Livestock that is kept on the farm such as pigs, chickens, ducks or buffalos do not serve as an actual income source for the farmers. They are not raised for mere production and later on for selling, but serve different purposes. According to these purposes livestock is comprised in different compartments.
In most farmhouseholds in the Philippines one or two or more pigs (Sus scrofa L., a commercial breed) are raised. They are mostly kept in special stalls for fattening. Pigs rather serve important social functions than as an additional food supply for the farmers' family or as a commercial farm product. They are often slaughtered on special occasions, like weddings or town fiestas. Therefore pigs are sometimes fattened long beyond their economically optimal time (Dalsgaard, 1997).
Pigs are either fed with commercial feeds or with available farm byproducts, such as rice bran or waste, like kitchen leftovers or both. They need approximately five months to grow to 50  60 kg. Either 6  8 weekold piglets are purchased and raised, or piglets are obtained from breeding. The pigs on the farm usually breed two times a year, if they are not sold or slaughtered before. Sometimes breeding pigs are kept for up to three years before slaughtering. Furthermore, pigs serve not only as an important converter of waste into capital, but also as a supplier of valuable fertilizer, i.e. manure, for vegetables and the fishpond (private conversations with B. Oficial, personal notes made during farm visits).
Most smallholder rice farms also keep a few poultry for egg and meat production. In this model only chickens (Gallus gallus or Gallus domesticus) are considered. Mostly different breeds of ducks can be found as well. They are seen roaming around the homestead. Keeping them in special stalls does not seem very common. Although the chickens also look for their own food while running around the homestead areas, they are also fed additional food, like kitchen leftovers or rice byproducts, like rice bran or broken rice. They need up to three months to reach a slaughtering weight of approximately 500 g (personal notes made during farm visits).
Description of a model for pigs and chickens
The development of a model for the growth performance of pigs and chicken was based on Parks' 'Theory of Feeding and Growth of Animals' (Parks, 1982).
The study of experiments on controlled feeding of steers, sheep and chickens led Parks (1982) to the notion that the growth of those animals under such conditions might be largely described by a simple firstorder linear inhomogenous differential equation;
dW/dt + gW(t) = hq(t) (2.2)
where g [t^{1}] and h [kg LW/kg food consumed] are some sort of metabolic parameters, W(t) [kg LW] denotes the live weight (LW) respective to lifetime (dW/dt therefore denotes the change of live weight in time) and q(t) [kg /day] the food intake .
Eqn. (2.2) is a balance equation where the term of the input hq(t) is distributed between growth dW/dt and nongrowth gW. The term hq(t) is the live weight equivalent of the food intake q(t). This means that for some metabolic reasons a portion of q(t) does not contribute to growth. On the one hand, not all components of the food are usable for the animal in terms of metabolizable energy and, on the other hand, only a portion of the absorbed chemical energy is used for building up new tissue. The rest is lost through heat produced by these processes. So h must have the unit of live weight per unit of food and is some kind of efficiency factor. The parameter h can be considered the efficiency of anabolic processes which are driven by the food or energy input. Surley this parameter strongly depends on the quality, i.e. energy content, of the food, state of the animal in general, external factors and the environment. The parameter g is responsible for catabolic processes. The animal needs, of course, energy for maintenance, various other daily life activities, internal and external work. These processes produce heat as well. The total value of this property increases the larger the animal gets. The parameter g has the unit of 'per time' and describes the rate by which stored energy or live weight is utilized by the animal's energy requirements. Of course, this parameter is also dependent on time and other external factors, like level of activity or environmental conditions, like temperature. In a first approximation the parameters g and h are considered constant.
Now it can be assumed that at a certain time in an animals live its food intake q(t) remains at a constant value q_{0}. This can either be due to the animals grade of maturity or to other external restrictions. Assuming futhermore that g and h are positive constant values as well, it can be seen that W approaches a final weight W_{f},
W(t) W_{f} = (h/g)q_{0} for t .
Now the parameters g and h have to be determined.
