Methods to calculate how range-size averages change with elevation (ERR)
For each species we calculated the average point of elevational occurrence (referred to as midpoint) and range-size, defined as maximum minus minimum elevation. To quantify how average range-sizes change with increasing elevation (ERR) we used a novel approach based on quantile binning (rather than even increments), which better reflects non-normal data distributions or variation in sampling efforts. We assessed four other ERR methods (Stevens 1992, Rohde et al. 1993, Vetaas and Grytnes 2002, Feng et al. 2016) and found comparable results, thus we selected the quantile binning method because it produced the most linear relationships, less skewed by outliers (see Supporting information). Species’ midpoint values were divided equally into twenty bins (ventiles), each bin representing 5% of each families’ Malesian richness. We then interpolated species’ presence between all points of observation (meaning potential presence within multiple bins) and distribution overlap to estimate species-richness curves, followed by calculating within-bin richness and average range-sizes. For each family, we used ordinary least squares regression (OLS) to test and quantify ERR slopes which then were used as the response variable for across-family analyses.