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Questions Popular methods to analyse community-trait-environment relationships constrain community patterns by trait and environment relationships. What if some traits are strongly associated with community composition but unrelated to environmental variables and vice versa? We take a different approach, unconstrained by this assumption using non-parametric methods. We applied this technique to lichen (fungal/algal and/or cyanobacterial symbioses) communities across environmental and fire age gradients by measuring richness and cover of four important functional traits: energy generation (type of photosynthetic symbiont), water relations (inferred from growth form), dispersal capability (from vegetative propagules) and microsite specificity (measured by substrate affinity). Location Denali National Park and Preserve, Alaska, USA. Methods We ordinated plots in species space and regressed trait and environmental variables against ordination axes, resulting in one- or two-dimensional trait and environment surfaces. We then superimposed these surfaces on the ordination to create a new visual display, the 'hilltop plot', which enabled simultaneous measurement and display of one- and two-dimensional, non-linear community-trait-environment associations. Results Most traits examined show non-linear relationships with community structure. Fire favoured simple cladoniiform lichens, species with higher vegetative dispersal capacity and specificity to grow on wood, but excluded the 'reindeer' lichens, which had lower cover even more than 20 yrs after fire. Forests had more sorediate lichens than non-forested habitats, whereas high elevation, rocky areas had more green algal and fruticose lichens. Cyanobacterial lichen richness was positively related to shrub cover, while tripartite (cyanobacteria and green algae in a single lichen) and foliose lichen richness was highest in areas with higher moss cover. Conclusions Different combinations of lichen functional traits peaked along environmental and disturbance gradients, which we interpreted as balancing energy generation, water relations, vegetative dispersal and habitat specificity. Our method of trait-environment-community analysis revealed numerous one- and two-dimensional, non-linear relationships between community composition and functional traits, environmental variables and fire age gradients, which informed mechanisms behind community assembly. Our results indicate non-parametric and non-linear methods of trait-environment-community analysis have the potential to detect patterns that would have been missed using current popular techniques. [ABSTRACT FROM AUTHOR]