Derivation of values for the parameters g and h
Analysing experimental growth data Spillman (1924) and others focused on data tables where response Y(n), let us concentrate here on animal live weight, is expressed to levels of n units of some material, like kg food intake. Spillman found that these curves can be described by what he called the law of diminishing returns. Written in a continous form, we obtain
W(F)=(AW_{0})[1exp(BF)]+W_{0 } W(0) = W_{0}, (2.3)
with W [kg LW] as weight and F [kg] as cumulative food consumed. A [kg LW] is the mature weight and B [kg food^{1}] a growth parameter which regulates the speed by which A is approached. The larger B, the faster A is reached. This equation resembles the form of the BGF. The difference is that the BGF is just an 'output' equation because it relates growth, e.g. fish length, to only time. Here we consider the growth of animals as input  output systems with F as input. Mathematically, this can be expressed as
dW/dt = (dW/dF)*(dF/dt),
the growth rate dW/dt is the product of growth efficiency dW/dF (change of live weight per food consumed) and food intake dF/dt (food consumed per time).
Comparing growth tables of various animals, various authors found that the shape of the curve always remained the same, only the parameters A and B changed from species to species. This led to the conclusion that those parameters are more than merely empirical, but reveal a real physiological relationship between the weight W of an animal and the cumulative food consumed by it to attain that weight. This evidence lends support to the notion to accept this formula as a first fundamental approach for developing a more general growth formula.
Comparing growth tables of various animals, various authors found that the shape of the curve always remained the same, only the parameters A and B changed from species to species. This led to the conclusion that those parameters are more than merely empirical, but reveal a real physiological relationship between the weight W of an animal and the cumulative food consumed by it to attain that weight. This evidence lends support to the notion to accept this formula as a first fundamental approach for developing a more general growth formula.
dF/dt=(CD)[1exp(t/t*)]+D, (2.4)
where t* [t] is a adjustment parameter. The greater t*, i.e. the later an animal reaches its puberty, the later it reaches the time of maximum food intake, i.e. maturity. C is the maximum food intake for mature animals [kg food/t] and D [kg food/t] the initial food intake at birth, hatching or weaning. A possible form of food intake is obtained by integrating (2.4) with F(0)=0 as a starting condition.
F(t)=C{tt*(1D/C)[1exp(t/t*)]} (2.5)
The parameter t* is called this way with reference to another growth model by Brody (1945). He assumed that the growth of animals can be described by
W=Wo*exp(ct), 0<=t<=t' (2.6)
W=A(1exp(k(tt*)), t'<=t. (2.7)
and created extensive listing of his growth parameters A, k [t^{1}], t* and c [t^{1}] which will be used futher on.
Fig. 15: The Ad Libitum feeding functions 2.4 and
2.5 with limiting function. C = 5, D = 1, t* = 2.
Assuming that D in (2.4) is small in relation to C, so that D/C is neglible, equations (2.4) und (2.5) become for large t
dF/dt C and F(t) C(tt*) for t .
So as the animal enters adulthood its food intake approaches its mature appetite and the cumulative food it has consumed up to age t asymptotically approaches the graph of C(tt*) (Fig.15).
That there is such a line of that form is indicated by several experiments on steers, chickens and ducks. Another notion that t*, as used here, is Brody's, is shown in the formula
W(t)=A{1exp[(BC)(tt*)]}
Here F(t)=C(tt*) is substituted in (2.3) assuming that W_{0} is small enough to be neglible. Replacing BC [t^{1}] by k makes this identical with Brody's equation (2.7). In this formulation the maturing rate k is identical with the product of the growth parameter B and the mature food intake C, which are measurable.
If Eqs. (2.3), (2.4) and (2.5) are suitable formulations of the growth of an animal with no restricted access to food, the live weight as a function of age is given by
W(t)=(A W_{0})[1exp<BC{tt*(1D/C)[1exp(t/t*)]}>]+ W_{0} (2.8)
Fig. 16: Ad libitum growth functions with A = 6,
BC = 0.091, t* = 10 and D = W_{0} = 0. The green line
represents Brody's formula 2.7. Reproduced according to Parks (1982).
Besides the parameters W_{0} and D, the parameters A, B, C and t* characterize the growth response of an animal under normal conditions with nutritious food freely available.
