Recognition of evolutionally stable behavioral strategy features

Kuzenkov O.A., Kuzenkova G.V.

Lobachevsky state University of Nizhny Novgorod, nstitute of information technologies, mathematics and mechanics, Russia, 603950, Nizhny Novgorod, Gagarina Ave. 23

One of the problems of modern biology is to study the quantitative and qualitative features of the zooplankton daily vertical migrations. The phenomenon of daily vertical movements of aquatic organisms has been studied by many scientists both empirically and theoretically for almost two hundred years, but the mechanisms that shape the features of migration behavior are still not fully understood. This is due to the wide variety of such migrations and the complexity of building the corresponding mathematical models. The purpose of this work is to create software for recognizing the quantitative and qualitative features of evolutionary stable strategies for daily vertical migrations of zooplankton.

The methodological basis of the investigation is an extreme principle of maximum fitness function. It is assumed that only that behavior strategy is realized in a population after a long period of evolution that provides it with the greatest fitness. The function of fitness is understood as the average temporal value of the coefficient of reproduction.

A mathematical model of population dynamics was proposed, and a numerical algorithm for calculating the optimal strategy on the base of variation calculus, as well as its approximation by a sinusoid, was implemented. The initial data for the algorithm are data on environmental conditions: the amount of food, the influence of the predator, the temperature distribution depending on the depth of immersion and the time of day. The obtained numerically solution is analyzed for the presence of an important qualitative feature: the implementation of pronounced vertical migrations against the background of random interference.

The work was supported by the Ministry of education and science of the Russian Federation (Project No. 14.Y26.31.0022).


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