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A Mathematical Model of the Functional Relationship Between Density and Spatial Distribution of a Population

Gosta Nachman
Journal of Animal Ecology
Vol. 50, No. 2 (Jun., 1981), pp. 453-460
DOI: 10.2307/4066
Stable URL: http://www.jstor.org/stable/4066
Page Count: 8
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A Mathematical Model of the Functional Relationship Between Density and Spatial Distribution of a Population
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Abstract

(1) A model of the functional relationship between the mean population density and the proportion of unoccupied patches in a patchy environment is proposed. (2) Provided a population is distributed according to the negative binomial distribution, the zero-term of this distribution can be set equal to the model predicted proportion of empty patches. The parameter k of the negative binomial will, for a given mean density mu, be a root in this equation. (3) The model is fitted to the data of the two-spotted spider mite (Tetranychus urticae) and its phytoseiid predator Phytoseiulus persimilis, and the density behaviour of 1/k is predicted. The agreement between observed and expected values of 1/k is relatively poor due to the large scatter of the empirical values of 1/k obtained by the method of maximum likelihood. A test for goodness of fit, however, reveals that the model provides better fit to the data than an alternative model of Taylor, Woiwod & Perry (1979) does, although the two models are qualitatively very similar.

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