[Previous]
[Contents]
[Next]
2.3 The Fishpond Model
Introduction
As pointed out in the introduction, aquaculture is a promising new feature which is expected to improve sustainability as well as the economic situation on smallscale Philippine farms through diversification and nutrient recycling. Not at least it is the purpose of this model to quantify the effect of integrating aquaculture on the whole farm performance. Since farmers are careful in adopting new technologies, a tool for assessing the impact of introducing aquaculture and later optimization may become an important contribution towards new, more sustainable resource management strategies.
The fishpond model which was to be incorporated into the whole farm model should be as simple as possible in order to keep the farm model clearly arranged. Moreover it should reflect the growth performance of Nile Tilapia Oreochromis niloticus (L.), which is the main cultured fish in the considered ponds. After the review of various fish models, none was found to suit this purpose. These models were partly very sophisticated physiological models, but too complex to be useful in the whole farm model (Wolfe et al, 1986; Hagiwara and Mitsch, 1994; van Dam, 1995, van Dam and Penning de Vries, 1995). Others lacked the right parameters or were developed for different conditions (Zweig, 1992; Anastßcio et al., 1993; From and Rasmussen, 1986). But most models used parameters and processes for which data on the specific conditions prevailing in the Philippines was not available (Bossel, 1989; Piedrahita et al., 1984; Cuenco et al., 1985; Liu and Chang, 1992; Ross et al., 1988). So an attempt was made to develop a simple statistical dynamic fish model on the basis of existing data, provided by the ICLARMCLSU experiment (Hopkins and Cruz, 1982). This set of fish growth experiments conducted by ICALRM and the Central Luzon State University, Mu±oz, Nueva Ecija, Philippines (CLSU) was especially designed to systematically develop and document integrated animalfish systems under tropical conditions, i.e. in the Philippines. Therefore parameters fitted to those experiments were expected to reflect well the conditions on Philippine smallscale farms. On the other hand, these experiments were conducted mostly using Nile Tilapia Oreochromis niloticus (L.), which is one of the most important cultured fish in the Philippines (Sevilleja, 1985).
Experiment design and data collection
From August 1979 to June 1981, 18 sets of experiments were conducted in twelve 0.1 ha ponds and twelve 0.04 ha ponds. The ponds had an average depth of 0.70.9 m. The raw data provided by ICALRM in a LOTUS 123 file contains data on experiments 112,14, all together 116 pond experiments (for the full description of the used data file, see appendix).
Ponds were mostly stocked in a standard polyculture of 85% Nile Tilapia (Oreochromis niloticus) as the main culture crop, 14% common carp (Cyprinus carpio) as a bottom stirrer and 1% snakehead (Channa striata) as a predator. The bottom stirrer was stocked to prevent weed growth in the ponds and the predator was0 there to diminish fry biomass, since mixed sex Tilapia were stocked. Fry are competitors for food and space and bias the values for average size and number in the end of each experiment. All experiments were doubled or tripled using essentially two different stocking densities of 8500 and 17 000 individuals per hectare.
Nutrient input in the ponds were either inorganic fertilizer or manure from pigs, peking ducks or chickens which were raised in stalls on the pond dikes. The manure from pigs and ducks was washed into the ponds during the daily cleaning. Chicken manure was collected and applied to the ponds three times a week.
The duration of the experiments was based on animal growth rates. While pigs and peking ducks need six months to reach market size, chicken require 45  49 days. Tilapias attain a locally marketable size of approximately 60 g in about 90 days. Thus, two independent fish cycles were possible within one pig or duck cycle, whereas two chicken cycles correspond to one fish production experiment (Hopkins and Cruz, 1982). Since after each chicken cycle the manure output would drop to zero, different chicken management strategies were chosen to maintain a constant flow of manure into the pond. In the pig and duck experiments the amount of manure applied was also regulated by the number and size of the livestock in the stalls above the ponds.
Fish size data was obtained by measurements before stocking, at biweekly intervals and at harvest. At the beginning of the experiments, individual fish weights and lengths were recorded in order to obtain a lengthweight relationship. Later on, only average data was considered for tilapia, tilapia recruits, carp and predators for 20  50 individuals, respectively.
Manure was analyzed for average dry matter content, nitrogen, phosphate, potash and crude fiber to determine the average daily nutrient input into the ponds. Daily measured water quality parameters were early morning water temperature and dissolved oxygen. This data was averaged over the sampling intervals.
Tab. 5: The livestockfish experiments considered in the regression
analysis.


