© 2006 International Council for the Exploration of the Sea
Modelling Caspian sturgeon population dynamics: a new paradigm and new technology
Institute of Cybernetics of the National Academy of Sciences, 9 F. Agayev Street, Baku, AZ 1141, Azerbaijan
*Correspondence to R. A. Karayev: tel: +994 12 4938030; fax: +994 12 4971786. e-mail: karayevr{at}yahoo.com.
Currently, many problems beset sustainable management of Caspian sturgeon stocks, some outside the traditional theory of fishery management. Successfully solving such problems requires different models of population dynamics, reflecting the phenomenological properties of sturgeon stocks, the consequences of their overexploitation, and issues relating to environmental pressure on the ecosystem in which they live. Of the many analytical tools available to address the various questions, problem-orientated models are few. Their development demands a new approach, a new modelling paradigm, and new modelling tools that meet the modern ideas of ecosystem analysis and cognitive theory. This paper offers one such new paradigm and describes a knowledge-based modelling technique that may provide realization of this paradigm. A problem-orientated version of knowledge-based models is described, the applicability of such models in attempting to solve the practical issues of sturgeon fisheries management is reviewed, and an example of model implementation is given.
Keywords: Caspian sturgeon, knowledge-based technologies, new paradigm, population dynamics, uncertainty
Received 15 November 2005; accepted 27 March 2006.
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Introduction |
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During the past few decades, Caspian sturgeon (Acipenser spp. and Huso huso) have been seriously impacted by, inter alia, damming of their spawning rivers, sea level fluctuations, overfishing (including extensive poaching), pollution of the sea and the rivers that run into it, and the accidental introduction of the invasive comb jelly Mnemiopsis leidyi. Long-term, multiple environmental and anthropogenic pressures such as these have resulted in wholesale depletion of sturgeon stocks, to the extent that between 1981 and 2005, the total allowable catch (TAC) of sturgeon in the Volga–Caspian Basin, the main commercial fishing area, dropped progressively by a factor of at least 50. Notwithstanding the optimism of some, it is now widely accepted scientifically that most Caspian species of sturgeon face disaster.
Such a huge reduction in stocks and catches has posed three crucial questions for those responsible for advising on management: (i) what anthropogenic and environmental factors have caused the stocks to decline? (ii) what are the threshold values of such factors which, if exceeded, will lead to stock collapse? (iii) what strategy can be applied to conserve, rebuild, ensure adequate reproduction of, and manage sturgeon stocks sustainably under the present environmental conditions?
To address these questions, a model of the system dynamics of sturgeon populations (Nikolskiy, 1974; Bolshakov et al., 1993) that takes into account species biology and environmental and fishery impacts needs to be developed. Currently no such model is available, and it has been known for a long time that it is virtually impossible to create such a model on the basis of traditional mathematical calculus. For example, Hempel and Sahrhage (1961) stated that "the dynamics of fish stock from an egg to an adult cannot be expressed mathematically". The long-term output from population modelling confirms the validity of this statement (Schnute and Richards, 2001). System dynamics can be modelled as a supplement to traditional fisheries assessment. It must be stressed, however, that continuous monitoring does not necessarily support stepwise improvement in solutions, and that there is currently no scientific method available to solve the above questions for Caspian sturgeon species.
The current situation is one of a "paradigm crisis" (sensu Kuhn, 1970). To a known degree, this is conditioned on the conservative nature of the initial provisions of population analyses created by the gnoseological basis of exact science (such as mathematics, mechanics, and physics). Today, under changed conditions, these provisions do not reflect reality in terms of the population dynamics of Caspian Sea sturgeon (Vlasenko et al., 1999; FAO, 2004). Further, they conceptually contradict the views of modern science (e.g. the theory of complex systems, cognitive psychology, fuzzy logic, knowledge engineering, possibility theory, determination analysis, and situational management) on how models of complex ecological systems should be built when opportunities for supervision (monitoring) are limited and experimental verification of the models is practically impossible.
Overcoming an existing problem situation requires the development of an essentially new paradigm of modelling that will reflect the complex dynamics of sturgeon stocks under their new conditions and, together, take into account features inherent in modelling complex "poorly-learned" systems. Already, first steps in this direction have shown that development of such a paradigm is crucial, but that such knowledge will be unable to solve the problem. Therefore, alongside developing a new paradigm it is critical that a technological platform for modelling be developed, one capable of providing the technical realization of a new paradigm.
This paper focuses on both these aspects and:
- the main theses of a contemporary paradigm of Caspian sturgeon population analysis are presented;
- a modelling technique in the form of problem-orientated expansion of knowledge-based technology is described as a means of realizing the new paradigm;
- an example is given of how a problem-orientated knowledge-based model can be used to estimate the efficiency of natural reproduction of Russian sturgeon (Acipenser gueldenstaedtii) in the lower Volga River, an important component of Caspian sturgeon stocks;
- finally, the appropriateness of the technology in solving practical Caspian sturgeon management issues is evaluated.
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The contemporary paradigm of population analysis |
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Thesis 1
It has long been thought that modelling the dynamics of Caspian fisheries requires an ecosystem approach. However, this issue has not yet been addressed from a theoretical perspective. Identification of sturgeon population dynamics with due consideration of both natural and anthropogenic factors is complicated. Here, as in solving other complicated problems, theory needs to address the limits in terms of the cognitive and creative abilities of man. Fishing at an optimal level is a theoretical rather than a practical consideration, and several recent general publications have stated this fact (e.g. Cadima, 2003). At present, wide-ranging natural and anthropogenic factors can be destructive and, if ignored, may lead to speculation and error in the strategy used to address them.
