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Mathematical Modeling for Population Dynamics and Evolutionary Dynamics
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Mathematical Modeling for Population Dynamics and 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 9081

Special Issue Editor

Dr. Galina P. Neverova

E-Mail Website
Guest Editor
Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia
Interests: ecosystem ecology; population dynamics; density-dependent regulation; modifying factors; natural selection; nonlinear dynamics; multistability

Special Issue Information

Dear Colleagues,

Mathematical modeling is a widely-used tool for studying the dynamics of population size and its genetic composition over time. Ecosystem functioning and its persistence significantly depend on population and evolutionary dynamics. Mathematical modeling allows us to investigate these processes, taking into account factors such as fertility rates, mortality rates, migration patterns, interspecies interaction, natural selection, and genetic mutation, and make predictions about how populations will change in the future. In recent years, there has been an increasing focus on using mathematical models to understand the impacts of human activities, such as habitat destruction and climate change, on population dynamics. In addition, there has been a trend towards the development of more sophisticated modeling techniques that take into account the complexity of real-world systems, including interspecific interactions and the influence of the environment. These advances in modeling will continue to enhance our understanding of population and evolutionary dynamics and allow us to make informed management decisions.  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 Population Dynamics and Evolutionary Dynamics.

Dr. Galina P. Neverova
Guest Editor

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Keywords

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

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Published Papers (7 papers)

