Influence of local carrying capacity restrictions on stochastic predator-prey models

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka-Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with site-restricted predator-prey model, we observe species coexistence also in one dimension. In addition, we report results on the steady-state prey age distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies

Metastability and anomalous fixation in evolutionary games on scale-free networks

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system's metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending on the network's degree distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter

Noise and Correlations in a Spatial Population Model with Cyclic Competition

Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al., Nature {\bf 418}, 171 (2002)]. To reach a better theoretical understanding of these phenomena, we consider a paradigmatic spatial model where three species exhibit cyclic dominance. Using an individual-based description, as well as stochastic partial differential and deterministic reaction-diffusion equations, we account for stochastic fluctuations and spatial diffusion at different levels, and show how fascinating patterns of entangled spirals emerge. We rationalize our analysis by computing the spatio-temporal correlation functions and provide analytical expressions for the front velocity and the wavelength of the propagating spiral waves.Comment: 4 pages of main text, 3 color figures + 2 pages of supplementary material (EPAPS Document). Final version for Physical Review Letter

Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetisation, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship to a reaction-diffusion model with pair annihilation and creation.Comment: Submitted to J. Phys. A (Letter to the editor

Bottleneck-induced transitions in a minimal model for intracellular transport

We consider the influence of disorder on the non-equilibrium steady state of a minimal model for intracellular transport. In this model particles move unidirectionally according to the \emph{totally asymmetric exclusion process} (TASEP) and are coupled to a bulk reservoir by \emph{Langmuir kinetics}. Our discussion focuses on localized point defects acting as a bottleneck for the particle transport. Combining analytic methods and numerical simulations, we identify a rich phase behavior as a function of the defect strength. Our analytical approach relies on an effective mean-field theory obtained by splitting the lattice into two subsystems, which are effectively connected exploiting the local current conservation. Introducing the key concept of a carrying capacity, the maximal current which can flow through the bulk of the system (including the defect), we discriminate between the cases where the defect is irrelevant and those where it acts as a bottleneck and induces various novel phases (called {\it bottleneck phases}). Contrary to the simple TASEP in the presence of inhomogeneities, many scenarios emerge and translate into rich underlying phase-diagrams, the topological properties of which are discussed.Comment: 14 pages, 15 figures, 1 tabl

When does cyclic dominance lead to stable spiral waves?

Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion

Solution of a one-dimensional stochastic model with branching and coagulation reactions

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001

The Resource Prospector Neutron Spectrometer System: RP's Bloodhound

The primary goal of the Resource Prospector Neutron Spectrometer System (NSS) is to locate and characterize hydrogen-bearing volatile deposits, especially subsurface ice, that may exist at the lunar poles. A key objective is to detect water-equivalent hydrogen concentrations of 0.5 wt% or greater while on a moving rover. A second objective is to determine approximate burial depth of enhanced hydrogen-bearing materials up to 1 meter below otherwise dry regolith. The instrument will be carried aboard a landed mobility system at the lunar poles. The instrument operates by measuring the changes in the leakage flux of low energy neutrons out of the regolith. These neutrons are produced by galactic cosmic rays, which are so energetic that they shatter the nuclei in surface materials. The neutrons interact with other nuclei and lose energy, becoming thermalized in the process. Hydrogen is most efficient at thermalizing neutrons owing to protons' similar mass - statistically, neutrons lose half their energy per collision with protons. With hydrogen in the soil, leakage fluxes of neutrons in the 0.5 eV to 500 keV energy range are reduced. A concentration of only1-2 wt% water-equivalent hydrogen results in a decrease in epithermal leakage flux of a factor of two. The leakage flux of thermal neutrons, from 0 to 0.5 eV in energy, can either increase or decrease depending on the hydrogen abundance and stratigraphy. As with the highly successful Lunar Prospector Neutron Spectrometer, the RP NSS detects both thermal and epithermal neutrons by using two helium-3 gas proportional counters, one covered by cadmium and the other uncovered. The former detects only epithermal neutrons with energies above approximately 0.5 eV, the latter detects both thermal (less than 0.5 eV) and epithermal energies (greater than 0.5 eV). When a neutron enters the detector tube and interacts with a helium-3 nucleus, the resulting reaction produces an energetic proton and triton that ionize the gas. The resulting electrons are accelerated toward a high-voltage anode and cascade, amplifying the net charge, which is collected at the anode. The number of electrons produced is proportional to the energy that the triton and proton deposit in the gas. A charge sensitive pre-amplifier converts the total charge to a step voltage output. A shaper amplifier then shapes this step into a uni-polar waveform with peaking time appropriate for the detection depending on the event rate. The integrated shaped waveform, representing the deposited triton/proton energy, is then measured. A histogram, or pulse height analysis, is performed to record the main capture peak and wall effect pulses. A threshold for detection is also required to limit the low amplitude counting rate such as noise floor. The system electronics consists of 2 modules - the Sensor Module (SM) front-end and the Data Processing Module (DPM) back-end circuits. SM is designed as a light-weight and low power front-end housing the two helium-3 proportional counter detectors, preamp and HVPS. It is mounted external to the rover body to detect the thermalized neutron flux with a minimum of host background. The DPM is located inside the rover; it digitizes the SM signals, performs pulse height analysis and accumulates the count rate for each spectral channel. The DPM controls high voltage and thresholding, and sends the science data to the host craft via an RS422 serial asynchronous protocol. The payload host provides all thermal management and control for the SM and DPM

Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. Here, we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions 1< d \leq 4, in contrast with mean-field theory which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.Comment: 5 pages, 4 figures, 2-column revtex4 format. Emphasis on the lattice predator-prey model with next-nearest-neighbor interaction (Rapid Communication in PRE

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001