Solutions to this management problem require at least a three-level analysis (Odum, 1983; Garcia et al., 2003; Karayev, 2003):
- at an ecosystem level – addressing the ecosystem of the Caspian Sea or the habitat of its population, its associated populations, and its natural and anthropogenic drivers;
- at a population level – addressing Caspian sturgeon population(s) as an element of the ecosystem and its/their relationship with associated fish populations (through food, competition, predators, etc.), and in knowledge of legal and illegal catches;
- at an organism level – addressing individual fish at various stages of their ontogenesis.
It is important that information on individual fish be included in such modelling. Monitoring eggs, pre-larvae, larvae, and fry produced naturally, and of juveniles released from hatcheries, provides important information on the survival rate of a generation and of its input into the general stock dynamics. Fish have a wide range of sensitive physiological, biochemical, and histo-physiological indicators that respond to anthropogenic impacts before any effect at a population level becomes clear; such indicators can help demonstrate the cause/effect relationship between environmental variation and the physiological condition of the fish, and can identify destructive processes before they become widely apparent.
Bioaccumulation of genotoxic substances that can damage a fish cell's genetic mechanism is one of the most dangerous effects of water pollution. Substances are hazardous not only because they result in genetic changes that may re-occur in future generations, but also because damage done to the DNA stimulates the so-called "principle of intensification": gene damage that may result in malfunctioning of various albumens. Preliminary studies in 1995 and 1996 reported by Chistyakov et al. (2002) revealed genotoxicity in tissues of mature adult sturgeon. They demonstrated that (i) substances genetically harmful to sturgeon originated mainly from inactive precursors (promutagens) produced by a system of microsomal oxidases in the fish liver, and (ii) the process entails depletion of tocopherol in the liver cells. The process is apparently that microsomal oxidases adapted to detoxification of certain substances during evolution encountered new substances (xenobiotic anthropogenic pollutants, such as PAH, PCB, dioxins, and their precursors), and their destructive effect was intensified.
Data on functional and genetic abnormalities of adult fish can be used as input data to physiological and genetic analyses at a population level, allowing for early diagnosis and forecasting of possible long-term effects at a population level, both critical factors in the context of sustainable exploitation of sturgeon stocks.
Thesis 2
A modeller needs to know the type of problem, and there will be many, with which he is dealing. An example is that proposed by Simon and Newell (1958), in which are identified three types of problem:
- well-structured or quantitatively expressed problems, in which the principal dependences are sufficiently clear to be expressed in numbers or symbols that ultimately gain a numerical value;
- poorly structured or combined problems that contain both qualitative and quantitative elements, but where they are qualitative, little known, indefinite components tend to dominate;
- non-structured or qualitatively expressed problems that describe important resources, qualities, and characteristics, and in which the quantitative inter-dependences are unknown.
Although not well established, and although the definition of some problems can change over time, this classification is revealing. First, all known population models are orientated towards well-structured problems (environmentally safe waterbodies; no overfishing; stable age structure and natural mortality; and reliable and complete statistics). The term "well-structured problems" does not necessarily mean that solving them will be easy; it is often very difficult to develop a mathematical model that reflects all the main features. Most non-structured problems can be solved heuristically; such a method does not contain a logical problem-solving procedure, but rather depends on the personality of the researcher. Basically, it contains intuitive speculation based on previous experience, often described as: "I don't know how, but I can do it."
Poorly structured problems are obviously an intermediate class between well- and non-structured problems. Current definitions typically refer to modelling stock dynamics as addressing poorly structured problems. The term "poorly structured" here means that we are not aware of some of the dependences between various stages of stock development, or how natural and anthropogenic factors impact such development. It also implies unpredictable historical changes in dependences in the Caspian Sea that cannot be considered in the original model. For instance, between 1981 and 1989, the annual flow of the Volga River was crucial to natural reproduction of sturgeon and access of juveniles to the sea, but from 1990 to 1999, when average summer flow increased to 69.1 km3, the importance of that flow became less significant. Other factors had a greater impact on stock rejuvenation: the number of breeders that reached the spawning grounds; the area of those spawning grounds; the physical condition of the spawning population; and the sex ratio and fecundity of the population.
There are many uncertainties of similar nature. Models of poorly structured problems can only be based on information provided by a person who participates in problem-solving, so there is often insufficient basis for compiling objective, unbiased models. Poor understanding of this resulted in the unsuccessful application of many "objective" mathematical models of population dynamics. Interrelationships presented mathematically do not become more objective, although some believe that it is possible to compile objective models of population dynamics. Other workers understand that compilation of models includes some subjectivity. Notwithstanding the intention of the model developer, some still assume that models reflect reality. The dependences developed for complex models are often based on an individual's (or a group of individuals') perception of the connection between certain parameters and the idea that cause/effect relationships taken from life remain true in the model.
The main methodological inference is that there are no natural-science-justified solutions to models of poorly structured complex problems. Modelling here follows a new principle, an unusual one for ichthyologists, not from formal mathematical calculus to deduced inferences and hypotheses, but from heuristic and empirical experience to formalization, and thence to inferences and hypotheses. Unlike traditional models, these reflect not the general biology of a species (or populations), but rather the biology of species (populations) within specific temporal and spatial limits, and within specific limits of knowledge. This view opens the question whether to apply to Caspian sturgeon species some universally available commercial software developed to international standards and recommended for use in different waterbodies.
