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.