1 2 Supporting Information 3 Freshwater Biology 4 5 6 Unifying research on the beta diversity-environmental heterogeneity 7 relationship in running water systems 8 9 Jani Heino, Adriano S. Melo & Luis Mauricio Bini 10 1 Table S1. Comparisons of three recent empirical studies on the BDEHR in stream invertebrates. Overall spatial level refers to the geographical area encompassing all region units in a study. Region unit level refers to a region unit within which local communities were situated, and beta diversity and habitat heterogeneity were measured. Grain size refers to a locality harbouring a local community. Mechanisms refer to the most important mechanisms that can be expected to occur at the spatial level of the region unit in each of the three studies. Spatial scale Study Heino et al. (2013) Astorga et al. (2014) Bini et al. (2014) Overall spatial level Region Unit level Grain size Landscape Stream Riffle site Regional Drainage basin Riffle site Continental Ecoregion Riffle site Mechanisms within a region unit Study Species sorting Mass effects Dispersal limitation Heino et al. (2013) Likely Very likely Unlikely Astorga et al. (2014) Likely Probable Probable Bini et al. (2014) Likely Unlikely Likely Dataset characteristics Study Number of region units No. of localities Localities per region unit Heino et al. (2013) 10 100 10 Astorga et al. (2014) 8 120 15 Bini et al. (2014) 30 689 10-62 Dataset characteristics Study Heino et al. (2013) Astorga et al. (2014) Bini et al. (2014) No. of taxa Habitat heterogeneity Chironomids included 168 Overall Yes ? Key variables only No 606 Overall Yes 2 Fig. S1. A test of the effect of using all environmental variables and key environmental variables only for calculating environmental heterogeneity among sites (average Euclidean distance to centroid) within a region unit. Also, shown are tests of removing an important taxonomic group (Diptera: Chironomidae) from the analyses of average biological distance to centroid (SØrensen dissimilarity coefficient, range: 0-1). The example data are from Heino et al. (2013). Subfigure (a) shows the relationship between beta diversity (all invertebrate species) and environmental heterogeneity (all environmental variables), (b) shows the relationship between beta diversity (Chironomidae omitted) and environmental heterogeneity (all environmental variables), (c) shows the relationship between beta diversity (all invertebrate species) and environmental heterogeneity (key five environmental variables), and (d) shows the relationship between beta diversity (Chironomidae omitted) and environmental heterogeneity (key five environmental variables). Region unit = a stream, n = 10 streams. 0.35 0.35 b) Average SØrensen distance to centroid a) 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 F = 0.048, R2 = 0.006, P = 0.831 F = 0.017, R2 = 0.001, P = 0.920 0.10 0.10 2 2.5 3 3.5 4 2 0.35 0.35 c) 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 2.5 1 1.2 1.4 1.6 1.8 4 F = 0.576, R2 = 0.067, P = 0.469 2 0.10 0.8 1 1.2 1.4 Average Euclidean distance to centroid 3 3.5 d) F = 0.462, R2 = 0.055, P = 0.516 0.10 0.8 3 1.6 1.8 2 References cited in Supporting Information Astorga A., Death R., Death F., Paavola R., Chakraborty M. & Muotka T. (2014) Habitat heterogeneity drives the geographical distribution of beta diversity: the case of New Zealand stream invertebrates. Ecology and Evolution, 4, 2693–2702. Bini L.M., Landeiro V.L., Padial A.A., Siqueira T. & Heino J. (2014) Nutrient enrichment is related to two facets of beta diversity for stream invertebrates across the United States. Ecology, 95, 1569-1578. Heino J., Grönroos M., Ilmonen J., Karhu T., Niva M. & Paasivirta L. (2013) Environmental heterogeneity and beta diversity of stream macroinvertebrate communities at intermediate spatial scales. Freshwater Science, 32, 142-154. 4