Stretched exponential as one of the alternatives for the power law to fit ranked species abundance data

A central object in community ecology is the species abundance distribution, SAD. We are interested in the power law and its allies for ranked species abundance data. We collected 12 large data sets consisting of many samples. The preliminary fitting result makes a robust impression (12 systems at three scales of integration) that the stretched exponential is an interesting alternative for the power law. For further work advanced statistics are required. Not only ‘our’ data but, quite often, other data as well, consist of sample × species cross tables. With cross tables, also 'within species over samples' characteristics can be studied. An integrated view on data-patterns in multi-sample sets may help to identify generative processes for and the formulation of a relatively simple model for species abundance data.