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Abstract Aim To investigate the biological meaning of equations used to apply the general dynamic model (GDM) of oceanic island biogeography proposed by R. J. Whittaker, K. A. Triantis and R. J. Ladle. Location Analyses are presented for 17 animal groups living on the Aeolian Islands, a volcanic archipelago in the central Mediterranean, near Sicily. Methods In addition to the mathematical implementation of the GDM proposed by Whittaker, Triantis and Ladle, and termed here logATT2 ( , where S is species number or any other diversity metric, t is island age, A is island area, and a, b, c and d are fitted parameters), a new implementation based on the Arrhenius equation of the species–area relationship (SAR) is investigated. The new model (termed powerATT2) is: . For logATT2 and powerATT2 models, equations were developed to calculate (1) the expected number of species at equilibrium (i.e. when the island has reached maturity) per unit area (Seq), and (2) the time required to obtain this value (teq). Whereas the intercept in the Gleason model (S = C + z log A) or the coefficient of the Arrhenius power model (S = CAz) of the SAR can be considered measures of the expected number of species per unit area, this is not the case for the parameter a of the ATT2 models. However, values of Seq can be used for this purpose. The index of ‘colonization ability’ (CAB), calculated as the ratio , may provide a measure of the mean number of species added per unit area per unit time. Results Both ATT2 models fitted most of the data well, but the powerATT2 model was in most cases superior. Equilibrial values of species richness (Seq) varied from c. 3 species km−2 (reptiles) to 100 species km−2 (mites). The fitted curves for the powerATT2 model showed large variations in d, from 0.03 to 3. However, most groups had values of d around 0.2–0.4, as commonly observed for the z-values of SARs modelled by a power function. Equilibration times ranged from about 170,000 years to 400,000 years. Mites and springtails had very high values of CAB, thus adding many more species per unit area per unit time than others. Reptiles and phytophagous scarabs showed very low values, being the groups that added fewest species per unit area per unit time. Main conclusions Values of equilibrial species richness per unit area are influenced by species biology (e.g. body size and ecological specialization). Theoretical and empirical evidence suggests that higher immigration rates should increase the z-values of the Arrhenius model. Thus, in the same archipelago, groups with larger z-values should be characterized by higher dispersal ability. Results obtained here for the parameter d conform to this prediction.