Mathematical Ecology of Plant Species Competition

The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials.

Anthony G. Pakes (Author), R. A. Maller (Author)

9780521102780, Cambridge University Press

Paperback / softback, published 12 March 2009

208 pages
22.9 x 15.2 x 1.2 cm, 0.31 kg

"...presents an interesting application of higher-level mathematical modeling to solving real world biological problems. It should be read by both applied mathematicians and biologists interested in competition theory." N.C. Kenkel, SIAM Reviews

Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology and to agronomists and botanists interested in population dynamics.

Preface
Part I. Introduction
Part II. Mathematical formulation of the models
Part III. Analysis of Model G: Introduction
Part IV. Analysis of Model G: no interior equilibrium
Part V. Analysis of Model G: one interior equilibrium
Part VI. Analysis of Model 2
Part VII. Application of the models
Part VIII. A single strain model with cropping and tillage
Bibliography
Indexes.

Subject Areas: Maths for engineers [TBJ], Plant ecology [PSTS], Maths for scientists [PDE]