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 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 Bifurcation Analysis of Time-Delay Model of Consumer with the Advertising Effect

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 417 ◽  
Author(s):  
Mahmoud A. Abd-Rabo ◽  
Mohammed Zakarya ◽  
Clemente Cesarano ◽  
Shaban Aly
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Delay Model ◽  
Advertising Effect ◽  
Reaction Diffusion Model ◽  
The Stability ◽  
Main Message ◽  
The Impact

Given the economic importance of advertising and product promotions, we have developed a diffusion model to describe the impact of advertising on sales. The main message of this study is to show the effect of advertising diffusion to convert potential buyers into actual customers which may result in persistent alteration in marketing over time. This work is devoted to studying the dynamic behavior of a reaction-diffusion model and its delayed version with the advertising effect. For the non-delay model, it is proven the existence of Hopf bifurcation. Moreover, the stability and direction of bifurcation of periodic solutions are detected. On the other hand, we consider there is a lag for responding of potential buyers to the advertising. Therefore, the time delay τ is deemed as an additional factor in the diffusion model. We have determined the critical values for the delay parameter that yield periodic solutions. Furthermore, the direction and the stability of bifurcating periodic solutions is studied. For supporting the theoretical analysis and demonstrate complex dynamic behaviors, numerical simulations including families of periodic curves are given.

scholarly journals Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1516
Author(s):  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Stelios Bekiros ◽  
Jinping Liu ◽  
Hadi Jahanshahi ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Linear Control ◽  
Control Law ◽  
Synchronization Problem ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions ◽  
Error System ◽  
The Stability ◽  
Complex Formations

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions.

scholarly journals Microbial competition reduces interaction distances to the low µm-range

2020 ◽  
Author(s):  
Rinke J. van Tatenhove-Pel ◽  
Tomaž Rijavec ◽  
Aleš Lapanje ◽  
Iris van Swam ◽  
Emile Zwering ◽  
...  
Keyword(s):  
Effective Interaction ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Dimensional System ◽  
Cellular Interactions ◽  
Natural Ecosystems ◽  
Concentration Gradients ◽  
Reaction Diffusion Model ◽  
The Impact ◽  
Three Dimensional System

AbstractMetabolic interactions between cells affect microbial community compositions and hence their function in ecosystems. It is well-known that under competition for the exchanged metabolite, concentration gradients constrain the distances over which interactions can occur. However, interaction distances are typically quantified in two-dimensional systems or without accounting for competition or other metabolite-removal, conditions which may not very often match natural ecosystems. We here analyze the impact of cell-to-cell distance on unidirectional cross-feeding in a three-dimensional system with competition for the exchanged metabolite. Effective interaction distances were computed with a reaction-diffusion model and experimentally verified by growing a synthetic consortium of 1 µm-sized metabolite producer, receiver and competitor cells in different spatial structures. We show that receivers cannot interact with producers ∼15 µm away from them, as product concentration gradients flatten close to producer cells. We developed an aggregation protocol and created variants of the receiver cells’ import system, to show that within producer-receiver aggregates even low affinity receiver cells could interact with producers. These results show that competition or other metabolite-removal of a public good in a three-dimensional system reduces the interaction distance to the low micrometer-range, highlighting the importance of concentration gradients as physical constraint for cellular interactions.

scholarly journals Why microbes secrete molecules to modify their environment: the case of iron-chelating siderophores

2019 ◽  
Vol 16 (150) ◽  
pp. 20180674 ◽  
Author(s):  
Gabriel E. Leventhal ◽  
Martin Ackermann ◽  
Konstanze T. Schiessl
Keyword(s):  
Iron Uptake ◽  
Large Fraction ◽  
Reaction Diffusion ◽  
Iron Particles ◽  
Diffusion Limitation ◽  
Iron Solubility ◽  
Reaction Diffusion Model ◽  
Particulate Iron ◽  
The Impact ◽  
Release Strategy

Many microorganisms secrete molecules that interact with resources outside of the cell. This includes, for example, enzymes that degrade polymers like chitin, and chelators that bind trace metals like iron. In contrast to direct uptake via the cell surface, such release strategies entail the risk of losing the secreted molecules to environmental sinks, including ‘cheating’ genotypes. Nevertheless, such secretion strategies are widespread, even in the well-mixed marine environment. Here, we investigate the benefits of a release strategy whose efficiency has frequently been questioned: iron uptake in the ocean by secretion of iron chelators called siderophores. We asked the question whether the release itself is essential for the function of siderophores, which could explain why this risky release strategy is widespread. We developed a reaction–diffusion model to determine the impact of siderophore release on iron uptake from the predominant iron sources in marine environments, colloidal or particulate iron, formed due to poor iron solubility. We found that release of siderophores is essential to accelerate iron uptake, as secreted siderophores transform slowly diffusing large iron particles to small, quickly diffusing iron–siderophore complexes. In addition, we found that cells can synergistically share their siderophores, depending on their distance and the size of the iron sources. Our study helps understand why release of siderophores is so widespread: even though a large fraction of siderophores is lost, the solubilization of iron through secreted siderophores can efficiently increase iron uptake, especially if siderophores are produced cooperatively by several cells. Overall, resource uptake mediated via release of molecules transforming their substrate could be essential to overcome diffusion limitation specifically in the cases of large, aggregated resources. In addition, we find that including the reaction of the released molecule with the substrate can impact the result of cooperative and competitive interactions, making our model also relevant for release-based uptake of other substrates.

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