Field Document 7
March 1984
| FI: DP/IND/75/031 Field Document 7 March 1984 |
A report prepared for the
Intensification of Freshwater Fish Culture and Training Project
by
Per Sparre
Consultant in Bioeconomic Modelling
This is one of a series of reports prepared during the course of the UNDP/FAO project identified on the title page. The conclusions and recommendations given in the report are those considered appropriate at the time of its preparation. They may be modified in the light of further knowledge gained at subsequent stages of the project.
The designations employed and the presentation of the material in this document do not imply the expression of any opinion whatsoever on the part of the United Nations or the Food and Agriculture Organization of the United Nations concerning the legal or constitutional status of any country, territory or sea area, or concerning the delimitation of frontiers.
FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS
Rome, 1984
Hyperlinks to non-FAO Internet sites do not imply any official endorsement of or responsibility for the opinions, ideas, data or products presented at these locations, or guarantee the validity of the information provided. The sole purpose of links to non-FAO sites is to indicate further information available on related topics.
This electronic document has been scanned using optical character recognition (OCR) software. FAO declines all responsibility for any discrepancies that may exist between the present document and its original printed version.
3. COUNTERPARTS AND ASSOCIATES
4.1 Training in Modelling Techniques
4.2 Outline of a Time Continuous Model
4.2.1 Outline of the metabolic growth model
4.2.2 The food suitability concept
4.2.3 A model of natural food production
4.2.4 Oxygen balance of the carp pond
4.3 A Simple Time Discrete Model for Hand Calculations
4.4 Microeconomics of Carp Production
4.6 Evaluation of Available Data and Advising on Further Data Needed
4.7 Discussion of the Usefulness of Bioeconomic Modelling in Fish Culture Research
5. CONCLUSIONS AND RECOMMENDATIONS
6. PROPOSALS FOR ORGANIZATION OF WORK
6.4 Group for Fish Growth Studies
6.5 Group for Natural Food Production Studies
6.6 Group for Ecosystem Studies
During recent decades a research programme on composite carp culture has been carried out in India. Composite culture is concerned with culture of the three Indian major carps, Catla catla (catla), Labeo rohita (rohu) and Cirrhinus mrigala (mrigala), along with the Chinese carps Hypophtalmichthys molitrix (silver carp) Ctenopharyngodon idella (grass carp) and Cyprinus carpio (common carp).
The Central Inland Fisheries Research Institute (CIFRI) has given very high priority to research on problems relating to carp culture. The Freshwater Aquaculture Research and Training Centre at Dhauli (FARTC) (Bhubaneswar) is making available to the Institute the necessary facilities for well planned laboratory and field research required for upgrading the technologies involved. The centre receives United Nations Development Programme/Food and Agriculture Organization of the United Nations assistance under the Intensification of Freshwater Fish Culture and Training Project (IND/75/031) and the regional project Establishment of a Network of Aquaculture Centres in Asia (RAS/76/003) in the form of equipment, fellowships and/or short-term consultants.
The background and outline of the IND/75/031 project have been given in UNDP/FAO report Outline Research Programmes for the Regional Aquaculture Lead Centres in Asia (ADCP/80/14 (En)). As part of the operation of the projects, Mr Per Sparre was assigned for two months as a consultant in bioeconomic modelling at the FARTC.
A large number of scientific publications demonstrate the breadth of carp culture research in India. More or less all aspects of carp culture have been investigated. However, little work has been done in the field of mathematical modelling and computerization and, as far as this subject is concerned, the consultant had to start from scratch.
To match the present state of carp culture research in other fields, a comprehensive model was required. The development of a carp pond model was initiated, including the following main elements:
physiological model for individual carp growth;
model of food intake and food competition (within species and between species);
model for phytoplankton and zooplankton production;
model for oxygen balance of a carp pond (to define the capacity of the pond);
microeconomic input/output model (as an extension to the biological model defined by i-iv).
Existing data are being evaluated and suggestions for future experiments were outlined
A detailed description of the models and the experimental design was given in the “lecture notes” prepared and given to the staff.
Due to the limited time available not all aspects of bioeconomic modelling were covered.
Emphasis was laid on the development of a “production function”, i.e., a model by which output (kilogrammes of carps produced) can be predicted from input (stocking, feeding, fertilization and environment).
