Predator-prey Competition Research Articles

Dynamics of a non-local intraspecific competition predator–prey model with memory effect

In the paper, we investigate a diffusive predator–prey model with nonlocal intraspecific prey competition and spatial memory under Neumann boundary conditions. Through stability and bifurcation analysis, we find that the memory-based diffusion coefficient and the spatiotemporal diffusive delay have important effects on the dynamics of the model. By using the spatiotemporal diffusive delay as a bifurcation parameter, the critical values are determined for the stability of the positive constant steady state and the associated Hopf bifurcation. We find that the system may admit no stability switch, one stability switch and multiple stability switches.

Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations.

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. To match the results of any computer simulation to observations or experiments carried out on the macroscale, a mapping is required between the microscopic probabilities that define the Monte Carlo algorithm and the macroscopic reaction rates that are experimentally measured. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities (subject to specific rules of interaction) is a very difficult problem, and there is currently no systematic, accurate analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using lattice Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely, restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka-Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka-Volterra model and its May-Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a more thorough and deeper understanding of coarse graining in spatially extended stochastic reaction-diffusion systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters, with a focus on ecological systems. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.

Flexible reprogramming of Pristionchus pacificus motivation for attacking Caenorhabditis elegans in predator-prey competition

Animals with diverse diets must adapt their food priorities to a wide variety of environmental conditions. This diet optimization problem is especially complex for predators that compete with prey for food. Although predator-prey competition is widespread and ecologically critical, it remains difficult to disentangle predatory and competitive motivations for attacking competing prey. Here, we dissect the foraging decisions of the omnivorous nematode Pristionchus pacificus to reveal that its seemingly failed predatory attempts against Caenorhabditis elegans are actually motivated acts of efficacious territorial aggression. While P.pacificus easily kills and eats larval C.elegans with a single bite, adult C.elegans typically survives and escapes bites. However, non-fatal biting can provide competitive benefits by reducing access of adult C.elegans and its progeny to bacterial food that P.pacificus also eats. We show that the costs and benefits of both predatory and territorial outcomes influence how P.pacificus decides which food goal, prey or bacteria, should guide its motivation for biting. These predatory and territorial motivations impose different sets of rules for adjusting willingness to bite in response to changes in bacterial abundance. In addition to biting, predatory and territorial motivations also influence which search tactic P.pacificus uses to increase encounters with C.elegans. When treated with an octopamine receptor antagonist, P.pacificus switches from territorial to predatory motivation for both biting and search. Overall, we demonstrate that P.pacificus assesses alternate outcomes of attacking C.elegans and flexibly reprograms its foraging strategy to prioritize either prey or bacterial food.

Dynamics of a Predator–Prey-Competition System with Pure Delays

This paper deals with the non-autonomous Lotka–Volterra type one prey-two competitive predator systems with pure time delays. Based on the the comparison method and construction of the multiple Lyapunov functional, some new sufficient conditions on the boundedness, permanence, extinction and global attractivity of the system are established. In addition, two examples with numerical simulations are presented to illustrate the obtained theoretical results.

Predator-prey behaviour in self-replicating interstellar probes

AbstractThe concept of a rapid spread of self-replicating interstellar probes (SRPs) throughout the Milky Way adds considerable strength to Fermi's Paradox. A single civilization creating a single SRP is sufficient for a fleet of SRPs to grow and explore the entire Galaxy on timescales much shorter than the age of the Earth – so why do we see no signs of such probes? One solution to this Paradox suggests that self-replicating probes eventually undergo replication errors and evolve into predator-prey populations, reducing the total number of probes and removing them from our view.I apply Lotka-Volterra models of predator-prey competition to interstellar probes navigating a network of stars in the Galactic Habitable Zone to investigate this scenario. I find that depending on the local growth mode of both populations and the flow of predators/prey between stars, there are many stable solutions with relatively large numbers of prey probes inhabiting the Milky Way. The solutions can exhibit the classic oscillatory pattern of Lotka-Volterra systems, but this depends sensitively on the input parameters. Typically, local and global equilibria are established with prey sometimes outnumbering the predators. Accordingly, we find this solution to Fermi's Paradox does not reduce the probe population sufficiently to be viable.

