A Technique for Analysis of Population Density Data

Erickson, Ralph O.; Stehn, J. R.

doi:10.2307/2421189

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Greig-Smith (1983) comments that the applications tested contagion more than ptp variation, that it would be difficult to apply and that the meaning of c is difficult to interpret. Erickson and Stehn (1945) are concerned only to divide the area into favourable and unfavourable parts for each species. They plotted log(x!y) against x, where x is some number of individuals and y is the number of quadrats containing x individuals.…”

Section: Previous Methodsmentioning

confidence: 99%

“…He cites Feller (1943) as showing that these cannot be distinguished on the basis of observed frequency distributions, and comments that ptp variability has been little studied. Indeed, in contrast to the large number of references to studies of contagion, he cites only 4 concerned with point-to-point variability - Ashby (1935), Stevens (1937), Singh and Das (1938) and Erickson and Stehn (1945). The Poisson parameter is simply the mean (and variance) of a Poisson distribution and presumably variation in this parameter reflects environmental heterogeneity, with the probability of occurrence of a species varying with the harshness, or otherwise, of the habitat.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum message length clustering, environmental heterogeneity and the variable Poisson model

Dale

2001

Community Ecology

View full text Add to dashboard Cite

One possible explanation of variation in vegetation is based on the variable Poisson model. In this model, species occurrence is presumed to follow a Poisson distribution, but the value of the Poisson parameter for any species varies from point to point, as a result of environmental variation. As an extreme, this includes dividing the given habitat into areas favourable to a community and areas which are unfavourable, or at least not occupied. The spatial area can then be viewed as a series of patches within which each species follows a Poisson distribution, although different patches may have different values for the Poisson parameter for any particular species.In this paper, I use a method of fuzzy clustering (mixture modelling) based on the minimum message length principle to examine the variation in Poisson parameter of individual species. The method uses the difference between the message length for the null, 1-cluster case and the message length for the optimal cluster solution, appropriately normalised, as a measure of the amount of pattern any analysis captures. I also compare the Poisson results with results obtained by assuming the within patch distribution is Gaussian. The Poisson alternative consistently results in a greater capture of pattern than the Gaussian, but at the expense of a much larger number of clusters. Overall, the Gaussian alternative is strongly supported. Other mechanisms that might introduce extra clusters, for example within-cluster correlation or spatial dependency between observations, would presumably apply equally to both models. The variable Poisson model, in the limit, converges on the individualistic model of vegetation, the Gaussian on something like the community unit model. With these data, the individualistic model is strongly rejected. Difficulties with comparing model classes mean this conclusion must remain tentative.Abbreviations: MML -Minimum Message Length, ptp -point-to-point.

show abstract

Section: Previous Methodsmentioning

confidence: 99%