Interspecific Competition Coefficients Research Articles

Coexistence and competitive exclusion in a time-periodic Lotka-Volterra competition-diffusion system

The evolutionary impact of both temporal periodicity and spatial heterogeneity on population ecology is a challenging problem. Hutson et al. (2001) [12] and Bai et al. (2022) [2] studied the effects of diffusion rates on the dynamics of a time-periodic Lotka-Volterra competition-diffusion system with identical interspecific competition abilities. In this paper, we consider the case of different interspecific competition coefficients. The obtained results can be divided into two groups. The first part focuses on the interplay between the diffusion intensities and the interspecific competition coefficients on the dynamics in the weak competition case. We provide some sufficient conditions on coexistence and competitive exclusion. The second part considers the dynamics for fixed diffusion coefficients and varying competition coefficients. We not only provide a complete classification on the dynamics when one of the interspecific competition coefficients is small, but also show the multiple coexistence periodic patterns by applying the bifurcation method.

Global dynamics of a Lotka-Volterra competition-diffusion system with nonlinear boundary conditions

In this paper, a Lotka-Volterra competition-diffusion system subject to nonlinear boundary conditions is considered with an aim to understand the nonlinear balance between two competing nonlinear mechanisms (namely, interior reaction and boundary flux). A complete picture on the global dynamics (including the existence, nonexistence, global stability, and steady-state bifurcation of semi-trivial positive steady-state solutions) has been studied in terms of inter-specific competition coefficients, the growth rate functions, and boundary reaction functions. Our results extend largely the relevant results in the existing literature on Lotka-Volterra competition-diffusion systems, even those with homogeneous boundary conditions.

The effects of evolution on the stability of competing species

Based on evolutionary game theory and Darwinian evolution, we propose and study discrete-time competition models of two species where at least one species has an evolving trait that affects their intra-specific, but not their inter-specific competition coefficients. By using perturbation theory, and the theory of the limiting equations of non-autonomous discrete dynamical systems, we obtain global stability results. Our theoretical results indicate that evolution may promote and/or suppress the stability of the coexistence equilibrium depending on the environment. This relies crucially on the speed of evolution and on how the intra-specific competition coefficient depends on the evolving trait. In general, equilibrium destabilization occurs when , when the speed of evolution is sufficiently slow. In this case, we conclude that evolution selects against complex dynamics. However, when evolution proceeds at a faster pace, destabilization can occur when . In this case, if the competition coefficient is highly sensitive to changes in the trait v, destabilization and complex dynamics occur. Moreover, destabilization may lead to either a period-doubling bifurcation, as in the non-evolutionary Ricker equation, or to a Neimark-Sacker bifurcation.

Dynamics of heterogeneous population due to spatially distributed parameters and an ideal free pair

Population movements are necessary to survive the individuals in many cases and depend on available resources, good habitat, global warming, climate change, supporting the environment, and many other issues. This study explores the spatiotemporal effect on the dynamics of the reaction-diffusion model for two interacting populations in a heterogeneous habitat. Both species are assumed to compete for different fundamental resources, and the diffusion strategies of both organisms follow the resource-based diffusion toward a positive distribution function for a large variety of growth functions. Depending on the values of spatially distributed interspecific competition coefficients, the study is conducted for two cases: weak competition and strong competition, which do not perform earlier in the existing literature. The stability of global attractors is studied for different conditions of resource function and carrying capacity. We investigated that in the case of weak competition, coexistence is attainable, while strong competition leads to competitive exclusion. This is an emphasis on how resource-based diffusion in the niche impacts selection. When natural resources are in sharing, either competition or predator-prey interaction leads to competitive exclusion or coexistence of competing species. However, we concentrate on the situation in which the ideal free pair is achieved without imposing any other additional conditions on the model's parameters. The effectiveness of the model is accomplished by numerical computation for both one and two space dimension cases, which is very important for biological consideration.

