Population Growth Model Research Articles

Локальная предельная теорема для ветвящихся случайных систем Гальтона–Ватсона с иммиграцией и бесконечной дисперсией

The paper considers a stochastic population growth model, which is the critical Galton-Watson stochastic branching system allowing immigration. We consider the case when the mathematical expectation of the law of influx of immigrant particles and the variance of the law of reproduction of aboriginal particles have infinite values. The asymptotic properties of transition probabilities are studied in the case when the states of the system are irreversible. For this case, a local limit theorem has been established.

Modification of the Leslie Model on Population Growth in the Bangka Belitung Islands Province

The Leslie model is one of the applications of Algebra in solving a population growth model. The birth rate and survival rate of a population are constituents of the Leslie Matrix. The advantage of this model is that it only requires data on the total female population. This study aims to modify the classic Leslie Model by adding correction values to matrix elements, especially birth rates and survival rates. The correction value is obtained from the minimum Euclidean distance for each birth rate and survival rate for each population age group. The Euclidean distance is used because it requires simple calculations. Based on the modified results, the Perron value obtained from the Leslie matrix is 0.9. If the constant value is zero, then the modification of the Leslie model will be the same as the classic Leslie model.

The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Survival, cause‐specific mortality, and population growth of white‐tailed deer in western Virginia

AbstractUnderstanding the role of recruitment in population dynamics of white‐tailed deer (Odocoileus virginianus) is important for management. In the central Appalachian Mountains, deer are part of a largely forested ecosystem that supports 3 carnivore species thought to be capable of influencing white‐tailed deer recruitment: black bears (Urus americanus), coyotes (Canis latrans), and bobcats (Lynx rufus). Yet little is known about predation, how other environmental factors influence recruitment, or the importance of neonate survival to white‐tailed deer population performance in the region. Our objectives were to identify causes of mortality for neonates, analyze effects of landscape attributes on survival of neonates, estimate survival rates for neonates and adult female white‐tailed deer, and to model population growth trends based on current vital rates and hypothetical harvest and neonate survival scenarios. During 2019–2020, we captured 57 neonate deer in Bath County, Virginia, USA, by monitoring 38 pregnant females equipped with global positioning system collars and vaginal implant transmitters and by conducting transect searches for recently born neonates. We observed 37 neonate mortalities and identified cause of death using field and genetic evidence. Mortalities included 28 predation events and 9 deaths from other causes (e.g., abandonment, malnutrition, disease). Black bears accounted for 48.6% of neonate mortalities, and 64.2% of predation events (n = 18), followed by bobcats (n = 5) and coyotes (n = 3). Annual survival for adult female deer was 0.871 and neonate survival to 12 weeks old was 0.310. Elevation was a significant predictor of neonate survival; mortality risk increased 20% for every 100‐m increase in elevation. Models of annual population growth using observed vital rates predicted an increasing population (λ = 1.10). A 10% increase in female harvest would still result in a potential population increase of 2% (λ = 1.02), but a 20% increase in harvest rate would result in a potential 7% decline (λ = 0.93). Neonate survival was higher near fertile valley bottoms and lower along forested ridges characterized by shallow, infertile soils and limited edge or early successional forests. While predation, largely influenced by black bears, was the leading cause of neonate mortality and contributed to low neonate survival, we observed little evidence of population decline, and suggest there is opportunity for a modest increase in harvest of female deer.

The numerical solution of a time-delay model of population growth with immigration using Legendre wavelets

The paper addresses a computational method to simulate more accurate models for population growth with immigration, focusing on integral equations (IEs) featuring a delay parameter in the time variable. The proposed method utilizes Legendre wavelets within the Galerkin scheme as a orthonormal basis. Legendre wavelets are known for their localized functions, offering suitable precision and stability in simulating time-delay biological models. This approach employs the composite Gauss-Legendre (CGL) quadrature rule to compute integrals appeared in the scheme. An error bound analysis demonstrates a convergence rate of order 2−Mk. Additionally, various numerical examples are presented to show the efficiency, accuracy and validate the theoretical error estimate of the novel technique.

