Population Growth Model Research Articles

Research on a Grey Prediction Model of Population Growth Based on a Logistic Approach

The classical population growth models include the Malthus population growth model and the logistic population growth model, each of which has its advantages and disadvantages. To address the disadvantages of the two models, this paper establishes a grey logistic population growth prediction model, based on the modeling mechanism of the grey prediction model and the characteristics of the logistic model, which uses the least-squares method to estimate the maximum population capacity. In accordance with the data characteristics of population growth, the weakening buffer operator is used to establish the weakening buffer operator grey logistic population growth prediction model, which improves its accuracy, thus improving the classic population prediction model. Four actual case datasets are used simultaneously, and the two classical grey prediction models are compared. The results of the six evaluation indicators show that the effects of the new model demonstrate obvious advantages. Finally, the new model is applied to the population forecast of Chongqing, China. The prediction results suggest that the population may reach a peak in 2020 and decline in the future. This finding is consistent with the logistic population growth model.

Modified analytical approach for generalized quadratic and cubic logistic models with Caputo-Fabrizio fractional derivative

In this paper, a modified reproducing kernel algorithm is proposed to solve a class of quadratic and cubic logistic equations with Caputo-Fabrizio fractional derivative in Hilbert space. These equations are the generalization of Verhulst’s model which describes population growth taking in account that individuals will compete for limited resources. A novel reproducing kernel function is constructed to create an orthogonal system and to calculate the analytical and approximate solutions in the desirable Sobolev space. The stability, convergence, and complexity of the proposed approach are discussed. Furthermore, the effects of the Caputo-Fabrizio fractional derivatives are studied in solving the population growth model comparing with those of the classical Caputo derivatives. The main motivation for using the proposed technique is high accuracy and low computational cost compared to other existing methods especially when involving fractional differentiation operators. In this orientation, the effectiveness, applicability, and feasibility of this technique are verified by numerical examples. In a numerical viewpoint, the obtained results indicate that the suggested intelligent method has many advantages in accuracy and stability using the new Caputo-Fabrizio derivative.

Simulating changes in polar bear subpopulation growth rate due to legacy persistent organic pollutants – Temporal and spatial trends

Although atmospheric concentrations of many conventional persistent organic pollutants (POPs) have decreased in the Arctic over the past few decades, levels of most POPs and mercury remain high since the 1990s or start to increase again in Arctic areas, especially polar bears. So far, studies generally focused on individual effects of POPs, and do not directly link POP concentrations in prey species to population-specific parameters. In this study we therefore aimed to estimate the effect of legacy POPs and mercury on population growth rate of nineteen polar bear subpopulations. We modelled population development in three scenarios, based on species sensitivity distributions (SSDs) derived for POPs based on ecotoxicity data for endothermic species. In the first scenario, ecotoxicity data for polar bears were based on the HC50 (the concentration at which 50% of the species is affected). The other two scenarios were based on the HC5 and HC95. Considerable variation in effects of POPs could be observed among the scenarios. In our intermediate scenario, we predicted subpopulation decline for ten out of 15 polar bear subpopulations. The estimated population growth rate was least reduced in Gulf of Boothia and Foxe Basin. On average, PCB concentrations in prey (in μg/g toxic equivalency (TEQ)) posed the largest threat to polar bear subpopulations, with negative modelled population growth rates for the majority of subpopulations. We did not find a correlation between modelled population changes and monitored population trends for the majority of chemical-subpopulation combinations. Modelled population growth rates increased over time, implying a decreasing effect of PCBs, DDTs, and mercury. Polar bear subpopulations are reportedly still declining in four out of the seven subpopulations for which sufficient long-term monitoring data is available, as reported by the IUCN-PBSG. This implies that other emerging pollutants or other anthropogenic stressors may affect polar bear subpopulations.

Effect Modeling Quantifies the Difference Between the Toxicity of Average Pesticide Concentrations and Time-Variable Exposures from Water Quality Monitoring.

Synthetic chemicals are frequently detected in water bodies, and their concentrations vary over time. Water monitoring programs typically employ either a sequence of grab samples or continuous sampling, followed by chemical analysis. Continuous time-proportional sampling yields the time-weighted average concentration, which is taken as proxy for the real, time-variable exposure. However, we do not know how much the toxicity of the average concentration differs from the toxicity of the corresponding fluctuating exposure profile. We used toxicokinetic-toxicodynamic models (invertebrates, fish) and population growth models (algae, duckweed) to calculate the margin of safety in moving time windows across measured aquatic concentration time series (7 pesticides) in 5 streams. A longer sampling period (14 d) for time-proportional sampling leads to more deviations from the real chemical stress than shorter sampling durations (3 d). The associated error is a factor of 4 or less in the margin of safety value toward underestimating and an error of factor 9 toward overestimating chemical stress in the most toxic time windows. Under- and overestimations occur with approximate equal frequency and are very small compared with the overall variation, which ranged from 0.027 to 2.4 × 1010 (margin of safety values). We conclude that continuous, time-proportional sampling for a period of 3 and 14 d for acute and chronic assessment, respectively, yields sufficiently accurate average concentrations to assess ecotoxicological effects. Environ Toxicol Chem 2020;39:2158-2168. © 2020 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Investigate future population projection of Bangladesh with the help of Malthusian model, Sharpe-lotka model and Gurtin Mac-Camy model

