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Background Perennity of giant rosette species in combination with a single 'big bang' reproduction followed by death of the genetic individual is relatively rare among plants. Such long-lived monocarpic plants are usually slow growing and can be found in deserts, bogs or in alpine regions of the tropics or sub-tropics. Due to their longevity, monocarpic perennials risk losing everything before reproduction, which make them particularly susceptible to disturbances. Because of the inherent difficulties in assessing whether long-lived populations are growing or declining, usually neither their demography nor the consequences of increasing grazing pressure are known. Methods We used integral projection modelling (IPM) to measure the growth rate and passage time to flowering of Rheum nobile , a monocarpic perennial, and one of the most striking alpine plants from the high Himalayas. Rosettes which were no longer found due to disturbances or grazing by yaks were either treated as missing or as dead in two series of analysis, thereby simulating demography with and without the impact of grazing cattle. Data were collected from plants at 4500 m a.s.l. in Shangri-la County, Yunnan Province, south-west China. In four consecutive years (2011–2014) and in two populations, 372 and 369 individuals were measured, respectively, and size-dependent growth, survival and fecundity parameters were estimated. In addition, germination percentage, seedling survival and establishment probability were assessed. Key results The probability of survival, flowering and fecundity were strongly size dependent. Time to reach flowering size was 33.5 years [95 % confidence interval (CI) 21.9–43.3, stochastic estimate from pooled transitions and populations]. The stochastic population growth rate (λ s) of Rheum nobile was 1.013 (95 % CI 1.010–1.017). When disturbance by grazing cattle (yaks) was accounted for in the model, λ s dropped to values <1 (0.940, 95 % CI 0.938–0.943). Conclusion We conclude that natural populations of this unique species are viable, but that conservation efforts should be made to minimize disturbances by grazing and to protect this slow-growing flagship plant from the high Himalayas. [ABSTRACT FROM AUTHOR]