Ecologists have long held that species' poleward range boundaries are set by environmental constraints rather than by interactions with other organisms. However, populations can be more sensitive to competition near their environmental limits which may prohibit their expansion into otherwise tolerable habitats. Analyzing empirical mechanistic niche models in the variable-environment coexistence theory framework, I show that interspecific competition can limit the northern range boundary of a globally-distributed aquatic duckweed plant. My competition model predicts the observed distribution of the duckweed and its primary competitor with remarkable accuracy, and uncovered a crucial role of temperature fluctuations in maintaining its northern range boundary. My results highlight how accounting for species interactions and partitioning coexistence mechanisms can clarify the factors shaping species' geographic distributions.