Skip to main content
SpringerLink
Log in

A Metaphysiological Approach to Modeling Ecological Populations and Communities

  • Conference paper
Frontiers in Mathematical Biology

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

Abstract

Modern theoretical ecology owes much to the modeling legacies of Vito Volterra, Alfred Lotka, and Georgii F. Gause. In 1949, Hutchinson and Deevey (1949) acknowledged their contribution by writing “Perhaps the most important theoretical development in general ecology has been the application of the logistic by Volterra, Gause, and Lotka to 2 species cases.” To this group we should add the name of C. S. Holling who, in the late 1950s (Holling, 1959), made important contributions to quantifying the rate at which consumers exploit resource populations in two species interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akçakaya, H. R., 1992. The population cycles of mammals: evidence for a ratio-dependent predation hypothesis. Ecological Monographs 62(1):119–142.

    Article  Google Scholar 

  • Arditi, R., and Ginzburg, L. R., 1989. Coupling in prey-predator dynamics: ratio dependence. Journal of Theoretical Biology 139:311–326.

    Article  Google Scholar 

  • Arditi, R., Perrin, N. and Saïah, H. 1991. Functional responses and heterogeneities: an experimental test with cladocerans. Oikos 60:69–75.

    Article  Google Scholar 

  • Arditi, R. and Saïah, H. 1992. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 73:1544–1551.

    Article  Google Scholar 

  • Berryman, A. A., 1992. The origins and evolution of prey-predator theory. Ecology 73:1530–1535.

    Article  Google Scholar 

  • Boucher, D. H. (ed.), 1985. The Biology of Mutualism: Ecology and Evolution, Oxford University Press, New York, p. 388.

    Google Scholar 

  • Bustamante, R.H. and W.M.Getz, in press. Analysis of a limpet fishery using a meta-physiological standard-growth model. Natural Resource Modeling (to appear).

    Google Scholar 

  • Burns, T. P., 1989. Lindeman’s contradiction and the trophic structure of ecosystems. Ecology 70:1355–1362.

    Article  Google Scholar 

  • Chitty, D., 1960. Population processes in the vole an their relevance to general theory. Can. J. Zool. 38:99–113.

    Article  Google Scholar 

  • Cohen, J. E., 1978. Food Webs and Niche Space. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Cohen, J. E., F. Briand, and C. M. Newman, 1990. Community Food Webs, Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  • DeAngelis, D. L., R. A. Goldstein, and R. V. O’Neill, 1975. A model for trophic interaction, Ecology 56:881–892.

    Article  Google Scholar 

  • DeVries, P. J. and I. Baker, 1989. Butterfly exploitation of an ant-plant mutualism: adding insult to herbivory. Journal of the New York Entomological Society 97(3):332–340.

    Google Scholar 

  • Emlen, J. M., 1984. Population Biology: The Coevolution of Population Dynamics and Behavior. Macmillan, New York, pp. 547.

    Google Scholar 

  • Erhlich, P. and L. Birch, 1967, The “balance of nature” and “population control”. American Naturalist 101:97–107.

    Article  Google Scholar 

  • Freeman, H. I., J. F. Addicott, and B. Rai, 1987. Obligate mutualism with a predator: stability and persistence of three species models. Theoretical Population Biology 32:157–175.

    Article  MathSciNet  Google Scholar 

  • Fretwell, S. D., 1987. Food chain dynamics: the central theory of ecology? OIKOS 50:291–301.

    Article  Google Scholar 

  • Getz, W. M., 1979. Invariant structures in a system of competitive logistic ordinary differential equations. SIAM J. Applied Math. 36:321–333.

    Article  MathSciNet  MATH  Google Scholar 

  • Getz, W. M., 1984. Population dynamics: a resource per capita approach. Journal of Theoretical Biology 108:623–644.

    Article  MathSciNet  Google Scholar 

  • Getz, W. M., 1991. A Unified Approach to Multispecies Modeling. Natural Resource Modeling 5:393–421.

    Google Scholar 

  • Getz, W. M., 1993. The metaphysiological and evolutionary dynamics of populations exploiting constant and interactive resources: beyond r-K selection. Evolutionary Ecology 7:1–19.

    Article  Google Scholar 

  • Ginzburg, L. R., 1986. The theory of population dynamics: I. Back to first principles. J. theor. Biol. 122:385–399.

    Article  MathSciNet  Google Scholar 

  • Ginzburg, L. R., 1992. Evolutionary consequences of basic growth equations. Trends Evol. Ecol. 7:133.

    Article  Google Scholar 

  • Ginzburg, L. R. and H. R. Akçakaya 1992. Consequences of ratio-dependent predation for steady-state properties of ecosystems. Ecology 73:1536–1543.

