Approaches to Mathematical Modeling of Biological Invasions PDF Download
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Author: Merlin C. Köhnke
Publisher:
ISBN: 9783832551513
Category :
Languages : en
Pages : 246
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Book Description
With potentially dangerous biological invasions increasing due to rises in international trade and travel, research in invasion biology becomes increasingly relevant. Mathematical models form an integral part of this research. This book presents: research on mathematical modeling of biological invasions, different forms of differential equations such as ordinary differential equations, reaction-diffusion models, and stochastic differential equations, detailed investigations as well as a thorough introduction to dynamical systems. Subjects range from theoretical to applied models on fascinating case studies, including: investigating how phenomena such as inducible defense or group defense can be incorporated into mathematical models, investigating how selective infections can influence the dispersal of invasive species, investigating how invasive mammals in New Zealand can be controlled to rescue the national bird, the Kiwi. The book is well suited not only for accomplished researchers but also for students with limited quantitative background interested in studying biological invasions.
Author: Merlin C. Köhnke
Publisher:
ISBN: 9783832551513
Category :
Languages : en
Pages : 246
Get Book
Book Description
With potentially dangerous biological invasions increasing due to rises in international trade and travel, research in invasion biology becomes increasingly relevant. Mathematical models form an integral part of this research. This book presents: research on mathematical modeling of biological invasions, different forms of differential equations such as ordinary differential equations, reaction-diffusion models, and stochastic differential equations, detailed investigations as well as a thorough introduction to dynamical systems. Subjects range from theoretical to applied models on fascinating case studies, including: investigating how phenomena such as inducible defense or group defense can be incorporated into mathematical models, investigating how selective infections can influence the dispersal of invasive species, investigating how invasive mammals in New Zealand can be controlled to rescue the national bird, the Kiwi. The book is well suited not only for accomplished researchers but also for students with limited quantitative background interested in studying biological invasions.
Author: Mark A. Lewis
Publisher: Springer
ISBN: 3319320432
Category : Mathematics
Languages : en
Pages : 362
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Book Description
This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.
Author: Sergei V. Petrovskii
Publisher: CRC Press
ISBN: 9781584885214
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Much of our current knowledge on biological invasion was derived from field studies, but many recent advances relied heavily on mathematics and computing, particularly mathematical modeling. While numerical simulations are clearly a useful approach, they have some serious drawbacks. Approximations errors and the number of parameter values can have a significant impact on the simulation results, the extent of which often remains obscure. Such difficulties do not arise, however, when the problem can be solved analytically. Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice. Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.
Author: Sergei V. Petrovskii
Publisher: CRC Press
ISBN: 9781420034967
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Much of our current knowledge on biological invasion was derived from field studies, but many recent advances relied heavily on mathematics and computing, particularly mathematical modeling. While numerical simulations are clearly a useful approach, they have some serious drawbacks. Approximations errors and the number of parameter values can have a significant impact on the simulation results, the extent of which often remains obscure. Such difficulties do not arise, however, when the problem can be solved analytically. Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice. Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.
Author: Andreas Deutsch
Publisher: Springer Science & Business Media
ISBN: 081764556X
Category : Mathematics
Languages : en
Pages : 386
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Book Description
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.
Author: Shandelle M. Henson
Publisher: CRC Press
ISBN: 1000806103
Category : Mathematics
Languages : en
Pages : 285
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Book Description
Mathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research. Features Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices along with datasets available on https://bit.ly/3fcLF3D
Author: Sarah P. Otto
Publisher: Princeton University Press
ISBN: 1400840910
Category : Science
Languages : en
Pages : 745
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Book Description
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
Author: João Canning-Clode
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110438666
Category : Science
Languages : en
Pages : 488
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Book Description
When organisms are deliberately or accidentally introduced into a new ecosystem a biological invasion may take place. These so-called ‘invasive species’ may establish, spread and ecologically alter the invaded community. Biological invasions by animals, plants, pathogens or vectors are one of the greatest environmental and economic threats and, along with habitat destruction, a leading cause of global biodiversity loss. In this book, more than 50 worldwide invasion scientists cover our current understanding of biological invasions, its impacts, patterns and mechanisms in both aquatic and terrestrial systems.
Author: Nanako Shigesada
Publisher:
ISBN: 9781383027846
Category : Biological invasions
Languages : en
Pages : 0
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Book Description
The phenomenon of organisms moving to and occupying new locations is called invasion. Whether humans travelling around the world or a virus entering a cell, this text covers the topic and introduces mathematical modelling of the phenomenon.
Author: Marc W. Cadotte
Publisher: Springer Science & Business Media
ISBN: 1402049250
Category : Science
Languages : en
Pages : 506
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Book Description
In this edited volume, global experts in ecology and evolutionary biology explore how theories in ecology elucidate the processes of invasion, while also examining how specific invasions inform ecological theory. This reciprocal benefit is highlighted in a number of scales of organization: population, community and biogeographic. The text describes example invaders in all major groups of organisms and from a number of regions around the globe.