Manure load

Stocking

culture periods

Experiment No. (Pond No.)

Animal type

kg DM/(ha*d)

density

(days)

  
(No./ha)
 
7 (17, 18, 24)



0

17000

30

1 (1, 5)



IF

8500

97,96

1 (8, 11)



IF

17000

101,95

1 (6, 9); 3 (2, 4)

pig

31  40

8500

98,101,106

1 (2, 3); 3 ( 6, 8)

pig

31  40

17000

97,98,99

2 (5, 6, 9); 3 (3)

pig

41  50

8500

90,96

1 (10); 2 (2, 3, 11); 3(1, 9)

pig

41  50

17000

76,96,103,108

1 (4); 3 (7, 10, 11)

pig

51  60

8500

93,95,102

1 (7, 12); 3 (5)

pig

51  60

17000

95,96,97

2 (1, 4, 7)

pig

61  70

8500

76

2 (8, 10, 12); 3 (12)

pig

61  70

17000

76,103

4 (2, 4, 11)

pig

81  90

8500

91,94,95

4 (6, 8, 9)

pig

81  90

17000

93,96,97

4 (3, 7, 10)

pig

101  110

8500

92,96,97

4 (1, 5, 12)

pig

101  110

17000

92,94,95

6 (13, 14, 20)

pig

131  140

16825

42

6 (19)

pig

151  160

16825

42

14 (4)

pig

66  86

28500

139

14 (5)

pig

66  90

28500

147

14 (9)

pig

66  91

28500

141

14 (10)

pig

67  86

28500

143

5 (2, 6, 7, 8, 9, 12)

pig

increasing

8500

156,157

5 (1, 3, 4, 5, 10, 11)

pig

increasing

17000

156,157

8 (13, 15, 16)

Duck

51  60

8500

101,102,104

8 (18, 20, 23)

Duck

51  60

17000

100,102,103

8 (13, 15, 17, 18, 21)

Duck

76  85

8500

86,87,88,101,104

8 (14, 19, 22, 24); 9 (16, 20, 23)

Duck

76  85

17000

75,79,87,94,95,101,103

9 (17, 19, 21)

Duck

131  140

8500

75,78,88

9 (14, 22, 24)

Duck

131  140

17000

78,79,86

11 (14, 21)

Chicken

5

17000

100

11 (17, 19)

Chicken

10

17000

100

11 (15, 22)

Chicken

15

17000

100

10 (15, 19, 22); 11 (13,20)

Chicken

20

17000

90,91,93,100

10 (16, 21, 23)

Chicken

61

17000

86,91,92

12 (14, 21)

Chicken

97

17000

93

10 (13, 14, 20)

Chicken

101

17000

90,95

12 (15, 20)

