Mathematical ecology of populations and ecosystems / John Pastor.

Format:

Book

Author/Creator:

Pastor, John.

Contributor:

Rudolph G. Schmieder Fund.

Language:

English

Subjects (All):

Ecology--Mathematical models.

Ecology.

Ecology--Mathematics.

Population biology--Mathematical models.

Population biology.

Physical Description:

xiv, 329 pages : illustrations ; 26 cm

Place of Publication:

Oxford ; Hoboken, NJ : Wiley-Blackwell Pub., 2008.

Summary:

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.

Contents:

1 What is mathematical ecology and why should we do it? 3

2 Mathematical toolbox 11

Part 2 Populations 51

3 Homogeneous populations: exponential and geometric growth and decay 53

4 Age- and stage-structured linear models: relaxing the assumption of population homogeneity 65

5 Nonlinear models of single populations: the continuous time logistic model 78

6 Discrete logistic growth, oscillations, and chaos 92

7 Harvesting and the logistic model 110

8 Predators and their prey 129

9 Competition between two species, mutualism, and species invasions 159

10 Multispecies community and food web models 176

Part 3 Ecosystems 187

11 Inorganic resources, mass balance, resource uptake, and resource use efficiency 189

12 Litter return, nutrient cycling, and ecosystem stability 218

13 Consumer regulation of nutrient cycling 238

14 Stoichiometry and linked element cycles 252

Part 4 Populations and ecosystems in space and time 271

15 Transitions between populations and states in landscapes 273

16 Diffusion, advection, the spread of populations and resources, and the emergence of spatial patterns 284

Appendix MatLab commands for equilibrium and stability analysis of multi-compartment models by solving the Jacobian and its eigenvalues 298.

Notes:

Includes bibliographical references (pages 305-317) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rudolph G. Schmieder Fund.

ISBN:

9781405177955

1405177950

9781405188111

1405188111

OCLC:

213407350