    Article  Google Scholar 

  • Gutierrez, A. P., 1992. Physiological basis of ratio-dependent prey-predator theory: the metabolic pool model as a paradigm. Ecology 73:1552–1563.

    Article  Google Scholar 

  • Gutierrez, A. P. and J. U. Baumgaertner, 1984. Multitrophic level models of predator-prey energetics. I. Age specific energetics models: pea aphid Acythosiphon pisum (Harris) (Homoptera: Aphididae) as an example. Canadian Entomologist 116:924–932.

    Google Scholar 

  • Gutierrez, A. P., J. U. Baumgaertner, and K. S. Hagen, 1981. A conceptual model for growth, development, and reproduction in the ladybird beetle Hippodamia convergences G.-M. (Coccinellidae: Coleoptera). Canadian Entomologist 113:21–33.

    Article  Google Scholar 

  • Gutierrez, A. P., W. J. Dos Santos, A. Villacorta, M. A. Pizzamiglio, C. K. Ellis, L. H. Carvalho, and N. D. Stone, 1991. Modelling the interaction of cotton and the cotton boll weevil. I. A comparison of growth and development of cotton varieties. J. Applied Ecology 28:371–397.

    Article  Google Scholar 

  • Hairston, N. G., F. E. Smith, and L. B. Slobodkin, 1960. Community structure, population control, and competition. Amer. Nat. 94:421–425

    Article  Google Scholar 

  • Hall, C. A. S., 1988. An assessment of several of the historically most influential theoretical models used in ecology and of the data provided in their support. Ecological Modelling 43:5–31.

    Article  Google Scholar 

  • Hanski, I., 1991. The functional response of predators: worries about scale. Tree 6(5):141–142.

    Google Scholar 

  • Hölldobler, B. and E. O. Wilson, 1990. The Ants. The Belknap Press of Harvard University Press, Cambridge, Masschusetts, pp. 732.

    Google Scholar 

  • Higashi, M., T. B. Burns, and B. C. Patten, 1989. Food network unfolding: an extension of trophic dynamics for application to natural ecosystems. J. theor. Biol. 140:243–261.

    Article  MathSciNet  Google Scholar 

  • Holling, C. S., 1959. Some characteristics of simple types of predation and parasitism. Canadian Entomologist 91:385–98.

    Article  Google Scholar 

  • Horn, H. S. and D. I. Rubenstein, 1984. Behavioral adaptations and life history. In: J. R. Krebs and N. B. Davies (eds.), Behavioral Ecology: An Evolutionary Approach, Second Edition, Sinauer Associates, Sunderland, Massachusetts, pp. 279–298.

    Google Scholar 

  • Hutchinson, G. E. and E. S. Deevey, 1949. Ecological studies on populations. Survey of Biological Progress 1:324–359.

    Google Scholar 

  • Jeffries, C., 1989. Mathematical Modeling in Ecology, Birkhäuser, Boston, pp. 193.

    Book  MATH  Google Scholar 

  • Lack, D., 1954.. The Natural Regulation of Animal Numbers. Oxford, University Press, London.

    Google Scholar 

  • Leslie, P. H., 1948. Some further notes on the use of matrices in population mathematics. Biometrika 35:213–245.

    MathSciNet  MATH  Google Scholar 

  • Levin, S. A., 1970. Community equilibria and stability, and an extension of the competitive exclusion principle. American Naturalist 104:413–423.

    Article  Google Scholar 

  • Lindeman, R. L., 1942. The trophic-dynamic aspect of ecology. Ecology 23:399–418.

    Article  Google Scholar 

  • Lotka, A. J., 1925. The Elements of Physical Biology. Republished in 1956 as: The Elements of Mathematical Biology, Dover, New York, pp. 465.

    MATH  Google Scholar 

  • MacArthur, R. H., 1972. Geographical Ecology: Patterns in the Distribution of Species. Harper and Row, New York, pp. 269.

    Google Scholar 

  • MacArthur, R. H. and E. O. Wilson, 1967. The Theory of Island Biogeography. Princeton University Press, Princeton, New Jersey, pp. 203.

    Google Scholar 

  • McLain, D. E., 1991. The r-K continuum and the relative effectiveness of sexual selection. Oikos 60:263–265.

    Article  Google Scholar 

  • May, R. M., 1973. Stability and complexity of Model Ecosystems. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • May, R. M., 1981. Models for two interacting populations. In: Theoretical Ecology, (2nd edition), Sinauer Associates, Sunderland, MA, 78–104.

    Google Scholar 

  • McLain, D. E., 1991. The r-K continuum and the relative effectiveness of sexual selection. Oikos 60:263–265.

    Article  Google Scholar 

  • Mueller, L. D., 1988. Density-dependent population growth and natural selection in food-limited environments: the Drosophila model. American Naturalist 132:786–809.

    Article  Google Scholar 

  • Murdoch, W., 1966. Community structure, population control, and competition—a critique. American Naturalist 100:219–226.

