生态学及群体生物发展中的VOLTERRA-HAMILTON模型VOLTERRA-HAMILTON MODELS IN

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.

Prologue
Chapter Ⅰ.Simple Growth of Populations and Individuals
1.1.Population Growth
1.2.Multiple—Species Communities
1.3.Indi4idual Growth
1.4.Multidimensional Growth in Individuals
1.5.A Plant Considered as a Population
1.6.A Simple Model of Tannin Production in a Plant
1.7.volterra’S Production Variable
　Chapter Summary
ChapterⅡ.Competitive Interactions Between Two Species
2.1.Gause—Witt Competition
　2.2.Hutchinson’S Competition with Social Effects
　Chapter Summary
ChapterⅢ.Medawar’S Growth Energy and Optimal Production
　3.1.Gompertz Growth and Medawar’S Energy of Growth
　3.2.The Calculus of Variations and Optimal Production
　3.3.Laird’S Law.The Principle of MaupertuiS and　Medawar’S Energy　
　Chapter Summary　
Chapter Ⅳ.Predation and Herbivory on Optimally ProducingTerrestrial and Marine Ecosystems
　4.1.The Crown—of-Thorns Starfish Predation on G.B.R
　4.2.Optimal Defense Theory of Rhoades
　4.3.Chemical Interactions Between Soft and Hard Corals—The Biology
　4.4.Introduction to the Model Description of a Viable　Community　
　4.5.Predictions on the Model　
　Chapter Summary　
Chapter Ⅴ.The Differential Geometry of Production Stability
　5.1.Quadratic Maupertuis Energy
　5.2.Non—Quadratic Maupertuis Energy
　Chapter Summary
ChapterⅥ.A Dynamical Theory of Heterochrony：Time.Sequencing Changes in Ecology，Evolution and Development
6.1.Krivan’S Growth Rate TransformationDefined by Ecological Constraints
　6.2.Constraints on Production and the ProjectiveGeometry of Sprays.The Adaptation Theorem
　6.3.Division of Labour in Colonial AnimalsWilson’S Ergonomics and Allometric Space
　6.4.Social Interactions，Curvature and ComplexityKwang Jeon’S Experiment
　6.5.Heterochrony and Environment in the Evolutionof a Colonial Individual
　6.6.Allometric Space and Wagner Geometry
　6.7.Allometric Growth and Heterochrony in Paleontology
　6.8.Remarks on the Dissociation of Growth，Maturationand Development in Ontogeny
　6.9.Progenesis and Myxomatosis，The Wild Rabbit Disease
　Chapter Summary
Appendix A：On the Fundamental Lemma of Variational Calculus
Appendix B：Fuzzy Differential Inclusions as Substitutes forStochastic Differential Equations in
Population Biology
　1.Introduction
　2.Fuzzy Differential Inclusions
　3.An Example of Non—Riemannian Type
　4.Targeting Growth in the Presence of Noise
　5.Final Remarks
References
Appendix C：Normal Coordinates and Log。Biomass
References
Some Frequently Used Formulas
Index