The Ricker Competition Model of Two Species: Dynamic Modes and Phase Multistability

The model of two species competing for a resource proposed by R. May and A.P. Shapiro has not yet been fully explored. We study its dynamic modes. The model reveals complex dynamics: multistable in-phase and out-of-phase cycles, and their bifurcations occur. The multistable out-of-phase dynamic modes can bifurcate via the Neimark–Sacker scenario. A value variation of interspecific competition coefficients changes the number of in-phase and out-of-phase modes. We have suggested an approach to identify the bifurcation (period-doubling, pitchfork, or saddle-node bifurcations) due to which in-phase and out-of-phase periodic points appear. With strong interspecific competition, the population’s survival depends on its growth rate. However, with a specific initial condition, a species with a lower birth rate can displace its competitor with a higher one. With weak interspecific competition and sufficiently high population growth rates, the species coexist. At the same time, the observed dynamic mode or the oscillation phase can change due to altering of the initial condition values. The influence of external factors can be considered as an initial condition modification, leading to dynamics shift due to the coexistence of several stable attractors.

Finding the right mix: a framework for selecting seeding rates for cover crop mixtures.

Cover crop mixtures have the potential to provide more ecosystem services than cover crop monocultures. However, seeding rates that are typically recommended (i.e. seeding rate of monoculture divided by the number of species in the mixture) are non‐optimized and often result in the competitive species dominating the mixture, and therefore limiting the amount of ecosystem services that are provided. We created an analytical framework for selecting seeding rates for cover crop mixtures that maximize multifunctionality while minimizing seed costs. The framework was developed using data from a field experiment, which included six response surface designs of two‐species mixtures, as well as a factorial replacement design of three‐species and four‐species mixtures. We quantified intraspecific and interspecific competition among two grasses and two legume cover crop species with grass and legume representing two functional groups: pearl millet [Pennisetum glaucum (L.) R.Br.], sorghum sudangrass [Sorghum bicolor (L.) Moench × Sorghum sudanense (Piper) Stapf], sunn hemp (Crotalaria juncea L.), and cowpea [Vigna unguiculata (L.) Walp]. Yield–density models were fit to estimate intraspecific and interspecific competition coefficients for each species in biculture. The hierarchy from most to least competitive was sorghum sudangrass > sunn hemp > pearl millet > cowpea. Intraspecific competition of a less competitive species was the greatest when the biculture was composed of two species in the same functional group. Competition coefficients were used to build models that estimated the biomass of each cover crop species in three‐species and four‐species mixtures. The competition coefficients and models were validated with an additional nine site‐years testing the same cover crop mixtures. The biomass of a species in a site‐year was accurately predicted 69% of the time (low root mean square error, correlation > 0.5, not biased, r 2 > 0.5). Applying the framework, we designed three‐species and four‐species mixtures by identifying relative seeding rates that produced high biomass with high species evenness (i.e. high multifunctionality) at low seed costs based on a Pareto front analysis of 10,418 mixtures. Accounting for competition when constructing cover crop mixtures can improve the ecosystem services provided, and such an advancement is likely to lead to greater farmer adoption.

Metacyclops minutus and Daphnia magna interspecific competition coefficients under CO2-mediated acidification

Metacyclops minutus and Daphnia magna interspecific competition coefficients under CO2-mediated acidification

Coexistence in a competition-diffusion-advection system with equal amount of total resources.

We consider a Lotka-Volterra competition-diffusion-advection system with the total resources for two competitors fixed at the same level. We reveal the combined effect of competition abilities and spatial variations on the coexistence of two competing species. It is obtained that when the ratio of advection rate α to diffusion rate d1 is appropriately large, the two competing species will always coexist if the inter-specific competition coefficients (b,c) in (0,1]×(0,1] and when the ratio is appropriately small, the two species will coexist if the inter-specific competition coefficients c is appropriately small and b is in (0,1].

Positive solution branches of two-species competition model in open advective environments

The effect of competition is an important topic in spatial ecology. This paper deals with a general two-species competition system in open advective and inhomogeneous environments. At first, the critical values on the interspecific competition coefficients are established, which determine the stability of semi-trivial steady states. Secondly, by analyzing the nonexistence of coexistence steady states and using the theory of monotone dynamical system, we find that the competitive exclusion principle holds if one of the interspecific competition coefficients is large and the other is in a certain range. Thirdly, in terms of these critical values, the structure and direction of bifurcating branches of positive equilibria arising from two semi-trivial steady states are given by means of the bifurcation theory and stability analysis. Finally, we show that multiple coexistence occurs under certain regimes.

