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From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an attractive alternative. (ii) The ability of physiologically structured population models to increase our un derstanding of the relation between mechanisms at the i-level and phenomena at the p-level will depend strongly on the development of dynamical systems lab facilities which are applicable to this class of models. (iii) Physiologically structured population models are ideally suited for the for mulation of evolutionary questions. Apart from the special case of age (see Charlesworth 1980, Yodzis 1989, Caswell 1989, and the references given there) hardly any theory exists at the moment. This will, hopefully, change rapidly in the coming years. Again the development of appropriate software may turn out to be crucial.
Table des matières
I. Frontiers in Cell and Molecular Biology.- Reflections on Mathematical Contributions to Understanding the Molecular Basis of Life From 1970 to the 21 st Century.- Genomes, Maps and Sequences.- Cell Protrusions.- Cell Motion and Orientation: Theories of Elementary Behavior Between Environmental Stimulation and Autopoietic Regulation.- II. Frontiers in Organismal Biology.- Pattern Formation in Tissue Interaction Models.- Toward Artificial Competence.- Norbert Wiener's Brain Waves.- Puzzles About Excitable Media and Sudden Death.- Immune Networks and Immune Responses.- III. Frontiers in Evolutionary Biology.- Evolution of Gene Families: A Clue to Some Problems of Neo-Darwinism.- The Changing Role of Population Genetics Theory.- Some Advantages and Disadvantages of Recombination.- The Morphometric Synthesis: A Brief Intellectual History.- Behavioral Ecology, Epidemiology and Population Genetics: The Undiscovered Country.- IV. Frontiers in Population Ecology.- Stochastic Demography and Life Histories.- On the Reciprocal Relationship Between Life Histories and Population Dynamics.- Structured Population Dynamics.- Modelling Social Animal Aggregations.- Spatial Chaos and its Role in Ecology and Evolution.- V Frontiers in Community and Ecosystem Ecology.- Speculations on the Future of Food Webs.- Lorenzo Camerano's Contribution to Early Food Web Theory.- On the Equilibrium of Living Beings by Means of Reciprocal Destruction.- Frontiers in Ecosystem Science.- Individual-Oriented Approaches to Modeling Ecological Populations and Communities.- A Metaphysiological Approach to Modeling Ecological Populations and Communities.- The Trophodynamics of Whole Ecological Communities.- Modeling Contact Structures in Biology.- VI. Frontiers in Applied Biology.- Conservation and SpatialStructure: Theoretical Approaches.- A Thousand and One Epidemic Models.- Uncertainty and Fisheries Management.- Ecological Risk Assessment in Aquatic Populations and Communities: The Next Generation.- VII. Mathematical Challenges.- Health Information in Developing Countries.- What Everyone Should Know About the Belousov-Zhabotinsky Reaction.- Avoiding Chaos.- Model Building as an Inverse Problem in Biomathematics.- Some Remarks on Estimation Techniques for Size-Structured Population Models.
