This monograph studies a series of mathematical models of the evolution of a population under mutation and selection. Its starting point is the quasispecies equation, a general non-linear equation which describes the mutation-selection equilibrium in Manfred Eigen’s famous quasispecies model. A detailed analysis of this equation is given under the assumptions of finite genotype space, sharp peak landscape, and class-dependent fitness landscapes. Different probabilistic representation formulae are derived for its solution, involving classical combinatorial quantities like Stirling and Euler numbers. It is shown how quasispecies and error threshold phenomena emerge in finite population models, and full mathematical proofs are provided in the case of the Wright–Fisher model. Along the way, exact formulas are obtained for the quasispecies distribution in the long chain regime, on the sharp peak landscape and on class-dependent fitness landscapes. Finally, several other classical population models are analyzed, with a focus on their dynamical behavior and their links to the quasispecies equation. This book will be of interest to mathematicians and theoretical ecologists/biologists working with finite population models.

This is a collection of refereed papers presented at the 4th International Conference on Mathematical Population Dynamics. The selection of papers and their organization were made by the following persons: O Arino, D Axelrod, V Capasso, W Fitzgibbon, P Jagers, M Kimmel, D Kirschner, C Mode, B Novak, R Sachs, W Stephan, A Swierniak and H Thieme.It features some of the new trends in cell and human population dynamics. The main link between the two traits is that human populations of concern here are essentially those subject to cell diseases, either the processes of anarchic proliferation or those by which some cell lines are killed by an infectious agent.The volume is divided into 3 main parts. Each part is subdivided into chapters, each chapter concentrating on a specific aspect. Each aspect is illustrated by one or several examples, developed in sections contributed by several authors. A detailed introduction for each part will enable the reader to refer to chapters of interest. An index and a bibliography for each part is also included for easy reference.This book will be useful for those interested in the subject matter.

Virus as Composition, Complexity, Quasispecies, Dynamics, and Biological Implications, Second Edition, explains the fundamental concepts surrounding viruses as complex populations during replication in infected hosts. Fundamental phenomena in virus behavior, such as adaptation to changing environments, capacity to produce disease, and the probability to be transmitted or respond to treatment all depend on virus population numbers. Concepts such as quasispecies dynamics, mutations rates, viral fitness, the effect of bottleneck events, population numbers in virus transmission and disease emergence, and new antiviral strategies are included. The book's main concepts are framed by recent observations on general virus diversity derived from metagenomic studies and current views on the origin and role of viruses in the evolution of the biosphere. - Features current views on key steps in the origin of life and origins of viruses - Includes examples relating ancestral features of viruses with their current adaptive capacity - Explains complex phenomena in an organized and coherent fashion that is easy to comprehend and enjoyable to read - Considers quasispecies as a framework to understand virus adaptability and disease processes

This volume brings together recent developments in quasispecies theory extended to variable environments and practical applications in elucidating viral dynamics and treatment designs. In particular, the existence of an error threshold in rugged fitness landscapes has opened the way to a new antiviral strategy termed lethal mutagenesis, which is now under intensive theoretical, experimental and clinical investigation. As such the book explains how an understanding of quasispecies dynamics within infected organisms has increased our knowledge of viral disease events. From a clinical perspective, population dynamics highlights important problems for viral disease control, such as the selection of drug-resistant mutants that often accompanies treatment failures, and suggests means of increasing the effectiveness of antiviral treatments. The book is intended for students and scientists interested in basic and applied aspects of biophysics, chemistry, biology, evolution and medical virology.

Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.

New viral diseases are emerging continuously. Viruses adapt to new environments at astounding rates. Genetic variability of viruses jeopardizes vaccine efficacy. For many viruses mutants resistant to antiviral agents or host immune responses arise readily, for example, with HIV and influenza. These variations are all of utmost importance for human and animal health as they have prevented us from controlling these epidemic pathogens. This book focuses on the mechanisms that viruses use to evolve, survive and cause disease in their hosts. Covering human, animal, plant and bacterial viruses, it provides both the basic foundations for the evolutionary dynamics of viruses and specific examples of emerging diseases. - NEW - methods to establish relationships among viruses and the mechanisms that affect virus evolution - UNIQUE - combines theoretical concepts in evolution with detailed analyses of the evolution of important virus groups - SPECIFIC - Bacterial, plant, animal and human viruses are compared regarding their interation with their hosts

Viroids and Satellites describes plant diseases and their causal agents while also addressing the economic impact of these diseases. The book discusses various strategies for state-of-the-art methods for the detection and control of pathogens in their infected hosts and provides pivotal information from the discovery of viroids through the analysis of their molecular and biological properties, to viroid pathogenesis, host interactions, and RNA silencing pathways. Students, researchers and regulators will find this to be a comprehensive resource on the topics presented. - Provides coverage of the basic biological properties of disease, along with applied knowledge - Features economic impacts, transmission, geographical distribution, epidemiology, detection, and control within each chapter - Organizes viroid diseases by viroid taxonomy and viroid species