Literature review and dataset
A search for the focal publications was primarily conducted in the Web of Science database (webofknowledge.com) and Google Scholar (scholar.google.com) using the keywords “Yunnan” or “Tibet” or “Sichuan” or “Himalaya” or “Hengduan” in combination with the terms “pollination” or “fruit set” or “seed set” or “hand poll*” or “supp* poll*”. To include more published pollination works conducted in this area, we also searched the Chinese publications database, CNKI (Chinese National Knowledge Infrastructure, www.cnki.net), using the keyword combinations mentioned above in Chinese. Some unpublished papers, theses and personal data graciously given by the authors were also added to this analysis. The following criteria were used to select the focal publications: (1) studies of flowering plants growing on the East Himalaya-Hengduan Mountains, including plants in northwestern Yunnan Province, western Sichuan Province, southern Gansu Province and southeastern Tibet; (2) studies that applied hand pollination on the studied plants and assed the reproductive success of both hand- and open-pollination treatments; and (3) studies whose results included average seed set/seed production, standard deviation and sample size and fruiting proportion and sample size. For the fruit data recorded, we extracted the numbers of flowers with and without fruit in both hand- and open-pollinated treatments. For the seed set or seed production data, we extracted the mean, standard deviation and sample size of both treatments. For those data exhibited in graphs, we extracted the dataset from the graphs with ImageJ 1.31 .
To understand the effects of plant reproductive features on the degree of pollen limitation, several key traits were extracted, including the capacity for autonomous self-reproduction, pollination type (generalized vs. specialized pollination) , flower shape (restricted vs. nonrestricted) , rewards type (nectariferous vs. nectarless)  and flowering time , from the collected studies, other studies on the same species or the Flora of China (www.iplant.cn). We assessed the capacity for autonomous self-reproduction by the reproductive success of bagged treatments and hand-pollination treatments from the collected papers or from other studies on the same species. The flowering time was separated into three categories: early spring (before May), summer (May to August), and autumn (August). The flowering time was separated into such way mostly based on the abundance of pollinators in different seasons in this region. The pollination pattern was assessed by the number of pollination functional groups according to the description in the paper. Specialized pollination plants had only one kind of pollination functional group (moth, bees, butterflies, ants, etc.); otherwise, a plant was regarded as having generalized pollination. The flower shape was separated into two types, one is the open flowers those were radial symmetry and whose nectars were easily to be reached (non-restricted flowers), and the other one was bilateral symmetry or those with a tubular shape that can limit pollinator’s behavior (restricted flowers). The rewards of a plant were also collected and separated into two categories, nectariferous vs. nectariless, based on the description in the paper or from the Flora of China. We also extracted the elevation from the publications if the authors provided it; otherwise, we extracted it from Google Maps based on the geographic coordinates or names the authors provided. The elevation was arranged as a continuous variable from 1213 meters to 4600 meters.
Given that studies of heteromorphic species had more than one data entry, such as Primula chungensis, which has three different morphs (long-, short- and homo-styled morph), we took the average of records as the final number for a species if the data did not differ significantly in the capacity for autonomous selfing, elevation, pollination type, flowering time or rewards type. In total, 108 datasets from 94 species and 26 families were collected from 76 studies, and Primulaceae (14.04%), Gentianaceae (8.77%), Scrophulariaceae (10.53%) and Orchidaceae (14.91%) represented most of the collected species in our study.
For the binary data, i.e., fruit set, we calculated the effect size with log odds ratios (ln(o)) obtained from a 2 X 2 table of the flowers with and without fruit in the hand- and open-pollinated treatments . For the continuous data, i.e., seed set and seed production, we calculated the effect size by Hedges’ d with the mean, standard deviation and sample size of the hand- and open-pollinated treatments . The standard error recorded in studies was transformed to standard deviation by dividing by the sqrt of the sample size. The effect size of each study was calculated in OpenMEE, a free meta-analysis software for ecology and evolution research . To include as many datasets as possible, we transformed the log odds ratios to Hedges’ d following Coopers’ method . The degree of pollen limitation was viewed as the reproductive success of hand-pollination treatment vs. open-pollination treatment, and the plant species were viewed as pollination limited if the effect size was positive and its 95% confidence interval did not overlap zero ; otherwise, it was not viewed as being pollination limited.
The overall effect size was calculated by the traditional method and phyloMeta method separately. For the traditional meta-analysis, we used a random model to calculate the overall effect size, which took into account the deviation from the true effect size that may be generated by differences between the studies. We calculated Rosenthal’s fail-safe numbers to test the presence of publication bias in the datasets . These numbers represent the number of nonsignificant, unpublished, or missing studies that would need to be added to a meta-analysis to change the results from significant to nonsignificant. If the fail-safe number is larger than five times the sample size plus 10, it is safe to conclude that the results are robust with the consideration of publication bias . Because the Rosenberg fail-safe number was 80721 in the present study, which was much larger than the critical value (1080), there was no evidence of publication bias in the dataset. The classical meta-analysis, as well as the calculation of Rosenberg fail-safe number, was conducted with the “metaphor” package  in R 3.6.0.
For the phylogenetic meta-analysis, we constructed a list of plant species (family/genus/species) with the aid of the “plantlist” package . The angiosperm APG III consensus tree was constructed , and the branch lengths were calibrated from the “ape” package , which is used for phylogenetic analysis. After that, the overall effect size of the phylogenetic meta-analysis was tested by the “metafor” package  with the aid of the constructed phylogenetic tree mentioned above. Since the heterogeneity of the dataset was significant, several explanatory variants were added in the analysis. In the analysis, the flowering time, the capacity of autonomous selfing, the pollination type, the flower shape and the reward type were set as discontinuous explanatory variables, and the elevation was set as a continuous explanatory variable. The Qm and p values were calculated for each explanatory variable, and the different categories within an explanatory variable were significantly different if the p value did not exceed 0.05. The correlation between the continuous explanatory variable (elevation) and the degree of pollen limitation was also calculated. We also applied multiple analysis to test for potential interaction among different modulators.