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Aim: Closely related species tend to resemble each other in their morphology and ecology because of shared ancestry. When exploring correlations between species traits, therefore, species cannot be treated as statistically independent. Phylogenetic comparative methods (PCMs) attempt to correct statistically for this shared evolutionary history. Almost all such approaches, however, assume that correlations between traits are constant across the tips of the tree, which we refer to as phylogenetic stationarity. We suggest that this assumption of phylogenetic stationarity might be often violated and that relationships between species traits might evolve alongside clades, for example, owing to the effects of unmeasured traits or other latent variables. Specific examples range from shifts in allometric scaling relationships between clades (e.g., basal metabolic rate and body mass in endotherms, and tree diameter and biomass in trees) to the differing relationship between leaf mass per area and shade tolerance in deciduous versus evergreen trees and shrubs. Innovation: Here, we introduce an exploratory modelling framework, phylogenetically weighted regression, which represents an extension of geographically weighted regression (GWR) used in spatial studies, to allow non‐stationarity in model parameters across a phylogenetic tree. We demonstrate our approach using empirical data on flowering time and seed mass from a well‐studied plant community in southeastern Sweden. Our model reveals strong, diverging trends across the phylogeny, including changes in the sign of the relationship between clades. Main conclusions: By allowing for phylogenetic non‐stationarity, we are able to detect shifting relationships among species traits that would be obscured in traditional PCMs; thus, we suggest that PWR might be an important exploratory tool in the search for key missing variables in comparative analyses. [ABSTRACT FROM AUTHOR]