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 : 61.94 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

Applied Population Ecology

Author : A. P. Gutierrez
ISBN : 0471135860
Genre : Science
File Size : 75.88 MB
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This book provides applied biologists and ecologists with the mathematical tools they need to understand the ever increasingly mathematical and complex area of population ecology.
Category: Science

Mathematical Ecology

Author : Thomas G. Hallam
ISBN : 9783642698880
Genre : Mathematics
File Size : 70.71 MB
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There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.
Category: Mathematics

Encyclopedia Of Theoretical Ecology

Author : Dr. Alan Hastings
ISBN : 9780520951785
Genre : Nature
File Size : 87.13 MB
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This major reference is an overview of the current state of theoretical ecology through a series of topical entries centered on both ecological and statistical themes. Coverage ranges across scales—from the physiological, to populations, landscapes, and ecosystems. Entries provide an introduction to broad fields such as Applied Ecology, Behavioral Ecology, Computational Ecology, Ecosystem Ecology, Epidemiology and Epidemic Modeling, Population Ecology, Spatial Ecology and Statistics in Ecology. Others provide greater specificity and depth, including discussions on the Allee effect, ordinary differential equations, and ecosystem services. Descriptions of modern statistical and modeling approaches and how they contributed to advances in theoretical ecology are also included. Succinct, uncompromising, and authoritative—a "must have" for those interested in the use of theory in the ecological sciences.
Category: Nature

Deterministic Mathematical Models In Population Ecology

Author : Herbert I. Freedman
ISBN : UCSD:31822010590610
Genre : Science
File Size : 31.34 MB
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Single-species growth; Pedration and parasitism; Predador-prey systems; Lotka-volterra systems for predator-prey interactions; Intermediate predator-prey models; Continous models; Discrete models; The kolmogorov model; Related topics and applications; Related topics; Aplications; competition and cooperation (symbiosis); Lotka-volterra competition models; Higher-oder competition models; cooperation (symbiosis); Pertubation theory; The implicit function theorem; Existence and Uniqueness of solutions of ordinary differential equations; Stability and periodicity; The poincare-bendixon theorem; The hopf bifurcation theorem.
Category: Science

The Background Of Ecology

Author : Robert P. McIntosh
ISBN : 0521270871
Genre : Nature
File Size : 54.29 MB
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The Background of Ecology is a critical and up-to-date review of the origins and development of ecology, with emphasis on the major concepts and theories shared in the ecological traditions of plant and animal ecology, limnology, and oceanography. The work traces developments in each of these somewhat isolated areas and identifies, where possible, parallels or convergences among them. Dr McIntosh describes how ecology emerged as a science in the context of nineteenth-century natural history.
Category: Nature

Matrices And Graphs Stability Problems In Mathematical Ecology

Author : D. Logofet
ISBN : 9781351091220
Genre : Science
File Size : 37.61 MB
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Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.
Category: Science

Population Ecology

Author : John H. Vandermeer
ISBN : 0691114412
Genre : Science
File Size : 40.78 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

Progress In Mathematical Ecology

Author : Sergei Petrovskii
ISBN : 9783038973126
Genre : Science
File Size : 47.7 MB
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This book is a printed edition of the Special Issue "Progress in Mathematical Ecology" that was published in Mathematics
Category: Science

Ecological And Evolutionary Modelling

Author : Cang Hui
ISBN : 9783319921501
Genre : Science
File Size : 47.64 MB
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Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify emerging ecological patterns and investigate their hidden mechanisms, we need to rely on the simplicity of mathematical language. Ecological patterns are emerging structures observed in populations, communities and ecosystems. Elucidating drivers behind ecological patterns can greatly improve our knowledge of how ecosystems assemble, function and respond to change and perturbation. Mathematical ecology has, thus, become an important interdisciplinary research field that can provide answers to complex global issues, such as climate change and biological invasions. The aim of this book is to (i) introduce key concepts in ecology and evolution, (ii) explain classic and recent important mathematical models for investigating ecological and evolutionary dynamics, and (iii) provide real examples in ecology/biology/environmental sciences that have used these models to address relevant issues. Readers are exposed to the key concepts, frameworks, and terminology in the studies of ecology and evolution, which will enable them to ask the correct and relevant research questions, and frame the questions using appropriate mathematical models.
Category: Science