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

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

Population Growth in Space and Time

How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual based model (IBM) with spatially localized dispersal and competition, and from a deterministic approximation to the IBM describing the dynamics of the first and spatial moments. The dynamical system incorporates a novel closure that gives a close approximation to the IBM in the presence of strong spatial structure. Population growth given by the spatial logistic equation can differ greatly from that of the non-spatial logistic model. Numerical simulations show that populations may grow more slowly or more rapidly than would be expected from the non-spatial model, and may reach their maximum rate of increase at densities other than half of the carrying capacity. Populations can achieve asymptotic densities substantially greater than or less than the carrying capacity of the non-spatial logistic model, and can even tend toward extinction. These properties of the spatial logistic equation are caused by a local dispersal and competition which effect spatial structure, which in turn affects population growth. Accounting for these spatial processes brings the theory of single-species population growth a step closer to the growth of real spatially-structured populations

Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective

Evolution takes place in an evolutionary setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals- the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the predator-prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator-prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather than different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species

Evolutionary Conservation Biology: Introduction

Evolution has molded the past and paves the future of biodiversity. As anthropogenic damage to the Earth's biota spans unprecedented temporal and spatial scales, it has become urgent to tear down the traditional scientific barriers between conservation studies of populations, communities, and ecosystems from an evolutionary perspective. Acknowledgment that ecological and evolutionary processes closely interact is now mandatory for the development of management strategies aimed at the long-term conservation of biodiversity. The purpose of this book is to set the stage for an integrative approach to conservation biology that aims to manage species as well as ecological and evolutionary processes. Human activities have brought the Earth to the brink of biotic crisis. Over the past decades, habitat destruction and fragmentation has been a major cause of population declines and extinctions. Famous examples include the destruction and serious degradation that have swept away over 75% of primary forests worldwide, about the same proportion of the mangrove forests of southern Asia, 98% or more of the dry forests of western Central America, and native grasslands and savannas across the USA. As human impact spreads and intensifies over the whole planet, conservation concerns evolve. Large-scale climatic changes have begun to endanger entire animal communities (Box 1.1). Amphibian populations, for example, have suffered widespread declines and extinctions in many parts of the world as a result of atmospheric change mediated through complex local ecological interactions. The time scale over which such biological consequences of global change unfolds is measured in decades to centuries

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

Speciation and the evolution of dispersal along environmental gradients

We analyze the joint evolution of an ecological character and of dispersal distance in asexual and sexual populations inhabiting an environmental gradient. Several interesting phenomena resulting from the evolutionary interplay of these characters are revealed. First, asexual and sexual populations exhibit two analogous evolutionary regimes, in which either speciation in the ecological character occurs in conjunction with evolution of short-range dispersal, or dispersal distance remains high and speciation does not occur. Second, transitions between these two regimes qualitatively differ between asexual and sexual populations, with the former showing speciation with long-range dispersal and the latter showing no speciation with short-range dispersal. Third, a phenotypic gradient following the environmental gradient occurs only in the last case, i.e., for non-speciating sexual populations evolving towards short-range dispersal. Fourth, the transition between the evolutionary regimes of long-range dispersal with no speciation and short-range dispersal with speciation is typically abrupt, mediated by a positive feedback between incipient speciation and the evolution of short-range dispersal. Fifth, even though the model of sexual evolution analyzed here does not permit assortative mating preferences, speciation occurs for a surprisingly wide range of conditions. This illustrates that dispersal evolution is a powerful alternative to preference evolution in enabling spatially distributed sexual populations to respond to frequency- dependent disruptive selection