Mathematical Model Of Population Dynamics Research Articles

Steady-state dynamics in a two-patch population model with and without Allee effect

Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.

Modeling the effects of plant resistance, herbivore virulence, and parasitism, on the population dynamics of aphids and parasitoids in wheat and soybean in different climates

Invasions by insects that become pests are an increasing problem for agriculture. Introductions of parasitoids from the regions of pest origin and breeding plants resistant to invasive pests can reduce the abundances and impacts of pests, while providing safe, sustainable alternatives to insecticides. However, impacts of parasitoids and plant resistance are likely to interact, and the abiotic environment, and in particular, climate change is likely to affect these interactions. Here I report results from simulations with mathematical models of population dynamics of aphids and parasitoids on resistant versus susceptible plants, parameterized with published results, designed to test the following hypotheses: (1) parasitoids can reduce abundances and frequencies of virulent aphids able to overcome plant resistance, (2) temperature regime affects the impacts of parasitoids on virulent aphids, and (3) the outcomes of these interactions vary with crop. Two systems were modeled: the soybean aphid, Aphis glycines, on soybean, and the Russian wheat aphid, Diuraphis noxia, on wheat. The parasitoids in the models are in the genus Aphelinus, species of which have a long association with biological control of invasive pests. In the simulations with these models, parasitoids reduced the abundances, and on wheat, the percent of virulent aphids. The impacts of parasitoids on virulent aphids were greater in southern locations than in northern locations, and the impacts on virulent aphids were greater on wheat than on soybean. Indeed, parasitoids actually increased the frequencies of virulent aphids on soybean when only susceptible plants were present, while reducing the abundance of all aphids. If one accepts that comparisons of population dynamics in southern versus northern locations indicate the likely affects of climate change in the northern locations, these results suggest that climate change would lead to decreased abundance and frequency of virulent aphids in northern locations.

A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

This study concentrates on the dynamics of a prey–predator model incorporating the fear effect in the birth and death rate of prey, whose physiological changes may give rise to undirect predation. In the presence and absence of time delay, single parameter numerical continuation with respect to two parameters, that are (i) fear level in the death rate of prey and (ii) conversion efficiency by which new predators are introduced through prey consumption in the system, is performed. Basic results on extinction and delay‐driven Hopf bifurcation criteria are investigated. Then, the model is extended to involve the spatial dynamics with and without time delay. Theoretical results for orientation and stability of Hopf bifurcation in spatial system are provided by applying the normal form recipe and also the center manifold theory. Classical reaction–diffusion‐type models, incorporating self‐diffusion, can induce regular (periodic) and irregular (chaotic) oscillations in space. However, space periodic oscillations are not common in prey–predator interactions. Here, it is shown that the dynamics of only diffusion involved model is periodically arranged in space and time. However, introducing a very small value of time delay in predator maturation, spatial dynamics with chaos is initiated as a result of the joint effect of time delay and diffusion. This reassures that time delay has a crucial role in population dynamics incorporated with the role of indirect predation and gives some useful intuition into underlying species interactions. Theoretical results of the model in this paper are supported with numerical experiments.

Sufficient Conditions for the Existence and Uniqueness of the Solution of the Dynamics of Biogeochemical Cycles in Coastal Systems Problem

The article considers a three-dimensional mathematical model of population dynamics based on a system of non-stationary parabolic advection-diffusion-reaction equations with lower derivatives describing the advective motion of the aquatic environment and non-linear source functions. In contrast to the previous authors’ works devoted to the description of this model and its numerical implementation, this article presents the results of an analytical study of the initial-boundary value problem corresponding to this model. For these purposes, the original initial-boundary value problem is linearized on a single time grid—for all nonlinear sources, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial—final data at each step of the time grid. For this chain of linearized problems, the existence and uniqueness of the solution of the initial-boundary value problem for the system of partial differential equations in the Hilbert space were researched. Numerical experiments were performed for model problems of the main types of phytoplankton populations in coastal systems under the influence of dynamically changing biotic and abiotic factors, the results of which are consistent with real physical experiments. The developed model, including the proposed model of biological kinetics, allows for the study of the productive and destructive processes of the shallow water body biocenosis to assess the state of the processes of reproduction of valuable and commercial fish participating in the food chain with selected species of summer phytoplankton.

Optimal Harvest Problem for Fish Population—Structural Stabilization

The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigated and an optimality system to the problem research is constructed. The solutions properties in various cases have also been investigated. Environmental conditions influence the fish population through recruitment. Modelling of recruitment rate is made by using a stochastic imitation of environmental conditions. In the case of stationary environment, a population model admits nontrivial equilibrium state. The parameters of fish population are obtained from this equilibrium condition. The variability of environment leads to large oscillations of generation size. The fluctuations of the fish population density follow the dynamics of recruitment rate fluctuations but have smaller gradients than recruitment. The dynamics of the optimal fishing effort is characterized by high variability. The population and the average size of individuals decrease under the influence of fishery. In general, the results of computer calculations indicate the stabilization of the population dynamics under influence of size structure. Optimal harvesting also contributes to stabilization.