A criterion of periodic point stability based on Lyapunov exponent

The logistics equation is the most classical model of population growth. Influenced by external environmental factors and growth inertia, the total population is in a state of periodic equilibrium. so, studying the stability of the periodic solution of the logistics equation is an important issue. If the logistics equation is considered as a function, the general method to judge the stability of the periodic point is to bring in the derivative of the function after iterating n times to take the value. The Lyapunov exponent is originally an important method used to judge the stability of dynamical systems. If the logistics map is considered as a discrete dynamical system, applying the Lyapunov exponent to the determination of the periodic solution will largely reduce the computational effort.

A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh

This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974–2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

Enhancing Ecological Efficiency in Biological Wastewater Treatment: A Case Study on Quality Control Information System

This study aimed to improve the control system of the biological stage of wastewater treatment using the quality control information system to support the concept of environmental efficiency management. In this case, the object of the study was the treatment facilities of Sumy city (Ukraine). For automatic control of wastewater quality, pH, oxidation reduction potential (ORP), electrical conductivity, and temperature indicators were taken, as well as hydrobiological analysis of activated sludge and mathematical modelling. The pH of wastewater at the input system has systematically unacceptable values (above 8.5 were recorded). Unacceptable concentrations of sulphur-containing toxicants arrive at the entrance of treatment facilities (0.22–1.3 mg/L). The response of activated sludge biocenosis to increasing concentrations of hydrogen sulphide in wastewater was analysed. Furthermore, a mathematical model of monoculture population growth, with two factors that affect population growth (nutrient concentration and monoculture production concentration), was implemented for the initial assessment of possible negative effects on wastewater treatment. The differential equation of the population dynamics of the i-th species of microorganisms in activated sludge was described. The applied system of automated monitoring of wastewater parameters with expert assessment of activated sludge and a unified mathematical model of approaches allows for a complex system of decision-making support to be realised. However, this requires the construction of mathematical models that would take into account the cause–effect relations that operate under conditions of incomplete technological information and the potential presence of emergencies due to natural disasters and military activities.

Global Asymptotic Stability Analysis of Fixed Points for a Density-Dependent Single-Species Population Growth Model

In a density-dependent single-species population growth model, a simple method is proposed to explicitly and directly derive the analytic expressions of reliable regions for local and global asymptotic stability. Specifically, first, a reliable region ΛLAS is explicitly represented by solving the fixed point and utilizing the asymptotic stability criterion, over which the fixed point is locally asymptotically stable. Then, two types of auxiliary Liapunov functions are constructed, where the variation of the Liapunov function is decomposed into the product of two functions and is always negative at the non-equilibrium state. Finally, based on the Liapunov stability theorem, a closed-form expression of reliable region ΛGAS is obtained, where the fixed point is globally asymptotically stable in the sense that all the solutions tend to fixed point. Numerical results show that our analytic expressions of reliable regions are accurate for both local and global asymptotic stability.

Two New Quadratic Scheme for Fractional Differential Equation with World Population Growth Model

Two New Quadratic Scheme for Fractional Differential Equation with World Population Growth Model

Comparative Study of the Gompertz and Logistic Growth Models on the Prevalence and Fatality of Covid-19 Pandemic in Nigeria

This study models the prevalence and fatality of the Covid-19 pandemic in Nigeria from February 2020 to July 2022. It is a comparative study of two prominent models: The Gompertz and Logistic population growth models. The data for this study was obtained from the website of Our World in Data, OWID (https//www.ourworldindata.org). The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were employed to compare the performance of the models, and the number of iterations before convergence and convergence tolerance for each model was also put into consideration. The study revealed that the Gompertz population growth model provides a better fit compared to the logistic growth in modelling the cumulative covid-19 cases and cumulative covid-19-related deaths in Nigeria. From the models, we obtained important features of the pandemic, such as the growth rate and asymptotes.

Extended stage duration and diminished fecundity in deltamethrin-resistant Triatoma infestans (Klug, 1834) of the Argentinean Chaco.

