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This book presents a comprehensive typology and a comprehensible description of spatiotemporal models used in population dynamics. The main types included are: reaction-diffusion systems, patch models, matapopulation approaches, host parasitoid models, cellular automata (interacting particle systems), tessellations and distance models. The models are introduced through examples and with informative verbal explanations to help understanding. Some of the cellular automation examples are models not yet published elsewhere. Possible extensions of certain model types are suggested.
[Numerical Analysis is a way to solve the real life mathematical, physical and engineering problems. Numerical Analysis can be used to answer the problems for which the analytical solution is not available.]
Although the spatial dimension of ecosystem dynamics is now widely recognized, the specific mechanisms behind species patterning in space are still poorly understood and the corresponding theoretical framework is underdeveloped. Going beyond the classical Turing scenario of pattern formation, Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation illustrates how mathematical modeling and numerical simulations can lead to greater understanding of these issues. It takes a unified approach to population dynamics and epidemiology by presenting several ecoepidemiological models where both the basic interspecies interactions of population dynamics and the impact of an infectious disease are explicitly considered. The book first describes relevant phenomena in ecology and epidemiology, provides examples of pattern formation in natural systems, and summarizes existing modeling approaches. The authors then explore nonspatial models of population dynamics and epidemiology. They present the main scenarios of spatial and spatiotemporal pattern formation in deterministic models of population dynamics. The book also addresses the interaction between deterministic and stochastic processes in ecosystem and epidemic dynamics, discusses the corresponding modeling approaches, and examines how noise and stochasticity affect pattern formation. Reviewing the significant progress made in understanding spatiotemporal patterning in ecological and epidemiological systems, this resource shows that mathematical modeling and numerical simulations are effective tools in the study of population ecology and epidemiology.
Takes the hallmarks of metapopulation theory to the next level by considering a group of communities, each of which may contain numerous populations, connected by species interactions within communities and the movement of individuals between communities. This book seeks to understand how communities work in fragmented landscapes.
Individual-based models are an exciting and widely used new tool for ecology. These computational models allow scientists to explore the mechanisms through which population and ecosystem ecology arises from how individuals interact with each other and their environment. This book provides the first in-depth treatment of individual-based modeling and its use to develop theoretical understanding of how ecological systems work, an approach the authors call "individual-based ecology.? Grimm and Railsback start with a general primer on modeling: how to design models that are as simple as possible while still allowing specific problems to be solved, and how to move efficiently through a cycle of pattern-oriented model design, implementation, and analysis. Next, they address the problems of theory and conceptual framework for individual-based ecology: What is "theory"? That is, how do we develop reusable models of how system dynamics arise from characteristics of individuals? What conceptual framework do we use when the classical differential equation framework no longer applies? An extensive review illustrates the ecological problems that have been addressed with individual-based models. The authors then identify how the mechanics of building and using individual-based models differ from those of traditional science, and provide guidance on formulating, programming, and analyzing models. This book will be helpful to ecologists interested in modeling, and to other scientists interested in agent-based modeling.
With one volume each year, this series keeps scientists and advanced students informed of the latest developments and results in all areas of the plant sciences. The present volume includes reviews on genetics, cell biology, physiology, comparative morphology, ecology and vegetation science.
Although the spatial dimension of ecosystem dynamics is now widely recognized, the specific mechanisms behind species patterning in space are still poorly understood and the corresponding theoretical framework is underdeveloped. Going beyond the classical Turing scenario of pattern formation, Spatiotemporal Patterns in Ecology and Epidemiology:
A book blending evolution and trophic dynamics, taking into account recent advances in both behavioral and population ecology, is long overdue. A central objective of this book is to consider whether adaptive behavioral decisions on the individual organism level might tend to stabilize trophic interactions. A second major goal of the book is to explore the implications of presumably adaptive behaviors on trophic dynamics and the implications of trophic dynamics for the evolution of adaptive behaviors. All evolutionary biologists, ecologists, and behavioral ecologists should find this exciting volume essential reading.
In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.
Ecological dynamics are tremendously complicated and are studied at a variety of spatial and temporal scales. Ecologists often simplify analysis by describing changes in density of individuals across a landscape, and statistical methods are advancing rapidly for studying spatio-temporal dynamics. However, spatio-temporal statistics is often presented using a set of principles that may seem very distant from ecological theory or practice. This book seeks to introduce a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics. We provide a step-by-step illustration of techniques that combine core spatial-analysis packages in R with low-level computation using Template Model Builder. Techniques are showcased using real-world data from varied ecological systems, providing a toolset for hierarchical modelling of spatio-temporal processes. Spatio-Temporal Models for Ecologists is meant for graduate level students, alongside applied and academic ecologists. Key Features: Foundational ecological principles and analyses Thoughtful and thorough ecological examples Analyses conducted using a minimal toolbox and fast computation Code using R and TMB included in the book and available online