Chicken

131

17000

93

Summary of all considered animalfish experiments.
IF = inorganic fertilizer; increasing = no fixed manure loads
but increasing inputs.
Other water quality parameters which were not recorded continuously over the entire project period, but rather sporadically were midmorning pH, total ammonia, conductivity, NO2, nitrate and phosphate. As can be seen in Tab. 5 data was not available for every experiment. For instance, data on experiments 13 and 15  18 are missing completely. Moreover, many data points and variables had missing values. The same problem has been recognized before (Prein, 1993) and a lot of missing values could be obtained through interviews and the original data sheets. But there were also external influences or catastrophes, like, e.g. typhoons in experiment no. 7, that prevented the completion of experiments. Experiments that were not used in the further analysis due to missing or incomplete data were Exp. 1 (Pond 8), Exp. 6, Exp. 7, and Exp. 8 (Pond 15).
Statistical Analysis
The starting point of the following statistical analysis was the notion
that fish growth can be described by the van Bertalanffy Growth
Function (BGF)
L(t) = A*(1exp(k*(tt_{0}))) , L(t_{0})=L_{0},
Other water quality parameters which were not recorded continuously over the entire project period, but rather sporadically were midmorning pH, total ammonia, conductivity, NO2, nitrate and phosphate. As can be seen in Tab. 5 data was not available for every experiment. For instance, data on experiments 13 and 15  18 are missing completely. Moreover, many data points and variables had missing values. The same problem has been recognized before (Prein, 1993) and a lot of missing values could be obtained through interviews and the original data sheets. But there were also external influences or catastrophes, like, e.g. typhoons in experiment no. 7, that prevented the completion of experiments. Experiments that were not used in the further analysis due to missing or incomplete data were Exp. 1 (Pond 8), Exp. 6, Exp. 7, and Exp. 8 (Pond 15).
At first the recorded data of the change in length of Nile Tilapia over the several growth periods and experiments was fitted to the BGF using nonlinear regression (LevenbergMarquardtAlgorithm). This resulted in values for A, k and t0 for 116 different experiments. From those data a set of experiments was selected for which the fitted values of the maximal Length A had a 95 % confidence interval of less than six centimeters. This set of experiments is listed in Tab. 6.
Then the relation of the growth parameters A and k to several environmental conditions was analyzed, also mostly using nonlinear regression and correlation methods. Since not all parameters were recorded over the entire projectperiod, the analysis of daily measured parameters was emphasized. Also special attention was paid to those variables which can be easily manipulated by the farmers, like manure load, stocking density and length of culture period. In addition, the parameters in the equation should be easy to measure in order to facilitate future validation by onfarm data. Thus relationships between the main growth parameters, A and k, and the following parameters were sought:
Analysis of the impact of the different mentioned water quality
parameters on the growth performance of tilapias was already conducted
by Hopkins and Cruz (1982) and Prein (1993) without significant
results or relations that were not appropriate for a dynamic model.
Tab. 6: Set of experiments and ponds that were used for the analysis
of the influence of environmental factors and management strategies
on Tilapia growth performance.
 
culture
   
average

cumulative

Length 95%
 
Exp. No.

Pond No.

Period

k

A

t_{0}

AM Temp.

man. input

confidence

R²

 
(days)
   
(°C)

(kg/ha)

intervall (cm)

