Supporting Information: Appendix S1 Vegetation structure We measured woody plant species density and average heights to ensure the habitats surveyed were comparable at different sites along the aridity gradient. We used a line transect through each 1km transect in which the birds were sampled. We identified points every 20m, and within a 10m radius of that point, we counted and measured the height of each woody plant. This was then used to calculate average height and density of woody plants in each transect. Results Trees within riparian habitats were significantly taller than the other two habitats (K-W Chi-squared = 516.5, df = 2, p < 0.001, confirmed using multiple comparison test after Kruskal-Wallis); thickened habitats contained significantly more low woody cover than riparian, and both thickened and riparian habitats had greater low woody cover than open habitats (K-W Chi-squared = 1563.7, df = 2, p < 0.0001, Figure S1). Habitat types were comparable between sites (i.e., all riparian, open and thickened habitats did not differ significantly in woody plant density and height between sites along the aridity gradient). Figure S1. Summary of the (a) density, and (b) maximum height of woody plants at each of the habitat types at each of the sites along the aridity gradient. Sites are increasingly arid from left to right. Ok Cl We Ro 100 80 0 20 40 60 80 0 20 40 60 80 60 40 % woody cover 20 0 Ne Ne Ok Cl We Ro Cl We Ro Cl We Ro 15 0 5 10 15 10 0 Ok Ok Thickened 5 10 5 0 Ne Ne Riparian 15 Open Woody plant height (m) Thickened 100 Riparian 100 Open Ne Ok Cl We Ro Ne Ok Cl We Ro Appendix S2 200 150 100 50 Chao 1 Mean Chao1Mean[Habitat == "Riparian"] Species accumulation curves for sampling in riparian, thickened and open habitats, based on Chao1 species richness estimator. 0 Riparian 20 Number of transects 40 Thickened 60 Sample[Habitat == "Riparian"] 80 Open Appendix S4 Models Fit for FRic, Using Environmental Correlates that Best Explained FD and sesFD FRic Rainfall: Habitat (R) Habitat (T) Prev 6 month Rainfall: Prev year Season Habitat (R) Habitat (T) x Season x Season d.f. AIC Akaike weighting Model 1 n.s. n.s. - P < 0.0001 P < 0.05 P < 0.001 n.s. 9 1566.7 0.99 Model 2 n.s. n.s. P < 0.001 - P < 0.01 P < 0.01 n.s. 9 1581.7 0.0005 Null model - - - - - - - 3 1649.2 ~0 (Best model) Best model (Model 1): FRic = 1.72 (±0.78) Wet Season + 0.0088 (±0.002) Rainfall over previous year + 3.77 (±1.11) Riparian Habitat in Wet Season Model 2 : FRic = 2.32 (±0.81) Wet Season + 0.0074 (±0.002) Rainfall over previous year + 3.81 (±1.43) Riparian Habitat in Wet Season Based on SES calculated assuming chance of each species occurring in random assemblages is linked to its abundance in the dataset (that is, constrained) Model 1 (Best model) Model 2 Null Model Habitat (O) Habitat (R) Habitat (T) Rain: prev 6 mo (mm) Rainfall: prev y Habitat (R) x Season Habitat (T) x Season Season d.f. AIC Akaike weighting P < 0.05 P< 0.0001 P < 0.05 - - P < 0.05 n.s. n.s. 8 656.9 0.99 n.s. P< 0.0001 n.s. n.s. - P < 0.05 n.s. n.s. 9 672.8 0.0004 - - - - - - - - 3 699.8 ~0 Best model (Model 1): sesFRic = -0.27 (±0.12) Open – 1.4 (±0.12) Riparian -0.31 (±0.13) Thickened + 0.54 (±0.21) Riparian Habitat in Wet Season Model 2 : Same explanatory variables as those for sesFD constrained, but not all with the same levels of significance, so given in tables below in more detail Based on SES calculated assuming chance of each species occurring in random assemblages is not linked to its abundance in the dataset (that is, not constrained) Rain: Habitat Habitat Habitat Habitat Habitat Rainfall: Akaike prev 6 (R) x (T) x Season d.f. AIC (O) (R) (T) prev y weighting mo (mm) Season Season Model 1 (Best model) Model 2 Null Model P< 0.0001 P< 0.0001 P< 0.0001 P< 0.0001 - P< 0.0001 - P< 0.0001 - - - P < 0.001 n.s. n.s. 8 610.1 0.99 n.s. - P < 0.001 n.s. n.s. 9 620.4 0.008 - - - - - 3 626.5 ~0 Best model (Model 1): sesFRic = -0.74 (±0.11) Open – 1.4 (±0.11) Riparian -0.94 (±0.12) Thickened + 0.71 (±0.20 Riparian Habitat in Wet Season Model 2 : Same explanatory variables as those for sesFD not constrained, so given in tables below in more detail sesFRic constrained by prevalence: Habitat Open Habitat Riparian Habitat Thickened Season Wet Rainfall.6mo.prev Habitat Riparian:Season Wet Habitat Thickened:Season Wet Value -0.25 -1.39 -0.29 0.11 -0.00006 0.53 0.18 Std.Error 0.155 0.162 0.176 0.150 0.00036 0.211 0.220 t-value -1.65 -8.57 -1.67 0.76 -0.15 2.55 0.82 p-value 0.11 0.0000*** 0.10 0.45 0.88 0.0115* 0.41 sesFRic not constrained by prevalence: Value Std.Error t-value p-value Habitat Open -0.672 0.140 -4.81 0.0000*** Habitat Riparian -1.32 0.146 -9.00 0.0000*** Habitat Thickened -0.866 0.159 -5.43 0.0000*** Season Wet -0.082 0.139 -0.59 0.55 Rainfall.6mo.prev -0.00025 0.00033 -0.75 0.45 Habitat Riparian:Season Wet 0.72 0.195 3.66 0.0003*** Habitat Thickened:Season Wet 0.30 0.202 1.48 0.14 Note that the levels of significance for each term in the mixed models using Fric and sesFric differ somewhat to those for FD and sesFD, but the direction of effects (t-value) are identical. Differences in the levels of significance are likely due to the “randomness” of null model sampling and the behaviour of convex hull volumes (Fric) relative to functional dendrograms (FD). Convex hull volumes are vulnerable to overinflation when a species that greatly differs to the community on a single axis is added, because the volume of the additional multidimensional shape that is added to the index may be as large or larger than the volume for the rest of the community.