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The generation of this map of the world’s mountains consisted of five steps (Fig. 1): (i) the identification and hierarchisation of named mountain ranges and the recording of range-specific information; (ii) the manual digitization of the ranges’ general shape; (iii) the definition of mountainous terrain (and the inventory’s outer borders) using a DEM-based algorithm; (iv) the automatic refinement of the digitized and named ranges’ inner borders; and (v) the preparation of the final layers. The resulting products consist of a refined mountain definition (GMBA Definition v2.0), two versions of the inventory (GMBA Inventory v2.0_standard & GMBA Inventory v2.0_broad), and a set of tools to work with the inventories.Step i: Identification and hierarchisation of mountain rangesIn a first step, we identified mountain ranges worldwide. To do so we adopted the mountain ranges identified in the GMBA Inventory v1.410,14 and searched existing resources in any languages for other named ranges not yet included. The ranges added could either be adjacent to, included in (child range or subrange) or including (parent range or mountain system) mountain ranges of the GMBA Inventory v1.4. The resources used for our searches included world atlases (e.g. The Times Comprehensive Atlas of the World19, Knaurs grosser Weltatlas20, Pergamon World Atlas21); topographic maps (e.g. http://legacy.lib.utexas.edu/maps/imw/, http://legacy.lib.utexas.edu/maps/onc/, https://maps.lib.utexas.edu/maps/tpc/, www.topomap.co.nz, https://norgeskart.no, www.ign.es/iberpix/visor/); encyclopaedias (www.wikipedia.org; www.britannica.com); online gazetteers and reference sites (e.g. www.wikidata.org, www.geonames.org (GeoNames), www.mindat.org); mountain classification systems (e.g. the International Standardized Mountain Subdivision of the Alps or SOIUSA for the Alps22, Alpenvereinseinteilung der Ostalpen23, Classification of the Himalaya24, www.peakbagger.com/rangindx.aspx (PEMRACS), www.carpathian-research-network.eu/ogulist, http://www.sopsr.sk/symfony-bioregio/lkpcarporog, www.dinarskogorje.com, https://bivouac.com/, https://climbnz.org.nz/); and national or regional landscape, geomorphological, or physiographic maps and publications4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42. The full list of the consulted sources and references is available on GitHub at https://www.github.com/GMBA-biodiversity/Inventory (GMBA Mountain Inventory v2.0 References.pdf).All identified mountain ranges were recorded in a Microsoft Access relational database (“Mountain database”, see below) and given a name, a unique 5-digit identifier (GMBA_V2_ID), and the corresponding Wikidata unique resource identifier (URI), when available. This URI gives access to a range’s name as well as to its Wikipedia page URL in all available languages and lists other identifiers for given mountain ranges in a variety of other repositories such as GeoNames or PEMRACS. The primary mountain range names were based on the resources used for range identification and were preferably recorded in English. Names used nationally, locally, as well as/or by indigenous people and local communities were extracted from Wikidata and recorded in a separate attribute field.In the process of cataloguing, we attributed a parent range to each of the mapped mountain ranges. Information about parent ranges is included in PEMRACS, often also in Wikidata as a property that can be extracted though a SPARQL query, in the corresponding Wikipedia pages description, and in regional hierarchical mountain classifications that exist for the European Alps (SOIUSA), the Carpathians, and the Dinaric Alps. When no such information was available, we relied on other sources of information that we found either using a general web search (leading to specific papers, reports, or web pages on mountain ranges) or by consulting (online) topographical maps and atlases at different scales. The information about parent ranges was used to construct a hierarchy of up to 10 levels using a recursive SQL query (see Step v). The result of this step was a relational database with a hierarchy of mountain systems and (sub-) ranges (Fig. 1, “Mountain database”).Step ii: Digitization of the mountain rangesIn a second step, we digitized all identified ‘childless’ mountain ranges (i.e. smallest mapping units, called ‘Basic’ as opposed to ‘Aggregated’ in the database) in one vector GIS layer. To do so, we used the Google Maps Terrain layers (Google, n.d.) as background and the WHYMAP named rivers layer42 as spatial reference since descriptions of mountain range areal extension is often given with reference to major rivers. The digitization, which was done in QGIS43 using the WGS 84 / Pseudo-Mercator (EPSG 