Comparing growth tables of various animals, various authors found that the shape of the curve always remained the same, only the parameters A and B changed from species to species. This led to the conclusion that those parameters are more than merely empirical, but reveal a real physiological relationship between the weight W of an animal and the cumulative food consumed by it to attain that weight. This evidence lends support to the notion to accept this formula as a first fundamental approach for developing a more general growth formula.
Determing the growth parameters A, B, C, and t* for various animals from steers to pigs, chickens and rats, follows the observation that the parameter AB is nearly constant for all species. Introducing AB [kg LW/kg food] as a new parameter, we obtain
W=(A W_{0}){1exp[(AB)F/A]}+ W_{0 } or versus time t
W=(A W_{0})[1exp<(AB)C/A{tt*(1D/C)[1exp(t/t*)]}>]+W_{0 } (2.9)
This property of AB may be related to Rubner's law, i.e. the amount of energy required for doubling birth weight is the same per kilogram for all animals or the near birth growth efficiency is a constant for all animals. This is also reflected by Eq. (2.9). When W is still very small the growth efficiency dW/dF approaches (AB).
The Growth Phase Plane
The Growth Phase Plane (GPP) is a useful device in organising data from experiments of controlled feeding. The GPP is obtained by considering the change of liveweight W in terms of food intake dF/dt (Fig.17). According to 2.4 is
dF/dt = q(t) = C*(1exp(t/t*)),
thus
t=t*ln(1q/C)
Inserting this into Eq. (2.9) yields for W_{0 }= D = 0
W=A<1exp{(AB)Ct*/A[ln(1q/C)+q/C]}>.
This in an expression for W(dF/dt)=W(q).
Data on experiments of controlled feeding of cattle (Taylor and Young, 1966, 1967, 1968), sheep (Clapperton and Blaxter, 1965, Blaxter, 1968) and chickens (Titus et al. 1934), further data on partial starvation of dogs (Kleiber, 1961) and men (Keys, 1950) revealed interesting features when plotted in the GPP.
Data of partial starvation experiments suggested an equation of exponential decrease for describing such phenomena as, e.g.
W=(W_{0}W_{f})exp(bt)+W_{f}
and experiments with controlled feeding implied a mathematical description, like
W=(W_{f} W_{0})[1exp(bt)]+W_{0} ,
at least for an animal approaching final weight, where b might be an estimate of Body's k and W_{f}, naturally, is significantly lower than the final weight from the ad Libitum feeding experiments.
Looking at the equilibruim weights W_{f} that were attained on different constant levels of controlled food intake q_{0}, it became obvious that those weights where all disposed on a linear straight line T_{0} through the origin which was described by T_{0}=A/C (Fig.17). Therefore final weight W_{f} attained on a controlled feeding regime or partial starvation could be described by
W_{f} =T_{0}q_{0.}
Fig. 17: The GPP is divided into regions of controlled
growth and partial starvation by the Taylor diagonal 0S and the
ad Libitum growth curve 0PS. With constant food intake q_{0}
animals at P growth towards Q and animals at T loose weight towards
Q. The state T is reached by setting animals that are at R on
a 'q_{0}diet'.The final weight at Q is given by W_{f}
= T_{0}q_{0}. Arrows show the direction of response
in time. The time axis is perpendicular to the plane of this figure.
Reproduced according to Parks (1982, p. 102).
Experimental evidence presented by Parks (1982) led to the belief that the 'Taylor diagonal' (according to Taylor and Young) T0=A/C of the GPP had a real biological significance because it seemed to separate the controlled feeding region and the partial starvation region of the GPP. When the phase point (q,W) is in the lower, i.e. controlled feeding region, it will tend to drift upwards towards the diagonal with a diminishing rate dW/dt approaching zero when approaching the diagonal and when the phase point (q,W) is in the partial starvation region it tends to drift downwards towards the diagonal, with the W axis (q=0) being the line of complete starvation. Furthermore, when the phase point is on the ad Libitum curve, it will generate a curve which is the lower bound of the controlled feeding region, and finally drift to the extreme point (C,A) on the diagonal where the growth rate (dW/dt) approaches zero. This means that the Taylor diagonal can be looked at as an energetic boundary of the live weight of an animal which can be maintained under a certain feeding regime. When the phase point is located in the controlled feeding region and a certain feeding regime q0 is maintained, then the final live weight W_{f} is given by
W_{f} = T_{0}q_{0}
The same final weight will be approached if the phase point lies in the partial starvation region and q_{0} is fed. This means that the energy intake is not sufficient to maintain body weight and the phase point drifts to same W_{f}.
