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Frequency Distribution Models in the Ecology of Plankton and Other Organisms

R. Morrison Cassie
Journal of Animal Ecology
Vol. 31, No. 1 (Feb., 1962), pp. 65-92
DOI: 10.2307/2333
Stable URL: http://www.jstor.org/stable/2333
Page Count: 28
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Frequency Distribution Models in the Ecology of Plankton and Other Organisms
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Abstract

1. Mathematical frequency-distribution models for the distribution of organisms in space are discussed with particular reference to plankton ecology. Appropriate models for random distribution and underdispersion are respectively the Poisson series and the binomial series. 2. The negative binomial is the formal mathematical opposite of the binomial and does provide a relatively good model for overdispersion, although there does not appear to be any biological situation which leads unequivocally to this distribution and no other. 3. The discrete log-normal distribution often gives a good fit for large-sample data, but has usually been regarded only as an approximate model. 4. Other more specialized `contagious' models are discussed, but do not appear to have any unique properties which are particularly appropriate to plankton. At least for the data under consideration, the best solution would be a distribution with positive skewness, intermediate between the negative binomial and discrete log-normal. 5. For small samples there is a tendency for the negative binomial to overestimate and the discrete log-normal to underestimate the frequency of zero counts. 6. A model, the `Poisson-log-normal' distribution, is proposed, in which the means of a continuous series of Poisson variates are distributed as a log-normal. This has the required degree of skewness and appears to estimate zero counts without bias. 7. A method is shown for separating the parameters of different populations from a polymodal distribution, using log-probability paper.

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