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Priority effects, the effects of early-arriving species on late-arriving species, are caused by niche preemption and/or niche modification. The strength of priority effects can be determined by the extent of niche preemption and/or modification by the early-arriving species; however, the strength of priority effects may also be influenced by the late-arriving species, as some species may be better adapted to deal with niche preemption and/or modification. Therefore, some combinations of species will likely lead to stronger priority effects than others. We tested priority effects for all pairwise combinations of 15 plant species, including grasses, legumes, and nonleguminous forbs, by comparing simultaneous and sequential arrival orders in a 10-week-long, controlled, pot experiment. We did this by using the competitive effect and response framework, quantifying the ability to suppress a neighbor as the competitive effect and the ability to tolerate a neighbor as the competitive response. We found that when arriving simultaneously, species that caused strong competitive effects also had weaker competitive responses. When arriving sequentially, species that caused strong priority effects when arriving early also had weaker responses to priority effects when arriving late. Among plant functional groups, legumes had the weakest response to priority effects. We also measured plant functional traits related to the plant economic spectrum, which were combined into a principal components analysis (PCA) where the first axis represented a conservative-to-acquisitive trait gradient. Using the PCA species scores, we showed that both the traits of the focal and the neighboring species determined the outcome of competition. Trait dissimilarities between the focal and neighboring species were more important when species arrived sequentially than when species arrived simultaneously. Specifically, priority effects only became weaker when the late-arriving species was more acquisitive than the early-arriving species. Together, our findings show that traits and specifically the interaction of traits between species are more important in determining competition outcomes when species arrive sequentially (i.e., with priority effects present) than when arriving simultaneously.