Aim: It is widely accepted that biodiversity can be determined by niche-relate processes and by pure area effects from local to global scales. Their relative importance, however, is still disputed, and empirical tests are still surprisingly scarce at the global scale. We compare the explanatory power of area and environmental heterogeneity as a proxy for niche-related processes as drivers of native mammal species richnessworldwide and with biogeographical regions.

Location: Global

Time Period: Data was collated form the IUCN (2013)

Major Taxa Studied: All mammal species, including possibly extinct species and species with uncertain presence.

Methods: We developed a random walk algorithm to compare the explanatory power of area and environmental heterogeneity on native mammal species richness. As measures for environmental heterogeneity, we used elevation and precipitation ranges, which are well known correlates of species richness.

Our global terrestrial mammal data comprised 4,954 native species derived from extent-of-occurrence distribution maps provided by IUCN (2013), from which species richness across an equal-area grid with cells of 12,364 km² (approximately 111 km x 111 km at the equator) was aggregated by Stein et al. (2015). This dataset was split into seven mammalian biogeographic regions (Olson et al. 2001; Kreft & Jetz 2010). We excluded introduced species, vagrant species, bats and species for which no specific localities were known. We removed grid cells with no indigenous terrestrial mammals present (excluding the biogeographic regions Antarctica and Oceania) and grid cells containing only water (oceans and large lakes).

We analysed two measures of environmental heterogeneity across the same 12,364 km² grid cells in all biogeographic regions of the globe (except for Antarctica and Oceania): elevation range and precipitation range. These two measures of environmental heterogeneity are known to be strong predictors of terrestrial mammal species richness at broad scales and are uncorrelated at this scale, whereas temperature and elevation are highly correlated (see Table S1.1 and Fig. S1.4 in Supporting Information S1; Rahbek 2005; Rodríguez et al. 2005; Tuanmu & Jetz 2015). The elevation and precipitation ranges were aggregated by Stein et al. (2015) from elevation and climate surfaces produced by Hijmans et al. (2005) at a 111 km x 111 km grain.

We analysed species richness as a function of area, elevation range and precipitation range for the globe and the six remaining biogeographic regions at scales ranging from one to 50 grid cells. Grid cells were selected using a new random walk algorithm that randomly selected neighboring cells from an initial grid cell (see Appendix S1; run in R 3.3.0 (R Core Team 2016)). Starting from an initial ("focal") cell, the second cell was randomly selected within the 8-cell neighborhood. The next cell was chosen from the 8-cell neighborhoods of the previously selected cells, excluding cells already selected. The algorithm stopped when a cell group had no not-yet-selected neighboring cells, or when the maximum of 50 cells was reached. Each cell served 50 times as focal cell (i.e. 50 iterations per focal cell). For further technical detail see the supplementary material (see Appendix S1). In comparison to rectangular or circular sampling procedures, this new random walk algorithm is able to adapt to any given spatial configuration of cells through a flexible neighbor selection, is random through randomized selection of neighbors and has a dynamic sampling window that allows observations of all possible realizations of a given spatial dataset including edge or peripheral grid cells such as coastlines (see also animations of moving window, traditional random walk and new random walk algorithms in Fig. S2.5). Due to the large pixel size of our analysis, reaching a coastline is a typical rather than special case. However, the observations were autocorrelated as the observed values at larger spatial scales depended on those at smaller spatial scales, similar to strictly nested quadrat construction algorithms (see Scheiner 2003, Storch et al 2012). We applied the random walk algorithm to create sets of nested areas for seven datasets: The global dataset with 10,704 grid cells, Nearctic with 1,731 grid cells, Palearctic with 4,257 grid cells, Indo-Malay with 690 grid cells, Neotropics with 1,553, Afrotropics with 1,771 and Australasia with 702 grid cells. Absolute values of variables per grid cell ranged from: species richness of 5-463, elevation ranges of 10 m a.s.l. - 8,235 m a.s.l. and precipitation ranges of 0 mm -11210 mm.