Now we can return to the starting point, where it was found that for a constant controlled feeding regime the final weight was given by
W_{f} = (h/g)q_{0}.
Moreover, we stated that h was some kind of efficiency factor with the unit of kg LW/kg food consumed. In Eqn. (2.9) we introduced a very similar efficiency factor, which was also found to be nearly constant for a wide range of different species, namely the parameter AB which also has the correct units. Taking AB as h intuitively as a first approach, we can also determine g which is now g = AB/T0. Equation 2.2 becomes
dW/dt+[(AB)C/A]W=(AB)q(t) or
dW/dt+[(AB)/T_{0}]W=(AB)q(t). (2.10)
In the STELLA model the growth performance for pigs and chickens was implemented using Eqn. 2.10. Parameters were taken from data tables listed in Parks (1982, p. 53).
For pigs and chickens alike only one age group was considered, respectively. Since the model concept allows simulation over one season and this is also the time pigs need to grow to market size, it was assumed that pig production starts with the beginning of the simulation. That means that simulation time is equal to pig age or pig lifetime.
singlepigweight(t) =
singlepigweight(t  dt) + (piggrowthrate) * dt
piggrowthrate =
(pigAB/pigTo)*singlepigweight+
pigAB*feedrate
There are different ways and units to express the actual feeding rate. Here feeding rate is expressed in percent ad Libitum food intake (feedrate, kg/d). This way pigs can never be fed more than they can actually theoretically consume. Ad Libitum food intake was modeled according to Eqn. 2.4. The parameter t* could not be calibrated due to the lack of appropriate data.
Since chickens need much less time to be ready to eat or reach market size, a variable Chickage [days] had to be introduced which was set to zero after each chicken lifetime cycle. This way several chicken cycles could be simulated.
Simulating the growth of chickens it was assumed that
c) chicken do not feed themselves, but are rather subjected to controlled feeding.
Chickage(t) = Chickage(t  dt) + (chickmaturing) * dt
chickmaturing = IF (chickslaughter= 0) THEN 1 ELSE Chickage
Chickslaughter is set to 1 if the individual animals reach a weight of 500g, which is about the weight when chicken are slaughtered and sold or eaten by the farmers. Apart from this slight modification growth rate was implemented as for pigs.
Verification and longterm analysis
Verification of the submodels for pigs and chicken was conducted checking the model's outcomes to a range of different external conditions. The internal logic and the structure of the model are already explained.
Longterm analysis also resulted in the expected outcomes. Chicken cycles repeated themselves ad infinitum and total chicken production grows according to this. Pigs approach their equilibrium weight with respect to the feeding regime. The variable that increases ad infinitum as well is the amount of purchased commercial food (that is, of course, if the livestock is fed at all; when no food is applied, equilibrium is reached at zero). This is also because after the first rice growth period no more rice production is simulated and hence no crop byproducts are provided for livestock nutrition.
Starting from the parameters given by Parks a sensitivity analysis was conducted. All major growth parameters were varied within a 20 % range and the simulated weight compared to a standard weight. Since the model is the same for pigs and chickens, the same parameters were considered as well. The results are listed in Tab. 9.