Pyrethroid-resistance is an emergent trait in populations of various insect species. For Triatoma infestans (Klug, 1834) (Heteroptera: Reduviidae), the major vector of Chagas disease in the southern part of South America, hotspot areas of pyrethroid-resistance have recently been found in the Chaco Province of Argentina. Resistant condition can reduce fitness of individuals in the absence of insecticide exposure, that is, fitness costs. We evaluated the existence of developmental and/or reproductive costs in T. infestans collected from two areas of pyrethroid-resistance in Chaco Province, Argentina. Three toxicological groups were defined from field-collected insects: susceptible (survival <20%), moderately resistant (survival between 20% and 80%) and highly resistant (survival >80%). Cohorts of the three toxicological groups were followed-up to study life cycle and reproductive parameters. Additionally, we parameterized matrix population growth models. First and IV nymphal stages of the resistant groups exhibited a longer stage duration than susceptible ones. The reproductive days and hatching success showed significant lower values revealing reproductive costs for the resistant groups. Matrix analysis showed lower population growth rates for the resistant groups. Our results support developmental and reproductive costs for pyrethroid-resistant individuals. This trait could be interpreted as lower population recovery ability for pyrethroid-resistant individuals compared to susceptible insects after alternative vector control actions.

Modelling population growth and sustainable harvesting

In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line analysis, graphing approximate solutions) to analyse their models. We then discuss how to use aspects of a species' behaviour to choose an appropriate model from among the ones developed. Finally, we show how a professor could apply what students have learned to develop general principles for sustainable harvesting of such species.

Patterns of asexual reproduction of the soybean aphid, Aphis glycines (Matsumura), with and without the secondary symbionts Wolbachia and Arsenophonus, on susceptible and resistant soybean genotypes.

Plant breeding is used to develop crops with host resistance to aphids, however, virulent biotypes often develop that overcome host resistance genes. We tested whether the symbionts, Arsenophonus (A) and Wolbachia (W), affect virulence and fecundity in soybean aphid biotypes Bt1 and Bt3 cultured on whole plants and detached leaves of three resistant, Rag1, Rag2 and Rag1 + 2, and one susceptible, W82, soybean genotypes. Whole plants and individual aphid experiments of A. glycines with and without Arsenophonus and Wolbachia did not show differences in overall fecundity. Differences were observed in peak fecundity, first day of deposition, and day of maximum nymph deposition of individual aphids on detached leaves. Bt3 had higher fecundity than Bt1 on detached leaves of all plant genotypes regardless of bacterial profile. Symbionts did not affect peak fecundity of Bt1 but increased it in Bt3 (A+W+) and all Bt3 strains began to deposit nymphs earlier than the Bt1 (A+W-). Arsenophonus in Bt1 delayed the first day of nymph deposition in comparison to aposymbiotic Bt1 except when reared on Rag1 + 2. For the Bt1 and Bt3 strains, symbionts did not result in a significant difference in the day they deposited the maximum number of nymphs nor was there a difference in survival or variability in number of nymphs deposited. Variability of number of aphids deposited was higher in aphids feeding on resistant plant genotypes. The impact of Arsenophonus on soybean aphid patterns of fecundity was dependent on the aphid biotype and plant genotype. Wolbachia alone had no detectable impact but may have contributed to the increased fecundity of Bt3 (A+W+). An individual based model, using data from the detached leaves experiment and with intraspecific competition removed, found patterns similar to those observed in the greenhouse and growth chamber experiments including a significant interaction between soybean genotype and aphid strain. Combining individual data with the individual based model of population growth isolated the impact of fecundity and host resistance from intraspecific competition and host health. Changes to patterns of fecundity, influenced by the composition and concentration of symbionts, may contribute to competitive interactions among aphid genotypes and influence selection on virulent aphid populations.

Stochastic Modeling of Bacterial Population Growth with Antimicrobial Resistance

In this paper we consider a stochastic model of bacterial population growth with antimicrobial resistance under the influence of random fluctuations. We analyze the model for the problem of persistence and extinction of bacterial cells. This analysis shows asymptotic extinction and conditional persistence for growing population. Moreover, we perform computer simulations in order to illustrate the model behavior. The model results have important implications for the eradication of bacterial cells and the emergence of resistance.