Thesis 3
The development of information technology has resulted in some modelling "illusions". One is a belief that it is possible to develop complex mathematical models that simplify prediction and guarantee calculation of reliable optimal levels of fishing (e.g. Beverton and Holt, 1957; Ricker, 1958; Nikolskiy, 1974; Dementyeva, 1976). However, there is now sufficient experience to show that uncertainties in the fish stock assessment process can create practically insurmountable obstacles that make the development of ever more complicated computer models a questionable activity. Without going into detail about the multiple sources of uncertainty (Shaffer, 1981; Soule, 1987; FAO, 1995), it is necessary to review the most critical, basic biological axioms. At present, scientists and managers who follow certain doctrines apply their own principles and methods to fish stock modelling that are based on a system of hypotheses. The problem of how to discriminate (select) between hypotheses, i.e. to select the most appropriate, is not generally known.
Modern gnoseology and the practice of cognition of the real world's complicated objects and processes show sceptism about such selection procedures, and raise queries as to where the ideology of selection originates. The answer is straightforward: according to Kuhn (1970), the existing paradigm states that the world is on the one hand governed by the laws of nature, and on the other, that scientific experiment allows these laws to be revealed. The first part of this paradigm is losing support. It is opposed by bootstrap philosophy (Chew, 1968; Capra, 1976), according to which nature is a mutually coordinated dynamic web that cannot be reduced to elementary blocks of substance or fundamental laws, equations, or principles. Indeed, the term "bootstrap" cannot refer to an individual model; it is applicable only to a combination of internally coordinated models, none of which is more fundamental than the other. As for the second part of the paradigm, according to Popper (1963, 1965) and from general philosophical perception, the role of experiment and observation in science is limited: a hypothesis cannot be confirmed experimentally or by observation. An experiment or an observation can only be shown not to contradict a hypothesis.
Under this thesis, stock assessment practitioners who develop a new paradigm should cease searching for reliable and universal methods and models of population analysis (stock assessment, TACs, quotas, and stock predictions), because there is no sense postulating what appears to be illusive from a research perspective. Instead, the results of population dynamics studies need to be presented through a range of models. Further, if this point of view were to be accepted, we would eventually dispute the traditional perception of the role of statistics, a widely used tool in population analysis. According to Fisher (1960), the role of statistics is to compress the observed data; taking this statement to its next step, the results of fisheries research presented statistically would be more compressed than in their original raw format. However, any new approach would require the use of original, uncompressed data to evolve new information. Further, if data compression was carried out before at a formal, logical level (during statistical data processing), the process should now be transferred to an intuitive level that allowed for various interpretations of the raw data and their direct use in extrapolation. This would require the development of largely new formats for presenting statistical data, appropriate to both the cognitive and linguistic needs of information technology. The solution could be a combination of the methods of modern cognitive psychology (Velichkovskiy, 1992), fuzzy logic (Zadeh, 1965), determination analysis (Chesnokov, 1982), situational management (Pospelov, 1986), the theory of possibility (Dubois and Prade, 1994), and knowledge engineering (Waterman, 1986; Saila, 1996; Salski et al., 1996).
Thesis 4
Because of the present unstable environmental situation and the significant impact of anthropogenic factors in the Caspian Sea (and elsewhere), uncertainty has become a feature of population dynamics. Although many agree with this statement, agreement has not been reflected in the development of theory, not even in its initial classification. According to Luce and Raiffa (1957), and considering the basic operational environment as deterministic, probabilistic, and uncertain, it would be expedient to introduce a new classification of population dynamics models that reflects the dialectics of development of modelling concepts and tools. As a framework of this new classification, one should consider deterministic, probabilistic (or stochastic), and uncertain (or fuzzy, according to Zadeh, 1973) models of population dynamics.
Such a classification should, I believe, receive priority among other population analytical classifications, i.e. productive, structural models (Cadima, 2003), continuous- and discrete-time models (Nikolskiy, 1974), integral-differentiation, statistical, and simulation models (Laevastu and Larkins, 1981), and graphical and analytical models (Beverton and Holt, 1957). The proposed classification would direct attention in a new direction, by stressing the need for caution when traditional or deterministic and stochastic approaches are being used. Caution is specifically needed in the use of stock estimation methods of a spatial nature that postulate the random (probabilistic) distribution of fish in a waterbody (e.g. Aksyutina, 1968), and also in methods of TAC determination that postulate the deterministic concepts of a population's reproductive variability (e.g. Malkin, 1995), or the principles of the precautionary approach (e.g. FAO, 1995; Caddy, 1998) in, for example, a "traffic light" approach (Caddy, 2002).
Thesis 5
Assessment accuracy (stock size, TACs, quotas, and catch forecasts) is one of the most crucial requirements of fisheries research today. However, uncertainty resulting from the phenomenological properties of sturgeon and uncontrolled environmental pressure (poaching, pollution, Mnemiopsis, etc.) requires that new approaches to address the problem over and above a simple modelling approach (FAO, 2004) be developed.
The "principle of incompatibility" (Zadeh, 1973) as applied to complex ecological, economic, and social systems could become the basis of a new approach to sturgeon management in the Caspian Basin. According to this principle, the more complicated the system, the less able one is to provide accurate and practical judgement of its performance. Accuracy and practicality are almost mutually exclusive in systems where the complexity is above a certain threshold level. The corollary of the principle is that the deeper the analysis of the real problem, the more uncertain will be its solution.
In the context of population dynamics modelling, the incompatibility principle results in three important inferences: (i) the accuracy of the primary data collected through monitoring is relative (the data do not lend themselves to interpretation of currently complete dynamics of the processes in time and space); (ii) the accuracy of models developed on the basis of the data will be even less precise than the accuracy of the data; and (iii) the accuracy (adequacy) of the models is measured by their ability to demonstrate a qualitative description of dynamics, not by their quantitative error (Laevastu and Larkins, 1981; Anon., 2004a). The models therefore need to be conceptually credible (Soule, 1987). In this context, therefore, any estimation of the error inherent in stock assessments must be speculative, because stock size cannot be identified either experimentally or directly by observation. Further, determination of the errors in stock assessments (Anon., 2003, 2004a) is bound to be difficult, because they contradict both the uncertainty factor and the principle of incompatibility.
