scholarly journals Feasibility conditions of ecological models: Unfolding links between model parameters

2021 ◽  
Author(s):  
Mohammad AlAdwani ◽  
Serguei Saavedra
Keyword(s):  
Species Coexistence ◽  
Equilibrium Points ◽  
Ecological Models ◽  
Model Systems ◽  
Model Parameters ◽  
Functional Responses ◽  
Population Dynamics Model ◽  
Analytic Expressions ◽  
Systematic Understanding ◽  
Mathematical Relationships

AbstractOver more than 100 years, ecological research has been striving to derive internal and external conditions compatible with the coexistence of a given group of interacting species. To address this challenge, numerous studies have focused on developing ecological models and deriving the necessary conditions for species coexistence under equilibrium dynamics, namely feasibility. However, due to mathematical limitations, it has been impossible to derive analytic expressions if the isocline equations have five or more roots, which can be easily reached even in 2-species models. Here, we propose a general formalism to obtain the set of analytical conditions of feasibility for any polynomial population dynamics model of any dimension without the need to solve for the equilibrium locations. We additionally illustrate the application of our methodology by showing how it is possible to derive mathematical relationships between model parameters, while maintaining feasibility in modified Lotka-Volterra models with functional responses and higher-order interactions (model systems with at least five equilibrium points)—a task that is impossible to do with simulations. This work unlocks the opportunity to increase our systematic understanding of species coexistence.

scholarly journals Is the addition of higher-order interactions in ecological models increasing the understanding of ecological dynamics?

2019 ◽  
Author(s):  
Mohammad AlAdwani ◽  
Serguei Saavedra
Keyword(s):  
Equilibrium Points ◽  
Explanatory Power ◽  
Higher Order ◽  
Ecological Models ◽  
Model Parameters ◽  
Ecological Communities ◽  
Ecological Dynamics ◽  
Higher Order Terms ◽  
Population Dynamics Models ◽  
The Stability

AbstractRecent work has shown that higher-order interactions can increase the stability, promote the diversity, and better explain the dynamics of ecological communities. Yet, it remains unclear whether the perceived benefits of adding higher-order terms into population dynamics models come from fundamental principles or a simple mathematical advantage given by the nature of multivariate polynomials. Here, we develop a general method to quantify the mathematical advantage of adding higher-order interactions in ecological models based on the number of free-equilibrium points that can be engineered in a system (i.e., equilibria that can be feasible or unfeasible by tunning model parameters). We apply this method to calculate the number of free-equilibrium points in Lotka-Volterra dynamics. While it is known that Lotka-Volterra models without higher-order interactions only have one free-equilibrium point regardless of the number of parameters, we find that by adding higher-order terms this number increases exponentially with the dimension of the system. Our results suggest that while adding higher-order interactions in ecological models may be good for prediction purposes, they cannot provide additional explanatory power of ecological dynamics if model parameters are not ecologically restricted.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

Dynamics of one-prey two-predator system with square root functional response and time lag

2015 ◽  
Vol 08 (03) ◽  
pp. 1550029 ◽  
Author(s):  
O. P. Misra ◽  
Poonam Sinha ◽  
Chhatrapal Singh
Keyword(s):  
Numerical Simulation ◽  
Functional Response ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Time Lag ◽  
Critical Value ◽  
Square Root ◽  
Basic System ◽  
Functional Responses ◽  
Predator System

Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey–predator forming groups have been considered by many authors in their models. In the present paper we have considered a model for one prey and two competing predator populations with time lag and square root functional response on account of herd formation by prey. It is shown that due to the inclusion of another competing predator, the underlying system without delay becomes more stable and limit cycles do not occur naturally. However, after considering the effect of time lag in the basic system, limit cycles appear in the case of all equilibrium points when delay time crosses some critical value. From the numerical simulation, it is observed that the length of delay is minimum when only prey population survives and it is maximum when all the populations coexist.

scholarly journals A global database of photosynthesis model parameters, and modelled photosynthetic responses from every major terrestrial plant clade

2020 ◽  
Author(s):  
Mina Rostamza ◽  
Gordon G. McNickle
Keyword(s):  
Carbon Capture ◽  
Vascular Plant ◽  
Model Parameters ◽  
Plant Responses ◽  
Functional Responses ◽  
Terrestrial Plant ◽  
Photosynthetic Rates ◽  
Global Database ◽  
Plant Photosynthesis ◽  
Average Plant