6<=n<=11

1

1

97

0.027

14.81

23.4

27.07

0

12.08 17.53

0.9563

3

1

96

0.017

18.7

20.7

27.84

4644

15.6  21.8

0.991

3

2

96

0.025

17.64

18.7

28.03

3706

16.0 19.3

0.9986

3

7

96

0.023

18.43

15.84

27.84

4995

15.9  20.96

0.9842

3

10

102

0.022

18.4

18.3

27.6

5535

16.8  20.1

0.9928

3

12

103

0.02

18.8

16.63

27.73

6378

15.7 21.8

0.9953

4

2

95

0.023

21.5

14.3

25.41

8573

20.2  22.8

0.9976

4

3

97

0.022

21.22

15.1

25.08

10287

19.6  22..8

0.9976

4

4

91

0.021

21.1

4.7

25.25

7747

18.6  23.7

0.9956

4

5

92

0.021

21.1

11.8

25.22

9950

18.6  23.7

0.9959

4

7

96

0.02

22.5

15.17

25.16

10090

20.34  24.7

0.9957

4

9

93

0.03

18.4

5

24.72

7766

16.4  20.3

0.9935

4

10

92

0.025

20.9

10.3

24.72

9812

19.8  22.0

0.999

4

12

95

0.022

20.25

12.6

24.82

9917

18.3  22.1

0.997

5

1

156

0.018

20.87

17.57

27.18

13733

19.9  21.8

0.9929

5

2

156

0.024

20.3

14

27.43

13592

19.8  20.8

0.9962

5

3

156

0.018

19.96

18.6

27.36

13620

18.8  21.1

0.9911

5

4

156

0.014

22.5

20.4

27.23

13411

21.2  23.8

0.9958

5

5

156

0.015

23.1

18.95

27.25

13478

21.9  24.3

0.9955

5

6

157

0.014

23.7

22.5

26.73

12689

20.6  26.8

0.9747

5

8

157

0.017

21.4

19.1

27.01

13722

18.9  23.0

0.983

5

9

157

0.012

27.7

20

27.05

12777

25.9  29.5

0.9965

5

10

156

0.016

22.6

16.3

27.45

12877

21.5  23.7

0.9952

5

11

157

0.015

21.7

22.9

26.87

13831

20.4  23.0

0.9937

5

12

157

0.02

21.7

15.3

27.06

14140

21.2  22.3

0.9969

10

13

95

0.0215

19.52

15.06

27.28

9643

16.7  22.3

0.9922

10

19

90

0.035

18.25

10.1

27.85

1847

16.5  20.0

0.9891

10

20

90

0.035

17.29

10.3

27.7

9246

15.9  18.7

0.9922

10

21

89

0.019

22.172

9.43

27.32

5391

20.2  24.1

0.9986

Results
One useful correlation was found between maximum length and average daily Nitrogen input (Fig. 9). As Nile Tilapia is a herbivorous fish, its characteristic diet is composed of plant matter and/or detritus of plant origin with or without macrophytes (Bowen, 1982). Therefore tilapia does not feed directly on the manure applied to the pond but indirectly through the food chain. Pig or chicken manure is decomposed by bacteria releasing inorganic nutrients which in turn increase primary productivity. Fish growth has been observed to be related to primary productivity or phytoplankton density (Almazan and Boyd, 1978). Increasing phytoplankton density increased fish growth, whereas above a certain level growth decreased due to oxygen shortages. Above a certain phytoplankton density shading prevents the lower water levels from producing oxygen by photosynthesis. Furthermore is must be taken into account that excess nitrogen input can cause high unionized ammonia concentrations, which may reduce fish growth or cause mortality (KnudHansen et al., 1991). This evidence suggests that fish growth is supported by increasing average daily nitrogen inputs in the pond up to certain level, from where it decreases. Although the data concerning this relationship was not unequivocal, it was assumed to follow the described pattern. A polynomial approach was chosen. In this regression the experiment with the outstanding value of A = 27.7 cm (Exp. 5, Pond 9) was omitted.
Fig. 9: A quadratic relation between maximal attainable
length and daily nitrogen input was assumed on the basis of evidence
found in literature that growth performance increases in relation
to nitrogen input up to certain level from
where it decreases.
L = 11.7 + 9.1*N  2*N² (r² = 0.6824, n = 28)
