I formulated responses of multiple functional traits of a community, which are defined as abundance-weighted mean traits of composite species, to environmental changes. The presented model of trait dynamics can include an arbitrary number of traits and multispecies interactions. The variance-covariance structure of species functional traits determines trait dynamics in communities by modifying the rate and the direction of the environmental effects transmitted to changes in relative abundances of species having particular functional traits. In addition, the interspecific interaction further modifies the effect of trait covariances. For the special case of competition with a single niche axis, the effect of interspecific interaction is limited so that the trait variance-covariance structure is the predominant factor of trait responses. This implies that the trait-based approach aggregating community properties in terms of functional traits is especially useful for species assemblies or ecological guilds in which composite species only weakly associate or compete with each other in a single resource niche space.