The Mathematics Behind Biological Invasions

  • Mark A. Lewis
  • Sergei V. Petrovskii
  • Jonathan R. Potts

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 44)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 1-18
  3. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 19-68
  4. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 69-105
  5. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 107-154
  6. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 155-193
  7. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 195-209
  8. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 211-232
  9. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 233-256
  10. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 257-285
  11. Mark A. Lewis, Sergei V. Petrovskii, Jonathan R. Potts
    Pages 287-305
  12. Back Matter
    Pages 307-362

About this book

Introduction

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.

Keywords

29B05, 92D40, 37N25, 35Q92, 62P10 biological invasions dynamical systems mathematical biology stochastic dynamics population spread

Authors and affiliations

  • Mark A. Lewis
    • 1
  • Sergei V. Petrovskii
    • 2
  • Jonathan R. Potts
    • 3
  1. 1.Department of Mathematics & StatisticalUniversity of AlbertaEdmontonCanada
  2. 2.Dept of MathematicsUniversity of LeicesterLeicesterUnited Kingdom
  3. 3.School of Mathematics & StatisticsUniversity of SheffieldSheffieldUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-32043-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-32042-7
  • Online ISBN 978-3-319-32043-4
  • Series Print ISSN 0939-6047
  • Series Online ISSN 2196-9973
  • About this book
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