Mathematical Ecology of Populations and Ecosystems
MATHEMATICAL ECOLOGY
Population ecologists study how births and deaths affect the dynamics of populations and communities, while ecosystem ecologists study how species control the flux of energy and materials through food webs and ecosystems. Although all these processes occur simultaneously in nature, the mathematical frameworks bridging the two disciplines have developed independently. Consequently, this independent development of theory has impeded the cross-fertilization of population and ecosystem ecology. Using recent developments from dynamical systems theory, this advanced undergraduate/graduate level textbook shows how to bridge the two disciplines seamlessly. The book shows how bifurcations between the solutions of models can help understand regime shifts in natural populations and ecosystems once thresholds in rates of births, deaths, consumption, competition, nutrient inputs, and decay are crossed.
Mathematical Ecology is essential reading for students of ecology who have had a first course in calculus and linear algebra or students in mathematics wishing to learn how dynamical systems theory can be applied to ecological problems.
Preface.
Acknowledgments.
Part I: Preliminaries.
1. What is Mathematical Ecology and Why Should We Do It?.
2. Mathematical Toolbox.
Part II: Populations.
3. Homogeneous Populations: Exponential and Geometric Growth and
Decay.
4. Age- and Stage-structured Linear Models: Relaxing The
Assumption Of Population Homogeneity.
5. Nonlinear Models of Single Populations: The Continuous Time
Logistic Model.
6. Discrete Logistic Growth, Oscillations, and Chaos.
7. Harvesting and the Logistic Model.
8. Predators and their Prey.
9. Competition between Two Species, Mutualism, and Species
Invasions.
10. Multispecies Community and Food Web Models.
Part III: Ecosystems.
11. Inorganic Resources, Mass Balance, Resource Uptake, and
Resource Use Efficiency.
12. Litter Return, Nutrient Cycling, and Ecosystem
Stability.
13. Consumer Regulation of Nutrient Cycling.
14. Stoichiometry and Linked Element Cycles.
Part IV: Populations and Ecosystems in Space and
Time.
15. Transitions between Populations and States in
Landscapes.
16. Diffusion, Advection, the Spread of Populations and
Resources, and the Emergence of Spatial Patterns.
Appendix: MatLab Commands for Equilibrium and Stability Analysis
of Multi-compartment Models by Solving the Jacobian and its
Eigenvalues.
References.
Index
cobwebs from the mind of someone
who has learnt this stuff at some time in the past. . . It would be
ideal as a text for a course taught in a mathematics department, to
convince mathematics students that their skills in differential
equations can be applied to ecological problems." (Austral Ecology,
2011)
"Its best feature a the scientific soundness t hat permeates the
whole book, founded on a robust mathematical treatment of most of
the arguments." (Ecoscience, June 2010)"I find the
publication extremely valuable in the analytical tools that it
provides and the depth in which they are covered." (The
Quarterly Review of Biology, June 2009)
"I would recommend this book to students or ecologists who work
in either population or ecosystems ecology. The mathematics is
dense at times, but Pastor does an excellent job of guiding us
through the equations and helping us understand what they mean in
an ecological context." (Ecology, June 2009)