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Article information
2021 , Volume 26, ¹ 2, p.21-43
Perevaryukha A.Y.
Simulation of three variants of population dynamics with large reproductive potential in a new environment
The research addresses mathematical description of three nontrivial avenues for development of population processes. Such events arise after invasions of aggressive species. Invasive processes do not lead to an equilibrium (stable balance) between ecosystems and the environment or regular cyclical changes. The method we have chosen allows simulation of several variants for the reaction of the environment to the appearance of a competitor with a large reproductive potential. We discarded the idea of interpreting the balance capacity of the ecological niche, but used threshold levels for the reaction of the environment instead. We have proposed models based on equations with delayed regulation and delayed activation of counteraction for the dynamics of invasive populations in an environment without mechanisms controlling their reproduction. Some species, when introduced into a new habitat, are able to demonstrate nonstationary and extreme regimes of growths due to uncompensated reproductive activity. The species with a large 𝑟-parameter deplete significant resources they need to live, which make stable development impossible, including orbitally stable cycles. We have developed new equations that describe the following scenarios: 1) boom-bust dynamics stabilization at the level of a small group after a single outbreak is the most common scenario for insect pests; 2) the destruction and disappearance of the invader during the oscillatory dynamics and with the regulation with delayed external pressure; 3) scenario for a threshold crisis — successful passage of a population with a logistic increase in the subcritical minimum while adapting to a suddenly intensified confrontation. It is a frequently observed variant that confirmed by experiments with bacterial colonies. The third variant of our modification of the equation describes the most interesting scenario of interspecies interaction with threshold regulation. Development of simulated situation here ends up in stable state after the deep crisis during phase of rapid growth of the population size. We substantiated the model scenario based on experimental data for introduction of the bacteriophage virus into bacterial colony with the CRISPR-Cas mechanism. Our models can be used to study variability of the immune response
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Keywords: computational scenarios of invasive processes, regulation and phenomenon of time lag in ecology, modelling of oscillations, biological suppression of invading species, crisis of aggressive population, excess value of r parameter, CRISPR-Cas adaptation
doi: 10.25743/ICT.2021.26.2.003
Author(s):
Perevaryukha Andrey Yuryevich
PhD.
Position: Senior Research Scientist
Office: St. Petersburg Federal Research Center of the Russian Academy of Sciences
Address: 197110, Russia, St-Petersburg, 14-line 39
E-mail: temp_elf@mail.ru
SPIN-code: 6070-5310 References:
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Perevaryukha A.Y. Simulation of three variants of population dynamics with large reproductive potential in a new environment // Computational technologies. 2021. V. 26. ¹ 2. P. 21-43
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