scholarly journals Population dynamics with threshold effects give rise to a diverse family of Allee effects

2020 ◽  
Author(s):  
Nabil T. Fadai ◽  
Matthew J. Simpson
Keyword(s):  
Cell Biology ◽  
Growth Models ◽  
Critical Density ◽  
Threshold Effect ◽  
Logistic Growth ◽  
Threshold Effects ◽  
Allee Effects ◽  
Growth Mechanisms ◽  
Local Growth ◽  
Local Threshold

AbstractThe Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.

scholarly journals Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200350
Author(s):  
Nabil T. Fadai ◽  
Stuart T. Johnston ◽  
Matthew J. Simpson
Keyword(s):  
Population Dynamics ◽  
Cell Biology ◽  
Allee Effect ◽  
Local Density ◽  
Growth Models ◽  
Logistic Growth ◽  
Allee Effects ◽  
Individual Level ◽  
Modelling Framework ◽  
Global Population

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

scholarly journals Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

2019 ◽  
Author(s):  
Nabil T. Fadai ◽  
Stuart T. Johnston ◽  
Matthew J. Simpson
Keyword(s):  
Population Dynamics ◽  
Cell Biology ◽  
Allee Effect ◽  
Local Density ◽  
Growth Models ◽  
Logistic Growth ◽  
Allee Effects ◽  
Individual Level ◽  
Modelling Framework ◽  
Global Population

AbstractWe present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

scholarly journals Threshold Effects of Infectious Disease Outbreaks on Livestock Prices: Cases of African Swine Fever and Avian Influenza in South Korea

2021 ◽  
Vol 11 (11) ◽  
pp. 5114
Author(s):  
Hyung-Chul Rah ◽  
Hyeon-Woong Kim ◽  
Aziz Nasridinov ◽  
Wan-Sup Cho ◽  
Seo-Hwa Choi ◽  
...  
Keyword(s):  
Avian Influenza ◽  
Infectious Diseases ◽  
Disease Outbreaks ◽  
African Swine Fever ◽  
Threshold Effect ◽  
Impact Response ◽  
Threshold Effects ◽  
Infectious Disease Outbreaks ◽  
Retail Prices ◽  
The Impact

In this paper we demonstrate the threshold effects of infectious diseases on livestock prices. Daily retail prices of pork and chicken were used as structured data; news and SNS mentions of African Swine Fever (ASF) and Avian Influenza (AI) were used as unstructured data. Models were tested for the threshold effects of disease-related news and SNS frequencies, specifically those related to ASF and AI, on the retail prices of pork and chicken, respectively. The effects were found to exist, and the values of ASF-related news on pork prices were estimated to be −9 and 8, indicating that the threshold autoregressive (TAR) model can be divided into three regimes. The coefficients of the ASF-related SNS frequencies on pork prices were 1.1666, 0.2663 and −0.1035 for regimes 1, 2 and 3, respectively, suggesting that pork prices increased by 1.1666 Korean won in regime 1 when ASF-related SNS frequencies increased. To promote pork consumption by SNS posts, the required SNS frequencies were estimated to have impacts as great as one standard deviation in the pork price. These values were 247.057, 1309.158 and 2817.266 for regimes 1, 2 and 3, respectively. The impact response periods for pork prices were estimated to last 48, 6, and 8 days for regimes 1, 2 and 3, respectively. When the prediction accuracies of the TAR and autoregressive (AR) models with regard to pork prices were compared for the root mean square error, the prediction accuracy of the TAR model was found to be slightly better than that of the AR. When the threshold effect of AI-related news on chicken prices was tested, a linear relationship appeared without a threshold effect. These findings suggest that when infectious diseases such as ASF occur for the first time, the impact on livestock prices is significant, as indicated by the threshold effect and the long impact response period. Our findings also suggest that the impact on livestock prices is not remarkable when infectious diseases occur multiple times, as in the case of AI. To date, this study is the first to suggest the use of SNS to promote meat consumption.

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

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe 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 both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, 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. As a solution, we propose simple and general 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 and validate 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.

scholarly journals Building reaction kinetic models for amiloid fibril growth

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1607311 ◽  
Author(s):  
Svetoslav Marinov Markov
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Reaction Kinetic ◽  
Growth Models ◽  
Reaction Network ◽  
Network Models ◽  
Point Of View ◽  
Logistic Growth ◽  
Sigmoidal Functions ◽  
Methodological Aspects

In this work we  discuss some methodological aspects of the creation and formulation of mathematical  models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We   propose several reaction network  models  for  the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using  the computer algebra system   Mathematica.

scholarly journals In search of a new economic model determined by logistic growth

2019 ◽  
Vol 31 (2) ◽  
pp. 339-368 ◽  
Author(s):  
R. G. SMIRNOV ◽  
K. WANG
Keyword(s):  
Economic Growth ◽  
Group Theory ◽  
Growth Models ◽  
Production Functions ◽  
Perfect Competition ◽  
Logistic Growth ◽  
Economic Data ◽  
Lie Group Theory ◽  
Wage Share ◽  
Economic Growth Models

In this paper, we extend the work by Sato devoted to the development of economic growth models within the framework of the Lie group theory. We propose a new growth model based on the assumption of logistic growth in factors and derive the corresponding production functions, as well as a compatible notion of wage share. In the process, it is shown that the new functions compare reasonably well against relevant economic data. The corresponding problem of maximisation of profit under conditions of perfect competition is solved with the aid of one of these functions. In addition, it is explained in reasonably rigorous mathematical terms why Bowley’s law no longer holds true in the post-1960 data.

Different policy instruments and the threshold effects on collaboration efficiency in China

2020 ◽  
Vol 47 (3) ◽  
pp. 348-359
Author(s):  
Hua Cheng ◽  
Zhiying Zhang ◽  
Zhongju Liao ◽  
Yong Wei ◽  
Joseph Martial Nkongo Mvondo
Keyword(s):  
Policy Instruments ◽  
Threshold Effect ◽  
Tax Incentives ◽  
Threshold Effects ◽  
Policy Makers ◽  
Tax Incentive ◽  
Important Means ◽  
University Industry ◽  
Positive Effect

Abstract University–industry R&D collaboration is an important means to improve innovation efficiency; many governments have issued policies to promote it. The most frequent policy instruments implemented by policy-makers to foster firms’ innovation are subsidies and tax incentives. The article elaborated on how subsidies and tax incentives influence the R&D collaboration efficiency through a panel dataset from 2009 to 2015 in China. The result showed that subsidies and tax incentives have a positive effect on collaboration efficiency, and the effect of subsidies on output is bigger than that of tax incentives. Taking the intensity of subsidy as a threshold variable, there is a significant single threshold effect on collaboration efficiency. However, there is no threshold effect when the intensity of the tax incentive used as the threshold variable.

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