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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: 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: Vitaly Volpert
Publisher: Springer
ISBN: 3034808135
Category : Mathematics
Languages : en
Pages : 784
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Book Description
If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.
Author: Frank Mathias Hilker
Publisher:
ISBN: 9783832510503
Category :
Languages : en
Pages : 0
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Book Description
Biological invasions are a severe ecological problem threatening biodiversity and causing substantial economic damages. Mathematical models of spatiotemporal spread have proven to be powerful tools in identifying the underlying mechanisms, thus contributing to the understanding of the factors that determine invasion processes and to the assessment of possible control methods. In this thesis, classical models are extended to combine spatial spread, population growth, disease transmission and community interactions. Applications are exemplarily found in the circulation of the Feline Immunodeficiency Virus (FIV) - an HIV-similar lentivirus that induces AIDS in cat populations - and in viral infections in phytoplankton that forms the basis for all food chains and webs in the sea. The joint interplay of epidemics, predation and environmental stochasticity in invasion models is shown to generate rich and novel patterns of spatiotemporal spread such as the blocking and reversal of invasion fronts or the spatial `trapping' of infection as well as its noise-induced escape. The results of this thesis can explain real-world phenomena and have important implications for understanding and controlling invasion processes in ecosystems and epidemiology.
Author: Jonathan M Jeschke
Publisher: CABI
ISBN: 1780647646
Category : Science
Languages : en
Pages : 187
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Book Description
There are many hypotheses describing the interactions involved in biological invasions, but it is largely unknown whether they are backed up by empirical evidence. This book fills that gap by developing a tool for assessing research hypotheses and applying it to twelve invasion hypotheses, using the hierarchy-of-hypotheses (HoH) approach, and mapping the connections between theory and evidence. In Part 1, an overview chapter of invasion biology is followed by an introduction to the HoH approach and short chapters by science theorists and philosophers who comment on the approach. Part 2 outlines the invasion hypotheses and their interrelationships. These include biotic resistance and island susceptibility hypotheses, disturbance hypothesis, invasional meltdown hypothesis, enemy release hypothesis, evolution of increased competitive ability and shifting defence hypotheses, tens rule, phenotypic plasticity hypothesis, Darwin's naturalization and limiting similarity hypotheses and the propagule pressure hypothesis. Part 3 provides a synthesis and suggests future directions for invasion research.
Author: Gil Rilov
Publisher: Springer Science & Business Media
ISBN: 354079235X
Category : Science
Languages : en
Pages : 642
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Book Description
Biological invasions are considered to be one of the greatest threats to the integrity of most ecosystems on earth. This volume explores the current state of marine bioinvasions, which have been growing at an exponential rate over recent decades. Focusing on the ecological aspects of biological invasions, it elucidates the different stages of an invasion process, starting with uptake and transport, through inoculation, establishment and finally integration into new ecosystems. Basic ecological concepts - all in the context of bioinvasions - are covered, such as propagule pressure, species interactions, phenotypic plasticity, and the importance of biodiversity. The authors approach bioinvasions as hazards to the integrity of natural communities, but also as a tool for better understanding fundamental ecological processes. Important aspects of managing marine bioinvasions are also discussed, as are many informative case studies from around the world.
Author:
Publisher:
ISBN:
Category : Engineering
Languages : en
Pages : 1076
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Book Description
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: Frithjof Lutscher
Publisher: Springer Nature
ISBN: 3030292940
Category : Mathematics
Languages : en
Pages : 385
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Book Description
This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.
Author: Jonathan M. Jeschke
Publisher: Cabi
ISBN: 9781780647654
Category : Biological invasions
Languages : en
Pages :
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Book Description
Author: Arthur James Wells
Publisher:
ISBN:
Category : Bibliography, National
Languages : en
Pages : 2142
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Book Description