Thesis 6
Some dominant natural and anthropogenic factors have influenced the abundance and biomass of sturgeon stocks, even allowing for the fact that sturgeon can adjust to some of them. For instance, certain periods in the recent history of sturgeon spawning in the Volga River can be associated with specific factors (Anon., 2001, 2001–2004):
- Until 1958, before the damming of the Volga, natural reproduction was the main source of recruitment to sturgeon stocks.
- From 1959 to 1972, with the construction of hydroelectric stations on the Volga, both the area in which sturgeon could reproduce naturally and the distance of their spawning migrations were reduced, so lowering natural recruitment. During the same period, catching of sturgeon in the open sea was banned, and sturgeon hatcheries were built. This ban on fishing for sturgeon in the open sea contributed to stock growth, but the contribution to the stock from artificial reproduction was equally influential in stock dynamics, because already by the early 1970s, hatchery releases were the main contributors to recruitment of beluga (Huso huso).
- From 1973 to 1977, a sudden drop in the level of the Caspian Sea resulted in a significant reduction in the area available for natural spawning, lessened juvenile survival, and an increase in salinity. This was a critical period for the survival of juveniles of the other (Acipenser) species of sturgeon. Even with large numbers of fecund sturgeon arriving at the spawning grounds, contraction of the area available for them to spawn meant that few naturally spawned sturgeon recruited to the stocks.
- Then, from 1978 to 1989, sea level rose again. This resulted in a lowering of the salinity in the northern Caspian, and an increase in the area of the feeding grounds, enhancing the survival of juvenile sturgeon. Concomitantly, the number of juvenile beluga released from fish hatcheries in the Volga delta increased, and unfavourable environmental conditions reduced natural restocking of all sturgeon species. At that time too, sturgeon suffered cumulative toxicosis, which had a negative impact on their reproductive organs. In 1981, extra controls were introduced in an attempt to enhance recruitment of naturally spawned fish.
- From 1990 to date, as the former Soviet Union broke up into sovereign states and economic pressures severely impacted those living in the littoral states, poaching in both the open sea and in rivers increased. This situation was exacerbated by the failure of the Caspian littoral states to agree on appropriate (and harmonized) control measures, so the then existing system of rational use of bioresources, and support for natural reproduction and conservation of sturgeon, gradually collapsed. Replenishment of stocks through wild spawning virtually ceased, and the number of juveniles released from hatcheries declined. Further, the quality of the juveniles (fingerlings or fry) released was generally poor, a consequence of the poor biotechnology being applied and the higher levels of pollution in the Volga River. The proportion of fry released with abnormalities rocketed, almost all having at least one of some 83 identified types of abnormality (e.g. hydrocephaly, no eyes, no nostrils, three gills, no abdominal wall and the intestines open to the water). Some fry even had two or more abnormalities, which would have led to instant death (Anon., 2004b). Indeed, there is doubt whether the generations released from hatcheries during the early part of this period (from 1990) will provide even a minimal contribution to stocks of sturgeon in the Caspian. Thankfully, the abnormalities in released fry have recently been curtailed.
The effectiveness of previous and proposed activities for sturgeon replenishment is seriously jeopardized by the factors above. To compound the problems, the invasive comb jelly Mnemiopsis leidyi was found in the Caspian for the first time in 1999, having been introduced accidentally in the ballast water of ships passing from the Black Sea through largely artificial waterways into the Caspian Sea. In 2000, M. leidyi spread almost throughout the Caspian and is now thought to have had a significantly negative impact on the biota, including natural forage for sturgeon; it is believed to be a species that can "cause a real environmental catastrophe" (Volovik and Korpakova, 2002).
Such a continuously changing environment in an enclosed waterbody such as the Caspian requires the development of system dynamics models with structural and parametric adaptability (Holling, 1978), a complex task well known to environmental modellers. The solution would be to review the performance and health of the Caspian ecosystem under its various and manifold pressures (Belyaeva et al., 1998; Sapozhnikov, 2002), to investigate the response of sturgeon populations to changing conditions, and to build a management model based on such multi-factorial zones of tolerance [note that the mono-factor law of tolerances of Lybich-Sheffold (Odum, 1983) would not work here].
Thesis 7
The variability of structural and parametric characteristics of environmental pressure places before model developers a range of questions far beyond Russell's axiom (Russell, 1931), formulated for "closed" (isolated) populations that inhabit environmentally safe waterbodies. The axiom of sturgeon stock modelling in the Caspian needs to be based on high-level postulates that reflect the general and specific biological bases for modelling stock dynamics:
- the structural sustainability of the life cycle of sturgeon set against a background of environmental variation;
- the long-term stability of the spatial and temporal distributions of sturgeon populations and subpopulations;
- the need for observed biological parameters of stocks to play a key role in an ecosystem analysis of system dynamics.
The importance of selecting a conceptual scheme for ecosystem modelling, collecting data, and processing existing primary data (the third point above) is interpreted by Nikolskiy (1974) as "analysis of variation of a population's biological parameters identifies much more sensitive changes in its living conditions than a direct analysis of the dynamics of the conditions would". Such an interpretation of the role of the population as a subject of modelling agrees with the widespread opinion of experts in complex systems: e.g. "the best model of a complex system is a complex system itself." It will always be necessary to analyse environmental dynamics, but the most reliable primary indicator of change comes through analysing changes in the population itself.
