• quantitative biogeography;
  • macroecology;
  • latitudinal and elevational gradients;
  • geometric range boundary constraints;
  • humped or parabolic diversity curve;
  • hotspot;
  • range size frequency distribution;
  • indicator group

Species richness has classically been thought to increase from the poles towards the Equator, and from high elevations down to sea-level. However, the largest radiation of butterflies in Madagascar, the subtribe Mycalesina (c. 67 spp.) does not exhibit such a monotonic pattern, either for empirical records or for interpolated species ranges. Instead, summation of mycalesine ranges generates a domed curve of species richness values approximately symmetric around mid latitudes within the island, a pattern most smoothly exhibited by the wider ranging and better known species, and a less symmetric curve peaking near mid elevations. Hotspots for the summation of 1183 species ranges and seven out of the ten groups of insects and vertebrates analysed (butterflies, cicindelid and enariine melonthid beeties, ctenuchiine moths, chameleons, frogs, birds, lemurs, tenrecs, and rodents) also occur at both mid latitudes and elevations. The most strongly parabolic pattern is shown by animals (637 spp.) whose ranges are confined to the highly linear rainforest biome. This rainforest species richness curve is resilient in shape even after controlling for particular effects of area and irregular sample effort. In sharp contrast, at least eight different environmental parameters for the rainforest biome tend to increase monotonically towards the northern, more tropical, boundary, a trend evident only in species richness gradients of more narrow-ranging species. The one-dimensional latitudinal species richness curves and hotspots observed in fact best reflect overall the geometric predictions of a null model for ranked range size partitions of the regional species pool. This analytical model is based on the uniform probability distribution, and assumes that species ranges are constrained by the position of biome or island boundaries. The same logarithmic equations applied iteratively to longitude also accurately predict hotspots for more realistic species ranges containing gaps, as shown for two-dimensional species richness patterns for the Madagascan rainforest dataset. Bio-geographic and conservation implications of the bounded range overlap concept are discussed.