Construction of the fitness function depending on a set of competing strategies based on the analysis of population dynamics

Abstract

The purpose of this work is to construct a fitness function that depends on the set of coexisting competing hereditary elements based on population dynamics in the “predator– prey” model with the logistic growth of prey. Materials and methods. The work uses the generalized Volterra model. The planktivorous fish plays the role of a predator. Many different species of zooplankton are considered as prey, which differ from each other in the hereditary strategies of daily vertical migrations. The model takes into account the intraspecific competition of prey. The peculiarity of the model consists of the presence of pairs of hereditary strategies in which the carriers of the first can displace the carriers of the second and vice versa — the carriers of the second can displace the carriers of the first, depending on the set of competing strategies in which they coexist. To restore the fitness function, the ranking method is used, which is reduced to the classification of ordered pairs of hereditary strategies into two classes “the first strategy displaces the second” and “the second displaces the first”. Results. The article presents a new methodology for constructing the fitness function. The technique involves two stages. First, the fitness function is reconstructed for a certain finite subset of elements on the basis of processing data on the long-term dynamics and comparing their competitive advantages. At the second stage, the form of the fitness function is derived for an arbitrary set of elements. It uses the features of interspecies interaction reflected in the model. With the help of the constructed fitness function, an evolutionarily stable regime of daily vertical migrations of zooplankton is modeled by numerically solving the minimax problem. Conclusion. The proposed method for constructing a fitness function that depends on a set of competing strategies is quite general and can be applied to a wide range of models of population dynamics. The strategy of diel vertical migrations of zooplankton constructed as a result of modeling is in good agreement with empirical data.