MATHEMATICAL ECOLOGY OF POPULATIONS AND ECOSYSTEMS

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Mathematical Ecology Of Populations And Ecosystems

Author : John Pastor
ISBN : 9781444358452
Genre : Science
File Size : 33.3 MB
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Population ecologists study how births and deaths affect the dynamics of populations and communities, while ecosystem ecologists study how species control the flux of energy and materials through food webs and ecosystems. Although all these processes occur simultaneously in nature, the mathematical frameworks bridging the two disciplines have developed independently. Consequently, this independent development of theory has impeded the cross-fertilization of population and ecosystem ecology. Using recent developments from dynamical systems theory, this advanced undergraduate/graduate level textbook shows how to bridge the two disciplines seamlessly. The book shows how bifurcations between the solutions of models can help understand regime shifts in natural populations and ecosystems once thresholds in rates of births, deaths, consumption, competition, nutrient inputs, and decay are crossed. Mathematical Ecology is essential reading for students of ecology who have had a first course in calculus and linear algebra or students in mathematics wishing to learn how dynamical systems theory can be applied to ecological problems.
Category: Science

Population Ecology

Author : John H. Vandermeer
ISBN : 0691114412
Genre : Science
File Size : 47.75 MB
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How can the future number of deer, agricultural pests, or cod be calculated based on the present number of individuals and their age distribution? How long will it take for a viral outbreak in a particular city to reach another city five hundred miles away? In addressing such basic questions, ecologists today are as likely to turn to complicated differential equations as to life histories--a dramatic change from thirty years ago. Population ecology is the mathematical backbone of ecology. Here, two leading experts provide the underlying quantitative concepts that all modern-day ecologists need. John Vandermeer and Deborah Goldberg show that populations are more than simply collections of individuals. Complex variables such as the size distribution of individuals and allotted territory for expanding groups come into play when mathematical models are applied. The authors build these models from the ground up, from first principles, using a much broader range of empirical examples--from plants to animals, from viruses to humans--than do standard texts. And they address several complicating issues such as age-structured populations, spatially distributed populations, and metapopulations. Beginning with a review of elementary principles, the book goes on to consider theoretical issues involving life histories, complications in the application of the core principles, statistical descriptions of spatial aggregation of individuals and populations as well as population dynamic models incorporating spatial information, and introductions to two-species interactions. Complemented by superb illustrations that further clarify the links between the mathematical models and biology, Population Ecology is the most straightforward and authoritative overview of the field to date. It will have broad appeal among undergraduates, graduate students, and practicing ecologists.
Category: Science

From Populations To Ecosystems

Author : Michel Loreau
ISBN : 1400834163
Genre : Science
File Size : 54.98 MB
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The major subdisciplines of ecology--population ecology, community ecology, ecosystem ecology, and evolutionary ecology--have diverged increasingly in recent decades. What is critically needed today is an integrated, real-world approach to ecology that reflects the interdependency of biodiversity and ecosystem functioning. From Populations to Ecosystems proposes an innovative theoretical synthesis that will enable us to advance our fundamental understanding of ecological systems and help us to respond to today's emerging global ecological crisis. Michel Loreau begins by explaining how the principles of population dynamics and ecosystem functioning can be merged. He then addresses key issues in the study of biodiversity and ecosystems, such as functional complementarity, food webs, stability and complexity, material cycling, and metacommunities. Loreau describes the most recent theoretical advances that link the properties of individual populations to the aggregate properties of communities, and the properties of functional groups or trophic levels to the functioning of whole ecosystems, placing special emphasis on the relationship between biodiversity and ecosystem functioning. Finally, he turns his attention to the controversial issue of the evolution of entire ecosystems and their properties, laying the theoretical foundations for a genuine evolutionary ecosystem ecology. From Populations to Ecosystems points the way to a much-needed synthesis in ecology, one that offers a fuller understanding of ecosystem processes in the natural world.
Category: Science

Methods And Models In Mathematical Biology

Author : Johannes Müller
ISBN : 9783642272516
Genre : Mathematics
File Size : 71.25 MB
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This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Category: Mathematics