Factors affecting the recovery of Mexican wolves in the Southwest United States

Abstract Recovering and maintaining large carnivore populations is a global conservation challenge that requires better knowledge of the factors affecting their populations, particularly in shared landscapes (i.e. non‐protected areas where people occupy and or utilize the land). The Mexican wolf (Canis lupus baileyi) is an endangered wolf subspecies being recovered on shared landscapes in the Southwest United States and Mexico. We used data from the U.S. program to model population growth, evaluate the impact of management removal and illegal killing relative to other demographic factors, and test hypotheses about factors influencing rates of management removal and illegal killing. From 1998 to 2019, the population growth averaged 12% per year. Rates of natural reproduction, illegal killing and other mortality remained consistent over the 22 years; while releases, translocations and management removals varied markedly between two time periods, phase 1:1998–2007 and phase 2:2008–2019. The number of wolves removed for conflict management was higher during phase 1 (average ~ 13 per year, rate = 24.8%) than phase 2 (average of ~5 per year, rate = 5.2%). This decrease in management removal resulted in the wolf population resuming growth after a period of population stagnation. Two factors influenced this decrease, a change in policy regarding removal of wolves (stronger modelling support) and a decrease in the number of captive‐reared adult wolves released into the wild (weaker modelling support). Illegal mortality was relatively constant across both phases, but after the decrease in management removal, illegal mortality became the most important factor (relative importance shifted from 28.2% to 50.1%). Illegal mortality was positively correlated with rates of reintroduction and translocation of wolves and negatively correlated with the rate of management removal. Synthesis and applications. Using management removal to reduce human–carnivore conflict can have negative population impacts if not used judiciously. Recovering and maintaining carnivore populations in shared landscapes may require greater tolerance of conflict and more emphasis on effective conflict prevention strategies and compensation programs for affected stakeholders.

Research on future demographic trends based on the Chinese population growth model

Population development plays a vital role in the healthy and orderly operation of our country. To understand the new trends and characteristics of population change can effectively grasp the basic national condition of population and promote the high-quality development of China's economy. Based on the new characteristics and influencing factors of China's population, this paper establishes the mathematical model of China's population growth in the new era, and predicts the change trend of short-term and long-term population in China. First, we adopt the classical GM (1,1) model to predict the short-and medium-term demographic changes, and the fitting effect is very good. Then, in the long-term prediction, based on China's population policy and the future trend of population development, we choose the logistic population block growth model, which also got relatively good results. Next, we selected the representative five provinces of Guangdong, Zhejiang, Hubei, Heilongjiang and Inner Mongolia for comparative analysis according to the above model, and concluded that the correlation coefficient of people such as age structure, urbanization rate, birth and mortality were the main factors affecting population change. Finally, we put forward corresponding policy suggestions by changing the age structure, urbanization rate, sex ratio model correlation coefficient, combined with our country's recent population policy.

Population Growth Model and Mortality of Pakistan Lobster (Panulirus polyphagus) in Estuary Waters of Tarakan City

Lobster Panulirus polyphagus has a fairly high economic value and is found in the estuary waters of Tarakan City. This research aims to study the growth and mortality model of Lobster P. polyphagus originating in the estuary waters of Tarakan City. The research method was carried out using a quantitative descriptive method. Sampling was conducted 14 times from December 2021-May 2022 using gill nets. The results showed that the male sex ratio was more than the female. Allometric growth of males and females is negative allometric with a thin body shape. The structure of the size obtained was mostly in males ranging from 18.3-20.6 cm, and females around 20.5-22.2 cm. The maximum length growth of P. polyphagus based on von Bertalanffy's growth model was 31.519 cm in males and 31.374 cm in females. The total mortality (Z) of P. polyphagus for males and females was 1.104 and 1.119; catch mortality (F) of 0.106 and 0.253; natural mortality (M) of 0.998 and 0.866; exploitation rate (E) of 0.096 and 0.226, respectively. The high natural mortality causes the extinction of the Lobster species, so good management is needed so that it is sustainable.

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

This study analyses an approach to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by an improper discretisation of the required source terms. The current work focuses on advection-diffusion models, in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used in heat and mass transfer problems or multiphase flows. The investigated scheme is applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. Further application of this work can be found in the method of manufactured solutions or in the immersed boundary method. This paper is dedicated to three aspects regarding proper inclusion of the source term in LBM schemes. Firstly, it identifies the differences observed between the ways in which source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the observed differences, and to identify their origin. Secondly, it analyses in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is valid for any source term discretization scheme. It is a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model and the Allen-Cahn equation. The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. The pitfalls of the commonly used acoustic and diffusive scalings are identified and discussed. Furthermore, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

Solving the stochastic dynamics of population growth.

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters.