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A mathematical model of the functional relationship between density and spatial distribution of a population

, : A mathematical model of the functional relationship between density and spatial distribution of a population. Journal of Animal Ecology 50(2): 453-460

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


DOI: 10.2307/4066

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