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Characteristics of the new modelling technique |
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The theses above open an essentially new concept on how sturgeon populations should be modelled. Realization of the concept with the help of existing technologies and traditional mathematical tools (algebra, differential and integral calculus, mathematical statistics, theory of probabilities, etc.) is practically impossible. The complex uncontrolled dynamics of the pressurized stocks under current management and laws cannot be adequately described by means of traditional mathematics (Schnute and Richards, 2001). However, one means of solving the problem would be to employ knowledge-based technologies, using the ideas and methods of artificial intelligence (Waterman, 1986).
Knowledge-based techniques were first used in ecological modelling at the end of the 1980s (Anon., 1990). In fisheries modelling, the use of such techniques has been documented by, inter alia, Aoki et al. (1989), Fuchs (1991), Saila (1992, 1996, 1997), Mackinson et al. (1999), and Mackinson (2000). However, there are limitations in using knowledge-based techniques to model poorly structured objects such as fish populations.
- Development of applied models often takes years and requires significant and continuous professional effort that is not always available.
- The phase of the process associated with the acquisition of expert knowledge inherently opens uncertainties, lowering confidence in the results.
- The modelling process is less efficient because of the cognitive features associated with working with poorly structured objects (Arbib, 1972). Modelling such objects requires less "verbal" knowledge of experts (in terms of the knowledge base of the model), but more "non-verbal" knowledge (i.e. intuition) of managers and scientists interactively working with the computer model.
To succeed in developing such knowledge-based modelling techniques for fish populations will require these restrictions to be overcome, so to do so we need to move in the direction of creating support technologies of a cognitive type (Schnute and Richards, 2001). Here I try to solve these issues by developing a transition version of the model, which I produce in the form of a problem-orientated expansion of knowledge-based technology. A list and the functions of the expansion mechanisms are reflected in the structure of the model.
Structure
The structure of models of Caspian sturgeon population dynamics will lie in problem-orientated expansion of the canonical structure of the system, based on knowledge (Waterman, 1986), i.e.
- <Structure of the model>:
- <Principles>
- <Lexicon>
- <conceptual scheme of dynamics formation>
- <Knowledge base>
- <Inference mechanism>
- <Model applications>
- <Lexicon>
- <Principles>
The structure is outlined in the sections below.
Principles
The principles of modelling are an engineering interpretation of the main theses of a new paradigm of population analysis. Here they are a multi-level hierarchy of multi-model feasibility, robustness, fuzziness, interactivity, and adaptability.
Lexicon
A lexicon is here the specialized (limited natural) language of Caspian sturgeon population analysis, for which the terms are simultaneously the formal notation for developing the specifications of the knowledge base and the inference mechanism, and their translation in applied programs (Ershov, 1985).
Conceptual scheme of dynamics formation
The "conceptual grammar" of population analysis (Schank, 1975), embodying the mechanisms of sturgeon stock dynamics, requires guidance in unfamiliar situations and assistance in making appropriate but approximate decisions under conditions of uncertainty. A discrete time t: t0; t0 + t1; ... ; t0 + tn is established, and two concepts are introduced: the condition of a population at time S(t), and the population trajectory T. Modelling population dynamics within a specified time frame is conducted by simulation and by studying its trajectory.
A schematic of the modelling procedure is given in Figure 1. The scheme is used to present the trajectory of a population's behaviour, which consists of a sequence of discrete conditions. Detailed design and review of the population model within a discrete period of time are conducted through a conceptual scheme of the life cycle of various generations (Figure 2). One peculiarity of the model is that each of its discrete conditions is formed by a closure of some initial (originating) set of facts and events. Closure is through an inference mechanism that applies current facts about and patterns within the population and its environment; these are retained in the knowledge base. The method of closure itself is not important – different methods can be applied: analytical, empirical, or heuristic. Any scheme of inductive inference developed in knowledge engineering can be used, for instance inference by analogy, inference by association, fuzzy situational inference, scenario-based inference, case-based reasoning, pseudo-physical logic-based inference, and the use of cartographic information from remote sensing systems and GIS technologies.
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). Distribution D = {Di}. Natural reproduction (NR) spawning areas: Volga, Ural, Terek, Sulak, Samur, Sefid-Rud, Kura, Araks, and Lenkoranka rivers. Artificial reproduction (AR) hatcheries (ARH): Russia, Azerbaijan, Kazakhstan, Iran, and Turkmenistan. Abiotic environmental factors influencing spawning, growth, and natural mortality A = {Ai} (i = 
). Structural and functional population characteristics S = {Si} (i = 
). Associated populations G = {Gi}, (i = 
), where 1 refers to food organisms, 2 to food competitors, 3 to predators, and 4 to parasite interactions. Interspecific relations with associated populations R = {Rij} (i = The modelling scheme is designed to solve real (poorly structured) issues of population analysis, the uncertain changing structure and condition being a priority for solution, but the laws of reproduction, growth, and mortality do not permit exhaustive analytical description.
Knowledge base
This refers to a paradigm's knowledge base (Pospelov, 1986), which contains the verbal knowledge of experts plus appropriate off-subject knowledge (of primary statistics, methods of diagnostic analysis, facts, historical events and stereotyped situations, alternative hypotheses, examples, and analogues) capable of stimulating the cognitive and creative activity of stock management.
The knowledge base (KB) is defined as KB = <D, L, M (P)>, where D refers to standard monitoring data and catch statistics, L to the patterns of natural and artificial reproduction, growth, and mortality at various stages of the life cycle, within various temporal and spatial locations in rivers and the sea, and M refers to the methods (probably several) used to solve the applications, each provided with a passport P = {Pi}, where Pi is the sections of the passport: the problem, the method annotation, the axioms (hypothesis, speculations, conditions, and application limits), the inference mechanism, basic data and their source, reference information, an estimate of adequacy, the level of development, and an archive of applications.
