DOI: 10.5061/dryad.1rn8pk0qs
title: Environmental heterogeneity predicts global species richness patterns better than area

description: 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.
 Results: We find that environmental heterogeneity explains species
 richness relationships better than area does, suggesting that
 niche-related processes are more prevalent than pure area effects at broad
 scales. Main Conclusions: Our results imply that niche-related processes
 are essential to understand broad-scale species-area relationships and
 that habitat diversity is more important than area alone for the
 protection of global biodiverstiy.
description: 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 km<sup>2</sup> (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. <b>Statistical Analyses</b> Quadratic polynomial linear regression models using all three variables (area, elevation range and precipitation range with their quadratic terms) were run on every dataset (Global, Nearctic, Palearctic, Indo-Malay, Neotropics, Afrotropics and Australasia) with mammal species richness as the response variable. The full model had the form lm(species.richness ~ area + area_squared + elevation + elevation_squared + precipitation + precipitation_squared). Model selection was done using AIC by stepwise removal of quadratic terms in all possible combinations from the full model for every dataset (see Table S1.3 for all tested model structures), but the full model always fit the data best (Table S1.3). Predictions for species richness were calculated from these models. All models were run inside a bootstrapping framework with 500 iterations over all available focal cells. To account for different species richness variances in different biogeographic regions, we did not necessarily use all available cells in a biogeographic region as focal cells. Instead, we took a random sample of focal cells for each biogeographic region (see Table S1.6 for sample sizes per region), so that all samples had the same sample precision with respect to species richness. We used a sample precision of +/- 4 species. This reduction of focal cells at the same time reduced spatial autocorrelation in the samples. Predictions of species richness were limited to a minimum of zero for all variables, as it is biologically impossible to have a negative numbers of species. To calculate which variable (area, elevation range or precipitation range) had the largest influence on species richness relationships, we partitioned the variance using polynomial models with all three predictors (full model). Variance partitioning was calculated using the varPart function from the modEvA package (Barbosa et al. 2016), which is based on R<sup>2</sup>-values. This was done by regressing species richness on the environmental and area variables simultaneously and separately and feeding the results (see code snippet in Table S1.7) into the varPart function. We used an R<sup>2</sup>-based method instead of an AIC-based method, because we were interested in explained variability instead of prediction-oriented model performance.