Tab. 9: Sensitivity analysis for the pig and chicken model
Pig Model  Chicken Model  

Sensitivity at  Sensitivity at  Sensitivity at  Sensitivity at  
Parameters  20 % deviation  50 % deviation  20 % deviation  50 % deviation 
W_{0} 




A (T_{0}) 




AB 




C 




t* 




growth period 




feeding 




Standard situation for pigs: A = 380, AB = 0.409, C = 8.7, t* = 60.9, growth period = 180 days, feeding rate = 50 % ad Libitum, initial weight = 12 kg, initial ad Lib. food intake = 10 % initial weight, simulated standard weight = 128.14 kg Standard situation for chicken: A = 3.25, AB = 0.331, C = 0.15, t* = 99.4, growth period = 90 days, feeding rate = 50 % ad Libitum, initial weight = 0.05 kg, initial ad Lib. food intake = 10 % initial weight, simulated standard weight = 0.53 kg
Data for Calibration and Validation
In order to test the validity of the parameters of Parks for Philippine conditions, the obtained growth curves from FARMSIM were compared to growth data from the Philippines. This data was also provided by Hopkins and Cruz (1982).
Fig. 18: One pig life cycle corresponded to two fish
cycles. Therefore the pigs in Exps. 1 and 2 are the same. One data
point represents the average weight of pigs belonging to one pond.
Fig. 19: One pig life cycle corresponded to two fish
cycles. Therefore the pigs in Exps. 3 and 4 are the same. One data
point represents the average weight of pigs belonging to one pond.
Fig. 20: Exp. 5 was a longterm experiment. Therefore
almost one pig life cycle corresponded to one fish experiment.
The outliers are omitted for calibration.
In their animalfish experiments, especially the pigfish experiments, they also recorded growth data from the pigs raised on the project site (Figs.1920).The single data points are the average weights of pigs belonging to a certain pond. Large whiteLandrace hybrid weanlings were purchased from commercial sources with initial weights of 11.9  19 kg. The pigs were fed commercial feeds: a starter ration while having an average weight less than 17 kg, a grower ration up to 60 kg and a finisher ration to a market size of 80  105 kg. These commercial feeds had an average protein content of 18 %, 16 % and 13 % of DM, respectively.
The feeding rate was adjusted such that the pigs would consume all of their ration in two onehour feedings sessions per day. This was equivalent to 3.5  7 % bodyweight per day. As stated above, one pig cycle related to two fish cycles. So pigs were the same in experiments 1 and 2, 3 and 4 and 5, respectively (Hopkins and Cruz, 1982).
Growth rates exhibited by the pigs were highly variable. Although the initial weights of pigs in Exps. 1 and 2 were about 40 % above those in Exps. 3 and 4, they attained a lower final weight. Hopkins and Cruz state that this observance might be due to 'runts' being included in groups of young animals by the weanling producer.
Growth data for chickens were not recorded in the Hopkins/Cruz animalfish experiments. Dayold broiler chickens were purchased from commercial suppliers and fed a commercial starter ration (21 % protein) ad Libitum until market size. A market size of 1.1  1.4 kg was attained in about 49 days. In interviews with farmers is was stated that chickens need up to three months to reach an eatable size of 500g per chicken.
Calibration of the growth parameters for pigs
For pigs the growth parameters AB = 0.409, A = 380 kg and C = 61 kg/week (8.7 kg/d) were used for calibration. These parameters were determined by Parks (1982) from data by Headley et al. (1961, cited in Parks). As stated above, pigs were fed in a way that they consumed 3.5  7 % of their bodyweight daily. Since animals usually eat relatively more when they are young than when they are grown up assuming sufficient food supply, it was assumed that feeding rate decreased linearly from 7 % to 3.5 %. With this assumption, Eqn. 2.10 turns to
dW/dt =  (AB/T_{0})W + AB*(0.07  (0.07 0.035)*t/T)W (2.11)
with T being the culture period. Pigs were said to need about six months to reach market size (see Figs. 17 and 18). So T was set to 180 days. Then 2.11 can easily be integrated to
W(t) = W_{0}*exp{(AB*0.07  AB/T_{0})*t  AB*0.000097*t²}. (2.12)
The validity of this formula ceases beyond 180 days, but this is enough to suit the purpose imposed here. The parameters in question are A, AB and C because the growth period and feeding rates are defined by the user and cannot be calibrated. Exps. 3, 4 and 5 were chosen as data for calibration because they showed the slightest deviations.