Global Dynamics of a Three Species Predator-Prey Competition Model with Holling type II Functional Response on a Circular Domain

This paper is devoted to the study of a three species ecosystem model consisting of a prey, a predator and a top predator. This model is given by a reaction diffusion system defined on a circular spatial domain and incorporates the Holling type II and a modified Leslie- Gower functional response. The aim of this paper is to investigate theoretically and numerically the asymptotic behavior of the interior equilibrium of the model. The conditions of boundedness, existence of a positively invariant and attracting set are proved. Sufficient conditions of local/global stability of the positive steady state are established. In the end, we present a numerical evidence of time evolution of the pattern formation.

Periodic solution to a multispecies predator-prey competition dynamic system with Beddington-DeAngelis functional response and time delay

In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).

GLOBAL ASYMPTOTIC STABILITY FOR A TWO-SPECIES DISCRETE RATIO-DEPENDENT PREDATOR–PREY SYSTEM

The dynamical behaviors of a two-species discrete ratio-dependent predator–prey system are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator–prey system, Indian J. Pure Appl. Math.42(1) (2011) 1–26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator–prey system with delays, Appl. Math. Comput.153 (2004) 337–351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system, Appl. Math. Comput.190 (2007) 500–509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.

Extinction in the Lotka-Volterra model

Birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey interaction. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.

Permanence of a discrete multispecies Lotka–Volterra competition predator–prey system with delays

In this paper, we propose a discrete multispecies Lotka–Volterra competition predator–prey system with delays. For general nonautonomous case, sufficient conditions are established for the permanence of the system.

On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system

In this paper, we propose a discrete multispecies general Gilpin–Ayala competition predator–prey model. By using new difference inequality and developing the analysis technique of Chen and Zhou [Y. Chen, Z. Zhou, Stable periodic solution of a discrete periodic Lotka–Volterra competition system, J. Math. Anal. Appl. 277 (2003) 358–366], sufficient conditions are established for the permanence and the global stability. An example shows the feasibility of our results.

Uniformly strong persistence of an nonlinear asymptotically periodic multispecies competition predator–prey system with general functional response

In this paper, an nonlinear asymptotically periodic multispecies competition predator–prey system with general functional response is studied. And we obtain sufficient conditions for the uniformly strong persistence of the system. In particular, our result extend the result in [F.Y. Wei, K. Wang, Uniform persistence of asymptotically periodic multispecies competition predator–prey systems with Holling III type of functional response, Appl. Math. Comput., in press].

Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka–Volterra type interactions defined on a d-dimensional lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous active-to-absorbing state phase transition. Field-theoretic arguments, supported by Monte Carlo simulation results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by essentially stationary localized clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka–Volterra system displays complex, correlated spatio-temporal patterns of competing activity fronts. Correspondingly, the population densities in our numerical simulations turn out to oscillate irregularly in time, with amplitudes that tend to zero in the thermodynamic limit. Yet in finite systems these oscillatory fluctuations are quite persistent, and their features are determined by the intrinsic interaction rates rather than the initial conditions. We emphasize the robustness of this scenario with respect to various model perturbations.

Permanence and global attractivity of a discrete multispecies Lotka–Volterra competition predator–prey systems

In this paper, we propose a discrete multispecies Lotka–Volterra competition predator–prey systems. For general non-autonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; for periodic case, sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained.

Uniform persistence of asymptotically periodic multispecies competition predator–prey systems with Holling III type functional response

In this paper, we studied the persistence of the asymptotically periodic multispecies competition predator–prey system with Holling III type functional response. Further, by use of the Standard Comparison Theorem, we improved the results of paper [C. Chen, F. Chen, Conditions for global attractivity of multispecies ecological competition-predator system with Holling III type functional response, Journal of Biomathematics 19(2) (2004) 136–140].

The competitive interactions of man and deer in prehistoric California

A hypothetical model concerning the structure of aboriginal California trophic systems is presented. The dynamics of each possible state of the system is generated theoretically and then tested using previously published data. It is determined that a state of competitive coexistence of a fish-regulated predatorprey competition relationship between the deer and human populations limited the growth of both populations and should be considered a determinant of aboriginal California population levels.