KB includes only information used to solve specific applications; solution of a wide range of tasks increases it. The following have been used to develop the methods:
- information on the biological basis of stock dynamics, i.e. on the biology of anadromous fish, with both one-step (spring form) and two-step (winter form) migrations (Pavlov et al., 2000);
- the results of routine research surveys conducted by CaspNIRKh (Russia), the Scientific Research Centre for Fisheries of Kazakhstan and its Atyrau affiliate, AzerNIRKh (Azerbaijan), and the International Sturgeon Research Institute (Iran);
- elements of fuzzy logic theory (Zadeh, 1973);
- modified methods of fuzzy determination analysis (single and multiple; Chesnokov, 1982);
- methods and models of knowledge engineering (Waterman, 1986; Saila, 1996);
- the principles and postulates of cognitive psychology (Kelly, 1955; Neves and Anderson, 1981; Velichkovskiy, 1992).
The roadmap used to develop the KB is:
- A fuzzy scale method of assessing population dynamics, individual fish, and environmental factors (single-parameter scales, multi-parameter situational scales; Karayev, 2001).
- A method of determination that includes the additive and multiple impact mechanisms of environmental and anthropogenic factors (varying freshwater flow, fluctuations in sea level, poaching, conditions of natural and artificial reproduction, etc.), as well as their effect on components of a generation's life cycle and the parameters of the entire population (Karayev, 2001).
- A method of determination analysis that specifies the impact of single environmental factors and/or of combined factors on various components of a generation's life cycle, as well as on parameters of the entire population (Chesnokov, 1982).
- A method of identifying environmentally permitted values of anthropogenic factors (poaching, pollution, legal fishing, etc.) in the context of agreed criteria of sustainable stock management (Bulgakov et al., 1995).
- A method of annually predicting stock biomass when historical data are incomplete (trawl and hydroacoustic surveys, catch records) and the environment is subject to seasonal variation.
Inference mechanism
An inference mechanism (IM) activates the inference control algorithm of a KB during implementation of modelling applications, i.e. IM = <I, P, A, E>, where I is the man–computer interface, P the decision planner, A the activator of methods included in the plan, and E is an explanatory component.
By means of interface I, a user gives a name to the task to be solved, enters all necessary data, supervises and corrects a course (plan) of action, receives a range of results (probably alternative ones), and comments on them to explain the course of the action. The inference mechanism therefore permits modelling the individual stages of a generation's life cycle as well as the general population dynamics. The mechanism designs a trajectory of a population's behaviour from a sequence of discrete periods. Temporally discrete values can include fishing/biological year (not calendar year), and seasonally discrete values that represent the spatio-temporal dynamics of species at various stages of their development.
Model applications
- Fuzzy (approximated) stock assessments should include multi-methods: a method of absolute stock assessment (a modified method of isolines on the basis of trawl and hydroacoustic data, with appropriate consideration given to the rarity and diffuseness of populations); a method of relative stock assessment based on analysing populations and environmental variation (the modified meta-heuristics of Nikolskiy, 1974); and a method of analogues (internal population analysis on the basis of determination).
- TACs need to be determined under conditions of uncertainty and risk resulting from extensive poaching and the currently critical condition of sturgeon populations.
- Assessment of the effectiveness of natural reproduction in the Volga and Ural rivers, the two rivers of maximum natural reproduction.
- Fuzzy (approximated) annual predictions of commercial stock size.
Stages and levels of model development
The process of developing knowledge-based models generalizes known schemes of constructing population dynamics models (e.g. Beverton and Holt, 1957; Ricker, 1958; Varley, 1962; Horafas, 1967; Nikolskiy, 1974). It includes identification, conceptualization, formalization, implementation, and testing.
At the identification stage, a model developer together with fisheries scientists identifies the problems to be solved in the population analysis, and very importantly, their scope. Questions to be answered include: are we developing a model for the entire Caspian, or a set of models for each species of sturgeon, beluga, Russian sturgeon, Persian sturgeon (Acipenser persicus), stellate sturgeon (A. stellatus), and ship sturgeon (A. nudiventris), or are we developing a set of models for each subpopulation that inhabits a certain part of the sea: Volga–Caspian, Ural–Caspian, Kura–Caspian, Iranian waters? According to current experience, the second modelling approach would seem to be most appropriate.
At the conceptualization stage, model developers and fisheries scientists identify the concepts, relationships, and inference mechanisms required to solve the problems. Sub-problems, scenarios, and limits of the KB compilations should also be reviewed.
At the formalization stage, key concepts and relationships within the population dynamics are expressed in a formal manner, usually within the framework of a selected knowledge presentation language (semantic networks, frameworks, production rules, object-orientated languages, neural networks, cognitive maps, etc.).
At the implementation stage, model developers transform the formalized knowledge into operating software. Realization has to be swift, because one of the objectives of implementation is to check decisions taken at previous stages. It is connected to the specifics of KB models, that there is a probability that the original program will be changed or even rejected during further development. It is worth noting that availability of vocabulary and open structure allow for gradual computerization of the model, from completely manual to completely computerized.
Testing includes validation and verification of a model, as well as its revision, if necessary, and assessment of its utility. Validation and verification mean that certain key questions have to be answered. For example, does the model adequately represent the biology of a certain species of sturgeon and its relationships with the environment? Does it appropriately describe historical events in the dynamics of sturgeon exploitation and management in the Caspian Sea? Does it allow identification of major natural and anthropogenic factors and their significance, whether they are critical for the population now or may be critical in future? Finally, does it cover all possible eventualities of population dynamics, and does it estimate possible situations that may be critical to the populations?
A different range of questions is set while assessing a model's utility. For instance, does the model offer non-standard solutions that are not familiar to fisheries scientists, but acceptable from a biological perspective? Are the inferences logical and understandable, and is the detail provided sufficient? Finally, does the model demonstrate an ability to simulate intuition?