For pigs Eqn. 2.12 was fitted to data from Hokins and Cruz (1982) varying parameters in different ways, omitting outliers (MarquardtLevenberg algorithm using SPSS 7.0) and using the parameters given by Parks (1982, p. 53) as start parameters (Tab. 10).
Tab. 10: Calibration results of fitting the pig growth model to the
experimental data of Exp. 34, Exp. 5 and both.
Calibration  Parameters 




av. W_{0}  12.467  17.98  15.22  
start  start W_{0}  12.5  18  15.2 
parameters  start T_{0}  43.61  43.61  43.61 
start AB  0.409  0.409  0.409  
varying  W_{0}  8.75  
all  T_{0}  43.95  n.R.  n.R. 
parameters  AB  0.458  
r²  0.99219  
keeping  T_{0}  196.1  
W_{0} fixed  AB  0.247  n.R.  n.R. 
r²  0.98665  
keeping W_{0}  AB  0.387  0.265  0.336 
and T_{0} fixed  r²  0.97731  0.94568  0.9389 
keeping W_{0}  T_{0}  40.7  28.33  34.98 
and AB fixed  r²  0.974  0.899  0.9135 
logistic fit  W_{0}  9.4  15.2  
A  140.98  n.R.  341.48  
K  0.02  0.012  
r²  0.99286  0.9782 
av. W_{0} = measured average initial weights in the experiment logistic fit was conducted using the formula: W(t) = (A*W_{0})/(W_{0}+(AW_{0})exp(kt)). n.R. = no results (i.e. the regression did not determine)
Calibrating the parameters a few simplifications arise using Eqn. 2.12. Calibrating merely A and keeping C fixed for instance results in the same value for A/C as keeping A fixed and change C. A and C depend on each other and occur only once in the growth equation. Therefore in the model the parameter T_{0} is considered rather than A and C separately. T_{0} can be looked at as the normed maximum weight that can be sustained if the animal consumes 1 kg food per day. So the model parameters in question here decrease to T_{0} and AB. The initial parameter W_{0} is also determined by the selected data set.
At first all parameters were varied. Then, in a second regression run, the parameter W_{0} was kept fixed because this parameter was given by the measured data. In a third and forth regession run AB and T_{0} were kept fixed respectively in order to test the parameters given by Parks as well as to test the validity of the GPPconcept.
Varying both parameters AB and T_{0} had no results, except for calibrating the parameters only for experiment 3 and 4. Taking both experimetns into consideration the best fit was obtained when only AB was calibrated to the experimental data. The results are visualized in Fig. 21.
Fig. 21: Fitting the model 2.12 to growth data of
Exp. 3 and 4 and Exp.5 (without outliers) keeping W_{0}
and T_{0} fixed. Initial value = 15.2 kg.
Validation of the model for pigs proved to be difficult because the other data available for pig growth on the Philippines which was not used for calibration was obtained under the same external conditions concerning feeding and raising. So no real validation with an independent data set under a range of different conditions could be carried out. Nevertheless the simulated weights are plottet versus the measured weights of the third pig growth experiment (see Fig. 22) using the same feeding regime, the calibrated parameter AB from above and the respective initial weight as inputs.
Fig. 22: Validation of the calibrated pig growth
model. Initial weight used here was 19.2 kg.
Chickens
Since there were no Philippine growth data on chicken available, only a rough estimation of the correctness of the parameters provided by Parks could be carried out.
Hopkins and Cruz stated that chickens needed roughly 49 days to reach a marketable size of 1.1  1.4 kg under a ad Libitum feeding regime. Food protein content was 21 %. Parks (1982, p. 53) gives values for this situation (Male ad Libitum food intake, food protein content 21 %) of A = 3.21 kg, AB = 0.391, C = 0.176 kg/d, t* = 18.3 weeks. Assuming an initial live weight of 0.05 kg at the start of the simulation and an initial food intake of 10 % liveweight, inserting this into Eqn. 2.10 and evaluating it at t = 49 yields W = 0.46 kg. Averaging the growth parameters from Parks over protein contents ranging from 25 % to 13 % results in values of A = 3.25 kg, AB = 0.331, C = 0.153 kg/d, t* = 14.2 weeks. Inserting this into the model also gives a final weight at t = 49 of W = 0.46 kg. To reach the size of 1.1  1.4 kg the simulated chickens needed up to 94 and 116 days, respectively, that is about twice as much as reported by Hopkins and Cruz.
