PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode

An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.Comment: accepted by Plasma Physics and Controlled Fusio

The filamentation instability driven by warm electron beams: Statistics and electric field generation

The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation.Comment: 10 pages, 6 figures, accepted by the Plasma Physics and Controlled Fusion (Special Issue EPS 2009

Adaptive Dynamics and Evolving Biodiversity

Population viability is determined by the interplay of environmental influences and individual phenotypic traits that shape life histories and behavior. Only a few years ago the common wisdom in evolutionary ecology was that adaptive evolution would optimize a population’s phenotypic state in the sense of maximizing som

On Scaling Up from Individual-Based Processes to Macroscopic Ecological Dynamics in Spatially-Extended Communities

How should ecologists scale up from the microscopic events affecting individuals, to the macroscopic processes affecting populations and communities? This question is becoming important in theoretical ecology due to the increasing use of individual-based models of spatially-extended populations and communities. We give here a dynamical system, derived from an individual-based stochastic process, that describes the principal features of such a stochastic process. The stochastic process models a multispecies community of organisms living in a spatial domain, containing organisms that (1) give birth and die with probabilistic rates which depend on other individuals in a specified neighborhood, and (2) move from one location to another. The dynamical system describes the change in the first and second spatial moments of the stochastic process, the first moments being the densities of species averaged over space, and the second moments being measures of the average spatial structure of the community in the vicinity of an individual. We show, by means of an example of two competing plant species, that the dynamics given by a simpler non-spatial model are qualitatively incorrect, whereas the dynamical system presented here gives a close approximation to the first and second moments of the underlying stochastic process

Competition and Predation in Simple Food Webs: Intermediately Strong Trade-offs Maximize Coexistence

Competition and predation are fundamental interactions structuring food webs. However, rather than following these neat theoretical categories, mixed interactions are ubiquitous in nature. Of particular importance are omnivorous species, such as intra-guild predators that can both compete with and predate on their prey. Here we examine trade-offs between competitive and predatory capacities by analyzing the entire continuum of food web configurations existing between purely predator-prey and purely competitive interactions of two consumers subsisting on a single resource. Our results show that the range of conditions allowing for coexistence of the consumers is maximized at intermediately strong trade-offs. Even though coexistence under weak trade-offs and under very strong trade-offs is also possible, it occurs under much more restrictive conditions. We explain these findings by an intricate interplay between energy acquisition and interaction strength

Symbiosis Without Mutualism and the Merger of Lineages in Evolution [Revised 3 June 1998]

A model for the coevolution of two species in facultative symbiosis is used to investigate conditions under which species merge to form a single reproductive unit. Two traits evolve in each species, the first affecting loss of resources from an individual to its partner, and the second affecting vertical transmission of the symbiosis from one generation to the next. Initial conditions are set so that the symbiosis is not mutualistic and vertical transmission is very rare. It is shown that a stable symbiotic unit with maximum vertical transmission of the partners can evolve in the face of continued exploitation of one partner by the other. Such evolution requires that eventually deaths should exceed births for both species in the free-living state, a condition which can be met if the victim, in the course of developing its defenses, builds up sufficiently large costs in the free-living state. This result expands the set of initial conditions from which the separate lineages can be expected to merge into symbiotic units, and argues against any automatic assumption of mutualism between organism with a long history of symbiosis

Relaxation Projections and the Method of Moments

Theory in spatial ecology has to steer a narrow and challenging course between the Scylla of oversimplification and the Charybdis of intractability. Until about 15 years ago, most of theoretical ecology was based on the mean-field paradigm, thus targeting well-mixed ecological systems. Although the underlying assumption of spatial homogeneity is violated for many, if not most, ecological populations and communities in the field, mean-field approaches appeared to be the only way forward. They even took center stage in certain areas, as in epidemiological systems (Bailey 1975; Anderson and May 1991), today recognized as typical examples of ecological processes for which space matters. It was only with the advent and ready availability of modern computer technology that explorations into critical effects of spatial heterogeneities became feasible (Levin 1974, 1976; Weiner and Conte 1981; Weiner 1982; Pacala and Silander 1985; Holsinger and Roughgarden 1985; Pacala 1986; Hogeweg 1988). Today, computer screens and journals abound with images of spatially extended simulations that have convincingly demonstrated that many predictions of classical ecological theory are inappropriate in the presence of spatially structured habitats or short-range ecological interactions. Despite their value as counterexamples to mean-field predictions and their usefulness in exploring the emergence of macroscopic effects resulting from microscopic ecological mechanisms, simulation studies often remain inconclusive. Are the reported phenomena robust under changed ecological parameters? Where, among the noisy dynamics of individual-based and stochastic models, is the ecological signal? How many (usually timeconsuming) spatial simulations have to be run before reliable conclusions can be drawn? These questions remind us that only part of our ecological understanding is based on description: on top of this, we look for mechanistic explanations and for reliable generalizations from observations

Insights from unifying modern approximations to infections on networks

Networks are increasingly central to modern science owing to their ability to conceptualize multiple interacting components of a complex system. As a specific example of this, understanding the implications of contact network structure for the transmission of infectious diseases remains a key issue in epidemiology. Three broad approaches to this problem exist: explicit simulation; derivation of exact results for special networks; and dynamical approximations. This paper focuses on the last of these approaches, and makes two main contributions. Firstly, formal mathematical links are demonstrated between several prima facie unrelated dynamical approximations. And secondly, these links are used to derive two novel dynamical models for network epidemiology, which are compared against explicit stochastic simulation. The success of these new models provides improved understanding about the interaction of network structure and transmission dynamics

Spatio-Temporal Processes in Plant Communities

Ecological systems evolve in space and time. Until recently, however, research in ecology separately has focused either on the spatial domain (patterns) or on the temporal domain (processes). In this paper we describe novel approaches for progressing towards an integration of pattern and process, a goal long called for in ecology. First, we present a sequence of alternative stochastic models of spatially extended processes. Second, we advance two new methods for the estimation, or calibration, of model parameters from spatio-temporal processes observed in the field. Third, we provide tools for reducing the complexity of spatially extended ecological processes to manageable dynamical systems. Steps and techniques are illustrated in the context of data from a montane grassland community from the Czech Republic