Development of the dynamic model of reproduction of sturgeon fish from the structural analysis of ecosystem processes

A. Yu. Perevaryukha

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 47 (2016) no. 1, pp. 34-43

Résumé

The article presents the formation of a species-specific dynamic model of the reproductive cycle of the population developed from the analysis of the conceptual graph model. Structural “Cognitive digraph” proposed previously interpreted the cumulative impact of a set of factors on the trouble of fishing of sturgeon stocks of the Caspian Sea fish. All known functions for calculation of the efficiency of reproduction do not contain preconditions for the implementation of such safety critical situations under slight excess of $\delta h$ allowable exemptions. We assumed the crucial role of overestimation of reproductive potential by fishing forecasts and implemented a new model. The proposed ODE system includes interconnected velocity of decrease in the number of generations of fish and the rates of individual development, which corresponds to the reduction of the productivity Allen curve. On the basis of numerical solution of differential equations we have obtained functional dependence, for which discrete iterations lead to the emergence of a stable cycle $p=2$ with the existence of an unstable state of equilibrium. The threshold point is attainable only under the external influence and realizes the situation of disproportionately significant reduction in reproductive efficiency. In the case of the Volga sturgeon Acipenser stellatus, this phenomenon has not been compensated by the artificial release of juvenile fish. All the characteristics of the operating system we obtained allow us to describe the character of the rapid degradation of the population, which was previously withstanding a huge catch for along time. Delayed decision to stop fishing leads to long-term degradation of biological resources. Restoring the abundance of fish is possible in the distant future at the expense of the least depleted in the new environment and partially isolated subpopulation groups. Accounting for the introduction of juvenile sturgeon technology by using a pulse action on the variables of the model shows a purely limited effectiveness. We have posed previously unknown scientific problem about the reasons for differences in reproduction curves closely related species of sturgeon.

Détail

Mots-clés : simulations of populations
Keywords: sturgeon of the Caspian Sea, overfishing, structuring feedback of ecosystems, threshold effects, unstable equilibrium.