Towards an extended framework for the general dynamic theory of biogeography.

Aim: The General Dynamic Model of island biogeography (GDM) explains patterns of species richness on volcanic hotspot archipelagos with respect to island age (T) and area (A), most commonly employing what we here call semi‐log ATT2 and LogATT2 models. These can be considered direct extensions of semi‐log and power law species‐area relationships (SARs), with a hump‐shaped function of T modelling drivers of biodiversity over and above area per se. We compare these and related models and investigate their conceptual and mathematical connections. Location: The Azores, Galapagos, Hawaii, Marquesas, Society Islands, Cape Verde Islands, Canary Islands and Aeolian archipelagos. Taxa: Vascular plants, birds, bryophytes, arthropods and molluscs. Methods: We gathered species richness data from databases and published sources, resulting in 34 datasets for various taxa. We used the Akaike information criterion corrected for small sample size (AICc) to compare the relative performance of models. We analysed the data at archipelago level and across archipelagos by using mixed effect models. We also calculated the relative time of expected peak diversity (Tpeak) from parameter estimates. Results: In almost three‐fourth of the cases the best model overall was one that contained only A or T rather than both predictors. There was greater variance between taxa than between archipelagos. Better dispersed taxa tended to reach peak diversity earlier. The most generally applicable of the models including T were the LogATT2 and LogTT2 models. These have important, previously unrecognized mathematical properties. Main Conclusions: SARs and species–time relationships should always be considered as potentially more parsimonious options. Considering the LogATT2 model as a modification of the power law S = cAz, where a lognormal function in T replaces the constant, c allows the construction of an extended framework for the GDM with incorporation of additional predictors such as measures of environmental heterogeneity and application beyond hotspot archipelagos. [ABSTRACT FROM AUTHOR]