with calving percentages of 70 and 48, respectively. Thus in both cases, 14% of the conceptions did not result in parturition: Improvement of disease control (not considered as a policy in the model) or in nutritional level could well decrease this pre-partum mortality, immediately resulting in an increase in productivity.
It is suggested that the abortion rate should be included in the calving rate as data to the model, i.e. to ask for the fertility rate. Parallel to the calculation of the probability of conception (), a stochastic probability of abortion could be built into the model.
The appraisal of the ILCA secondary production model with data from extensive semi-arid production systems in Mali and Kenya has revealed that, for such systems, the model needs some adaptations.
The forage intake of uncontrolled grazing animals is calculated by using almost solely the digestibility of the forage on offer. Availability and crude protein content of the forage and the time available for grazing are only used for possible adjustments. It is suggested that the forage availability per animal per day should play a more important role in the forage intake algorithm.
Due to its definition, the a factor used as a calibration factor for intake causes considerable variation in the outcome of the simulation processes. The functioning of this a factor in the model needs close examination.
Emphasis is given to the complicated reproductive physiology of Zebu cows under extensive range conditions. Scene proposals are advanced to make the assumed multiplicative effects match more closely to Zebu cow physiology.
Finally the mortality subroutine has been discussed, and some modifications are proposed.
The authors wish to thank Dr F.M. Anderson for his fruitful comments and Dr H. Berman and Mr P.N. de Leeuw for their supply of material for this appraisal.
Cartwright T C and Doren P E. 1984. Letter to the editor. Agric. Systems 15:249–251.
Conrad H R, Pratt A D and Hibbs J W. 1964. Regulation of feed intake of herbage by ruminants: Physiological and physical factors limiting feed intake. J. Anim. Sci. 25:227–235.
Diallo A. 1978. Transhumance: comportement, nutrition et productivité d'un troupeau zébus de Diafarabé. Thesis CPS, Bamako, Mali.
Elliot R C, Fokkema K and French C H. 1961. Herbage consumption studies on beef cattle. Rhodesian Agric. J. 58:124–130.
ILCA/APRU (International Livestock Centre for Africa/Animal Production Research Unit, Botswana). 1978. Mathematical modelling of livestock production systems: Application of the Texas A & M University beef cattle production model to Botswana. ILCA Systems Study No. 1. ILCA, Addis Ababa.
ILCA/IER (International Livestock Centre for Africa/L'Institut d'Economie Rurale du Mali). 1978. Evaluation of the productivities of Maure and Peul cattle breeds at the Sahelian station, Niono, Mali. ILCA Monograph No.l. ILCA, Addis Ababa.
van Keulen H, Ketelaars J J M, Butterworth M H and Anderson F M. 1984. Modelling activities in the framework of livestock research: considerations of a workshop held at Addis Ababa, 1983. CABO Report No. 53. CABO, Wageningen, the Netherlands.
Konandreas P A. (Unpublished). Modelling forage . intake and animal performance when the quality of forage on offer is highly variable: the case of transhumance in Mali. Draft paper, ILCA.
Konandreas P A and Anderson F M. 1982. Cattle herd dynamics: an integer and stochastic model for evaluating production alternatives. ILCA Research Report No. 2. =ILCA, Addis Ababa.
Konandreas P A, Anderson F M and Trail J C M. 1983. Economic tradeoffs between milk and meat production under various supplementation levels in Botswana. ILCA Research Report No. 10. ILCA, Addis Ababa.
Moore C P. 1984. Early weaning for increased reproduction rates in tropical beef cattle. World Anim. Rev. 49:39–50.
Sanders J O and Cartwright T C. 1979. A general cattle production systems model. II. Procedures used for simulating animal performance. Agric. Systems 4:289–309.
Semenye P P. 1982. Preliminary report of cattle productivity in Olkarkar, Merueshi and Mbirikani group ranches. Documents prepared for the Program Committee. ILCA, Kenya.
Traoré G. 1978. Evaluation de la disponibilité et de la qualite de fourrage au cours de la transhumance de Diafarabé. Thesis CPS, Bamako, Mali.
Wagenaar K T, Diallo A and Sayers A R. (in press). The productivity of transhumant Sudanese Fulani cattle in the Niger Inner Delta in Mali. ILCA Research Report.
Whelan M B, Spath E J A and Morley F H W. 1984. A critique of the Texas A & M model when used to simulate beef cattle grazing pasture. Agric.Systems 14:81–84.
Comment–In the TAMU model the equation from Conrad is used He had a co-efficient which related the amount of dry faecal output per day to liveweight, and assumed a constant faecal output. Conrad referred to lactating cows. With feed digestibilities at which the digestive tract is not limiting, then of course the intake normalizing factor should be metabolic weight. It is suggested that faecal output may be higher in animals grazing poor-quality pasture because they may have a higher inner capacity.
Comment–There is real variation in faecal output. It is not so constant and not within such a small variation as is often assumed. You have to deal with a factor of 2 or even 3 in faecal output.
Comment– In the way you use reference intake, it is assumed that digestibility is the determining actor of that intake, so in fact any possibility of detecting other possibly limiting factors is lost. Therefore it is not an objective reference intake but, in my opinion, simply a way to adjust model output. A whole range of factors, such as mineral deficiencies and disease conditions, may explain the reference intake.
Reply– I concluded that digestibility is the only forcing factor at the moment. The program has possibilities to use quantity of feed as a limiting factor as well as nitrogen percentage or distance walked per day. I agree with you entirely that there are more factors determining intake, which are not operational in the model at the moment. There is obviously a certain level of accuracy which you can reach when you want to apply a model. There are factors that are neglected because they are, for the moment, too difficult to model, or they are not yet fully understood, but there is no reason not to try to build a model based on the actual state of knowledge and possibilities.
Comment–We could say that the modeling problem lies between the ground and the animal's mouth, in that nobody is challenging the partition of energy or protein within the animal. We do understand quite well those factors that affect the handling of the food after it gets into the rumen at least.
Comment – But if an animal is sick, it will certainly have a lower intake, as with mineral deficiencies. The supply of animal drinking water is also important for intake. You should try to estimate the level of production in a system given the quality of the feeds available and subsequently compare it with the observed levels of production. If there is a difference between them, then we should look for the factors which explain it.
Comment – You give the impression that you are trying to simulate observed data. You are getting a set of data from Mali, and then you are changing the model to make it fit the data.
Reply– I believe that the use of models in general is limited to the kind of situation for which you have created it. If we apply the ILCA model as developed for ranches in Botswana to a ranch in Kenya, we will have no major problems. But if we use it for a significantly different set of data, i.e. data from pastoral systems under suboptimal conditions, like in Mali, we have to change scene of the assumptions in the model. With the data from Mali, we can at least approach the mortality or fertility subroutine more realistically, and then use this modified model for pastoral systems in Kenya. I will not say that one model will be applicable everywhere, neither will I say that the model is only applicable for the situation in which you validate it. There must be something in between.
