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Abstract: Lianas are structural parasites of trees and reduce individual host tree growth, survival and fecundity. Thus, liana infestation is expected to affect tree population growth rates, with potentially different effects in different species depending on the frequency of liana infestation and the impact of liana infestation on population growth rates. Previous studies have documented the myriad negative effects of lianas on trees and variation in liana infestation among tree species; however, no study has quantified the impact of liana infestation on individual tree species population growth rates. Lianas are increasing in abundance in multiple Neotropical sites, which may have profound consequences for tree species composition if lianas differentially affect host tree species population growth. Here, we use long‐term data to evaluate the effects of liana infestation on the reproduction, growth, survival and ultimately population growth rates of dozens of tree species from Barro Colorado Island, Panama. We then test whether liana infestation affects tree species differentially with respect to two axes of life‐history variation: adult stature and position along the fast–slow axis, a measure of shade tolerance. Liana infestation decreased tree growth, survival and reproduction, with the strongest effects on survival in fast‐growing, light‐demanding species and on reproduction in large‐statured species. In combination, these effects reduced tree population growth rates such that liana‐infested populations declined by an average of 1.4% annually relative to conspecific liana‐free populations. The reduction in population growth rates was greatest among fast‐growing species and smaller in slow‐growing species. Synthesis. Our results demonstrate that liana infestation has strong negative effects on tree population growth rates, which vary systematically among tree species with tree life history. The finding that liana infestation is more harmful to fast‐growing tree species appears to be at odds with the general expectations in the literature. We propose that this is likely due to survivorship bias, as infestation greatly decreases survival in fast‐growing species such that the observable sample is biased towards those that survived and liana‐free. In combination with data on how tree species vary in liana infestation rates, these results provide a basis for predicting the impacts of changes in liana abundance on tree species composition. [ABSTRACT FROM AUTHOR]