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Abstract Question Which functional diversity indices have the power to reveal changes in community assembly processes along abiotic stress gradients? Is their power affected by stochastic processes and variations in species richness along stress gradients? Methods We used a simple community assembly model to explore the power of functional diversity indices across a wide range of ecological contexts. The model assumes that with declining stress the influence of niche complementarity on species fitness increases while that of environmental filtering decreases. We separately incorporated two trait‐independent stochastic processes – mass and priority effects – in simulating species occurrences and abundances along a hypothetical stress gradient. We ran simulations where species richness was constant along the gradient, or increased, decreased or varied randomly with declining stress. We compared observed values for two indices of functional richness – total functional dendrogram length ( FD ) and convex hull volume ( FR ic) – with a matrix‐swap null model (yielding indices SESFD and SESFR ic) to remove any trivial effects of species richness. We also compared two indices that measure both functional richness and functional divergence – R ao quadratic entropy ( R ao) and functional dispersion ( FD is) – with a null model that randomizes abundances across species but within communities. This converts them to pure measures of functional divergence ( SESR ao and SESFD is). Results When mass effects operated, only SESR ao and SESFD is gave reasonable power, irrespective of how species richness varied along the stress gradient. FD , FR ic, R ao and FD is had low power when species richness was constant, and variation in species richness greatly influenced their power. SESFR ic and SESFD were unaffected by variation in species richness. When priority effects operated, FR ic, SESFR ic, R ao and FD is had good power and were unaffected by variation in species richness. Variation in species richness greatly affected FD and SESFD . SESR ao and SESFD is had low power in the priority effects model but were unaffected by variation in species richness. Conclusions Our results demonstrate that a reliable test for changes in assembly processes along stress gradients requires functional diversity indices measuring either functional richness or functional divergence. We recommend using SESFR ic as a measure of functional richness and either SESR ao or SESFD is (which are very closely related mathematically) as a measure of functional divergence. Used together, these indices of functional richness and functional divergence provide good power to test for increasing niche complementarity with declining stress across a broad range of ecological contexts.