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.