A new formulation of the geometric series with applications to oribatid (Acari, Oribatida) species assemblages from human-disturbed Mediterranean areas

The mathematical properties of the geometric series are revisited and the model is applied to oribatid mite (Acari, Oribatida) assemblages from Mediterranean areas that have been disturbed by human activity. In the past, the geometric series has been considered an ideal form of Fisher's log model. However, in some cases data fit both models or the geometric series offers a better fit. Data presented in this paper and collected from areas heavily disturbed by human activity show that the species abundance distribution of oribatids is in almost all cases well fitted by the geometric series, indicating a common trend in the response to disturbance of this assemblage. The proposed new version of the model allows interesting applications in environmental monitoring because it is easy to outline the quantitative relationship between the abundance of the most abundant species, the total number of individuals and the total number of species in the sample.