    Article  Google Scholar 

  • Odum, E. P., and L. J. Biever, 1984. Resource quality, mutualism and energy partitioning in food chains. American Naturalist 124:360–376.

    Article  Google Scholar 

  • Oksanen, L., 1991. Trophic levels and trophic dynamics: a consensus emerging? TREE 6(2):58–60.

    MathSciNet  Google Scholar 

  • Oksanen, L., S. D. Pretwell, J. Arruda, and P. Niemela, 1981. Exploitation ecosystems in gradients of primary productivity. American Naturalist 118:240–261.

    Article  Google Scholar 

  • Pella, J. J. and P. K. Tomlinson, 1969. A generalized stock production model. Bull. Inter-Am. Trop. Tuna Comm. 13:421–458.

    Google Scholar 

  • Pierce, N. E., 1987. The evolution and biogeography of associations between lycaenid butterflies and ants. Oxford Surveys in Evolutionary Biology, 4:89–116.

    Google Scholar 

  • Pimm, S. L., 1982. Food Webs, Chapman and Hall, London, pp. 219.

    Google Scholar 

  • Pitcairn, M. J., W. M. Getz, and D. W. Williams, 1990. Resource availability and parasitoid abundance in the analysis of host-parasite data. Ecology, 71:2372–2374.

    Article  Google Scholar 

  • Power, M. E., 1990a. Benthic turfs versus floating mats of algae in river food webs. Oikos 58:67–79.

    Article  Google Scholar 

  • Power, M. E., 1990b. Effects offish in river food webs. Science 250:411–415.

    Article  Google Scholar 

  • Power, M. E., 1992. Top-down and bottom-up forces in food webs: do plants have primacy? Ecology 73:733–746.

    Article  Google Scholar 

  • Rescigno, A. and Richardson, I. W., 1973. The deterministic theory of population dynamics. In: R. Rosen (ed.), Foundations of Mathematical Biology: Vol III, Supercellular Systems. Academic Press, New York, 283–360.

    Google Scholar 

  • Slobodkin, L. B., F. E. Smith, and N. C. Hairston, 1967. Regulation in terrestrial ecosystems and the implied balance of nature. American Naturalist 101:109–124.

    Article  Google Scholar 

  • Sykes, R. M., 1973. The trophic dynamics aspects of ecosystem models. Proc. 16th Conf. Great Lakes Res, pp. 977–988, Intl. Assoc. Great Lakes Res.

    Google Scholar 

  • Tilman, D., 1982. Resource Competition and Community Structure. Princeton University Press, Princeton, New Jersey, pp. 296.

    Google Scholar 

  • Ulanowicz, R. E., 1986. Growth and Development, Springer-Verlag, London.

    Book  MATH  Google Scholar 

  • Vadas, R. L., 1989. Foob web patterns in ecosystems: a reply to Pretwell and Oksanen. Oikos 56:339–343.

    Article  Google Scholar 

  • Volterra, V., 1926. Fluctuations in the abundance of species considered mathematically. Nature 118:558–560.

    Article  MATH  Google Scholar 

  • Wang, Y. H., A. P. Gutierrez, G. Oster, and R. Daxl, 1977. A population model for cotton growth and development: coupling cotton-herbivore interactions. Canadian Entomologist 109:1359–1374.

    Article  Google Scholar 

  • White, T., 1978. The importance of a relative shortage of food in animal ecology. Oecologia 33:71–86.

    Article  Google Scholar 

  • Wright, D. H., 1989. A simple, stable model of mutualism incorporating handling time. American Naturalist 134:664–667.

    Article  Google Scholar 

  • Wolin, C. L., 1985. The population dynamics of mutualistic systems. In: D. H. Boucher (ed.), The Biology of Mutualism, Oxford University Press, New York, pp. 248–269.

    Google Scholar 

  • Wootton, J. T., and M. E. Power, 1993. Productivity, consumers, and the structure of a river food chain. Proc. Natl. Acad. Sci. (USA), 90: 1384–1387.

    Article  Google Scholar 

  • Yodzis, P., 1989. Introduction to Theoretical Ecology, Harper and Row, New York, pp. 384.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Environmental Sciences, Policy, and Management, University of California, Berkeley, CA, 94720, USA

    Wayne M. Getz

Authors
  1. Wayne M. Getz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ecology & Evolutionary Biology, Princeton University, Princeton, New Jersey, 08544-1003, USA

    Simon A. Levin

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Getz, W.M. (1994). A Metaphysiological Approach to Modeling Ecological Populations and Communities. In: Levin, S.A. (eds) Frontiers in Mathematical Biology. Lecture Notes in Biomathematics, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50124-1_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-50124-1_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-50126-5

  • Online ISBN: 978-3-642-50124-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation