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.
Table of Contents
1. Stability Concepts in Ecology and Mathematics 2. Leslie Matrix Model: A Challenge to Linear Algebra 3. Modifications of the Leslie Model 4. Lotka-Volterra Models of n-Species Communities 5. Stability Analysis on Community Graphs 6. Trophic Chains and Stability in Vertical-Structured Communities 7. Ecological Niche Overlap and Stability in Horizontal-Structured Communities 10. Stability in "Box" Models of Spatial Distribution