A model of carp production is considered useful if it can give the answer to:
“If a pond has given characteristics (area, depth, soil, etc.), and if the production strategy (stock density, species composition, feeding rates, food types, fertilizer types, fertilization rates and length of production period) is given - how many kilogrammes of each species can then be harvested at the end of the production period?”
Having solved this central problem, the remaining problems of the microeconomics are relatively simple ones. One such problem is to maximize the net return (measured in rupees) subject to various constraints on the production. A constraint is. e.g., limitation of investment.
The consultancy was carried out from 2 September to 3 November 1981 at the FARTC with the following terms of reference:
Review, in consultation with scientific staff of the Centre, and determine usefulness and application of bioeconomic modelling in the Centre's research programme.
Describe data requirements, evaluate available data and advise on the collection of further data needed.
Initiate work on bioeconomic modelling and assist in the procurement of essential hardware and software for the purpose.
Train counterpart staff in modelling techniques.
The following FARTC scientists were designated as associate and counterparts to the consultant:
| Mr M. Ranadhir | (associate) | Economist |
| Mr B.R. Shirsat | (counterpart) | Economist |
| Mr N.K. Tripathy | (counterpart) | Fish culturist |
| Dr C.R. Das | (counterpart) | Fish culturist |
| Mr D.N. Swamy | (counterpart) | Fish feed technologist |
| Mr M. Rout | (counterpart) | Statistician |
The order of the items of the terms of reference was changed, as the consultant considered it necessary to give some training in modelling techniques before a meaningful discussion on their usefulness could be initiated. And, before an evaluation of available data and advice on future data collection can be given, some outline of the purpose of data collection must be available, i.e., one must have some idea of which type of parameters in which type of model one wishes to estimate before an evaluation of data can be carried out. Thus, the order of the following sections 4.1 to 4.6 indicates the chronological order of the development.
Lecture notes containing the essential parts of the training programme were prepared and 17 copies were made available to the staff.
Some time was spent in discussing the differences between empirical and analytical models and the usefulness of these two approaches. An empirical approach was defined as a model in which only the relationships between input (stocking, supplemental food, fertilizers, etc.) and output (harvest) were described, i.e., a model which does not contain a description of the biological production processes going on in the pond. The analytical model contains the same elements as the empirical input/output model and, in addition, it attempts to describe the biological processes of the carp production. It was recommended to apply the analytical approach and to concentrate on the links between biology and microeconomics. A production function describing the physical output as the number of surviving carps multiplied by final individual body weight was suggested. By using this as an example, some basic features of modelling techniques were illustrated. A comparison between this (analytical) model and an empirical model (the so-called Cobb-Douglas model) was made.
A model by which the dynamics of tissue-flows is described in terms of differential equations was discussed. This model is considered a somewhat sophisticated approach, e.g., it was not possible to apply the model before the FARTC received the HP 3000 computer from FAO and the staff at the FARTC had obtained a certain level in computerization of models. However, the consultant was requested to take most aspects of the carp-ecosystem into consideration and in his opinion the present model is the simplest one. It was recommended to initiate the modelling work with a simpler model and a suggestion for a simple approach was given (see next section). The time continuous model contains the compartments and the flows shown in Figure 1. A box symbolized a state variable and a full arrow symbolizes a flow of biomass (e.g., in units of kg/h). The oxygen balance model is used to determine the production capacity of the pond.
Each arrow corresponds to a differential equation of the model. The food competition between carp species and within carp species was modelled by aid of so-called “food suitability coefficients”. A physiological model for growth of a single carp was suggested (the Ursin metabolic growth model).
Some important compartments of the ecosystem were not given a detailed treatment because of the consultant's concern about the complexity of the model and the counterpart staff's limited background in modelling techniques.
Some time was spent in explaining how the model could be computerized and the computer calculations were illustrated by hand calculations.
A “growth model” describes the growth of an individual carp as a function of:
The Ursin metabolic growth model was suggested. This model considers the body weight change per time unit as an input/output system:
w(t) is the body weight of the carp at time t and dw/dt is the weight increase per time unit (e.g., measured in g/day).
The input term is the food intake per time unit:
where R(t) is the total food intake until time t by an individual carp.
