## Illustration of abundance weighting procedure for FD and Hulls.

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Figures are generally photos, graphs and static images that would be represented in traditional pdf publications.

Calculations are shown for a simplified community of three species with unequal abundances (abundance represented by the size of circles). Subscripts are for species i and trait j. Trait values for species are standardized to a mean of zero and standard deviation of one (Z-scores). Trait values for species are then multiplied by the proportional relative abundance (bound between zero and one), which results in a translation towards the origin, more so for rare species and less so for abundant species (see Appendix 1 for calculation). This modified distribution is then used for subsequent metric calculation. Weighing by the CV involves multiplying each standardized trait value by the CV (a positive value). This “stretches” trait axes with CV>1, effectively spreading species further apart along that axis, and “compresses” trait axes with CV<1, effectively crowding species closer together along that axis. We performed CV weighting prior to abundance weighting.