The other correlation used in the model was found between maximum length A and the average early morning water temperature over the whole experiment period (Fig.10). Since fish are poikilothermic, thermal variations will have an important impact on all of the animals' physiological functions. It is generally accepted that tilapias cease growing significantly at temperatures below 20—C and above 3036—C. Between those extreme temperatures optimal growing temperatures have been observed (Caulton, 1982). Therefore, despite the lack of data for average early morning water temperatures between 25.5—C and 26.5—C, a quadratic correlation between early morning water temperature and max. length with a maximum around 26—C was assumed. But as it was figured that for climatic reasons the actual average early morning temperature could significantly exceed the interval used in the regression (Fig.11), a bellshaped curve was correlated to the data for stability reasons.
Fig. 10: Since fish are poikilothermic it can be
assumed that growth performance increases up to a certain level
from where it decreases. Although data density is not very high
it can be interpreted as support for this thesis.
The early morning water temperature followed a well defined pattern
throughout the year (Fig. 11).
This pattern was fitted to a quadratic function:
T(t) = 22.37 + 0.0586*t  0.0015*t² ,
where T is the early morning water temperature and t is the day
of year (R² = 0.715, n = 668).
Fig. 11: The data points are the average temperatures
between two fish sampling dates. I.e. that each experiment and
pond has several temperature measurements from where the average
early morning temperature over the whole experiment period is
obtained.
In order to put the twodimensional correlation of maximum lenght
to average early morning water temperature and average daily nitrogen
input into one formula a multiple nonlinear regression was performed.
This was feasible because daily Nitrogen input is obviously independent
from the time of year. The result was a 2D surface in a 3D 'growth
performance space' (Fig. 12).
Fig.12: Final growth performance dependencies used
by FARMSIM.
L(T,N) = 5.24*exp((T  26.3)²/2.38) + 12.6 + 5.34*N  1.26*N²
(r²=0.775, n=27)
In all regressions the parameter k was always significantly correlated to the parameter A. Since no significant correlations of k to environmental parameters were found and in the regressions of the BGF k was always linearly correlated to A, different approaches to correlate k to A were tried. In the end a linear approach was chosen:
k = 0.0550.001668*A (r²=0.52, n=29)
As the maximum weight of the fish is more interesting than the maximum length, the highly significant correlation between weight and length was implemented.
W = 0.01065 * L^{3.258 }
where W is in g and total length is in cm and for which n=612,
r² = 0.973, size range: 0.7 to 211 g, 4.3 to 22.0 cm (Prein,
1993).
So the model derived from the experimental data using a simple
BGF is defined as:
W = 0.01065 * L^{3.258 } where
L(t) = A*(1exp(k*(tto))) and
A = 5.24*exp((T  26.3)²/2.38) + 12.6 + 5.34*N  1.26*N²
and
k = 0.0550.001668*A.
As an average initial length L(t0)=5 cm was selected for the model implementation. T is the average early morning water temperature over the growth period of the fish and N is the daily nitrogen input in the pond (kg N/(ha*d)) also averaged over the experimental period. T is simply calculated as the mean of the early morning water temperature between the day of stocking T1 and the day of harvest T2:
average early morning water temperature =_{ }dt / (T_{2}T_{1})
T(t) = 22.37 + 0.0586*t  0.0015*t²
So the average early morning temperature Tav. throughout the growth
period is determined by
Tav. = ((22.37*(T_{2}  T_{1}) + (0.0586/2)*(T_{2}²
 T_{1}²)  (0.00015/3)*(T_{2}³  T_{1}³))/(T_{2}
 T_{1})
for T_{1} < T_{2} < 365. For the case that
T2 < T1 < 365 the formula has to be changed to
Tav. = ((22.37*(T_{2}  T_{1 }+ 365) +
(0.0586/2)*(T_{2}²  T_{1}² + 365²)

