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Mathematical Modeling of Evolutionary Dynamics
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Mathematical Modeling of Evolutionary Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 6199

Special Issue Editors

Prof. Dr. Efim Ya. Frisman

E-Mail Website
Guest Editor
Institute for Complex Analysis of Regional Problems, Far Eastern Branch, Russian Academy of Sciences, Birobidzhan 679016, Russia
Interests: population genetics; evolutionary biology; mathematical ecology; predator–prey interactions; ecogenetic dynamics; optimal harvest problems; mathematical modelling; nonlinear dynamics
Dr. Oksana L. Zhdanova

E-Mail Website
Guest Editor
Institute for Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, Vladivostok 690041, Russia
Interests: population genetics; population dynamics; mathematical modelling; numerical analysis; predator–prey interactions; ecogenetic dynamics

Special Issue Information

Dear Colleagues,

Basic concepts of general biology considering population evolution and ecosystem dynamics were developed with the idea that ecology can influence evolution and vice versa, even over short timescales—i.e., ecological and evolutionary processes are interrelated. In particular, the author of evolutionary theory, Charles Darwin; the creators of the “genetic” evolutionary synthesis R. Fisher, S. Wright, J. Haldane, and S.S. Chetverikov; and the founders of theoretical ecology (dynamic theory of ecosystems), P. Verhulst and V. Volterra (as well as G.F. Gauze), recognized the intertwined nature of ecological and evolutionary processes. Later, the perception that evolution and ecology happened on very different time scales became widely accepted. It took several decades to experimentally confirm that natural selection based on life history and genetic variation can influence population dynamics. As a result, there has recently been a higher level of research interest in eco-evolutionary dynamics. There has still been no complete synthesis of ecological and genetic theories and ideas. Meanwhile, the ecological-genetic approach provides new prospects for understanding the evolutionary dynamics of natural populations and communities; moreover, it allows for predicting changes associated with altering external conditions and anthropogenic impacts.

This Special Issue aims to select and publish original research articles, review papers, and perspective papers presenting achievements in the theory and applications of mathematical models in various fields of evolutionary dynamics.

We look forward to receiving your contributions.

Prof. Dr. Efim Ya. Frisman
Dr. Oksana L. Zhdanova
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • population dynamics
  • community dynamics
  • eco-evolutionary dynamics
  • population genetics
  • nonlinear dynamics
  • multistability
  • numerical analysis
  • natural selection

Published Papers (6 papers)