3857) coordinate reference system, consisted in the drawing of shapes (polygons) that roughly followed the core area of each mountain range. In general, the approximate shape and extent of the mountain ranges we digitized could be distinguished based on the terrain structure as represented by the shaded relief background that corresponded to the placement and orientation of the range’s name label on a topographical map, atlas or other resource. As the exact placement and orientation of mountain range labels in each specific source can be influenced by cartographic considerations (e.g. avoiding overlaps with other features), the final approximation of the mountain range was obtained by consulting a variety of sources for each mountain range. Occasionally, the mountain terrain’s geomorphological characteristics strongly hampered the accuracy of our visual identification of mountain subranges within larger systems. This was particularly the case in old, eroded massifs such as the Brazilian Highlands or the highlands of Madagascar, where individual mountain ranges are not separated by deep well-defined valleys and have a very complex topography. In these cases, we referred to available topographical descriptions of range extent and to the river layer (see above). Other complex regions included Borneo and the Angolan Highlands, whereas subranges in mountain systems such as the European Alps, the Himalayas, and the North American Cordillera were comparatively easy to map. Moreover, the density of currently available mountain toponymical information varied quite strongly between regions. Accordingly, regional variation in the size of the smallest mountain range map units can be considerable. The result of this step was a (manually) digitized vector layer of named mountain ranges shapes (Fig. 1, “Manual mountain shapes”).Step iii: Definition of mountainous terrainIn a third step, we defined mountainous terrain (GMBA Definition v2.0). To distinguish mountainous from non-mountainous terrain, we developed a simple algorithm which we implemented in ArcMap 10.7.144. This algorithm is based on ruggedness (defined as highest minus lowest elevation in meter) within eight circular neighbourhood analysis windows (NAWs) of different sizes (from 1 pixel (≈ 250 m) to 20 (≈ 5 km) around each point, Fig. 2c) combined with empirically derived thresholds for each NAW (Fig. 2). The decision to use multiple NAW sizes was made because calculating ruggedness based on only a small or a large NAW comes at the risk of identifying the many local irregularities typically occurring in flat or rolling terrain as mountainous or of including extensive flat ‘skirts’ through the smoothing and generalization of large NAWs3. Accordingly, our approach ensures that any point in the landscape classified as mountainous showed some level of ruggedness not only at one but across scales. This also resulted in a smooth and homogeneous delineation of mountainous terrain, very suitable for our mapping purpose.Fig. 2Elevation range thresholds for the eight neighbourhood analysis windows (NAW) and their contribution to calculations of the GMBA Definition v2.0. (a) distribution of elevation range values (ruggedness) for NAWs (numbered I to VIII) in mountain regions as defined by the geometric intersection of K1, K2 and K3. (b): plot of the minimum elevation range versus the area of the NAW (n = 920). (c) NAWs and their corresponding threshold values. (d) percent overlap between GMBA Definition v2.0 (intersection of eight NAW-threshold pairs) and area defined by each individual NAW-threshold pair. (e) percent eliminated by each NAW-threshold pair (I to VIII) from the mountain area defined by the other 7 NAW-threshold combinations. Highlighted bars in the two graphs represent the combination of three NAW-threshold pairs that results in the highest overlap with the GMBA Definition v2.0.Full size imageWe used the median value of the 7.5 arc second GMTED2010 DEM45 as our source map. To reduce the latitudinal distortion of the raster, and thus the shape and area of the NAWs, we divided the global DEM into three raster layers corresponding to three latitudinal zones (84° N to 30° N, 30° N to 30° S and 30° S to 56° S) excluding ice-covered Antarctica and projected the two high latitude zones to Lambert Azimuthal Equal Area and the equatorial zone to WGS 1984 Cylindrical Equal Area. We used these reprojected DEM layers to produce eight ruggedness layers, each using one of the eight NAWs.To determine the threshold values of our algorithm, we selected 1000 random points within the area defined by the geometric intersection (Fig. 1b) of the three commonly applied mountain definitions, i.e. the definitions by UNEP-WCMC46, GMBA15, and USGS3. These layers (referred to as K1, K2, and K3, respectively by