Despite the very simplifying assumptions of keeping the growth parameters g and h in Eqn. 2.2 constant, the main features of the growth performance of pigs are reflected well by the model. In the regression analysis, where only the efficiency parameter AB or rather B are fitted to the growth data, the results vary with respect to the imposed parameter of Parks. Data of experiments 3 and 4 which reveal the slightest deviations the fitted parameter AB is almost the same as the start parameter. Also when the data of all experiments were fitted to the assumed formula keeping only T0 fixed, the resulting parameter AB was 0.39 (this result is not tabulated. Resulting W0 was 11.73, r™ = 0.957). This could be interpreted as support to the theory of the GPP with respect to the existence of the Taylor diagonal. Although A and C are far from the values attained in the Philippine experiments, their relation revealed good results. This is not astonishing because A and C are obtained from regression of ad Libitum feeding experiments but all that counts according to the theory of the GPP is their relation T0 = A/C (i.e. the slope of the Taylor diagonal) which is used in the model. This seems to be at least useful for a first approach.
Although it was stated by Hopkins and Cruz that pigs in all experiments were raised using the same methods they show different growth performance. Keeping those natural fluctuations in mind the parameter AB = 0.336 as obtained in the last regression keeping W0 and T0 fixed, seems to be a good average for Philippine conditions. Validating the model with data from Exp. 1, an overestimation is observed. The reason for this might be that the maximal weight attained in Exp. 1 were generally a little lower than in the other experiments. Hopkins and Cruz presumed that there were runts included as stated above.
Looking at results for e.g. Exps. 3 and 4 it can be seen that simulated data are a little overestimated for the lower range of the regression interval and underestimated for the upper range. The slope of the data curves resembles more a sigmoide function. Therefore a fit to the logistic equation was tried. The results are better but the logistic equation is a mere output model, i.e. weight is only related to time. Of course, a model that relates output, i.e. weight, to input ,i.e. food intake, is much more useful for the purposes of a farm simulation.
Fig. 23: The logistic funtion mirros the shape of
the real pig growth curve best.
It is clear that growth performance of any animal strongly depends, among a lot of other factors, also on the quality of the food and the genetic strain. But as long as there are no relations known as to the dependency of the growth parameters to the quality of the food or the breed, simplifying assumptions have to be used. So the higher growth performance using Parks parameters can be caused by different food for which no information was available or also genetic differences which are known to exist.
In the final implementation of the model the fitted parameters of the final regression are used (AB = 0.336, T_{0} = 43.61, W0 = 15.2, t* = 60.9).
The use of Parks' parameters for chickens did not result in a good accordance to the growth of chickens described in the Philippine experiments. Using Parks' parameters, chickens needed about twice as much time to reach the weight of the chickens of Hopkins and Cruz. Parks' parameters rather reflected the growth performance of chickens observed by the farmers, assuming that chickens that feed freely on the farm have an average food intake of about 50 % ad Libitum.
Sensitivity analysis reveals that the feeding rate and the growth period are the most crucial parameters of the models. Naturally, the models behave the same under a different set of parameters. It must be stated that in the pig model the starting parameter AB, as given by Parks, differs by 18 % from the final calibrated growth parameter AB. Still this results in a deviation from the standard value of only 10 % with ad Libitum feeding and 180 days' growth period. So for the parameters of the chicken model it must be presumed that the values used here differ significantly from the ones in the Hopkins and Cruz experiment, because there a deviation of over 50 % was observed. But all this gives no hint of the actual growth parameters onfarm. The feeding rate of chickens on the farm is difficult to determine, since chickens mostly feed freely on the homestead. In the further development of the RESTORE project some data on the growth of poultry and livestock might be available so that the parameters can be calibrated to Philippine farm conditions. Since the most sensitive parameters are the ones defined by the user (growth period and feeding rate), they have to be handled carefully in the model.