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From the Chapman & Hall Microbiology Series this unique resource offers specific experimental and practical applications of mathematical modeling in microbial ecology. The text presents a variety of systems, ranging from subcellular systems to ecosystems, and shows how to test whether the models provide a good representation of the system. The book also encourages further development and application of modeling to burgeoning problems associated with microbial ecology, such as the pollution and destruction of pesticides and herbicides.
From the Chapman & Hall Microbiology Series this unique resource offers specific experimental and practical applications of mathematical modeling in microbial ecology. The text presents a variety of systems, ranging from subcellular systems to ecosystems, and shows how to test whether the models provide a good representation of the system. The book also encourages further development and application of modeling to burgeoning problems associated with microbial ecology, such as the pollution and destruction of pesticides and herbicides.
Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.
This book introduces the concept of bacterial communication systems from a mathematical modeling point of view. It sheds light on the research undertaken in the last three decades, and the mathematical models that have been proposed to understand the underlying mechanism of such systems. These communication systems are related to quorum sensing mechanisms and quorum sensing regulated processes such as biofilm formation, gene expression, bioluminescence, swarming and virulence. The book further describes the phenomenon of noise, and discusses how noise plays a crucial role in gene expression and the quorum sensing circuit operationusing a set of tools like frequency domain analysis, power spectral density, stochastic simulation and the whitening effect. It also explores various aspects of synthetic biology (related to bacterial communication), such as genetic toggle switch, bistable gene regulatory networks, transcriptional repressor systems, pattern formation, synthetic cooperation, predator-prey synthetic systems, dynamical quorum sensing, synchronized quorum of genetic clocks, role of noise in synthetic biology, the Turing test and stochastic Turing test.
Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
The National Research Council's (NRC) Board on Agriculture and Natural Resources invited professional societies associated with agriculture and ecology to participate in a two-day workshop to explore leadership and a common vision for ecologically based pest management (EBPM). These proceedings describe the challenges of and opportunities for EBPM discussed by participants in the workshop.
Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "behave" realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985).
Basic modelling, analysis and simulation of systems that have proven effective in real ecological applications.