ABSTRACTPlant photosynthesis is a major part of the global carbon cycle and climate system. Carbon capture by C3 plants is most often modelled using the Farquhar-von-Caemmerer-Berry (FvCB) equations. We undertook a global synthesis of all parameters required to solve the FvCB model. The publicly available dataset we assembled includes 3663 observations from 336 different C3 plant species among 96 taxonomic families coming from every major vascular plant clade (lycophytes, ferns, gymnosperms, magnoliids, eudicots and monocots). Geographically, the species in the database have distributions that span the majority of the globe. We used the model to predict photosynthetic rates for a hypothetical average plant in each major terrestrial plant clade and find that generally plants have dramatically increased their photosynthetic abilities through evolutionary time, with the average monocot (the youngest clade) achieving maximum rates of photosynthesis almost double that of the average lycophyte (the oldest clade). We also solved the model for different hypothetical average plant functional types (PFTs) and find that herbaceous species generally have much higher rates of photosynthesis compared to woody plants. Indeed, the maximum photosynthetic rate of graminoids is almost three times the rate of the average tree. The resulting functional responses to increasing CO2 in average hypothetical PFTs would suggest that most groups are already at or near their maximum rate of photosynthesis. However, phylogenetic analysis showed that there was no evidence of niche conservatism with most variance occurring within, rather than among clades (K=0.357, p=0.001). This high within-group variability suggests that average PFTs may obscure important plant responses to increasing CO2. Indeed, when we solved the model for each of the 3663 individual observations, we found that, contrary to the predictions of hypothetical average PFTs, that most plants are predicted to be able to increase their photosynthetic rates. These results suggest that global models should seek to incorporate high within-group variability to accurately predict plant photosynthesis in response to a changing climate.

scholarly journals Horizontal Gene Transfer Can Help Maintain the Equilibrium of Microbial Communities

2017 ◽  
Author(s):  
Yuhang Fan ◽  
Yandong Xiao ◽  
Babak Momeni ◽  
Yang-Yu Liu
Keyword(s):  
Population Dynamics ◽  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Microbial Communities ◽  
Transfer Rate ◽  
Species Coexistence ◽  
Focal Points ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Evolutionary Advantage

Horizontal gene transfer and species coexistence are two focal points in the study of microbial communities. The evolutionary advantage of horizontal gene transfer has not been well-understood and is constantly being debated. Here we propose a simple population dynamics model based on the frequency-dependent interactions between different genotypes to evaluate the influence of horizontal gene transfer on microbial communities. We find that both structural stability and robustness of the microbial community are strongly affected by the gene transfer rate and direction. An optimal gene flux can stablize the ecosystem, helping it recover from disturbance and maintain the species coexistence.

scholarly journals Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

2020 ◽  
Author(s):  
Ibrahim M. ELmojtaba ◽  
Fatma Al-Musalhi ◽  
Asma Al-Ghassani ◽  
Nasser Al-Salti
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Environmental Transmission ◽  
Estimated Parameters ◽  
Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

scholarly journals Bifurcation Analysis of a Two-Dimensional Neuron Model under Electrical Stimulation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Chunhua Yuan ◽  
Xiangyu Li
Keyword(s):  
Electrical Stimulation ◽  
Hopf Bifurcation ◽  
Dynamic Characteristics ◽  
Neuron Model ◽  
Equilibrium Points ◽  
Model Parameters ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Firing Characteristics

The two-dimensional neuron model can not only reproduce abundant firing patterns, but also satisfy the research of dynamical behavior because of its nonlinear characteristics. It is the most simplified model that includes the fast and slow variables required for neuron firing. In this paper, the dynamic characteristics of two-dimensional neuron model are described by both analytical and numerical methods, and the influence of model parameters and external stimuli on dynamic characteristics is described. The firing characteristics of the Prescott model under external electrical stimulation are studied, and the influence of electrophysiological parameters on the firing characteristics is analyzed. The saddle-node bifurcation and Hopf bifurcation characteristics are studied through the distribution of equilibrium points. It is found that there are critical saddle-node bifurcation and critical Hopf bifurcation in the Prescott model. And the value range of the key parameters that cause the critical bifurcation of the model is obtained by analytical methods.

scholarly journals Predator-prey nutrient competition undermines predator coexistence

2019 ◽  
Author(s):  
Toni Klauschies ◽  
Ursula Gaedke
Keyword(s):  
Nutrient Limitation ◽  
Uptake Rate ◽  
Species Coexistence ◽  
Logistic Growth ◽  
Nutrient Competition ◽  
Functional Responses ◽  
Predator Prey ◽  
Natural Systems ◽  
Prey System ◽  
Flow Through

AbstractContemporary theory of predator coexistence through relative non-linearity in their functional responses strongly relies on the Rosenzweig-MacArthur equations (1963) in which the (autotrophic) prey exhibits logistic growth in the absence of the predators. This implies that the prey is limited by a resource which availability is independent of the predators. This assumption does not hold under nutrient limitation where both prey and predators bind resources such as nitrogen or phosphorus in their biomass. Furthermore, the prey’s resource uptake-rate is assumed to be linear and the predator-prey system is considered to be closed. All these assumptions are unrealistic for many natural systems. Here, we show that predator coexistence on a single prey is strongly hampered when the prey and predators indirectly compete for the limiting resource in a flow-through system. In contrast, a non-linear resource uptake rate of the prey slightly promotes predator coexistence. Our study highlights that predator coexistence does not only depend on differences in the curvature of their functional responses but also on the type of resource constraining the growth of their prey. This has far-reaching consequences for the relative importance of fluctuation-dependent and -independent mechanisms of species coexistence in natural systems where autotrophs experience light or nutrient limitation.

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