Aim Mac Nally and Lake proposed a statistic (η) for determining whether the diversity in archipelagos is better generated by several small patches (SS-dominance) or by a few large patches (SL-dominance). The η statistic improves the study of the generation of diversity in systems of patches, but the dependence of η on a particular species–area relationship may reduce its effectiveness. In this paper we show that η may be affected by the criterion used to distinguish between large and small patches. We propose alternative measures (ranked m-dominance indices) for the detection of SS/SL dominance, which separate the effects of each class of patch size on the generation of diversity.
Location We use previously published species lists from three archipelagos: lizard species on 25 islands in the Gulf of California; non-introduced species of reptiles of the Canary Islands (order Squamata); and finch species from 19 islands of the West Indies. We also use one artificial data set.
Methods Presence–absence data and the rank order of patch areas are used to define the m-dominance indices, interpreted as measures of preferential size of patches occupied by m species. A Monte Carlo procedure is implemented for testing the significance of the observed indices. Row and column totals in the simulated presence–absence matrices are kept fixed in order to maintain differences in species richness among sites and differences in occurrence frequencies among species, but the allocation of each occurrence to a specific ranked area is randomized. The analyses are exemplified with the three published data sets taken from the literature, and a hypothetical patch system neither SS- nor SL-dominated.
Results The new m-dominance indices identified correctly the hypothetical patch system, while η was positive, suggesting an incorrect SL-dominant result. For the lizard data set, the standardized ranked m-dominance was significantly large for small m, confirming an SL-dominated system. Islands of varying size in the Canary archipelago hosted restricted reptile species, but matrix sparseness seems to have caused the non-significant results for the m-dominance indices in this case. The overall pattern of the West Indies system shows that medium-large islands are dominant, but most Monte Carlo analyses were not significant, also possibly as a result of matrix sparseness.
Main conclusions The m-dominance indices have the virtue of summarizing composition–area relationships, and including Monte Carlo procedures for testing whether patch size and the type of species distribution (species restricted to m patches, m = 1,…,s) are random or not. When m is as low as 1 or 2, the m-dominance indices may typify the role of restricted species on the generation of diversity in the system of patches. The procedure developed here can be generalized to include other ordinal properties of patches, such as isolation or habitat heterogeneity.