Models of relative abundance distributions. 1, Model fitting by stochastic models

The present paper studies possibilities to discriminate between 9 stochastic models of relative abundance distributions (RADs). It develops a new test statistic for fitting based on least square distances and tests the applicability of methods described so far. The paper identifies three basic shapes of RADs termed power fraction, random assortment and Zipf-Mandelbrot type shape. It is shown that even a correct identification of the shape of a given data set requires that this data set is replicated more than 10 times. Estimates of necessary sample sizes for real animal or plant communities revealed that for communities with 20 to 100 species at least 200 to 500 times the species number is necessary for a correct model identification. The implications of these findings for the applicability of models of relative abundance distributions are discussed.