Trait variation within populations is an important area of research for empirical and theoretical ecologists. While differences between individuals are doubtlessly ubiquitous, their role for species coexistence is much less clear and highly debated. Both unstructured (random) and structured (linked to space, time or inheritance) intraspecific trait variation (ITV) may modify species interactions with nontrivial consequences for emerging community compositions. In many ecosystems, these compositions are further driven by prevalent disturbance regimes. I therefore explored the effects of unstructured as well as spatially structured ITV under disturbances in a generic ecological model of competing sessile species. Using spatially explicit, individual‐based simulations, I studied how intraspecific variation in life history traits together with interspecific tradeoffs and disturbance regimes shape long‐term community composition. I found that 1) unstructured ITV does not affect species coexistence in the given context, 2) spatially structured ITV may considerably increase coexistence, but 3) spatially clumped disturbances reduce this effect of spatially structured ITV, especially if interspecific tradeoffs involve dispersal distance. The findings suggest that spatially structured ITV with individual trait responses to local habitat conditions differing among species may create or expand humps in disturbance–diversity relationships. Hence, if present, these forms of spatially structured ITV should be included in ecological models and will be important for reliably assessing community responses to environmental heterogeneity and change.