On steady state of some Lotka-Volterra competition-diffusion-advection model

In this paper, we study a shadow system of a two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. We show that for any given migration, if the product of interspecific competition coefficients of competitors is small, then the shadow system has coexistence state; otherwise we can always find some migration such that it has no coexistence state. Moreover, these findings can be applied to steady state of the two-species Lotka-Volterra competition-diffusion-advection model. Particularly, we show that if the interspecific competition coefficient of the invader is sufficiently small, then rapid diffusion of the invader can drive to coexistence state.

Spiraling Asymptotic Profiles of Competition‐Diffusion Systems

AbstractThis paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction‐diffusion systems with strongly competitive interactions of Lotka‐Volterra type, when the matrix of the interspecific competition coefficients is asymmetric and the competition parameter tends to infinity. Unlike the symmetric case, when it is known that the nodal set consists of a locally finite collection of curves meeting with equal angles at a locally finite number of singular points, the asymmetric case shows the emergence of spiraling nodal curves, still meeting at locally isolated points with finite vanishing order. © 2019 Wiley Periodicals, Inc.

On a competitive system with ideal free dispersal

In this article we study the long term behavior of the competitive system{∂u∂t=∇⋅[α(x)∇um]+u(m(x)−u−bv)inΩ,t>0,∂u∂t=∇⋅[β(x)∇v]+v(m(x)−cu−v)inΩ,t>0,∇um⋅nˆ=∇v⋅nˆ=0on∂Ω,t>0, which supports for the first species an ideal free distribution, that is a positive steady state which matches the per-capita growth rate. Previous results have stated that when b=c=1 the ideal free distribution is an evolutionarily stable and neighborhood invader strategy, that is the species with density v always goes extinct. Thus, of particular interest will be to study the interplay between the inter-specific competition coefficients b,c and the diffusion coefficients α(x) and β(x) on the critical values for stability of semi-trivial steady states, and the structure of bifurcation branches of positive equilibria arising from these equilibria. We will also show that under certain regimes the system sustains multiple positive steady states.

Specific interactions leading to transgressive overyielding in cover crop mixtures

Growing mixtures of species instead of sole crops is expected to increase the ecosystem services provided by cover crops. This study aimed at understanding the interactions between species and investigating how they affect the performance of the mixture. Four species were combined in six bispecific mixtures in a field experiment. The performance of each species when grown in a mixture was compared to its performance as a sole crop at different sowing densities, to characterise the influence of intra- and interspecific competition for each species. Intra- and interspecific competition coefficients were quantified using a response surface design and the hyperbolic yield-density equation. Interactions between the four species ranged from facilitation to competition. Most of the mixtures exhibited transgressive overyielding. Without nitrogen (N) fertilisation, high complementarity between species allowed to achieve the highest biomass. With N fertilisation, high dominance of one mixture component should be avoided to achieve good performance. A revised approach in the use of the land equivalent ratio for the evaluation of cover crop mixtures is also proposed in this study. It allows to better identify transgressive overyielding in mixtures and to better characterise the effect of one species on the other within the mixture.

Community diversity and total abundance: Quantitative predictions from competition niche theory

Lotka–Volterra niche competition theory (LVNCT) is based on Lotka–Volterra competition equations with competition coefficients between pairs of species determined by the intensity of their niche overlap though the MacArthur–Levins niche overlap formula. Here I study analytically and numerically the predictions of LVNCT concerning total abundance and biodiversity, measured by the Shannon equitability index. Firstly, a set of simplifying assumptions that render the LVNCT amenable of analytical treatment are considered. In particular I derive an approximated formula for the total abundance, as the inverse of the mean value of the interspecific competition coefficients, which works pretty well both for the transient and steady regime and for a wide range of the typical niche width σ. Secondly, I analyze, by means of simulations, the effect of relaxing the above simplifying assumptions when considering more realistic conditions. It turns out that the approximated formula for the total abundance is quite robust and its potential implications for management are discussed. I also analyze the predicted relationship between community productivity and diversity.

Global dynamics of a competition model with nonlocal dispersal II: The full system

In this paper, we study logistic models with non-local dispersal for two competing species. In the weak competition case, the global asymptotic behavior of solutions is completely classified provided one of the following conditions is valid:•one diffusion rate is small;•one diffusion rate is large;•two diffusion rates are close. This is a continuation of the work [16]. Our results illustrate the effects of non-local dispersals and interspecific competition coefficients in the competition system with spatially heterogeneous environments.

Global dynamics of a competition model with non-local dispersal I: The shadow system

Equations with non-local dispersal have been widely used as models in biology. In this paper we focus on logistic models with non-local dispersal, for both single and two competing species. We show the global convergence of the unique positive steady state for the single equation and derive various properties of the positive steady state associated with the dispersal rate. We investigate the effects of dispersal rates and inter-specific competition coefficients in a shadow system for a two-species competition model and completely determine the global dynamics of the system. Our results illustrate that the effect of dispersal in spatially heterogeneous environments can be quite different from that in homogeneous environments.

On multidimensional discrete-time Beverton–Holt competition models

Following Ackleh et al. (2005), we study the multidimensional discrete-time competitive Beverton–Holt equations with equal interspecific competition coefficients. It is shown that competitive exclusion occurs if only one species has the largest carrying capacity. Otherwise, all the species with the largest carrying capacity coexist. In the former case, the system is globally asymptotically stable. In the latter case, the system has a linear stable manifold.

Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems

In this paper we study the interactions between diffusion and heterogeneity of the environment in the classical diffusive Lotka--Volterra competition systems. In the weak competition case, we establish the uniqueness, hence the global asymptotic stability, of coexistence steady states under various circumstances, and thereby we obtain a complete understanding of the change in dynamics when one of the interspecific competition coefficients is small.

On the effects of migration and inter-specific competitions in steady state of some Lotka-Volterra model

Shadow systems are often used to approximate reaction-diffusion systems when one of the diffusion rates is large. In this paper, we investigate in a shadow system the effects of migrationand interspecific competition coefficients on the existence of positive solutions. Our study shows that for any given migration, if the interspecific competition coefficient of the invader issmall, then the shadow system has coexistence state; otherwisewe can always find some migration such that it has no coexistence state. Moreover, thesefindings can be applied to steady state of a two-species Lotka-Volterracompetition-diffusion model. Particularly, we show that if the interspecificcompetition coefficient of the invader is sufficiently small, then rapid diffusion of the invader can drive tocoexistence state.

Evaluating the impact of herbivory by a grasshopper, Cornops aquaticum (Orthoptera: Acrididae), on the competitive performance and biomass accumulation of water hyacinth, Eichhornia crassipes (Pontederiaceae)

The water hyacinth grasshopper, Cornops aquaticum is being considered for release in South Africa as a biocontrol agent for water hyacinth, Eichhornia crassipes. The release decision was to be based on C. aquaticum’s potential efficacy, in addition to its host specificity. An additive series analysis of competition between E. crassipes and a similar free-floating macrophyte, water lettuce ( Pistia stratiotes), was used to assess the impact of C. aquaticum on E. crassipes competitive ability and potential for biomass accumulation. The data was analyzed using an inverse linear model where the competitive performance of both plant species was estimated using multiple linear regressions of the inverse of biomass yield. Eichhornia crassipes was 24 times more competitive than P. stratiotes without C. aquaticum herbivory but this was reduced to 12 in the presence of herbivory which equated to a 50% reduction in its competitive performance. Pistia stratiotes competitive ability increased from 3.8 to 4.8 (i.e. 21%) when E. crassipes was damaged by C. aquaticum. The interspecific competition coefficients from E. crassipes on P. stratiotes were also no longer statistically significant in the presence of C. aquaticum herbivory. Biomass accumulation of E. crassipes was significantly reduced by C. aquaticum herbivory at both planting densities tested. By comparison with similar studies on two of the most abundant, widespread and damaging biocontrol agents already released in South Africa, C. aquaticum has a greater impact on E. crassipes, suggesting it will be a valuable addition to the South African biological control program.