Abstract The negative impact of invasive plants on native species has been well documented, but little is known about the specific role that invaders play on the population decline of native species. Here we used demographic models to evaluate how the alien grass Megathyrsus maximus affects the population dynamics of the native cactus Harrisia portoricensis . Demographic data gathered for H. portoricensis in grass-invaded and non-invaded areas were used to construct matrix projection models. Our demographic analysis includes numerical simulations, life table response experiments, life-cycle parameters and a systematic evaluation of the effects of matrix dimensionality. Results revealed that, while positive λ values can be achieved in grass-free areas dominated by native vegetation, population growth rates of H. portoricensis are reduced in grass-invaded areas ( λ = 0.88–0.91). Models predicted that H. portoricensis populations in grass-invaded areas might become extinct in the next 14–59 years, suggesting that the long-term persistence of this cactus may be linked to the fate of the grass invasion. Overall, our data show that the conversion of native forests into grass-dominated areas is having detrimental impacts on the population dynamics of native species, creating novel regeneration barriers that native species cannot surpass. Under this scenario, management strategies designed for the conservation of H. portoricensis should consider grass-eradication and control policies and long-term monitoring of populations. The information derived from this work may help us understand the mechanisms by which invasive species are gaining dominance over native species, which is crucial for managing and predicting biological invasions.