A nonlinear deterministic model of age-dependent population growth is formulated in terms of joint integral equations in the total population size function and the total birth rate function. Existence of a unique solution of the model equation is established using Banach fixed point theorem. Then we investigate the total population size of Malthusian model, Sharpe-Lotka linear model and Gurtin Mac-Camy model for some specific age group and compare our investigated solutions with the total population of Bangladesh by using numerical method “Newton divided difference formula”. In our present study, we also investigate future population projection of Bangladesh with the help of Malthusian model, Sharpe-Lotka model and Gurtin Mac-Camy model.

Feasibility of Using Aeration to Cool Wheat Stored in Slovenia: A Predictive Modeling Approach Using Historical Weather Data

The use of aeration, which refers to cooling of a grain mass using low-volume airflow rates with ambient air, is an under-utilized component of management programs. A model simulation study was conducted for the country of Slovenia by examining historical weather data for 10 selected sites to determine if sufficient cooling hours <15 °C were available in August and September to cool stored wheat. The weather data were then coupled with a degree-day model to determine if a generation of Sitophilus oryzae (L.), the rice weevil, could be produced in the absence of aeration, using a start date of 1 August. The weather data for September was used to classify Slovenia into different risk zones, depending on the number hours <15 °C. Three sites from each zone, from warmest to coolest, Portorož, Novo Mesto, and Lesce, were further examined using a web-based aeration model and insect population growth model for S. oryzae developed by Texas A&M University Beaumont TX for cooling stored rough rice, to predict bin temperatures and population growth from 1 August to 30 November. The results show that, for most of Slovenia, in the absence of aeration, a complete generation of S. oryzae could occur based on an infestation beginning 1 August. The use of aeration immediately cooled stored wheat in the three selected sites, resulting in a dramatic decrease in predicted populations of S. oryzae in aerated wheat compared to unaerated wheat. The results show that the use of aeration may be expanded in Slovenia for management of stored commodities, and it could help alleviate dependence on insecticides for insect pest management after harvest.

Similar solutions for nonlinear Langevin equations with the drift and diffusion coefficients separable in time and space

The exact solution is obtained for a class of nonlinear Langevin equations, driven by Gaussian white noise, with drift and diffusion coefficients separable in time and space. In addition, the solutions for particular cases of the drift and diffusion coefficients have also been recovered and compared; it is shown that these systems can share similar solutions for specific ranges of the time-dependent drift and diffusion coefficients. The application of the system to population growth models is also discussed.

External Threats and Internal Geography

This paper examines how external military threats influence the distribution of population across cities. We argue that such threats reduce government investment, and thus population growth, in cities, particularly in non-democratic countries where governments have broad discretion in how investments are allocated. To test these hypotheses, we construct a measure of external military threat that varies both across cities within the same country and over time and examine its relationship with the growth of a set of large cities over the period 1950-2015. Results from models of city population growth incorporating both city and country-year fixed effects imply that external military threats are associated with slower city growth in non-democracies, but not democracies. Back-of-the-envelope calculations using our baseline estimates imply that post-1950 military threats had resulted in an average increase in population concentration among large cities of approximately 36% by 2015.

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania.

Climate change in a conceptual atmosphere–phytoplankton model

Abstract. We develop a conceptual coupled atmosphere–phytoplankton model by combining the Lorenz'84 general circulation model and the logistic population growth model under the condition of a climate change due to a linear time dependence of the strength of anthropogenic atmospheric forcing. The following types of couplings are taken into account: (a) the temperature modifies the total biomass of phytoplankton via the carrying capacity; (b) the extraction of carbon dioxide by phytoplankton slows down the speed of climate change; (c) the strength of mixing/turbulence in the oceanic mixing layer is in correlation with phytoplankton productivity. We carry out an ensemble approach (in the spirit of the theory of snapshot attractors) and concentrate on the trends of the average phytoplankton concentration and average temperature contrast between the pole and Equator, forcing the atmospheric dynamics. The effect of turbulence is found to have the strongest influence on these trends. Our results show that when mixing has sufficiently strong coupling to production, mixing is able to force the typical phytoplankton concentration to always decay globally in time and the temperature contrast to decrease faster than what follows from direct anthropogenic influences. Simple relations found for the trends without this coupling do, however, remain valid; just the coefficients become dependent on the strength of coupling with oceanic mixing. In particular, the phytoplankton concentration and its coupling to climate are found to modify the trend of global warming and are able to make it stronger than what it would be without biomass.

