Although functional and phylogenetic diversities are increasingly used in ecology for a variety of purposes, their relationship remains unclear, and this relationship likely differs among taxa, yet most recent studies focused on plants. We hypothesize that communities may be diverse in functional traits due to presence of: many phylogenetic lineages, trait divergence within lineages, many species and random functional variation among species, weak filtering of traits in favorable environments, or strong trait divergence in unfavorable environments. We tested these predictions for taxa showing higher (ants), or lower (spiders, ground beetles) degrees of competition and niche construction, both of which might decouple functional traits from phylogenetic position or from the environment. Studying > 11,000 individuals and 216 species from coastal heathlands, we estimated functional as minimum spanning trees using traits related to the morphology, feeding habits and dispersal, respectively. Relationships between functional and phylogenetic diversities were overall positive and strong. In ants, this relationship disappeared after accounting for taxonomic diversities and environments, whereas in beetles and spiders taxonomic diversity is related to functional diversity only via increasing phylogenetic diversity. Environmental constraints reduced functional diversity in ants, but affected functional diversity only indirectly via phylogenetic diversity (ground beetles) and taxonomic and then phylogenetic diversity (spiders and ground beetles). Results are consistent with phylogenetic conservatism in traits in spiders and ground beetles. In ants, in contrast, traits appear more phylogenetically neutral with any new species potentially representing a new trait state, tentatively suggesting that competition or niche construction might decouple phylogenetics from trait diversity.