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This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed.
Contents:
- Simple Growth of Populations and Individuals
- Competitive Interactions between Two Species
- Medawar's Growth Energy and Optimal Production
- Predation and Herbivory on Optimally Producing Terrestrial and Marine Ecosystems
- The Differential Geometry of Production Stability
- A Dynamical Theory of Heterochrony: Time-Sequencing Changes in Ecology, Evolution and Development
- Appendices: On the Fundamental Lemma of Variational Calculus
- Fuzzy Differential Inclusions as Substitutes for Stochastic Differential Equations in Population Biology
- Normal Coordinates and Log-Biomass
- References
- Some Frequently Used Formulas
- Index
Readership: Students and researchers in biomathematics, biostatistics, ecology and invertebrate evolution.