Development of a knowledge-based model is completely different from developing algorithmic models. Having compiled a conceptual scheme, the developer needs to build a knowledge base and inference mechanisms on the basis of his scheme. The process is difficult and time-consuming, develops continually, and is at a number of levels, usually four: demonstration, research prototype, testing, and operation. The demonstration version needs to show that the model can solve some problems of population dynamics, and to prove that the approach is appropriate and that the model can be produced. The research prototype would be a program of medium size that can demonstrate its utility in producing reliable results for the whole problem, but is not yet reliable because of incomplete testing. A model being tested is generally of quite high quality and fairly reliable. It should be able to pass a complete suite of tests and be robust, insensitive to changes in the basic biological and environmental axioms. Operating models will have been completely tested, maintained, and approved by relevant fisheries organizations and institutes.
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Example of a model application: assessment of the current effectiveness of natural reproduction by sturgeon |
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Current method
Currently, an indicator of Possible Commercial Return (PCR), calculated by an empirical formula (Alekhina and Finayeva, 2001) is being used to assess the effectiveness of natural reproduction:
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The deficiencies of the PCR assessment method are:
- the result cannot be used in direct assessment of the commercial return, the way it is applied in many reports; it can only be referred to as an output of a consultation that describes possible harvesting of the generation in a single river;
- the formula is an attempt by its developers to compress empirically the factors that impact natural reproduction, but such compression does not include natural reproduction and is illogical, confirmed simply by checking the dimensions;
- if the environment and the condition of the stock change, the factors impacting natural reproduction and their significance can also change; for instance, between 1990 and 1999, when average summer flow of the Volga River was high, the factors that dominated the impact of restocking became the number of breeders, the female proportion, and the fecundity of the whole population;
- by default, the formula assumes that the environment and its stocks are stable at the time of harvesting;
- the formula provides a spot assessment of the PCR and does not consider the reality that (M, N, W)
R multiplied by coefficient K will be adjusted for possible changes in the lifetime of a generation.
New method (assessing the effectiveness of natural reproduction, and fuzzy situational inference)
Method conceptualization
Modelling technology on the basis of knowledge allows assessment of the effectiveness of natural reproduction in compliance with the principle of data development and comparative assessment of the PCR, which in turn reflects the cognitive mechanisms of identification and extrapolation (Neves and Anderson, 1981; Velichkovskiy, 1992). Therefore, the new method of assessing the effectiveness of natural reproduction is based on the following theses:
- The assessment is based on multiple reference situations taken from monitoring statistics (the method of reference images; Velichkovskiy, 1992).
- Each reference situation includes a range of the major factors and an assessment of the PCR; their combination is the situational model of natural reproduction.
- Reference situations are developed on the basis of approximated (according to Zadeh, 1973) assessments of those factors that are fuzzy in terms of parameters, but structurally true (M, N, W) R (the fuzzy situational model of natural reproduction).
- The PCR is assessed by a system of fuzzy situational inference (Karayev et al., 2000). The fuzzy current situation of natural reproduction is classified into multiple reference fuzzy representations; the closest to the reference situation is then identified by means of a proximity test and a three-step selection scheme. Assessment of the PCR of the reference situation is accepted as the PCR for the current situation, with certain probability. It is of course possible that none, or two or more, of the close reference situations will be found, so final selection and research needs to be conducted by the decision-maker.
Method formalization
Let us suppose that there are representative statistics (Table 1) which, according to fisheries scientists and ichthyologists, can be used for comparative assessment of the effectiveness of natural reproduction (i.e. PCR) in year t0.
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The original data for the current year t0 are M0 = 1.2 g, N0 = 0.6 per trawl, and W0 = 105 km3. I now present the situation for each year in Table 1 as a fuzzy situational model (FSM). In order to do this, I use the definition of a linguistic variable given by Zadeh (1973) and the fuzzy situational inference technique. The linguistic variable is described as <ß, T, X, F>, where ß is the linguistic variable, T a term-set of linguistic (verbal) values of the variable, X the range of definition (quantitative scale) of each of the verbal values of the variable, and F is a semantic rule that allocates a membership function identified through X against each verbal meaning.
For instance, a linguistic variable of the parameter "river flow"(W) will be presented as: <"Flow", T, [50, 150], F>, where T= {LOW_FLOW, MIDDLE_FLOW, HIGH_FLOW}, and F is a membership function of these verbal values of linguistic variable (Figure 3) identified by the base scale 50/150 (km3). The linguistic variables for M, N, and R are identified in a similar manner. Thus, a linguistic variable is identified on a numerical scale, but it possesses a verbal value in a natural language. Linguistic variables and their values are therefore used for qualitative verbal description of a quantitative value. It is important that any linguistic variable and its verbal values be related to some numerical (base) scale. Linguistic variables allow formalization of quantitative information on an object presented verbally by fisheries scientists and ichthyologists. To comply with the above definitions, a fuzzy situational model is developed for each year listed in Table 1, e.g.,
- Natural reproduction FSM (1980): {M/<0.6/LOW>; N/<0.95/HIGH>; W/<0.4/MIDDLE>};
- Natural reproduction FSM (t0): {M0/<0.6/MIDDLE>; N0/<0.7/MIDDLE>; W0/<0.27/MIDDLE>}.
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Assessment of the PCR for the current year is made through fuzzy situational inference (Karayev et al., 2000), the procedure for which implements fuzzy classification of FSM (t0) of the current year on the set FSM (1977) ÷ FSM (1983).