(0.00015/3)*(T_{2}³  T_{1}³ + 365³))/(T_{2}
 T_{1})
According to this regression analysis, maximum fish yield at each
water temperature level is obtained by an average daily nitrogen
input of 2.12 kg N/ha. The absolute maximum of 23.5 cm can be
achieved at a daily N input of 2.12 kg N/ha and an average early
morning water temperature of 26.3 °C.
Implementation
In the actual implementation of the fishpond model the fish culture
period (culture_period, days)
was set to 90 days. After each culture period all fish is harvested
and fish production starts again with new harvest dates and
therefore also new average water temperatures. After the first
harvest each new fish cycle starts with an initial length of 0
cm per fish. This is not realistic, but it can be assumed that
the time until individual fish reach a new initial length of 5
cm is a fallow period. Since in one season more than one fish
cycle is possible, the total harvest is accumulated in a variable
called totalPond [kg FW].
totalPond(t) = totalPond(t  dt) + (PondRate)
* dt
PondRate = IF(DOY=dateofharvest) THEN
Pond ELSE 0
Pond = (FishWeight/1000)*Stocking*Pondsize
culture_period = 90
dateofstocking =
MOD(StartDOY+INT(TIME/culture_period)*culture_period,365)
dateofharvest = IF(culture_period+dateofstocking<=365)
THEN culture_period+dateofstocking
ELSE culture_period+dateofstocking365
In the regression formula for the maximal attainable fish length
the nitrogen input is averaged over the whole culture period.
It is calculated 'backwards' in a way. In a dynamic model this
is not possible. Therefore fluctuations in daily nitrogen application
are buffered by dividing the total nitrogen input in the pond
(Ninput, kg N/ha) accumulated
over the culture period (Pondage,
days). This also made the introduction of the variable culture_time
necessary. After each fish cycle the nitrogen input is accumulated
from the beginning (newPond,
kg N/(ha*d)).
NperHectarperDay = IF(Ninput/Pondage<4.5)
THEN Ninput/Pondage ELSE 4.5
Ninput(t) = Ninput(t  dt) + (dailyNAppl
 newPond) * dt
dailyNAppl = ((RiceBranTo_Fish*0.01)/Pondsize)+
((fert*0.299*0.019)/Pond size)+
NtoFish/Pondsize
newPond = IF(DOY=dateofharvest) THEN
Ninput ELSE 0
Pondage(t) = Pondage(t  dt) + (culture_time)
* dt
culture_time = IF (DOY=dateofharvest)
THEN Pondage+1 ELSE 1
For the description of NperHectatperDay
and dailyNAppl
see chapter 2.6.
Verification and longterm stability
After implementation in STELLA the model was verified by running on different sets of parameters and perturbation in the forcing function. The outcome of the model and the response to external inputs was as expected.
Running the model over a long time reveals no surprises. Every ninety days the fishpond is newly stocked and fish growth starts all over again. The only thing that increases steadily in time is the accumulated fish yield. The model is periodically stable in the long run.
Sensitivity analysis
The behavior of the BGF is dictated by the growth parameters A and k. Since k was correlated linearly to A, the latter is the main parameter which rules fish growth in this case. After it was decided to relate maximal attainable length A to daily average nitrogen input in the pond, and average early morning water temperature, different regression formulas were tried using also two different data sets. The first data set was the same as listed in Tab. 5 and in the second data set two experiments were added which had a 95 % confidence interval larger than 6 cm. This, of course, resulted in regression formulas with different parameters and different qualities of fit. Naturally, the final parameters of the regression formulas also depended on the initial starting parameters.
A different regression approach was, for instance, a quadratic relation for both parameters. This did not result in a good fit. Other formulas of the same kind as used here showed similar results (see Tab. 7). The decision for the final regression formula was, of course, mainly dictated by the quality of the fit, but secondly also by aesthetic considerations. As the parameter sets for the regression formula for A differed according to the data set used and initial values, a sensitivity analysis concerning these parameters was conducted. Subject of the sensitivity analysis were the parameters in the formula describing the maximal attainable length A,
A = P1*exp((TP2)²/P3) + P4 + P5*N  P6*N² (2.1)
which had a 95 % confidence interval that exceeded a 20 % fluctuation.
These were all parameters, except P2.
Tab. 7: Comparison of the final parameters of formula 2.1 and
the parameters using a slightly different data set in the regression
analysis.
Parameter