The rate of food intake is modelled by:
where h and m are species specific parameters; f is the so-called “feeding level”; f is a real number between 0 and 1.0. A starving carp is said to get feeding level 0, and a carp eating at maximum rate is said to get feeding level 1.0. A fish eating half of what it can possibly eat gets feeding level 0.5…etc. (To be discussed in next section).
The exponent m (the “anabolic exponent”) accounts for the fact that small fish can eat relatively more than large fish; m is species-specific.
Figure 1. Illustration of flows and compartments of a model considered sufficient for a description of the carp pond ecosystem.
The anabolic coefficient h is species-specific and is assumed to be a function of:
The output-term consists of three components:
Faecal loss is modelled by:
where F(t) is the total faeces production until time t. β is the fraction of food intake absorbed. Thus
is the rate of food absorption. β is assumed to be a function of feeding level and the composition of food.
The food used as energy for feeding catabolism is modelled by
where α is the fraction of food absorbed used as energy for feeding catabolism.
The fasting catabolism is modelled by
where k and n are species-specific parameters. k is assumed to be a function of environmental factors. Thus, to describe the growth of a single carp, the following parameters are required:
h, m, α, β, k and n
An experimental design for estimation of these parameters was suggested.
The experiments should be carried out under laboratory conditions. A detailed description was given in the lecture notes.
To model food competition within carp species and between carp species, the concepts of “available food” and “food suitability” were introduced.
The six carp species are known to have different feeding behaviour and food preferences. To determine the optimum combination of carp species and food composition, a model which describes the sharing of food by the carps is required. Let j be index of carp species and i index of food type, e.g.,
| J | Carp | i | Food |
| 1 | Catla | 1 | Phytoplankton |
| 2 | Silver carp | 2 | Zooplankton |
| 3 | Rohu | 3 | Rice (or wheat) bran |
| 4 | Grass carp | 4 | Groundnut oil cake |
| 5 | Mrigal | ||
| 6 | Common carp | etc. |
As a measure of food suitability the coefficients Gij were introduced. Gij = (suitability of food type i as food for carp species j).
The suitability coefficients Gij are real numbers between 0 and 1.0 and for each species the sum of the Gij's is 1.0, i.e.,
∑i Gij = 1.0
Silver carp is known to be a surface feeder, mainly feeding on phytoplankton, so G12 is expected to take a high value, whereas common carp is known to be a bottom feeder, so that G16 is expected to take a low value … etc. Let Xi (t) be the number of kg of food type i in the pond at time t.
The “available” food of type for carp is defined
Xi (t) Gij
Thus the food is weighted by its suitability. The total available food for carp j is defined
θj (t) = ∑ Xi (t) Gij
The feeding level, fj, is defined:
HSj is species-specific parameter, the so-called half situation constant.
By this model for feeding level, it has been recognized that there is an upper limit for food intake. The figure shows feeding level as a function of available food.
Experiments by which the food suitability coefficients and the half-saturation constant can be estimated were suggested. These experiments should be performed in experimental ponds. An important detail of the experiments is stomach content analysis.
A model of primary and zooplankton production was suggested. Primary production is assumed to be a function of:
A model for grazing mortality on algae caused by zooplankton and carps was outlined.
Production of zooplankton was modelled in a way similar to that used for carp production.
The various processes shown in Figure 1 were discussed but, due to lack of time, no detailed experimental design for estimation of the parameters was prepared.
Oxygen content of the pond water is assumed to be the major limiting factor for the total production.
A model for oxygen dynamics was suggested. The oxygen content is assumed to be a function of:
It was recommended to take oxygen measurements in connection with all the experiments suggested.
A simple time discrete model containing some of the elements of the time continuous model was discussed. A numerical example based on observations from an actual case study was given. The estimation of parameters was discussed but, due to limited time and computation facilities (only a pocket calculator was available for the purpose) no proper estimation was made. It was recommended to initiate the modelling work at the FARTC by a simple model along the lines of the present model. A FORTRAN programme for simulation of carp production was developed. Training in FORTRAN programming was given to the counterparts. By the simple model, some aspects of microeconomics were illustrated. The pond was treated as an input/output system and it was explained how output (net return) could be maximized by computer simulation techniques. The development of a production function was given the highest priority and, due to the limited time available, other aspects of microeconomics were not given detailed treatment. Furthermore, the counterpart staff were not beginners in several fields of microeconomics, so it was considered less important to cover these aspects.