In order to identify situations close to the current one, a degree of fuzzy proximity, 
(t0, 19XX) ( = 
), is used. Candidates for the reference situations are identified in a three-level scheme:
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> 0.5 (for instance, = 0.6 ÷ 1.0) are selected as reference ones, and can be used to forecast the PCR for a specific year.
Method implementation
The knowledge base required for this task includes the statistics of the parameters for natural reproduction (e.g. Table 1), the linguistic variables M, N, W, and R, algorithms for constructing the linguistic variables and the fuzzy situational model, and an algorithm for fuzzy situational inference. The input data are M0, N0, and W0. The inference mechanism is implemented by the following succession:
- Step 1. The FSMs for each year in Table 1 (from 1977 to 1983) are developed using the FSM algorithm and linguistic variables M, N, and W.
- Step 2. The FSM (t0) for the current year is developed in the same manner.
- Step 3. The FSM (t0) is classified by the fuzzy situational inference algorithm on the set FSM (1977) ÷ FSM (1983), i.e. the proximity of the current situation to each of the situations between 1977 and 1983 is identified {
(t0, 19XX)}.
- Step 4. A three-level scheme is used to select situations where
(t0, 19XX) > 0.5. For this example, (t0, 1977) = 0.31, (t0, 1978) = 0.42, (t0, 1979) = 0.37, (t0, 1980) = 0.41, (t0, 1981) = 0.15, (t0, 1982) = 0.67, and (t0, 1983) = 0.51. (Values of > 0.5 are emboldened.)
- Step 5. The situation with the greatest proximity is then selected from the emboldened ones, i.e.
(t0, 1982) = max.
- Step 6. The PCR in this situation is presented as a possible value of the PCR for the current year, i.e. R(t0)
R(1982) 3200 t {R < 0.89/MODERATE>}.
- Step 2. The FSM (t0) for the current year is developed in the same manner.
Discussion of the new method
The fuzzy situational inference method has a range of benefits, important for practical use:
- The fuzzy situational model of natural reproduction is open to change and can be extended or updated by changing factors and their assessment scales.
- The PCR is calculated not through a formal empirical scheme, but on the basis of real and/or near-real situational models that are developed within certain spatial and temporal limits, and which give due consideration to the environment and the status of the population within those limits. The models are stable within the same limits.
- Unlike the traditional PCR assessment based on a reduction principle, the fuzzy situational model is based on the principle of statistical data development, allowing intuitive extrapolation and interpretation from previous experience.
- The logic of fuzzy situational inference is similar to the natural human thinking process, encouraging extrapolation and interpretation.
- If made more complicated by adding a weighting coefficient, the model for natural reproduction can also consider the impact of individual factors on its effectiveness.
- In approximated (fuzzy) form, due consideration can also be given to changes that may take place in the environment before the generation can become part of the catch.
- Fuzzy situational inference can be presented as a system command shell that can be adjusted to specific conditions of single spawning areas (e.g. Volga, Ural, Terek, Kura, and Sefid-Rud rivers) and various periods (a list of the main factors that can be included in the shell is given in Table 2).
- The suggested method is universal, although not in the accepted sense of the word; it cannot be applied directly to any river and period of time. However, it is universal in that it can adjust the system shell to the condition of a river in a period of time, and also to the hypothesis of the researcher to enable him to solve his task with the help of the available inference mechanism. In knowledge-based models, unlike in traditional mathematical models, the data are separate from the algorithm, so the algorithm of fuzzy situational inference does not need to change.
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Capacity of knowledge-based models |
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Traditional mathematical models have some significant deficiencies:
- biological and environmental assumptions made by the researcher are implicit in the model, so even minor changes unavoidable in population analysis may appear to be crucial to applying the model;
- it is practically impossible to conduct multi-factor modelling; in most known models, it is replaced by single-factor modelling and the values of some factors are fixed;
- there is no capacity to model qualitative (non-numerical) relationships, which dominate research into poorly structured populations;
- there is no interaction between the model and the person operating it; in the case of uncertainty, that person becomes an integral and active component of the modelling;
- the language of mathematical models is usually difficult to understand for those not well versed in mathematics, generating the distrust of non-mathematicians in the results of such models.
Knowledge-based models do not have these deficiencies. However, they require thorough, time-consuming development of the knowledge base. An important advantage is the fact that they permit systematization of original monitoring data and presentation in a compact knowledge-based format that can be used for both strategic and tactical analysis. In the context of current fisheries research, at least four important issues relating to the use of knowledge-based models can be listed:
- they can amend, sometimes even replace, basic scientific research;
- they can provide a development technology for multi-model (non-universal) methods of stock assessment, TAC and quota allocation, and for predicting the PCR;
- they can be used to help coordinate future research, in this case in the Caspian Basin;
- they provide the technology for the archiving and use of important information as expert knowledge, which may be irretrievably lost if it is not documented.
In my opinion, therefore, a new paradigm of population analysis and knowledge-based models can open a fresh page in the theory of fisheries management in general, and of Caspian sturgeon fisheries in particular.
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Acknowledgements |
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I thank G. B. Cleiner and R. M. Kachalov of CEMI (the Central Economics and Mathematics Institute) of the Russian Academy of Sciences, N. G. Bulgakov of the Faculty of Biology of Moscow State University, and Z. M. Kuliev, formerly of AzerNIRKh, the Azerbaijan Fisheries Research Institute, for their support, advice, and interest in this work. I further acknowledge the input of Russian and Kazakh colleagues in providing me additional understanding of sturgeon issues and problems; such information is the foundation of knowledge-based models and helps define their adequacy. Finally, I acknowledge with thanks the constructive comments on the submitted manuscript of Saul B. Saila and an anonymous reviewer, which itself had benefited from extensive English language correction by the Journal editor, Andrew I. L. Payne.
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