Appendix 1 Definition of the main Allee effect-related concepts. Adapted from Berec et al. (2007). The reference was given as followed. Allee effect: a positive causal relationship between any component of fitness and population density or size. Component Allee effect: positive relationship between any measurable component of individual fitness, such as reproduction and survival, and population size or density. A population may suffer one to more component Allee effects. However, a component Allee effect in a population may not always generate a demographic Allee effect, which depends on more complex factors, such as life-history traits, resource availability, predation and disturbance. Demographic Allee effect: positive relationship between total individual fitness, usually quantified by the per capita population growth rate, and population size or density. The demographic Allee effect is defined as a strong Allee effect, if there is an Allee threshold (critical population size or density below which the per capita population growth rate becomes negative). Otherwise, it is called a weak Allee effect. Ecological Allee effect: ecological-level mechanism resulting in a positive relationship between any measurable fitness component and population size or density. Genetic Allee effect: genetic-level mechanism (such as sampling effect, genetic drift, inbreeding) resulting in a positive relationship between any measurable fitness component and population size or density. Pollination-driven Allee effect: decreased reproduction or reproductive failure at low density or in small populations due to decreased pollination success or pollination failure, which is the most common and well-documented mechanism resulting in an Allee effect in a plant species. Predation-driven Allee effect: a general term for any component Allee effect in survival or reproduction due to increased predation rate at low density or small prey populations. Reference Berec L., Angulo E., Courchamp F. 2007. Multiple Allee effects and population management. Trends in Ecology & Evolution 22, 185-191. Appendix 2 An individual of Bombus richardsi was visiting Pedicularis rex, which is a large subalpine herbaceous perennial and endemic to the East Himalaya. P. rex is self-compatible but absolutely depends on bumblebees for reproduction in natural populations. Appendix 3 location of the focal patches of Pedicularis rex in 2011, dp represents dense patch and sp indicates sparse patch. Patch size (the number of flowering individuals) was indicated as the number in the parentheses. Sp1patch included only one individual on an open space. The other three sparse patches (sp4, sp5 and sp6) were distributed dispersedly along a narrow path downhill from sp1. Sp2 and dp5 patches belonged to a large population having hundreds of flowering individuals. Dense patches were distributed much more continuously along another road downhill from sp1.