Description and analysis of a mathematical model of population growth of Aedes aegypti

This article proposes a mathematical model based on ordinary nonlinear differential equations that describes the dynamics of population growth of the mosquito Aedes aegypti throughout its life cycle. Then, a modification is made to the model by implementing a time delay, initially constant and then distributed over time. In addition, h, the population growth threshold, is established, the equilibrium points (trivial equilibrium, coexistence equilibrium) of the population are found and an analysis of local stability of the coexistence equilibrium is performed. If $$h>1$$ , this results in the population of adult aquatic mosquitoes persisting in the environment, approaching a equilibrium of coexistence, regardless of whether the time delay is considered or not. Finally, numerical simulations are carried out using Matlab software using the functions ode45 and dde23, with a value of $$ h>1 $$ , which allow the solutions of the initial model of ordinary differential equations to be compared to the solutions when the delay is implemented.

Stability in terms of two measures for population growth models with impulsive perturbations

In this paper, we establish some criteria for the stability of trivial solution of population growth models with impulsive perturbations. The working tools are based on the theory of generalized ordinary differential equations. Here, the conditions concerning the functions are more general than the classical ones.

Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration

We considered the time-inhomogeneous linear birth–death processes with immigration. For these processes closed form expressions for the transition probabilities were obtained in terms of the complete Bell polynomials. The conditional mean and the conditional variance were explicitly evaluated. Several time-inhomogeneous processes were studied in detail in view of their potential applications in population growth models and in queuing systems. A time-inhomogeneous linear birth–death processes with finite state-space was also taken into account. Special attention was devoted to the cases of periodic immigration intensity functions that play an important role in the description of the evolution of dynamic systems influenced by seasonal immigration or other regular environmental cycles. Various numerical computations were performed for periodic immigration intensity functions.

Human resilience to Holocene climate changes inferred from rodent middens in drylands of northwestern Patagonia (Argentina)

We reconstruct the Holocene vegetation, climate, and archaeological history for drylands of northwestern Patagonia, Argentina, based on multiproxy analysis (plant macrofossil, pollen, and parasites) of rodent middens integrated with a database of 14C dates associated with human occupations. The local scale corresponds to the Huenul paleoecological and archaeological locality, emplaced in north-western Patagonia (Neuquén Province, Argentina). The rodent midden record from the Huenul series reflects subtle vegetation changes driven by climatic variability at millennial timescale. Drier than present environmental conditions prevailed during the early Holocene (10,500–9400 cal yr BP), peaking during the mid-Holocene (9200–5500 cal yr BP), when wetter than present conditions established during the late Holocene (4400–2500 cal yr BP). These environmental and climatic dynamics agree with other paleoclimatic records from northern Patagonia, suggesting the winter precipitation dynamics related to the Southern Westerlies as a common driver. The diachronic distribution of anthropogenic radiocarbon dates from the western area of the South American Arid Diagonal between 32°–40°S conforms to a fitted exponential model of steady background population growth, not suggesting significant demographic changes that may have been the result of the impact of climate change. This record indicates that these human populations coped successfully with aridity, particularly during the mid-Holocene. These findings reinforce the need to integrate multi-scalar interdisciplinary analyses to assess the impact of climate change in human societies.

El modelo del ciclo de vida del producto desde una perspectiva en las ventas del periodo 2016 – 2018 en el sector calzado de la ciudad de Ambato

Plasticaucho S.A is a company dedicated to the manufacture and commercialization of footwear, being one of the biggest footwear companies in the province of Tungurahua, satisfying its customers under strict quality processes, thanks to this the company is recognized at a national level under product lines, areas and commercial channels. For this reason, the following research work emphasizes a model of population growth based on the life cycle of the product that responded to a quantitative approach, not an experimental one of longitudinal character and relational reach, including the description of the participants, the design of the study and the evaluation instrument. It was sought to nuance: 1) to locate the lines of products according to the CVP; 2) to classify the commercial zones; 3) to identify the participation of the distribution channels. To reach these elements, we explored the sales budget (pairs), seasonality (months) and the 10 percent growth rate. The sales reports for the years 2016, 2017 and 2018 were used to develop the logistical model for population growth, thus demonstrating the approval of the limited life of the products and the seasonality of sales with the calculation of the Fisher coefficient with a result of: 0.08338, which helped to locate in which stage of the CVP each line, zone and commercial channel is located, attaching the stage of turbulence in the study as an emphasis for decision making. After the study carried out in the company Plasticaucho S.A, it is suggested that in the school, relax and sports footwear, the innovation of designs with avant-garde products should be promoted as a market demand and new marketing strat

Modelling the dry season inundation pattern of Yala Swamp in Kenya

Ecological processes in wetlands rely on the natural variability of inundation cycle guided by different seasons. Human-induced modifications have, however, influenced the seasonality and the period of inundation, altering its inherent variability. The adjustments have further affected the functioning of many global wetlands by shifting their natural equilibrium. In a quest to understand the wetland’s inundation pattern, cellular automata and Markov chain analysis (CA–MCA) model was used to simulate the 2029 dry season inundation variation of Yala Swamp in Kenya. The model utilised parameters obtained from Tasselled Cap Wetness Index, supervised classification, population growth model and elevation for the years 1986, 2006, 2015 and 2019. The study established that inundation characteristics in the swamp varied as the years progressed from 1986 to 2019. Consistency was found between inundation variation and changes in land-use practices. Consequently, the area covered by the wetland decreased in its spatial extent by approximately 35%. The model projected that the swamp would additionally lose 12% of its inundated area by 2029, should the current practices continue. It is therefore essential to regulate anthropogenic activities to control the variability in the swamps inundation.

Evolutionary tracking is determined by differential selection on demographic rates and density dependence.

Recent ecological forecasts predict that ~25% of species worldwide will go extinct by 2050. However, these estimates are primarily based on environmental changes alone and fail to incorporate important biological mechanisms such as genetic adaptation via evolution. Thus, environmental change can affect population dynamics in ways that classical frameworks can neither describe nor predict. Furthermore, often due to a lack of data, forecasting models commonly describe changes in population demography by summarizing changes in fecundity and survival concurrently with the intrinsic growth rate (r). This has been shown to be an oversimplification as the environment may impose selective pressure on specific demographic rates (birth and death) rather than directly on r (the difference between the birth and death rates). This differential pressure may alter population response to density, in each demographic rate, further diluting the information combined to produce r. Thus, when we consider the potential for persistence via adaptive evolution, populations with the same r can have different abilities to persist amidst environmental change. Therefore, we cannot adequately forecast population response to climate change without accounting for demography and selection on density dependence. Using a continuous‐time Markov chain model to describe the stochastic dynamics of the logistic model of population growth and allow for trait evolution via mutations arising during birth events, we find persistence via evolutionary tracking more likely when environmental change alters birth rather than the death rate. Furthermore, species that evolve responses to changes in the strength of density dependence due to environmental change are less vulnerable to extinction than species that undergo selection independent of population density. By incorporating these key demographic considerations into our predictive models, we can better understand how species will respond to climate change.

Effects of colored noises on the statistical properties of a population growth model with Allee effect**Research is supported by the National Natural Science Foundation of China (11801224), Natural Science Foundation of Jiangsu Province (BK20180856).

We study a stochastic population growth model with Allee effect, it is driven by correlated multiplicative and additive colored noises. The influences of noises on the statistical properties of the stochastic model are discussed. Applying an approximative Fokker-Planck equation, we first obtain the stationary probability distribution (SPD) of the stochastic model, and then present a more detailed discussion of how the noises determine the behaviors of the SPD, mean, variance and skewness of the population size. The research of the shape of SPD shows that the phenomenological bifurcation may occur when the noise intensity passes through a critical value. We also find that the additive and multiplicative noises have different effects on the moments (mean, variance and skewness) of population density.

Generalized wavelet quasilinearization method for solving population growth model of fractional order

The primary aim of this study is to introduce and develop a generalized wavelet method together with the quasilinearization technique to solve the Volterra's population growth model of fractional order. Unlike the existing operational matrix methods based on orthogonal functions, we formulate the wavelet operational matrices of general order integration without using the block pulse functions. Consequently, the governing problem is transformed into an equivalent system of algebraic equations, which can be tackled with any classical method. The applicability of the proposed method is demonstrated via an illustrative comparison of the numerical outcomes with those found by other known methods. The experimental outcomes demonstrate that the proposed method is fast, accurate, simple, and computationally reliable.

Numerical schemes for studying biomathematics model inherited with memory-time and delay-time

The effect of inherited memory-time and delay-time in the formulation of a mathematical population growth model is considered. Two different numerical schemes are introduced to study analytically the propagation of population growth. We provide a graphical analysis that shows the impact of both memory-time and delay-time acting on the behavior of population density. We concluded that both delay-time and time-fractional-derivative play the same role as delaying the propagation of the nonlinear population growth.