Lianas are structural parasites of trees that reduce the growth, survival and reproduction of their hosts. Given that co-occurring tree species differ strongly in the proportion of individuals that are infested by lianas (liana prevalence), lianas could differentially impact tree species and thereby influence tree community composition. Surprisingly, little is known about what governs variation in liana prevalence. Here, we apply an approach inspired by disease ecology to investigate the dynamics of liana prevalence over 11 years on Barro Colorado Island, Panama. We followed the fate of 1,938 individual trees from 21 tree species, recording deaths and change in liana infestation status. With these data, we fit species-specific Markov chain models to estimate four rates: colonization by lianas (analogous to disease transmission), shedding or loss of lianas (analogous to host recovery), baseline mortality of uninfested trees (baseline mortality) and additional mortality of infested trees (parasite lethality). Models explained 58% of variation in liana prevalence among tree species, and revealed that host shedding of lianas and parasite lethality were the most important contributors to interspecific variation in liana prevalence at our site. These rates were also strongly related to shade tolerance, with light-demanding species having greater rates of shedding and lethality, and lower rates of liana prevalence. An indirect path analysis with a structural equation model revealed that both greater rates of liana shedding and liana-induced lethality contribute to the observed lower rates of liana prevalence for light-demanding tree species. Synthesis. Our approach revealed that the prevalence of liana infestation among tree species is driven via indirect pathways operating on the rates of shedding and lethality, which relate to the ability (or inability) of trees to shed and/or tolerate lianas. Shade-tolerant trees have greater proportions of trees infested by lianas because they are both less able to shed lianas and more able to tolerate infestation.