A model for net return of carp production during, say, one year, was suggested. Let P and C be production and costs (measured in Rs) resp.
Net return thus becomes
NR = P - C
The production of carps is
where
t1 = length of production period (production is said to start at time 0 and to end at time t1)
Nj (t1) = number of surviving carps species j at time t1
wj (t1) = average body weight at time t1 of carp species j
Nj (t1) Wj (t1) = kg of carp species j harvested
Pj = kg price of carp species j
The number of surviving carps is modelled by
Nj (t1) = Nj (0) exp (-Mj t1)
where Nj (0) is the number of fingerlings stocked at the beginning of the production period.
Mj is the coefficient of mortality. Mj is a function of disease frequency, poaching, escapement, etc.
Wj (t1) is a function of:
Density and species composition
Natural food production
Supplemental food
Initial body weight
Length of production period
Environment (soil, temperature, etc.)
Wj (t1) is determined by the growth model. Natural food production is determined by the model for primary and secondary production.
The costs are:
Cost of fingerlings
Cost of supplemental food
Cost of fertilizers
Fixed costs (pond preparation, netting, etc.)
The decision variables are:
Number of carps stocked
Species composition
Rate of supplementary feeding
Rate of fertilization
Length of production period
The problem is to determine the combination of decision variables which produce the maximum net return. Not all combinations of input variables are possible in practice, e.g., limitation of available oxygen in the pond determines an upper limit of the carp production. Another constraint on the production could be limitation of investment, e.g., the fish farmer may be unable to invest more than, say, Rs 5 000/year in the carp production.
How the production strategy subject to various constraints could be optimized by aid of operation research techniques was discussed. The data requirements for microeconomic analysis were dealt with and forms for future data collection were suggested. Data already available are being evaluated and FORTRAN programmes for the analysis of available data are being developed at the Danish Institute for Fisheries and Marine Research. (To be transferred to Dhauli for the HP-3000 computer).
An important aspect of fish production is the risk of losses caused by, for example, disease, poaching, water and oxygen supply failures, blooms of noxious algae.
These factors of stochastic nature can be taken into consideration by application of probabilistic modelling.
The natural mortality, M, may be considered the sum of three random variables
= Mdisease + Mpoaching + Mresidual
From knowledge of probability distributions of the three components, the probability distribution of N, the number of survivors, can be derived. Similarly, the feeding level, f, may be considered a random variable depending on oxygen concentrations and blooms of noxious algae. From knowledge of the probability distribution of f the distribution of the final body weight can be derived.
Finally, the probability distributions of harvested biomass can be derived from the distribution of number of survivors and final body weight.
When evaluating a planned production strategy, it is important to know the risks involved. Less risky strategies may be preferable even if they do not give the highest expected (planned) harvest.
Some aspects of probabilistic modelling were discussed. However, it was recommended to concentrate on deterministic models during the initial phase.
Data on experimental fish culture have been collected from all parts of India during the last decade (case studies). Out of a total of 263 case studies, 210 were considered useful for the type of modelling work suggested by the consultant. Forms for future data collection on commercial fish culture were designed. These new forms do not differ markedly from the forms already in use.
Proposals for experiments by which some of the parameters in the production function can be estimated were elaborated. These parameters were:
Experiments for estimation of parameters in the model for natural food production were outlined.
Time was spent in discussions on the usefulness of different types of models, and the role of the model maker in the research work at the FARTC. Special attention was paid to the priority that should be given to the biological aspects compared to economic aspects. Generally speaking, the opinion of the consultant is that they are of equal importance. However, because FARTC basically is a biological research station, it was recommended to concentrate on the microeconomics and to give the highest priority to the development of a production function. FARTC is in position to develop high level research in this field. It was recommended that the research work on microeconomics should be closely related to the biological research work and that no firm discrimination between biology and microeconomics should be made. The economist should extend his research field to include some biology and the biologist should include some microeconomics in his research field. It is expected to be a useful model only if all major fields of the research work in FARTC are covered.
The actual utilization of the model to determine the optimum combination of input is illustrated by Figure 2.
Figure 2. The interactive process for determination of optimum production strategy
Figure 2 shows an iterative procedure where combinations of inputs are tested by a simulation of production, i.e., by a prediction of the harvest subject to the combination of inputs. From an evaluation of the output the input combination is then improved and a new simulation is made … etc.
