Lotka-Volterra Competition Model Research Articles

Tractable models of ecological assembly

AbstractEcological assembly is a fundamental and yet poorly understood process. Three main obstacles hinder the development of a theory of assembly, and when these issues are sidestepped by making strong assumptions, one can build an assembly graph in which nodes are ecological communities and edges are invasions shifting their composition. The graph can then be analysed directly, without the need to consider dynamics. To showcase this framework, we build and analyse assembly graphs for the competitive Lotka–Volterra model, showing that in these cases sequential assembly (in which species invade a community one at a time) can reach the same configurations found when starting the system with all species present at different initial conditions. We discuss how our results can advance our understanding of assembly both from an empirical and a theoretical point of view, informing the study of ecological restoration and the design of ecological communities.

Scaling up biodiversity-ecosystem functioning relationships: the role of environmental heterogeneity in space and time.

The biodiversity and ecosystem functioning (BEF) relationship is expected to be scale-dependent. The autocorrelation of environmental heterogeneity is hypothesized to explain this scale dependence because it influences how quickly biodiversity accumulates over space or time. However, this link has yet to be demonstrated in a formal model. Here, we use a Lotka-Volterra competition model to simulate community dynamics when environmental conditions vary across either space or time. Species differ in their optimal environmental conditions, which results in turnover in community composition. We vary biodiversity by modelling communities with different sized regional species pools and ask how the amount of biomass per unit area depends on the number of species present, and the spatial or temporal scale at which it is measured. We find that more biodiversity is required to maintain functioning at larger temporal and spatial scales. The number of species required increases quickly when environmental autocorrelation is low, and slowly when autocorrelation is high. Both spatial and temporal environmental heterogeneity lead to scale dependence in BEF, but autocorrelation has larger impacts when environmental change is temporal. These findings show how the biodiversity required to maintain functioning is expected to increase over space and time.

The Dynamics of a Lotka-Volterra competition model with nonlocal diffusion and free boundaries

This paper is concerned with a Lotka-Volterra competition model with nonlocal diffusion and free boundaries, which describes the evolution of an invasive species with free boundaries in a one-dimensional habitat and a native species in the whole space. We prove the well-posedness of the model and obtain a spreading-vanishing dichotomy for the invasive species. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local model. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the local model, where the spreading has finite speed whenever spreading happens.

Bistability of a two-species competition model with stage structure

In this paper, we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure. Using the theory of generalized saddle-point behaviors, it is shown that there exists a [Formula: see text]-separatrix [Formula: see text] on its state space such that Species 2 wins the competition whenever the initial distribution is above [Formula: see text], while Species 1 wins the competition whenever the initial distribution is below [Formula: see text]. Combining with the previous conclusions of the system, we give a complete classification for global competitive dynamics. Furthermore, we carefully analyze the changes of the competition outcome after introducing the stage structure. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion

<p style='text-indent:20px;'>In this paper, we shall study the convergence rates of Tikhonov regularizations for the recovery of the growth rates in a Lotka-Volterra competition model with diffusion. The ill-posed inverse problem is transformed into a nonlinear minimization system by an appropriately selected version of Tikhonov regularization. The existence of the minimizers to the minimization system is demonstrated. We shall propose a new variational source condition, which will be rigorously verified under a Hölder type stability estimate. We will also derive the reasonable convergence rates under the new variational source condition.</p>

Study on fungal growth process based on K-means clustering and Lotka-Volterra interspecific competition Model

The carbon cycle has a great impact on the environmental changes of the Earth, and fungus play a crucial role in the decomposition of ground litter and woody fibers in nature, so it is very necessary to study the growth process of fungus. First, we used the K-means Clustering Algorithm to classify the different species of fungus into four categories according to their growth rates as well as their moisture tolerance. This not only measures the similarity between various fungus more intuitively, but also reduces the difficulty of subsequent modeling work. Second, we considered environmental accommodation, intra- and interspecific competition, and used this to modify the Lotka-Volterra interspecific competition Model and to derive the relationship between fungal growth rate and time. Then, we used this model for long-term and short-term prediction of fungal growth. In the short term, the growth rate of fungi increased rapidly with time; in the long term, the fungal population tended to be stable.

Asymptotic Properties of a Lotka-Volterra Competition and Mutualism Model Under Stochastic Perturbations

Asymptotic Properties of a Lotka-Volterra Competition and Mutualism Model Under Stochastic Perturbations

The Minimal Wave Speed of a Lotka-Volterra Competition Model

The minimal wave speed selection for the traveling waves of a 3-species competition system with monostable nonlinearity was considered. First, a comparison method was used to establish minimal-speed selection mechanisms through construction of subtle upper and lower solutions. Then, the speed selection about the threshold values of competition coefficients and the estimations were obtained. Finally, some numerical simulations were performed to show that the obtained results extend those in the previous literatures.