Sayre and co-authors12) were obtained from the Global Mountain Explorer47. We eliminated 80 clearly misclassified points (i.e., points that fell within lakes, oceans, or clearly flat areas according to the shaded relief map we used as a background) and used the remaining 920 to sample the eight ruggedness layers. For each of the 8 layers, we retained the lowest of the 920 ruggedness values as the threshold for the layer’s specific NAW (Fig. 2c). The eight threshold values were then used to reclassify each of the eight layers by attributing the value 1 to all cells with a ruggedness value higher than or equal to the corresponding threshold and the value 0 to all other cells. Finally, we performed a geometric intersection (see Fig. 1b) of the eight reclassified layers to derive the new mountain definition.After these calculations, we reprojected the three raster layers to WGS84 and combined them through mosaic to new raster. To eliminate isolated cells and jagged borders, we then generalized the resulting raster map by passing a majority filter (3 × 3 pixels, majority threshold) three times. This layer corresponds to the GMBA Definition v2.0.The resulting mountain definition (GMBA Definition v2.0) distinguishes itself from previous ones because of the empirically derived thresholds method used to develop it and the use of eight NAWs. In line with the previous GMBA definition, it relies entirely on the ruggedness values within NAWs. The GMBA Definition v2.0 was used to determine the outer delineation of this inventory’s mountainous terrain. As expected, it includes neither the wide ‘skirts’ of flat or undulating land around mountain ranges nor the topographical irregularities that are both typically included when other approaches are applied. It also successfully excludes extensive areas of rolling non-mountainous terrain such as the 52,000 km2 Badain Jaran Desert sand dunes in China. However, this mountain definition is conservative and only includes the highest, most rugged cores of low mountain systems, as for example in the Central Uplands of Germany, and therefore excludes some lower hill areas still considered by some as mountains.As a further step towards generalization, we considered that small ( More

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Study origin and designThe MeadoWatch project (MW) is a project run collaboratively between the University of Washington (UW) and the United States National Park Service to monitor the phenology of alpine and subalpine wildflower species across large elevational gradients in Mount Rainier National Park (Fig. 2). MW was established in 2013 with the goal of understanding long-term effects of climate change on Mount Rainier National Park wildflower communities using community-science approaches. The first MW transect was established along Reflection Lakes, Skyline, and Paradise Glacier trail system in 2013 (9–11 plots). In 2015, MW expanded to include a second transect (15–17 plots) along the Glacier Basin trail (Fig. 1a). The MW transects span around 5 km each, over a 400 m altitudinal gradient (Reflection Lakes: 1490m–1889m a.s.l.; Glacier Basin: 1460m–1831m a.s.l.)Fig. 2Alpine meadows, plot extension, and target species. (a) Species-rich alpine meadow in Mount Rainier National Park (Mount Tahoma), showing many of the target species in the foreground. (b) MW volunteer coordinator Anna Wilson at a plot, indicating the arm span that defines the plot area (personal likeness used with confirmed consent). (c) Species composition and proportion of reports per species in each of the transects; species common to both trails are highlighted with striped shadowing. Photographs: A. John (a), L. Felker (b).Full size imagePlots are located along the side of each trail, marked with a colored survey marker. The area of each plot is defined by the arm-span of volunteers when they position themselves over the plot marker looking away from the trail (Fig. 2b). While less accurate than marking the corners of plots, this approach was used to avoid establishing permanent structures in wilderness areas within the National Park. The surveyed area in each plot is, on average, 1.25 m2. Each plot is also equipped with temperature sensors (HOBO Pendant Logger, Onset Computer Corp.) buried approximately 4 cm below the ground. Sensors are placed at the start of each fall season and removed at the beginning of each summer season for data downloading. The HOBO sensors provide an estimate for the date of snow disappearance and in-situ temperature at 3 hours intervals. Once plots are covered in snow, soil temperatures remain at 0 °C and show no diurnal variation, so that daily changes in temperatures above 1 °C can be used to determine the earliest date without snow cover20. We use these approaches to provide dates of snow appearance and disappearance, snow cover duration, and minimum soil temperatures for each year and plot. Occasionally, temperature data during the snow disappearing window were lost due to sensor failure or loss of sensors (which occurs because plots are not permanently marked and/or well-meaning visitors remove sensors). This, and the lack of temperature sensors in the first year of the project, resulted in approx. 