In every step the production strategy is improved and eventually the iteration will give the optimum combination. By aid of a computer, thousands of combinations may be tested. As an example of an operations research approach, linear programming was demonstrated by small numerical examples and it was explained that the trial and error method described above could be replaced by operations research techniques.
The consultant visited the Central Inland Fisheries Research Institute (CIFRI) in Barrackpore, West Bengal, on 20 October. The work of the consultant was discussed with Dr A.V. Natarajan, Director of CIFRI, and Dr V.R.P. Sinha, National Project Director, IND/75/031. The echosystem aspects especially were discussed at this meeting and some extensions of the model developed by the consultant were suggested by Dr Natarajan. It was pointed out by Dr Natarajan that some important compartments of the model needed a more detailed treatment, such as the detritus and benthos compartments. The consultant agreed with these comments, and the discussion was encouraging to the consultant. However, due to the limited time available, the consultant had omitted several aspects of bioeconomic modelling. The attempt was to cover those aspects for which data were already available.
The physical conditions for advanced research utilizing modelling techniques will be available at the FARTC. The experimental facilities are already available; a large amount of relevant data have been collected and expertise in experimental research work exists. After the HP-3000 computer from FAO is operating, the physical conditions will be optimum. However, the theoretical background in modelling techniques and computerization of the FARTC staff has yet to be sufficient for an optimum utilization of available facilities. Of course, it is hoped that a certain background has been developed during this consultancy.
As the modelling approach contains all aspects of fish culture research, it is necessary that the total scientific staff should obtain a certain minimum level in modelling techniques. The development of a useful model cannot be made by a small group of mathematicians, economists or statisticians of biological research work. As FARTC is a biological station and the carp pond is a biological system, the biologist is considered the key person. If modelling is not considered a multidiscipline research field, little (or no) applicable results are expected. The bioeconomic model of carp culture should not be considered as one of the many research projects of equal status but as a project which receives its input from all other (sub-) projects and which attempts to combine the findings of all types of carp culture research into one conclusion on optimum management of carp production.
Recommendations
A new multidisciplinary project on the development of a bioeconomic model of carp production should be initiated at the FARTC along the lines suggested in the lecture notes. To create the necessary background for the project, the following programme should be implemented:
1.1 Study groups on basic mathematics, statistics, FORTRAN programming and modelling techniques should be established in the FARTC. The necessary textbooks should be made available in sufficient numbers. For training in practical applications, a number of “scientific” pocket calculators should be purchased. Designated FARTC scientists should receive training in modelling and computerization for a sufficient length of time at suitable Indian institutes.
1.2 After achieving a certain background in the disciplines mentioned under item 1.1 above, fellowship for training for a duration of about two months in research institutes with a tradition of modelling work should be arranged.
Experiments for estimation of parameters in the metabolic growth model should be carried out as soon as possible. Some of the experiments had already been initiated before the arrival of the consultant.
Experiments for estimation of “food suitability coefficients” should be initiated as soon as possible. These experiments can probably be integrated in already existing plans by introduction of minor modifications.
Collection of economic data from commercial carp production units (case studies) should be continued (with some minor extensions of the existing programme). A data base for the HP- 3000 computer should be developed (probably a suitable data base is already available on the market).
The microeconomic model for carp production should be tested on as many case studies as possible. Data on production limiting factors should be evaluated in order to define constraints to the production planning.
Optimum production strategies should be searched and cost-benefit analyses should be made for comparison of alternative production strategies. (Some initial work in this field is possible with existing data).
For optimum utilization of the HP- 3000 computer, it is recommended that FARTC employ a scientist with education in computer science and operations research. (If this is not possible it is recommended that FAO offer a consultancy in this field). The person in question should be able to develop the necessary software for a carp pond simulation programme and programmes for analysis of experimental data, and data on fish culture economics. The next consultancy in bioeconomic modelling should start after the arrival of the computer and the consultant should advise and assist in the development of software.
Investigations on the impact of detritus and benthos on the carp pond ecosystem should be initiated.
Experiments on natural food production as a function of fertilization and environment should be initiated.
The impact of diseases and the treatment of these should be evaluated in the context of cost-benefit analysis.
At a later state of the development, probabilistic modelling should be initiated in order to develop methods of risk analysis.
