Interactions Between Organisms and Their Environment

  • Ronald W. Shonkwiler
  • James Herod
Part of the Undergraduate Texts in Mathematics book series (UTM)


This chapter is a discussion of the factors that control the growth of populations of organisms. Evolutionary fitness is measured by the ability to have fertile offspring. Selection pressure is due to both biotic and abiotic factors and is usually very subtle, expressing itself over long time periods. In the absence of constraints, the growth of populations would be exponential, rapidly leading to very large population numbers. The collection of environmental factors that keep populations in check is called environmental resistance, which consists of density-independent and density-dependent factors. Some organisms, called r-strategists, have short reproductive cycles marked by small prenatal and postnatal investments in their young and by the ability to capitalize on transient environmental opportunities. Their numbers usually increase very rapidly at first, but then decrease very rapidly when the environmental opportunity disappears. Their deaths are due to climatic factors that act independently of population numbers. Adifferent lifestyle is exhibited byK-strategists, who spend a lot of energy caring for their relatively infrequent young, under relatively stable environmental conditions. As the population grows, density-dependent factors such as disease, predation, and competition act to maintain the population at a stable level. A moderate degree of crowding is often beneficial, however, allowing mates and prey to be located. From a practical standpoint, most organisms exhibit a combination of r- and K-strategic properties. The composition of plant and animal communities often changes over periods of many years, as the members make the area unsuitable for themselves. This process of succession continues until a stable community, called a climax community, appears.


Stationary Point Phase Portrait Tree Ring Parental Investment Prey Size 
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References and Suggested Further Reading

  1. [1] Environmental Resistance:
    W. T. Keeton and J. L. Gould, Biological Science, 5th ed., Norton, New York, 1993.Google Scholar
  2. [2] Partitioning of Resources:
    J. L. Harper, Population Biology of Plants, Academic Press, New York, 1977.Google Scholar
  3. [3] Population Ecology:
    R. Brewer, The Science of Ecology, 2nd ed., Saunders College Publishing, Fort Worth, TX, 1988.Google Scholar
  4. [4] Ecology And Public Issues:
    B. Commoner, The Closing Circle: Nature, Man, and Technology, Knopf, New York, 1971.Google Scholar
  5. [5] Natural Population Control:
    H. N. Southern, The natural control of a population of tawny owls (Strix aluco), J. Zool. London, 162 (1970), 197–285.CrossRefGoogle Scholar
  6. [6] A Doomsday Model:
    D. A. Smith; Human population growth Stability or explosion, Math. Magazine, 50–4 (1977) 186–197.MATHCrossRefGoogle Scholar
  7. [7] Budworm, Balsalm Fir, And Birds:
    D. Ludwig, D. D. Jones, and C. S. Holling, Qualitative analysis of insect outbreak systems: The spruce budworm and forests, J. Animal Ecol., 47 (1978), 315–332.CrossRefGoogle Scholar
  8. [8] Predator or Prey:
    J. D. Murray, Predator–prey models: Lotka–Volterra systems, in J. D. Murray, Mathematical Biology, Springer-Verlag, Berlin, 1990, Section 3.1.Google Scholar
  9. [9] Linearization:
    S. H. Strogatz, Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry, and Engineering, Addison–Wesley, New York, 1994.Google Scholar
  10. [10] A Matter of Wolves:
    B. E. McLaren and R. O. Peterson, Wolves, moose, and tree rings on Isle Royale, Science, 266 (1994), 1555–1558.CrossRefGoogle Scholar
  11. [11] Predator–prey With Child Care, Cannibalism, And Other Models:
    J. M. A. Danby, Computing Applications to Differential Equations, Reston Publishing Company, Reston, VA, 1985.Google Scholar
  12. [12] Chaos In Biological Populations:
    P. Raeburn, Chaos and the catch of the day, Sci. Amer., 300-2 (2009), 76–78.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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