A new family of Fisher-curves estimates Fisher's alpha more accurately.

Fisher's alpha is a satisfactory scale-independent indicator of biodiversity. However, alpha may be underestimated in communities in which the spatial arrangement of individuals is strongly clustered, or in which the total number of species does not tend to infinity. We have extended Fisher's curve to allow for an accurate calibration of Fisher's alpha in such communities. In spite of its good performance, the use of this extended curve is complicated by its optimization procedure. Therefore, we have simulated the extended Fisher curve by modifying the smooth expolinear curve, using three ecologically meaningful parameters only, i.e. Fisher's alpha, a coefficient describing the effects of clustering and the maximum number of species. The resulting equations successfully describe species-individual relationships from both spatial and temporal observations on both plant and animal communities. This family of equations combines three advantages: Fisher's alpha can be quantified more accurately, the number of estimated parameters is flexible and can be kept to a minimum, while all parameters can legitimately be compared across sites.