Some of the projects suggested above may be accomplished by units already existing at the FARTC. These projects are:
To cover the modelling and computerization aspects, two new units are suggested:
The present proposals for organization of work deal only with those aspects covered by the present consultancy. As modelling deals with all aspects of fish culture research, these proposals should be considered as a part of a larger organization plan. Important aspects not covered by the models suggested so far are:
Fish culture technology
Food technology
Nutritional requirements of carps
Fish diseases
Genetics
Extension work
From a modelling point of view it is important that a certain uniformity of the work in all units is implemented. All research work carried out at the FARTC should result in some estimates of some parameters in the “carp culture model”. At a later stage of development, the six above-mentioned fields should also be included in the modelling work.
Because of the multidisciplinary nature of modelling work, the most important aspect of organization is the cooperation between the units of the FARTC. It is of crucial importance that experiments in the various units are planned so that results can be utilized for estimation of parameters in the models, e.g., when measuring nutritive values and utilization of different food types, it is important that the experiments are performed for a range of carp body weights representative for the entire production (from fingerlings to marketable carps). Results obtained from, say, experiments with fingerlings only, may be of great value in themselves but they may not suffice for parameter estimation in a model also covering the production of 1 kg carps. Similarly, it is important that the entire range of temperatures observed in actual carp production is covered by the experimental design. Thus, more or less all experiments to be performed at the FARTC should be evaluated from a parameter estimation point of view. Whenever an experiment is performed, all observations relevant to estimation of parameters should be collected, e.g., an experiment designed to estimate density dependence of some disease frequency may at the same time be utilized to estimate oxygen consumption, primary production, etc.
It is proposed that a “coordination group” be established at the FARTC to ensure that maximum output is obtained from all experiments. This group should consist of representatives from all major scientific units at the FARTC. The members of the group must be those scientists with the strongest background in modelling work and statistical analysis.
The duties of the coordination group should be:
Development of the “carp culture model”, i.e., aggregation of submodels (such as models for individual growth of carps, primary production, etc.) into a total model.
Evaluation of projects from a parameter estimation point of view, i.e., to give priority to projects in accordance with the importance of the parameters to be estimated from the project in question.
To advise on experimental design, to secure optimum utilization of experimental facilities and manpower.
As the members of the coordination group are representatives of other units of FARTC, membership of this group is a part-time job. It is suggested that the members of the coordination group be the associate and counterpart staff of this consultancy. In addition, it is recommended to expand the group by: a chemist, a fish disease expert and a computer scientist (system analyst).
As the duties of the coordination group are of a theoretical nature, it is somewhat difficult to estimate the number of time per year necessary for meaningful work. The consultant estimates that an average of about 30 percent of time per member should be spent on the coordination and modelling work.
All members of the coordination group should be able to develop models and to transfer models into computer programmes.
In connection with the installation of the HP- 3000 computer, it is recommended that a computer unit be established. Members of the unit should be: one system analyst and two to four assistants (operators). Sooner or later all work by the coordination group will be transferred to the computer unit.
The major tasks of the system analyst are: to develop and maintain data base systems and to assistin development of software for the modelling work. A system analyst with a certain knowledge of operations research and statistical analysis would be preferable.
In the initial phase, the system analyst should give training to the members of the coordination group in order to bring them to a level at which they are able to computerize models.
This economics unit already exists and consists of 2 economists and 1 statistician.
Because economics are linked to all aspects of fish culture, as the modelling work is, the economics unit will probably be the unit most concerned with model development. The main tasks of the economics section should be to: collect and analyse data on commercial carp production; carry out cost-benefit analysis for alternative production strategies, and develop microeconomic models of carp production.
To carry out experiments for the estimation of growth parameters a group of (at least) two physiologists (or fish food technologists) should be established. Some of these experiments are already being performed by a fish food technologist at the FARTC.
The task of this group is to carry out experiments for estimation of parameters in models of: secondary production (phytoplankton + weed); zooplankton production and production of benthic animals.
These aspects are closely related to water quality, so it is recommended that the group consist of a chemist and a fish culturist.
The task of this group is primarily to carry out experiments to estimate parameters in models of carp growth as a function of the environment, i.e., the estimated carp production as a function of:
density of carps
species composition
secondary production
zooplankton and benthos production
supplementary feeding
water quality
An important detailed project is the estimation of food suitability coefficients. The group should consist of two fish culturists.
