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 : 63.5 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

From Populations To Ecosystems

Author : Michel Loreau
ISBN : 1400834163
Genre : Science
File Size : 29.11 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

Stability And Complexity In Model Ecosystems

Author : Robert McCredie May
ISBN : 0691088616
Genre : Mathematics
File Size : 54.28 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

Individual Based Models And Approaches In Ecology

Author : D. L. DeAngelis
ISBN : 9781351090360
Genre : Mathematics
File Size : 90.60 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

Ecological Modeling In Risk Assessment

Author : Robert A. Pastorok
ISBN : 9781420032321
Genre : Technology & Engineering
File Size : 49.27 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

Methods And Models In Mathematical Biology

Author : Johannes Müller
ISBN : 9783642272516
Genre : Mathematics
File Size : 56.48 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

Mathematical Ecology

Author : Thomas G. Hallam
ISBN : 9783642698880
Genre : Mathematics
File Size : 40.82 MB
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Category: Mathematics

Mathematical Models

Author : Richard Haberman
ISBN : 9780898714081
Genre : Mathematics
File Size : 82.39 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

Self Organization In Complex Ecosystems Mpb 42

Author : Ricard V. Solé
ISBN : 9781400842933
Genre : Science
File Size : 63.33 MB
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Can physics be an appropriate framework for the understanding of ecological science? Most ecologists would probably agree that there is little relation between the complexity of natural ecosystems and the simplicity of any example derived from Newtonian physics. Though ecologists have long been interested in concepts originally developed by statistical physicists and later applied to explain everything from why stock markets crash to why rivers develop particular branching patterns, applying such concepts to ecosystems has remained a challenge. Self-Organization in Complex Ecosystems is the first book to clearly synthesize what we have learned about the usefulness of tools from statistical physics in ecology. Ricard Solé and Jordi Bascompte provide a comprehensive introduction to complex systems theory, and ask: do universal laws shape the structure of ecosystems, at least at some scales? They offer the most compelling array of theoretical evidence to date of the potential of nonlinear ecological interactions to generate nonrandom, self-organized patterns at all levels. Tackling classic ecological questions--from population dynamics to biodiversity to macroevolution--the book's novel presentation of theories and data shows the power of statistical physics and complexity in ecology. Self-Organization in Complex Ecosystems will be a staple resource for years to come for ecologists interested in complex systems theory as well as mathematicians and physicists interested in ecology.
Category: Science