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Research

28 pages, 5839 KiB  
Article
Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect
by Oksana Revutskaya, Galina Neverova and Efim Frisman
Mathematics 2024, 12(4), 535; https://doi.org/10.3390/math12040535 - 8 Feb 2024
Cited by 1 | Viewed by 766
Abstract
This study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number [...] Read more.
This study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number of breeding pairs. The growth rate is regulated by limiting juvenile survival, where an increase in population size decreases the survival of immature individuals. We consider the following selective proportional exploitation: harvesting of juveniles and harvesting of mature males. Depending on the values of population parameters, selective harvesting can lead to the stabilization of population dynamics by dampening oscillations or the emergence and amplification of fluctuations in population size. The model reveals multistability domains in which different dynamic modes coexist, and variations in initial conditions can lead to changes in dynamic modes. Depending on the values of the population parameters, the proposed models with harvest reveal the hydra effect, indicating an increase in the equilibrium abundance of the exploited group after reproduction but before harvesting, with an increase in the harvesting rate. Selective harvesting, resulting in the hydra effect, increases the remaining population size due to reproduction and the number of harvested individuals. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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22 pages, 699 KiB  
Article
Mathematical Modeling of Two Interacting Populations’ Dynamics of Onchocerciasis Disease Spread with Nonlinear Incidence Functions
by Kabiru Michael Adeyemo, Umar Muhammad Adam, Adejimi Adeniji and Kayode Oshinubi
Mathematics 2024, 12(2), 222; https://doi.org/10.3390/math12020222 - 9 Jan 2024
Viewed by 956
Abstract
The transmission dynamics of onchocerciasis in two interacting populations are examined using a deterministic compartmental model with nonlinear incidence functions. The model undergoes qualitative analysis to examine how it behaves near disease-free equilibrium (DFE) and endemic equilibrium. Using the Lyapunov function, it is [...] Read more.
The transmission dynamics of onchocerciasis in two interacting populations are examined using a deterministic compartmental model with nonlinear incidence functions. The model undergoes qualitative analysis to examine how it behaves near disease-free equilibrium (DFE) and endemic equilibrium. Using the Lyapunov function, it is demonstrated that the DFE is globally stable when the threshold parameter R0≤1 is taken into account. When R0>1, it suffices to show globally how asymptotically stable the endemic equilibrium is and its existence. We conduct the bifurcation analysis by looking at the possibility of the model’s equilibria coexisting at R0<1 but near R0=1 using the Center Manifold Theory. We use the sensitivity analysis method to understand how some parameters influence the R0, hence the transmission and mitigation of the disease dynamics. Furthermore, we simulate the model developed numerically to understand the population dynamics. The outcome presented in this article offers valuable understanding of the transmission dynamics of onchocerciasis, specifically in the context of two populations that interact with each other, considering the presence of nonlinear incidence. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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16 pages, 12663 KiB  
Article
Modeling Study of Factors Determining Efficacy of Biological Control of Adventive Weeds
by Yuri V. Tyutyunov, Vasily N. Govorukhin and Vyacheslav G. Tsybulin
Mathematics 2024, 12(1), 160; https://doi.org/10.3390/math12010160 - 4 Jan 2024
Viewed by 1094
Abstract
We model the spatiotemporal dynamics of a community consisting of competing weed and cultivated plant species and a population of specialized phytophagous insects used as the weed biocontrol agent. The model is formulated as a PDE system of taxis–diffusion–reaction type and computer-implemented for [...] Read more.
We model the spatiotemporal dynamics of a community consisting of competing weed and cultivated plant species and a population of specialized phytophagous insects used as the weed biocontrol agent. The model is formulated as a PDE system of taxis–diffusion–reaction type and computer-implemented for one-dimensional and two-dimensional cases of spatial habitat for the Neumann zero-flux boundary condition. In order to discretize the original continuous system, we applied the method of lines. The obtained system of ODEs is integrated using the Runge–Kutta method with a variable time step and control of the integration accuracy. The numerical simulations provide insights into the mechanism of formation of solitary population waves (SPWs) of the phytophage, revealing the factors that determine the efficacy of combined application of the phytophagous insect (classical biological method) and cultivated plant (phytocenotic method) to suppress weed foci. In particular, the presented results illustrate the stabilizing action of cultivated plants, which fix the SPW effect by occupying the free area behind the wave front so that the weed remains suppressed in the absence of a phytophage. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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19 pages, 2691 KiB  
Article
Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks
by Vladislav Soukhovolsky, Anton Kovalev, Yulia Ivanova and Olga Tarasova
Mathematics 2023, 11(19), 4212; https://doi.org/10.3390/math11194212 - 9 Oct 2023
Viewed by 1012
Abstract
Three models of abundance dynamics for forest insects that depict the development of outbreak populations were analyzed. We studied populations of the Siberian silkmoth Dendrolimus sibiricus Tschetv. in Siberia and the Far East of Russia, as well as a population of the pine [...] Read more.
Three models of abundance dynamics for forest insects that depict the development of outbreak populations were analyzed. We studied populations of the Siberian silkmoth Dendrolimus sibiricus Tschetv. in Siberia and the Far East of Russia, as well as a population of the pine looper Bupalus piniarius L. in Thuringia, Germany. The first model (autoregression) characterizes the mechanism where current population density is dependent on population densities in previous k years. The second model considers an outbreak as analogous to a first-order phase transition in physical systems and characterizes the outbreak as a transition through a potential barrier from a low-density state to a high-density state. The third model treats an outbreak as an effect of stochastic resonance influenced by a cyclical factor such as solar activity and the “noise” of weather parameters. The discussion focuses on the prediction effectiveness of abundance dynamics and outbreak development for each model. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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19 pages, 1768 KiB  
Article
Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions
by Xiangjun Dai, Hui Jiao, Jianjun Jiao and Qi Quan
Mathematics 2023, 11(18), 3838; https://doi.org/10.3390/math11183838 - 7 Sep 2023
Viewed by 1176
Abstract
In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a [...] Read more.
In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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18 pages, 16303 KiB  
Article
Three-Dimensional Cellular Automaton for Modeling of Self-Similar Evolution in Biofilm-Forming Bacterial Populations
by Samvel Sarukhanian, Anna Maslovskaya and Christina Kuttler
Mathematics 2023, 11(15), 3346; https://doi.org/10.3390/math11153346 - 31 Jul 2023
Cited by 1 | Viewed by 1385
Abstract
Bacterial populations often form colonies and structures in biofilm. The paper aims to design suitable algorithms to simulate self-similar evolution in this context, specifically by employing a hybrid model that includes a cellular automaton for the bacterial cells and their dynamics. This is [...] Read more.
Bacterial populations often form colonies and structures in biofilm. The paper aims to design suitable algorithms to simulate self-similar evolution in this context, specifically by employing a hybrid model that includes a cellular automaton for the bacterial cells and their dynamics. This is combined with the diffusion of the nutrient (as a random walk), and the consumption of nutrients by biomass. Lastly, bacterial cells divide when reaching high levels. The algorithm computes the space-time distribution of biomass under limited nutrient conditions, taking into account the collective redistribution of nutrients. To achieve better geometry in this modified model approach, truncated octahedron cells are applied to design the lattice of the cellular automaton. This allows us to implement self-similar realistic bacterial biofilm growth due to an increased number of inner relations for each cell. The simulation system was developed using C# on the Unity platform for fast calculation. The software implementation was executed in combination with the procedure of surface roughness measurements based on computations of fractional dimensions. The results of the simulations qualitatively correspond to experimental observations of the population dynamics of biofilm-forming bacteria. Based on in silico experiments, quantitative dependencies of the geometrical complexity of the biofilm structure on the level of consumed nutrients and oxygen were revealed. Our findings suggest that the more complex structure with a fractal dimension of the biofilm boundaries (around 2.6) corresponds to a certain range of nutrient levels, after which the structure degenerates and the biofilm homogenizes, filling the available space provided and tending towards a strictly 3D structure. The developed hybrid approach allows realistic scenario modeling of the spatial evolution of biofilm-forming bacterial populations and specifies geometric characteristics of visualized self-similar biofilm bacterial structures. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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21 pages, 8419 KiB  
Article
Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions
by Matvey Kulakov and Efim Frisman
Mathematics 2023, 11(9), 2072; https://doi.org/10.3390/math11092072 - 27 Apr 2023
Cited by 2 | Viewed by 1072
Abstract
The inhomogeneous population distribution appears as various population densities or different types of dynamics in distant sites of the extended habitat and may arise due to, for example, the resettlement features, the internal population structure, and the population dynamics synchronization mechanisms between adjacent [...] Read more.
The inhomogeneous population distribution appears as various population densities or different types of dynamics in distant sites of the extended habitat and may arise due to, for example, the resettlement features, the internal population structure, and the population dynamics synchronization mechanisms between adjacent subpopulations. In this paper, we propose the model of the spatio-temporal dynamics of two-age-structured populations coupled by migration (metapopulation) with long-range displacement. We study mechanisms leading to inhomogeneous spatial distribution as a type of cluster synchronization of population dynamics. To study the spatial patterns and synchronization, we use the method of constructing spatio-temporal profiles and spatial return maps. We found that patterns with spots or stripes are typical spatial structures with synchronous dynamics. In most cases, the spatio-temporal dynamics are mixed with randomly located single populations with strong burst (outbreak) of population size (solitary states). As the coupling parameters decrease, the number of solitary states grows, and they increasingly synchronize and form the clusters of solitary states. As a result, there are the several clusters with different dynamics. The appearance of these spatial patterns most likely occurs due to the multistability of the local age-structured population, leading to the spatio-temporal multistability. Full article
(This article belongs to the Special Issue Mathematical Modeling for Population Dynamics and Evolutionary Dynamics)
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