Samara, Samara, Russian Federation
Krasnodar, Krasnodar, Russian Federation
The paper considers mathematical models of the evolution of new biological species from a common ancestor, depending on the adaptability to the environment in the presence of a particular trait in the genotype. Equations describing the change in the number of individuals with dominant and recessive traits, taking into account their fertility, are presented. The calculation of the time for which the population of the species consumes vital environmental resources has also been made. Within the framework of this model, the growth rate of the population in conditions of a shortage of a food source is investigated. A mathematical model of the population growth of the species, the limits of applicability and methods of its continuation using equations describing the factor of population decline due to sudden changes in the environment are presented and described. The article presents criteria for the applicability of critical points of one mathematical model as initial conditions for another. The results of the calculations can be used in the framework of population genetics, as well as for environmental studies. On their basis, it is possible to make assumptions about the possibility of further evolutionary development of a biological species.
Driving forces of evolution, mathematical modeling, emergence of new species from a common ancestor, bottleneck effect
1. Lyubich Yu.I. Basic concepts and theorems of evolutionary genetics of free populations. Successes of Mathematical Sciences, 1971, vol. 26, no. 5(161), pp. 51-116 (In Russ.).
2. Atassi A.N., Khalil H.K. A separation principle for the stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 1999, vol. 44, no. 9, pp. 1672-1687.
3. Rassadina E.V., Antonova Zh.A. Ecology of populations and communities. Teaching aid, 2015 (In Russ.).
4. Perevaryukha A.Yu. Scenarios for the passage of the “bottleneck” state by an invasive species in a new model of population dynamics. Izvestiya of higher educational institutions. Applied nonlinear dynamics, 2018, vol. 26, no. 5, pp. 63-80 (In Russ.).
5. Perevaryukha A.Yu. Scenarios of oscillations and mortality in a new continuous model of the eruptive phase of invasion of an alien species. Mathematical physics and computer modeling, 2019, no. 1 (In Russ.).
6. Trubetskov D.I. Phenomenon of the mathematical model of Lotka-Volterra and similar ones. Izvestia of higher educational institutions. Applied nonlinear dynamics, 2011, vol. 19, no. 2, pp. 69-88 (In Russ.).
7. Caplat P., Coutts S., Buckley Y.M. Modeling population dynamics, landscape structure, and management decisions for controlling the spread of invasive plants. Annals of the New York Academy of Sciences, 2012, vol. 1249, no. 1, pp. 72-83.
8. Hamilton M.B. Population genetics. John Wiley & Sons, 2021.
9. Hartl D.L., Clark A.G., Clark A.G. Principles of population genetics. MA: Sinauer associates, 1997, vol. 116, 542 p.
10. Henson S.M. Nonlinear population dynamics: models, experiments and data. J. theor. Biol., 1998, vol. 194, pp. 1-9.
11. Barros L.C., Bassanezi R.C., Tonelli P.A. Fuzzy modelling in population dynamics. Ecological modelling, 2000, vol. 128, no. 1, pp. 27-33.
12. Peach M.B., Rouse G.W. Phylogenetic trends in the abundance and distribution of pit organs of elasmobranchs. Acta Zoologica, 2004, vol. 85, no. 4, pp. 233-244.
13. Perevaryukha A.Yu. Modeling fluctuations of aggressive alien species in continuous models with independent regulation. Bulletin of Samara University. Natural Science Series, 2018, no. 4 (In Russ.).