A mathematical model of population dynamics for the internet gaming addiction

As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.

A fast and accurate analytical-numerical method for solving the prey-predator model

We consider the prey-predator mathematical model of population dynamics. For this model, we propose a new analytical-numerical method. Our proposed analytical-numerical method is much faster in terms of computation and more accurate in terms of approximation than an available existing multistage variational iteration method. Our proposed method is promising to be extended for solving other mathematical models.

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part II

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part II

The formation of spreading front: the singular limit of three-component reaction-diffusion models.

Understanding the invasion processes of biological species is a fundamental issue in ecology. Several mathematical models have been proposed to estimate the spreading speed of species. In recent decades, it was reported that some mathematical models of population dynamics have an explicit form of the evolution equations for the spreading front, which are represented by free boundary problems such as the Stefan-like problem (e.g., Mimura et al., Jpn J Appl Math 2:151-186, 1985; Du and Lin, SIAM J Math Anal 42:377-405, 2010). To understand the formation of the spreading front, in this paper, we will consider the singular limit of three-component reaction-diffusion models and give some interpretations for spreading front from the viewpoint of modeling. As an application, we revisit the issue of the spread of the grey squirrel in the UK and estimate the spreading speed of the grey squirrel based on our result. Also, we discuss the relation between some free boundary problems related to population dynamics and mathematical models describing Controlling Invasive Alien Species. Lastly, we numerically consider the traveling wave solutions, which give information on the spreading behavior of invasive species.

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I

Approaches to modeling population dynamics using discrete-time models are described in this two-part review. The development of the scientific ideas of discrete time models, from the Malthus model to modern population models that take into account many factors affecting the structure and dynamics, is presented. The most important and interesting results of recurrent equation application to biological system analysis obtained by the authors are given. In the first part of this review, the population dynamic effects that result from density-dependent regulation of population, the age and sex structures, and the influence of external factors are considered.

Enhanced ability of information gathering may intensify disagreement among groups

Today's society faces widening disagreement and conflicts among constituents with incompatible views. Escalated views and opinions are seen not only in radical ideology or extremism but also in many other scenes of our everyday life. Here we show that widening disagreement among groups may be linked to the advancement of information communication technology by analyzing a mathematical model of population dynamics in a continuous opinion space. We adopted the interaction kernel approach to model enhancement of people's information-gathering ability and introduced a generalized nonlocal gradient as individuals' perception kernel. We found that the characteristic distance between population peaks becomes greater as the wider range of opinions becomes available to individuals or the more attention is attracted to opinions distant from theirs. These findings may provide a possible explanation for why disagreement is growing in today's increasingly interconnected society, without attributing its cause only to specific individuals or events.

Combined impacts of the Allee effect, delay and stochasticity: Persistence analysis

We study a combined influence of the Allee effect, delay and stochasticity on the base of the phenomenological Hassell mathematical model of population dynamics. This bistable dynamical model possesses a wide variety of regimes, both regular and chaotic. In the persistence zone, these regimes coexist with the trivial equilibrium that corresponds to the extinction of the population. It is shown that borders of the persistence zone are defined by the crisis and saddle-node bifurcation points. Noise-induced transitions from the persistence to the extinction are studied both numerically and analytically. Using numerical modeling, we have found that the persistence zone can decrease and even disappear under the influence of random noise. For the theoretical study of this phenomenon, we apply the stochastic sensitivity analysis and Mahalanobis metrics.

Population Dynamics: Mathematical Modeling and Reality

Application of mathematical modeling for analysis of natural phenomena relies on model reduction techniques, which inevitably raises the question of whether the results of simulation reflect real processes. This work analyzes problems that arise when the results obtained by mathematical modeling of population processes are compared to data collected by monitoring of natural ecosystems. The source of these problems is that the type of dependencies between variables that describe the population dynamics, as well as the choice of numerical values assigned to the parameters of the mathematical model, are often impossible to justify, even based on the monitoring data from a particular ecosystem. This paper proposes an approach to mathematical modeling that would take the impact of the entire complex of biotic and abiotic factors on the population dynamics into account. Its central feature is consideration of ecosystem monitoring data and incorporating them directly into mathematical models of population dynamics. This approach would make it possible, in particular, to evaluate the extent to which individual environmental factors influence both the variations in population abundance recorded during monitoring and those characteristics of population processes that are not directly measured during monitoring, but are obtained by mathematical modeling.

A Population Dynamics Model of Mosquito-Borne Disease Transmission, Focusing on Mosquitoes’ Biased Distribution and Mosquito Repellent Use

We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the model clearly shows the existence of thresholds for mosquito repellent efficacy and its utilization rate in the human population with respect to the elimination of mosquito-borne diseases. Further, theresults imply that the suppression of mosquito-borne diseases becomes more difficult when the mosquitoes' distribution is biased to a greater extent around thehuman population.

Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis

This work is designed to formulate and analyse a mathematical model for population dynamics of financial crime with optimal control measures. Necessary conditions for the existence and stability of financial crime steady states are derived. The financial crime reproduction number is determined. Based on construction of suitable Lyapunov functionals, crime-free equilibrium point of the formulated model is shown to be globally asymptotically stable when the crime reproduction number is below unity, while a unique crime-present equilibrium is proved to be globally asymptotically stable whenever the crime reproduction number exceeds unity. Sensitivity analysis is carried out to determine the relative importance of model parameters in financial crime spread. Furthermore, optimal control theory is employed to assess the impact of two time-dependent optimal control strategies, including public enlightenment campaign (preventive) and corrective measure, on the financial crime dynamics in a population. The cost-effectiveness analysis is carried out to determine the least costly and most effective strategy of the singular and combined implementations of the intervention strategies, when the available resources to combat the spread of financial crime are limited.

Analysis of Integrodifference Equations with a Separable Dispersal Kernel

Integrodifference equations are a class of infinite-dimensional dynamical systems in discrete time that have recently received great attention as mathematical models of population dynamics in spatial ecology. The dispersal of individuals between generations is described by a ‘dispersal kernel’, a probability density function for the distance that an individual moves within a season. Previous authors recognized that the dynamics are reduced to a finite-dimensional problem when the dispersal kernel is separable. We prove some open questions from their work on the dynamics of a single population and then extend the idea to investigate the dynamics of two spatially distributed species in (i) a competitive relation, and (ii) a predator-prey relation. In all cases, we discuss how the dynamics of the population(s) depend on the amount of suitable space that is available to them. We find a number of bifurcations, such as period-doubling sequences and Naimark-Sacker bifurcations, which we illustrate through simulations.

Ecological network analysis in modeling of plant population dynamics

One of the most popular tools used in the process of modeling are ecological networks. Population dynamics of threatened plant species – Pulsatilla patens (L.) Mill. and commonly occurring taxon – Carex digitata L., was modeled using the package STELLA. The population of P. patens was studied in the years 2009-2011, at 16 sites, while the population of C. digitata was observed in the years 1987-2015, at the two sites in the natural and secondary oak-hornbeam forest Tilio cordatae-Carpinetum betuli Tracz. 1962 in the Supraśl Forest Division, Knyszyńska Forest. The input parameters for model construction were changes in the number of individuals and calculated on their basis birth and death rates. The proposed mathematical model of population dynamics implies that the probability of P. patens becoming a threatened species, evaluated on the basis of changes in the number of individuals is small, however it increases for C. digitata (in particular in the anthropogenically disturbed community). The results of simulations show that P. patens makes dynamically developing population characterized by an increase in the number of individuals with time in the period studied, disregarding the effect of natural and anthropogenic disturbances. In both C. digitata communities studied, a decrease in the number of individuals in the period studied is noted, and the rate of the decrease is much higher in the anthropogenically disturbed community, which means that the population is dynamically ageing.

La genealogia come disciplina ausiliaria della genetica

Genealogy as an auxiliary discipline of genetics. Beyond their historiographical interest, genealogical studies have long been attracting the interest of geneticist as they can provide emnpirical support or contribute to falsifying purely mathematical models of population dynamics. We briefly trace the history of the interactions between genealogy and genetics starting from the end of the XIX century, focusing in particular on matrimonial isonymy and on the distribution and disappearance of surnames. We analyze critically the theoretical models adopted, pointing at their conceptual limits, that history studies have allowed to identify. We then analyze some recent experiences and research proposals, in paricular the studies on the repetition of the ancestors (MRCA), carried out in vivo by exploring quantitatively the genealogically well-known complex constituted by the European nobility in the modern age.

Science, states, and salmon: Communicating through disagreement over a Cold War fault line

How are scientific communication and knowledge-production possible even in a politicized atmosphere pervaded by distrust and animosity? This essay takes the Soviet–Japanese Fisheries Convention of the Northwest Pacific Ocean of 1956 as a case study to consider the nature and characteristics of scientific disputes in highly politically-charged contexts outside frameworks of nation-states or international bodies. It shows that disagreements in this atmosphere were both scientific and political. What counted as evidence, reliable data, responsible resource management, and risk were contingent and deeply conditioned by geopolitics, political economies, and epistemological traditions. No purely scientific solution to the debate was possible. Methods to enable fruitful dialogue despite disagreement had to be both social and epistemic. Mathematical models of population dynamics proved particularly useful in this regard.

Auto-organização e formação de padrão em sistemas físicos e biológicos

Neste trabalho apresentamos uma breve discussão sobre a descrição matemática do fenômeno formação de padrão em sistemas biológicos, observando os modelos matemáticos de dinâmica de populações. Listamos vários exemplos de sistemas físicos, químicos e biológicos que exibem este fenômeno enfatizando, em cada um, os parâmetros principais envolvidos em seu entendimento. Mostramos que, no caso das populações, o fenômeno padrão pode ser modelado ao modificarmos a equação de Fisher-Kolmogorov, considerando uma interação não-local para o termo de competição. Apresentamos um estudo analítico e numérico da equação de Fisher-Kolmogorov com difusão e analisamos o papel dos termos de crescimento, difusão e competição na formação dos padrões.