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Research

24 pages, 4215 KiB  
Article
The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations
by Oksana Revutskaya, Galina Neverova, Oksana Zhdanova and Efim Frisman
Mathematics 2023, 11(24), 4971; https://doi.org/10.3390/math11244971 - 15 Dec 2023
Viewed by 646
Abstract
This paper proposes and studies a discrete-time model for a sex-structured population with non-overlapping generations under density-dependent regulation of survival. The population is assumed to have genetic variety among individuals in terms of reproductive potential, controlled by a single autosomal diallelic locus. We [...] Read more.
This paper proposes and studies a discrete-time model for a sex-structured population with non-overlapping generations under density-dependent regulation of survival. The population is assumed to have genetic variety among individuals in terms of reproductive potential, controlled by a single autosomal diallelic locus. We consider a panmictic population with Mendelian inheritance rules. We examine the stability model and show that increasing the average value of reproductive potential destabilizes the population dynamics. The scenario of stability loss in fixed points via period doubling or Neimark–Sacker bifurcations depends on the intensity of the self-regulation. The growth rate at which the population survives and develops is shown to depend on the fitness of the genotypes and the secondary sex ratio. As a result, the asymptotic genetic composition of the population is determined by the values of the reproductive potentials of the heterozygote and homozygotes, the initial conditions, and the parameter describing the ratio of newborn females to males. With disruptive selection, the influence of external factors changing the current genetic composition of a population can alter the direction of evolution and lead to the extinction of a successful developing population or a gradual population recovery due to evolutionary rescue after a noticeable decline in its abundance. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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18 pages, 1496 KiB  
Article
Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility
by Yuri V. Tyutyunov
Mathematics 2023, 11(15), 3378; https://doi.org/10.3390/math11153378 - 2 Aug 2023
Cited by 3 | Viewed by 1096
Abstract
Combining explicit modelling of predator movements with the Kostitzin demo-genetic equations, we study conditions promoting natural selection of consumer motility. The model is a system of partial differential equations describing spatial movements of predators pursuing the diffusing prey. Local predator–prey interactions are described [...] Read more.
Combining explicit modelling of predator movements with the Kostitzin demo-genetic equations, we study conditions promoting natural selection of consumer motility. The model is a system of partial differential equations describing spatial movements of predators pursuing the diffusing prey. Local predator–prey interactions are described by the classical Rosenzweig–MacArthur model, which additionally accounts for the Allee effect affecting reproduction of predators. Spatial activity of predators is determined by the coefficients of diffusion and indirect prey-taxis. The latter characterizes the predator ability to move directionally up the gradient of taxis stimulus (odor, pheromone, exometabolite) continuously emitted by prey. Assuming that the consumer movement ability is governed by a single diallelic locus with recessive ‘mobile’ and dominant ‘settled’ alleles, the predator population in the model consists of three competing genotypes differing by diffusion and taxis coefficients; other parameters characterizing the genotypes are assumed to be equal. Numerical simulations with different spatial patterns imitating habitat deterioration demonstrate that the direction of selection among the consumer genotypes alternates, depending on the degree of habitat deterioration affecting the overall production of the prey population. Theoretical implications of the results are discussed in relation with problems of biological control, predator interference, and evolution of animal motility. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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22 pages, 3741 KiB  
Article
The Evolutionary Mechanism of Formation of Biosphere Closure
by Sergey Bartsev and Andrey Degermendzhi
Mathematics 2023, 11(14), 3218; https://doi.org/10.3390/math11143218 - 21 Jul 2023
Cited by 2 | Viewed by 1013
Abstract
In accordance with the ideas of V.I. Vernadsky, the Earth’s biosphere can exist only because of the high degree of closure of the cyclic matter transformations carried out by all living organisms by using the energy from the Sun. In the course of [...] Read more.
In accordance with the ideas of V.I. Vernadsky, the Earth’s biosphere can exist only because of the high degree of closure of the cyclic matter transformations carried out by all living organisms by using the energy from the Sun. In the course of its evolution, the Earth’s biosphere has undergone a number of cardinal transformations, but, at least for the last 20 million years, the gas composition of the atmosphere, and primarily the concentration of carbon dioxide, has remained practically unchanged. Nevertheless, the high degree of closure of material flows in the Earth’s biosphere seems paradoxical, since closure is not an adaptive feature of an individual undergoing natural selection for traits that give an advantage here and now (the Vernadsky–Darwin paradox). The stages in the formation of the closure of the Earth’s biosphere are considered in the context of four epochs that differ in the energy available to living organisms: (1) geochemical energy; (2) solar energy; (3) energy of oxidative phosphorylation; and (4) consumption of living flesh, predation. The paper considers possible options for resolving the VD paradox using as the example models of closed ecological systems (CES) with low species diversity. The fundamental inapplicability of ecological models with rigid metabolism for the description of CES is shown. Three mechanisms for resolving the VD paradox are proposed and the conditions for their implementation are assessed: (1) a stochastic mechanism: random selection of closing organisms (decomposers) with the corresponding stoichiometric ratios; (2) changing the consumption stoichiometry by switching catabolic pathways to different types of substances (proteins, fats, carbohydrates); and (3) changing the consumption stoichiometry by choosing food, depending on the state of internal nutrient pools. The present study leads to the conclusion that the Vernadsky–Darwin paradox can be resolved in nature by combining the mechanisms that simultaneously provide both a current competitive advantage and the ability to close trophic chains with a wide variation in the composition of material flows. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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21 pages, 6364 KiB  
Article
Control Factors for the Equilibrium Composition of Microbial Communities in Open Systems: Theory and Experiments
by Andrey Degermendzhi and Alexander Abakumov
Mathematics 2023, 11(14), 3183; https://doi.org/10.3390/math11143183 - 20 Jul 2023
Viewed by 674
Abstract
The present paper is a summary of the authors’ theoretical and experimental research dealing with the patterns of stable equilibrium coexistence of microbial populations in flow systems interacting through specific density-dependent growth regulators (RFs). The discovered “paradoxical” lack of dependence of the background [...] Read more.
The present paper is a summary of the authors’ theoretical and experimental research dealing with the patterns of stable equilibrium coexistence of microbial populations in flow systems interacting through specific density-dependent growth regulators (RFs). The discovered “paradoxical” lack of dependence of the background steady-state levels (concentrations) of RFs on their input values is confirmed experimentally and theoretically through the introduced sensitivity coefficients. This effect has been termed “autostabilization” of RFs. An important theorem (formula) of “quantization” suggesting the integer value of the sum of all sensitivity coefficients, which is equal to the difference between the number of RFs and the number of populations of one trophic level, has been proven. A modification of the “quantization” formula for an arbitrary trophic web is shown. A new criterion for intra- and inter-population microbial interactions for RFs is proposed—the response of growth acceleration to a perturbation in population size. This criterion makes it possible to quantify interspecific complex relationships, which has been previously impossible. The relationship between the new coefficients of inter-population interactions and the accuracy of model verification has been shown theoretically. Based on this criterion and the autostabilization effect, a method for experimental search for unknown RFs is proposed. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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24 pages, 13264 KiB  
Article
Role of Photosynthesis Processes in the Dynamics of the Plant Community
by Alexander Abakumov and Svetlana Pak
Mathematics 2023, 11(13), 2924; https://doi.org/10.3390/math11132924 - 29 Jun 2023
Viewed by 1118
Abstract
The dynamics of the main photosynthetic structures are studied by mathematical modeling methods in this work. Chlorophyll portion variability in phytoplankton and formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their [...] Read more.
The dynamics of the main photosynthetic structures are studied by mathematical modeling methods in this work. Chlorophyll portion variability in phytoplankton and formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are conducted to simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models are tested for biological adequacy, and their effectiveness is compared. For the model selected as a result of the comparison, the optimal control problem was formulated and solved. This way reduces the space of the initial components of the model system. The main conclusion is that a step-by-step description of photosynthetic transformations gives a result close to the experimental description of phytoplankton production dynamics. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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12 pages, 302 KiB  
Article
On Oscillations in a Gene Network with Diffusion
by Vladimir Golubyatnikov, Natalia Ayupova and Natalia Kirillova
Mathematics 2023, 11(8), 1951; https://doi.org/10.3390/math11081951 - 20 Apr 2023
Cited by 1 | Viewed by 864
Abstract
We consider one system of partial derivative equations of the parabolic type as a model of a simple 3D gene network in the presence of diffusion of its three components. Using discretization of the phase portrait of this system, comparison theorems, and other [...] Read more.
We consider one system of partial derivative equations of the parabolic type as a model of a simple 3D gene network in the presence of diffusion of its three components. Using discretization of the phase portrait of this system, comparison theorems, and other methods of the qualitative theory of differential equations, we show uniqueness of the equilibrium solution to this system and find conditions of instability of this equilibrium. Then, we obtain sufficient conditions of existence of at least one oscillating functioning regime of this gene network. An estimate of lower and upper bounds for periods of these oscillations is given as well. In quite a similar way, these results on the existence of cycles in 3D gene networks can be extended to higher-dimensional systems of parabolic or other evolution equations in order to construct mathematical models of more complicated molecular–genetic systems. Full article
(This article belongs to the Special Issue Mathematical Modeling of Evolutionary Dynamics)
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