Stability And Complexity In Model Ecosystems

Author : Robert McCredie May
ISBN : 0691088616
Genre : Mathematics
File Size : 46.97 MB
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What makes populations stabilize? What makes them fluctuate? Are populations in complex ecosystems more stable than populations in simple ecosystems? In 1973, Robert May addressed these questions in this classic book. May investigated the mathematical roots of population dynamics and argued-counter to most current biological thinking-that complex ecosystems in themselves do not lead to population stability. Stability and Complexity in Model Ecosystems played a key role in introducing nonlinear mathematical models and the study of deterministic chaos into ecology, a role chronicled in James Gleick's book Chaos. In the quarter century since its first publication, the book's message has grown in power. Nonlinear models are now at the center of ecological thinking, and current threats to biodiversity have made questions about the role of ecosystem complexity more crucial than ever. In a new introduction, the author addresses some of the changes that have swept biology and the biological world since the book's first publication.
Category: Mathematics

Mathematical Models

Author : Richard Haberman
ISBN : 9780898714081
Genre : Mathematics
File Size : 81.44 MB
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The author uses mathematical techniques to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow.
Category: Mathematics

Ecological Modeling In Risk Assessment

Author : Robert A. Pastorok
ISBN : 9781420032321
Genre : Technology & Engineering
File Size : 45.10 MB
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Toxic chemicals can exert effects on all levels of the biological hierarchy, from cells to organs to organisms to populations to entire ecosystems. However, most risk assessment models express their results in terms of effects on individual organisms, without corresponding information on how populations, groups of species, or whole ecosystems may respond to chemical stressors. Ecological Modeling in Risk Assessment: Chemical Effects on Populations, Ecosystems, and Landscapes takes a new approach by compiling and evaluating models that can be used in assessing risk at the population, ecosystem, and landscape levels. The authors give an overview of the current process of ecological risk assessment for toxic chemicals and of how modeling of populations, ecosystems, and landscapes could improve the status quo. They present a classification of ecological models and explain the differences between population, ecosystem, landscape, and toxicity-extrapolation models. The authors describe the model evaluation process and define evaluation criteria. Finally, the results of the model evaluations are presented in a concise format with recommendations on modeling approaches to use now and develop further. The authors present and evaluate various models on the basis of their realism and complexity, prediction of relevant assessment endpoints, treatment of uncertainty, regulatory acceptance, resource efficiency, and other criteria. They provide models that will improve the ecological relevance of risk assessments and make data collection more cost-effective. Ecological Modeling in Risk Assessment serves as a reference for selecting and applying the best models when performing a risk assessment.
Category: Technology & Engineering

Mathematical Ecology

Author : E. C. Pielou
ISBN : UOM:39015001560690
Genre : Science
File Size : 49.78 MB
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Population dynamics; Spatial patterns in one-species populations; Spatial relations of two or more species; Many-species populations.
Category: Science

Individual Based Models And Approaches In Ecology

Author : D. L. DeAngelis
ISBN : 9781351090360
Genre : Mathematics
File Size : 42.2 MB
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Until fairly recently, populations were handled as homogenized averages, which made modeling feasible but which ignored the essential fact that in any population there is a great variety of individuals of different ages, sizes, and degrees of fitness. Recently, because of the increased availability of affordable computer power, approaches have been developed which are able to recognize individual differences. Individual-based models are of great use in the areas of aquatic ecology, terrestrial ecology, landscape or physiological ecology, terrestrial ecology, landscape or physiological ecology, and agriculture. This book discusses which biological problems individual-based models can solve, as well as the models' inherent limitations. It explores likely future directions of theoretical development in these models, as well as currently feasible management applications and the best mathematical approaches and computer languages to use. The book also details specific applications to theory and management.
Category: Mathematics

A Biologist S Guide To Mathematical Modeling In Ecology And Evolution

Author : Sarah P. Otto
ISBN : 9781400840915
Genre : Science
File Size : 21.26 MB
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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
Category: Science