Parameters

Final

95 % confidence

95 % confidence


using a different

parameters

interval of the

interval in % deviation


data set*
 
final fit

from the final fit

P1 
4.56

5.34

[3; 14]

[156 %; +162 %]

P2 
26.2

26.3

[26.1; 26.5]

[0.007%;+0.007%]

P3 
0.4

2.38

[5; 10]

[310%; +320%]

P4 
9

12.6

[4:20]

[68%: +58%]

P5 
12.9

5.34

[1; 9]

[80%; +68%]

P6 
3.48

1.26

[2; 0.4]

[58%; 68%]

Using these parameters according to the slightly
different data set the r² value of
Eqn. 2.1 was 0.766.
To test the influence of the parameters in Eqn. 2.1 on the final simulated length, the parameters considered were varied by 20  50 %, respectively. This rather large variation is due to the high uncertainty of the fitted parameters. As a reference value two values were selected because it was expected that the parameters were sensitive also depending on the forcing functions. One reference value was close to the maximum value (at the maximum value of 23.5 cm the parameter P3 has no influence), namely A = 22.04 cm at T = 27 —C and N = 1.5 kg N/(ha*d), and the other was a value at the lower end of the possible scale, namely A = 11.12 cm at T = 22.37 —C and N = 4.5 kg N/(ha*d). The results are listed in Tab. 8.
Tab. 8: Sensitivity analysis of the parameters of Eqn. 2.1 at
two different
reference values and two different levels.
 Sensitivity at
 Sensitivity at
 Sensitivity at
 Sensitivity at

Parameter
 A = 22.04 cm.
 A = 22.04 cm.
 A = 11.12 cm.
 A = 11.12 cm.

