Advertisement

Biogeography

  • Frank C. Hoppensteadt
  • Charles S. Peskin
Part of the Texts in Applied Mathematics book series (TAM, volume 10)

Abstract

Bacteria in our guts, insects in a field, trees in a forest and plants borne by air and water around the world are among many examples whose spatial distributions are important and interesting to study. Mechanisms of dispersal include making small random moves, being carried along by air or water, and being attracted to certain areas by chemical signals, nutrients, light, etc. Patterns of organisms can be formed by dispersal or aggregation. On the other hand, immobile organisms, like some bacteria on plant roots, can find themselves in habitats where nutrition fluctuates, for example by nutrients being washed through the soil in regular cycles. Patterns of organisms can also be formed by uneven distribution of nutrients or toxins.

Keywords

Markov Chain Random Walk Cellular Automaton Stochastic Differential Equation Diffusion Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Annotated References

  1. 1.
    N.T.J. Bailey, The theory of infectious diseases and its applications, Charles Griffin, London, 1975.zbMATHGoogle Scholar
  2. An excellent resource for epidemic modeling.Google Scholar
  3. 2.
    C.S. Rolling, The functional response of invertebrate predators to prey density, Ottawa Entom. Soc. Canada, 1966.Google Scholar
  4. 3.
    P. Gerhardt, et al. Manual of methods of general bacteriology, Am. Soc. Microbiology, Washington, D.C., 1981.Google Scholar
  5. 4.
    A.E. Mourant, A.C. Kopec, and K. Domaniewicz-Sobczak, The distribution of blood groups and other polymorphisms, 2nd ed., Oxford Univ. Press, New York, 1976.Google Scholar
  6. An introduction to the use of genetics in anthropology.Google Scholar
  7. 5.
    W. Feller, An introduction to probability theory and its applications, vol I, J. Wiley-Interscience, New York, 1968.zbMATHGoogle Scholar
  8. A broad, reliable and sophisticated description of probability theory.Google Scholar
  9. 6.
    J. Gardner, Mathematical games, Sci. Am. October (1970), 120 - 123.Google Scholar
  10. 7.
    J.M. Greenberg, M.B. Hassard, and S. Hastings, Pattern formation and periodic structures in systems modeled by reaction-diffusion equations, Bull. Amer. Math. Soc. 84 (1978), 1296 - 1327.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 8.
    B. Platt, Masters thesis, University of Utah, 1985.Google Scholar
  12. 9.
    A. Einstein, Investigation on the theory of Brownian movement, Dover, New York, 1956.Google Scholar
  13. Probably the only thing in science written by Einstein that non physicists will able to understand.Google Scholar
  14. 10.
    J. Fourier, The analytical theory of heat, Dover, New York, 1898. Fourier’s original and profound work on the heat equation.Google Scholar
  15. 11.
    H.S. Carslaw, and J.C. Jaeger, Conduction of heat in solids, 2nd ed., Oxford Univ. Press, New York, 1986.zbMATHGoogle Scholar
  16. An excellent source for solutions of the heat equation in various geometries.Google Scholar
  17. 12.
    D. Ludwig, Stochastic population theories, Lect. Notes in Biomathematics, vol. 3, Springer—Verlag, New York, 1974.CrossRefGoogle Scholar
  18. 13.
    J.D. Murray, Mathematical biology, Springer—Verlag, New York, 1989. A compendium of pattern formation models.Google Scholar
  19. 14.
    F. C. Hoppensteadt, Mathematical methods in population biology, Cambridge Univ. Press, Cambridge, 1982.Google Scholar
  20. 15.
    R.A. Fisher, The genetical theory of natural selection, Dover, New York, 1930.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  • Charles S. Peskin
    • 2
  1. 1.College of Natural ScienceMichigan State UniversityEast LansingUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations