Abstract
The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.
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Literature
Andrewartha, H. G. and L. C. Birch. 1954.The Distribution of an Abundance of Animals Chicago and London: The University of Chicago Press.
Bliss, G. A. 1946.Lectures on the Calculus of Variations Chicago: The University of Chicago Press.
Bliss, L. C., G. M. Courtin, D. L. Pattie, R. R. Reiwe, D. W. K. Whitfield and P. Widden. 1973. “Arctic Tundra Ecosystems” inAnnual Review of Ecology and Systematics (Johnston, R. C., Ed.), Palo Alto: Annual Reviews Inc..
Brillouin, L. 1962.Science and Information Theory. New York: Academic Press.
Eidel'man, S. D. 1969.Parabolic Systems. Amsterdam and London: North-Holland Publishing Co.
Elton, C. S. 1958.The Ecology of Invasions by Animals and Plants. London: Chapman and Hall.
El'sgol'ts, L. E. 1966.Introduction to the Theory of Differential Equations with Deviating Arguments (translated by R. J. McLaughlin). San Francisco: Holden Day, Inc.
Feller, W. 1966.An Introduction to Probability Theory and Its Applications, Vol. II. New York: John Wiley.
Fisher, R. A. 1958.The Genetical Theory of Natural Selection. New York: Dover.
Gauss, G. F. 1934.The Struggle for Existence. New York: Dover.
Hutchinson, G. E. 1957. “Concluding Remarks.”Cold Spring Harbor Quart. Biol.,22, 415–427.
Hutchinson, G. E. 1968. “When are Species Necessary?” InPopulation Biology and Evolution (Lewontin, R. C., Ed.) Syracuse: Syracuse University Press.
Leigh, E. G. 1977. Personal communication.
MacArthur, J. W. 1975. “Environmental Fluctuations and Species Diversity”. InEcology and Evolution of Communities (Cody, M. L. and J. Diamond, Eds.), Cambridge: Harvard University Press.
MacArthur, R. and J. MacArthur. 1961. “On Bird Species Diversity.”Ecology,42, 594–598.
——. 1972.Geographicdal Ecology: Patterns in the Distribution of Species. New York: Harper and Row.
May, R. M. 1973.Stability and Complexity in Model Ecosystems. Princeton: Princeton Univeristy Press.
Pianka, E. R. 1974.Evolutionary Ecology. New York: Harper and Row.
Pielou, E. C. 1969.An Introduction to mathematical Ecology. New York and London: Wiley-Interscience.
Rescigno, A. and I. W. Richardson. 1973. “The Deterministic Theory of Population Dynamics”. InFoundations of Mathematical Biology, Vol. III, Supercellular Systems. New York and London: Academic Press.
Rogers, T. D. 1977. “Ecological Capacity and Species Packing”Bull. Math. Biol.,39, 99–107.
Shannon, C. E. 1949.The Mathematical Theory of Communication. Urbana: The University of Illinois Press.
Sommerville, D. M. Y. 1958.An Introduction to the Geometry of n-Dimensions. New York: Dover Publications.
Volterra, V. 1937. “Principes de Biologie Mathematique”.Acta Biotheretica,3, 1–36.
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Rogers, T.D. Diversity and diffusion in multidimensional niche space. Bltn Mathcal Biology 41, 129–138 (1979). https://doi.org/10.1007/BF02460873
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DOI: https://doi.org/10.1007/BF02460873