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Frontiers in Mathematical Biology

  • Conference proceedings
  • © 1994

Overview

Editors:
  1. Simon A. Levin

    1. Ecology & Evolutionary Biology, Princeton University, Princeton, USA

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Part of the book series: Lecture Notes in Biomathematics (LNBM, volume 100)

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Table of contents (36 papers)

  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 21st 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
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Keywords

About this book

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.

Editors and Affiliations

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

    Simon A. Levin

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