Frontiers in Mathematical Biology

1. Front Matter

   Pages I-X

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2. Frontiers in Cell and Molecular Biology

   1. Front Matter

      Pages 1-1

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   2. Reflections on Mathematical Contributions to Understanding the Molecular Basis of Life: From 1970 to the 21^st Century

      • Charles Delisi

      Pages 2-27

   3. Genomes, Maps and Sequences

      • Michael S. Waterman

      Pages 28-52

   4. Cell Protrusions

      • George Oster, Alan S. Perelson

      Pages 53-78

   5. Cell Motion and Orientation

      • Wolfgang Alt

      Pages 79-101

3. Frontiers in Organismal Biology

   1. Front Matter

      Pages 103-103

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   2. Pattern Formation in Tissue Interaction Models

      • J. D. Murray, G. C. Cruywagen, P. K. Maini

      Pages 104-116

   3. Toward Artificial Competence

      • Lee A. Segel

      Pages 117-121

   4. Norbert Wiener’s Brain Waves

      • Steven H. Strogatz

      Pages 122-138

   5. Puzzles about Excitable Media and Sudden Death

      • A. T. Winfree

      Pages 139-158

   6. Immune Networks and Immune Responses

      • Randall Rose, Alan S. Perelson

      Pages 159-172

4. Frontiers in Evolutionary Biology

   1. Front Matter

      Pages 173-173

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   2. Evolution of Gene Families: A Clue to Some Problems of Neo-Darwinism

      • Tomoko Ohta

      Pages 174-185

   3. The Changing Role of Population Genetics Theory

      • W. J. Ewens

      Pages 186-197

   4. Some Advantages and Disadvantages of Recombination

      • Sarah P. Otto, Marcus W. Feldman, Freddy B. Christiansen

      Pages 198-211

   5. The Morphometric Synthesis: A Brief Intellectual History

      • Fred L. Bookstein

      Pages 212-237

   6. Behavioral Ecology, Epidemiology and Population Genetics: The Undiscovered Country

      • Marc Mangel, Bernard D. Roitberg

      Pages 238-251

5. Frontiers in Population Ecology

   1. Front Matter

      Pages 253-253

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   2. Stochastic Demography and Life Histories

      • Shripad Tuljapurkar

      Pages 254-262

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.

• Mathematicall biology
• biomathematics
• ecology
• ecosystem
• ecosystem ecology
• evolution
• evolutionary biology
• mathematical ecology
• molecular biology
• pattern foormation
• theroetical biology

• Ecology & Evolutionary Biology, Princeton University, Princeton, USA

  Simon A. Levin

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