 20% deviation
 50% deviation
 20% deviation
 50 % deviation

P1 
0.19

0.49





P3 
0.04

0.17



0.03

P4 
0.59

1.5

1.2

2.96

P5 
0.35

0.9

2.1

5.4

P6 
0.13

0.34

2.4

6

Sensitivity analysis of the parameters with a reference value
using medium nitrogen input and low temperatures resulted in a
high sensitivity of the parameters P4 and P5 causing a 35 % deviation
of the reference value.
The sensitivty of the weightlength relationship was not analysed
because uncertainity seemed to be low.
Forcing functions
The range of the temperature fluctuations is clear. Imposing the bellcurve shaped relationship between temperature and maximal length the sensitivity of the Eqn. 2.1 to the variation of temperature is well defined and needs no further investigation. There are several uncertainties about the formula describing the course of temperature throughout the year, but because the model only uses average temperatures, a sensitivity analysis of the temperature model was omitted.
The final length A is naturally very sensitive towards the quadratic relationship to daily nitrogen input. The disadvantage of polynomial approaches is that they very quickly reveal senseless results as soon as the actual input data are out of the range of the data where the formula had originally been fitted to. In the case of daily nitrogen input is was figured that an input of less than 0 kg N/ha*d and more than 4.5 kg N/ha*d would be improbable in real life and so this approach was thought to be rather accurate. Nevertheless, there has to be a threshold from where nitrogen application data is treated differently. So if any nitrogen fertilization should occur above 4.5 kg N/(ha*d), it is treated as 4.5 kg N/(ha*d). This might not reflect the real situation but avoids instabilities if there really are treatments above 4.5 kg N/ha*d (see implementation of NperHectaperDay p. 58).
Validation
The model uses the early morning water temperature averaged over the whole growth period, and the regression formula for the temperature was obtained using the average temperatures of the (usually) biweekly sampling intervals. Therefore the simulated average water temperatures were plotted against the measured average water temperatures over the whole experimental period (Fig. 13) in order to obtain an idea whether the chosen approach provides good results.
Fig. 13: This is no validation of the temperature equation because the simulated average temperatures are not independent from the measured average temperatures. This is only a visualization whether the equation which was fitted to biweekly measurements also holds for average temperature over larger time intervals.
An evaluation of the model was carried out using data which were not used in the regression (Fig. 14). The measured initial fish length L0, the average early morning water temperature calculated by the equation above and the measured average daily nitrogen input in the pond during the experimental period were fed into the BGF of the form
L(t) = (A  L_{0})*(1exp(k*t) + L_{0}, L(0)=L_{0}.
This equation was evaluated at the end of the experimental period and the simulated final fish length was plotted against the measured final fish length.
Additionally, growth performance data from buffalofish experiments (Edwards et al., 1994a, b; AIT 1986; Shevgoor et al. 1994) in Thailand were also used to validate the model assuming the same water temperatureday of year relation as in the Philippines. Those experiments were conducted under similar condition, i.e. tropical climate and smallscale fish farming, and were therefore considered comparable to the animalfish experiments in the Philippines.
Fig. 14: Validation of the fish growth model using
an independent data set. The measured average daily nitrogen input,
simulated average early morning water temperature and the growth
period served as input into the model.
Discussion
Looking at the R™ values of the regressions of the fish length data to the BGF justifies this rather simplistic approach. Indeed the shape of the length growth curve of Tilapia seems to follow the form described by Bertalanffy. The relations of the growth parameters to environmental conditions, like water temperature and nitrogen input, on the other hand of course emerge from the general assumptions concerning fish growth for which evidence was presented above. Those factors are far from being a complete picture of fish growth and are only of limited applicability. The quadratic relationship of max. length and daily nitrogen input in the pond has to be handled carefully.
Concerning the range of average temperatures that could be attained, the temperature curve releases the possible values. Since there are no reasonable days of year (DOY) beyond 0 and 365, this range is fixed. So average temperature can have a maximum of 28.1 —C at DOY 195 and a minimum of 22.37 —C at DOY 0 imposing the described relationship. The deviations from these values in real life should be less than 10 % (see Fig. 11). The model is not sensitive to temperature fluctuations of that range. With the constraints concerning the range of the forcing function daily nitrogen input (0  4.5 kg N/(ha*d)) the boundaries of the model are defined. There is one absolute maximum value for A of 23.5 cm at N = 2.12 and T = 26.6 and one absolute minimum of 11.1 cm at N = 4.5 and T = 22.37. All other simulated results will lie within these values, assuming the mentioned constraints of the input parameters. Taking also the initial value of 5 cm and the growth period into consideration, all simulated fish lengths will lie within the interval [5 cm; 23.5 cm].
The parameters of the regression formula 2.1 become very sensitive when the forcing functions are at the upper or lower range of their definition interval. This is especially true for the parameters P4  P6, which basically describe the response of maximal length A to daily nitrogen input. This means that simulation results in those ranges have to be treated extra carefully because a high uncertainty is attached to them.
For the correlation of early morning water temperature to the time of year, a sinusoidal connection was favored at first for aesthetic reasons but the quadratic approach resulted in a better fit. The temperatures averaged over the whole experimental period can be modeled with this equation satisfyingly.
The relation of fish length to fish weight was only fitted up to a length of 22 cm. It is assumed that the regression formula is also acceptable up to a length of 23.5 cm.
Generally the simulation of the fish growth reflects the real situation well. But looking at Fig. 14, a few constraints to the model become visible. As one can see, two ponds of experiment 12 are quite underestimated and experiments 1 and 8 are overestimated. In the ponds of experiment 12 the average daily nitrogen input is 4.58 kg N per hectare and day, and therefore lies out of the range of the actual interval, which was used to obtain this formula. As stated above, the model becomes unstable around a daily Ninput of 4.5 kg/ha*d. Moreover, it shows that extremely high fertilizer input does not necessarily mean low fish yields. Other factors may have become more important here that are not considered in the model. Only the general trend is reflected by this simulation approach.
The reasons why experiments 1 and 8 are overestimated are not clear. The fact that the whole of these experiments are not simulated well gives support to the notion that certain conditions prevailing in those experiments were responsible for this. Experiment 8 was a duckfish trial. Duckfish experiments were not used for the regressions, still the other duckfish experiment (Exp. 9) shows better results.
The buffalofish experiments of Edwards are also mostly overestimated. This might be due to the different buffalo manure consistency. Buffalo manure content is low in nitrogen and to obtain the same nitrogen loading rates as, for instance, with pig or chicken manure much more dry matter has to be applied to the pond. This results in an increased turbidity, which in turn decreases photosynthetic activity. Therefore high buffalo manure loading rates have a stronger negative effect than high pig manure loading rates. This might be the reason for the overestimation of parts of Edward's experiments.
Most other experiments lie within a 2.5 cm deviation from the perfect fit, which is tolerable considering that the fluctuations in length of experiments under the same feeding regime revealed even higher deviations. This is even more astonishing because fishponds are known to be rather complex systems. So it can be stated that this simple statistical model gives at least a good average picture of expected fish yields in small ponds in the Philippines under 'normal' conditions.
To get a better estimation of the quality of the model, onfarm data of fish trials have to be obtained. This proves to be difficult because in everyday life on the farm there is no such thing as fixed sampling intervals or fixed daily feeding rates. Monitoring is timeconsuming and therefore most data have to be collected from farmers' recall, which might be inappropriate. Still this model was also developed from the point of view of easy validation, and the parameters needed for evaluation are the most simple ones to obtain: length of culture period, and average daily nitrogen input and initial length. Water temperature is calculated by the regression formula. This will give support to easy onfarm testing of this submodel.
[Previous]
[Contents]
[Next]