D. Mouillot et al., The Fractal Model: a new model to describe the species accumulation process and relative abundance distribution (RAD), OIKOS, 90(2), 2000, pp. 333-342
Quantifying a sampled collection of taxa is a widespread problem in ecology
. A number of diversity indices have been proposed and used in numerous wor
ks in spite of a lack of statistical characteristics and tests of compariso
n. These Relative Abundance Distributions (RAD) can also be described using
graphic representations exhibiting both the number of taxa and the quantit
ative distribution of the individuals which constitute these taxa. Fitting
these RADs to deterministic or stochastic models remains problematic for di
fferent reasons like scale dependence or complexity of the numerical proced
ures. In our study, we introduce a new model to describe RAD and ecological
succession. This model is a Fractal Model based on the assumption that dur
ing an ecological succession/accumulation process, at each step of the succ
ession, K new species appear which are k times more abundant with K = k(d)
(where d is a fractal dimension). We use a Monte-Carlo procedure with a Kol
mogorov-Smirnov distance to fit this model and to estimate parameters. Thro
ugh the study of entomological data from a Mediterranean Man And Biosphere
reserve, we demonstrate the qualities of the new Fractal Model. Thus, the F
ractal Model was rejected for none of the 13 RADs tested. In addition, the
parameters (K, k and d) are independent of the Hill family diversity indice
s and of three evenness indices and are able to provide additional informat
ion concerning both the diversity of the sampled ecosystem and development
of this biodiversily during the species accumulation process in this ecosys
tem.