Some Novel Results in Two Species Competition

We investigate the classical two species ODE and PDE Lotka-Volterra competition models, where one of the competitors could potentially go extinct in finite time. We show that in this setting, classical theories and intuitions do not hold, and various counter intuitive dynamics are possible. In particular, the weaker competitor could avoid competitive exclusion, and the slower diffuser may not win. Numerical simulations are performed to verify our analytical findings.

Carrying simplex in the Lotka-Volterra competition model with seasonal succession with applications

We investigate the dynamics of the Poincar \begin{document}$ \acute{\rm e} $\end{document} -map for an \begin{document}$ n $\end{document} -dimensional Lotka-Volterra competitive model with seasonal succession. It is proved that there exists an \begin{document}$ (n-1) $\end{document} -dimensional carrying simplex \begin{document}$ \Sigma $\end{document} which attracts every nontrivial orbit in \begin{document}$ \mathbb{R}^n_+ $\end{document} . By using the theory of the carrying simplex, we simplify the approach for the complete classification of global dynamics for the two-dimensional Lotka-Volterra competitive model with seasonal succession proposed in [Hsu and Zhao, J. Math. Biology 64(2012), 109-130]. Our approach avoids the complicated estimates for the Floquet multipliers of the positive periodic solutions.

Time delays and chaos in two competing species revisited

This paper reexamines the Lotka-Volterra competition model with two delays. The steady state is shown to be locally asymptotically stable without delay. If the two delays are identical, then the model becomes a one-delay system. The critical value of the delay is determined when stability might be lost. If the delays are different, then the stability switching curves are analytically defined and numerically verified. It is demonstrated that the unstable two-delay system may exhibit periodic behavior, multistability, quasi period-doubling cascade and even complicated dynamics depending on model parameters.

Spreading speed of the periodic Lotka-Volterra competition model

In this paper, we study the minimal speed (spreading speed) selection mechanism of traveling waves to a periodic diffusive Lotka-Volterra model with monostable nonlinearity. The method of upper and lower solutions pair is applied to establish the existence of traveling waves. We prove that the nature of nonlinear selection is to find a lower solution pair with the first species decaying in a faster rate. By novel constructions of various upper and lower solutions, we obtain a number of new results on the minimal speed determinacy. Numerical simulations are carried out to illustrate all of our discoveries.

Quantifying the bioprotective effect of Lactobacillus sakei CTC494 against Listeria monocytogenes on vacuum packaged hot-smoked sea bream

In this study, the bioprotective potential of Lactobacillus sakei CTC494 against Listeria monocytogenes CTC1034 was evaluated on vacuum packaged hot-smoked sea bream at 5 °C and dynamic temperatures ranging from 3 to 12 °C. The capacity of three microbial competition interaction models to describe the inhibitory effect of L. sakei CTC494 on L. monocytogenes was assessed based on the Jameson effect and Lotka-Volterra approaches. A sensory analysis was performed to evaluate the spoiling capacity of L. sakei CTC494 on the smoked fish product at 5 °C. Based on the sensory results, the bioprotection strategy against the pathogen was established by inoculating the product at a 1:2 ratio (pathogen:bioprotector, log CFU/g). The kinetic growth parameters of both microorganisms were estimated in mono-culture at constant storage (5 °C). In addition, the inhibition function parameters of the tested interaction models were estimated in co-culture at constant and dynamic temperature storage using as input the mono-culture kinetic parameters. The growth potential (δ log) of L. monocytogenes, in mono-culture, was 3.5 log on smoked sea bream during the experimental period (20 days). In co-culture, L. sakei CTC494 significantly reduced the capability of L. monocytogenes to grow, although its effectiveness was temperature dependent. The LAB strain limited the growth of the pathogen under storage at 5 °C (<1 log increase) and at dynamic profile 2 (<2 log increase). Besides, under storage at dynamic profile 1, the growth of L. monocytogenes was inhibited (<0.5 log increase). These results confirmed the efficacy of L. sakei CTC494 for controlling the pathogen growth on the studied fish product. The Lotka-Volterra competition model showed slightly better fit to the observed L. monocytogenes growth response than the Jameson-based models according to the statistical performance. The proposed modelling approach could support the assessment and establishment of bioprotective culture-based strategies aimed at reducing the risk of listeriosis linked to the consumption of RTE hot-smoked sea bream.

Spreading dynamics of a Lotka-Volterra competition model in periodic habitats

Spreading speed of spatio-temporal nonlinear dynamical system can sometimes be determined either by its corresponding linear system with an explicit speed formula, or by the complicated nonlinear system itself with the existence of a pushed wavefront. In this paper, the spreading speed (the minimal speed of wavefronts) for a Lotka-Volterra competition model in spatially periodic habitats is investigated. We establish new results on the linear and nonlinear selections in terms of the spatio-periodic coefficient functions. In the case of nonlinear selection, lower and upper bound estimates of the minimal speed are provided.

Forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats

This paper is mainly concerned with the forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats. We first show that there exist two positive numbers c1∗ and c2∗ such that the system admits a forced wave provided that the forcing speed c∈(−c2∗,c1∗) by the iterative techniques combining with some known results for the forced moving KPP equations. Meanwhile, we use some delicate analysis to obtain the asymptotic behaviors at infinity of the forced waves with nonzero forcing speed c∈(−c2∗,0)∪(0,c1∗). Then, based on the comparison argument, we prove that the gap formations exist for c>c1∗ and c<−c2∗. Finally, some numeric simulation results are presented to confirm our theoretical results, which also contains the critical cases of c=c1∗ and c=−c2∗.

Temperature Shapes Ecological Dynamics in Mixed Culture Fermentations Driven by Two Species of the Saccharomyces Genus.

Mixed culture wine fermentations combining species within the Saccharomyces genus have the potential to produce new market tailored wines. They may also contribute to alleviating the effects of climate change in winemaking. Species, such as S. kudriavzevii, show good fermentative properties at low temperatures and produce wines with lower alcohol content, higher glycerol amounts and good aroma. However, the design of mixed culture fermentations combining S. cerevisiae and S. kudriavzevii species requires investigating their ecological interactions under cold temperature regimes. Here, we derived the first ecological model to predict individual and mixed yeast dynamics in cold fermentations. The optimal model combines the Gilpin-Ayala modification to the Lotka-Volterra competitive model with saturable competition and secondary models that account for the role of temperature. The nullcline analysis of the proposed model revealed how temperature shapes ecological dynamics in mixed co-inoculated cold fermentations. For this particular medium and species, successful mixed cultures can be achieved only at specific temperature ranges or by sequential inoculation. The proposed ecological model can be calibrated for different species and provide valuable insights into the functioning of alternative mixed wine fermentations.

The path to a 2025 nuclear-free Taiwan: An analysis of dynamic competition among emissions, energy, and economy

Taiwan intends to be nuclear free by 2025. This study employs the Lotka–Volterra competition model for sustainable development to analyze the emissions–energy–economy (3Es) issue to make appropriate policy suggestions for a nuclear-free transition. It also offers a new approach to naming the 3E relationship. The literature review shows that the environmental Kuznets curve accompanies the feedback and conservation hypotheses. In the 3E dynamics relationship analysis, the model shows a good mean absolute percentage error (&lt;15%) for the model estimation. The key findings are as follows: 1) the fossil fuel-led economy exists; 2) CO2 emissions are reduced with nuclear energy consumption; 3) renewable energy is far from scale; 4) a complementary effect exists between fossil fuel and nuclear energy consumption; and 5) gas retrofitting and phasing out of nuclear seem imminent. In the energy transition, Taiwan drastically cuts nuclear energy without considering energy diversity due to which troubles might ensue. The priority issue for Taiwan’s energy mix is energy security. To deal with these concerns, this study suggests the government could improve energy efficiency, build a smart grid, develop carbon capture and storage, and reconsider putting nuclear energy back into the energy mix before renewable energy is scaled.

Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka–Volterra competition model

A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which the diffusion coefficients, resource functions and competition rates are all spatially heterogeneous, the positive equilibrium solution is globally asymptotically stable when it exists. Secondly the existence and global asymptotic stability of the positive and semi-trivial equilibrium solutions are obtained for the model with arbitrary number of species under the assumption of spatially heterogeneous resource distribution. A new Lyapunov functional method is developed to prove the global stability of a non-constant equilibrium solution in heterogeneous environment.

Stability switching curves in a Lotka–Volterra competition system with two delays

This study is devoted to consider the dynamic properties of a Lotka–Volterra competition model with two discrete delays. First, it reviews stability conditions of the no-delay model as a benchmark. Second, it examines the delay model and analytically establishes the stability switching curve on which stability is switched to instability and vice versa. Finally, numerical simulations are performed to confirm the theoretical results such as Hopf bifurcations and, further, demonstrate a wide variety of dynamics ranging from simple limit cycle to the existence of multi-stability and the birth of chaotic dynamics.

Coexistence and bistability of a competition model with mixed dispersal strategy

In this paper, we investigate a Lotka–Volterra competition model with Danckwerts boundary conditions in a one-dimensional habitat where one species assumes pure random diffusion while another one undergoes mixed movement (both random and directed movements). We focus on the joint influence of advection rate, intrinsic growth rate and interspecific competition coefficient on the competition outcomes. It turns out that there exist some critical curves which separate the stable region of the semitrivial steady states from the unstable one. The locations of these curves determine whether coexistence or bistability occurs. More precisely, there are various tradeoffs between advection rate, intrinsic growth rate and interspecific competition coefficient that allow the transition of competition outcomes including competition exclusion, coexistence and bistability. We illustrate our results in various parameter spaces.