20% of cases of missing data. In those cases, we used a data imputation method to estimate the missing values based on data from nearby plots and a parallel temperature data collection with 890 total observations. These estimates were highly reliable in filling the data gaps (see Appendix C in16 for further details).Focal speciesWe originally targeted 16 native wildflower species along each transect, which were chosen based on their abundance, ease of identification, and presence in the plot. Four of those target species were present on both transects. In 2016 we replaced one species with a different one (see further information below), making for a total of 17 species monitored (Fig. 2c). The focal species are: American bistort* (Polygonum bistortoides), avalanche lily (Erythronium montanum), bracted lousewort* (Pedicularis bracteosa), broadleaf arnica (Arnica latifolia), cascade aster (Aster ledophyllus; synonym Eucephalus ledophyllus), glacier lily (Erythronium grandiflorum), Gray’s lovage (Ligusticum grayi), magenta paintbrush (Castilleja parviflora), mountain daisy (Erigenon peregrinus; synonym Erigeron glacialis), northern microseris (Microseris alpestris; synonym Nothocalais alpestris), scarlet paintbrush (Castilleja miniata), sharptooth angelica (Angelica arguta), sitka valerian* (Valeriana sitchensis), subalpine lupine* (Lupinus arcticus; synonym Lupinus latifolius var. subalpinus), tall bluebell (Mertensia paniculata), Canby’s licorice-root (Ligusticum canbyi), and western anemone (Anemone occidentalis). Asterisks denote species monitored along both trails.Due to challenges in species identification, we dropped Canby’s licorice-root (Ligusticum canbyi) as a target species in 2016. Consequently, Ligusticum canbyi has limited replication in the database (Fig. 2c). While we included the phenological records of this species for the sake of completeness, we recommend focusing on the other 16 species, which are both better represented (in terms of data coverage) and are free of any potential misidentification issues.For additional information on the species, methods, identification cues, and image resources see: http://www.meadowatch.org, https://www.youtube.com/channel/UCGBFTKxf8FIWswMDxBavpuQ, and the appendices therein16.Data collection and volunteer trainingDuring the summer months, MW volunteers and scientists collect reproductive phenology data with a frequency between 3 and 9 trail reports per week. Each report records the presence or absence of 4 phenophases for each target species present in each of the plots. The phenophases are ‘budding’, ‘flowering’, ‘ripening fruit’, and ‘releasing seed’. Phenophases were defined as follows:BuddingThe beginning growth of the flower which has not yet opened. A plant is considered budding if buds are present, but the stamen and pistils are not yet visible and available to pollinators.FloweringThe generally “showy” part of the plant that holds the reproductive parts (stamens and pistils). A plant is considered flowering when at least one flower is open, and the stamens and pistils are visible and available for pollination and reproduction.Ripening fruitThe fruit develops from the female part of the flower following successful pollination. In the target species, fruits can take many forms, from hard, fleshy capsules, juicy berries, to a feathery tuft on the end of a seed. A plant is in the ripening fruit stage when reproductive parts on at least one reproductive stalk are non-functional and the formation of the fruit part is clearly ongoing (visible), but seeds are not yet fully mature and not yet being dispersed.Releasing seedAfter the fruit ripens, seeds are released to be dispersed by gravity, wind, or animals. A plant is considered in the releasing seed stage if seeds are actively being released on at least one reproductive stalk (but there are still seeds present).A full description, including illustrations for each species’ phenophase and identification cues is available in http://www.meadowatch.org/volunteer-resources.html, as well as in Annex 1 – Supplementary Documentation. Multiple phenophases can be present simultaneously, depending on the species, and are noted independently. Additionally, volunteers are also asked to record the presence of snow (‘snow covered plot’, ‘partially covered plot’, or ‘snow-free plot’), and, since 2017, the presence of damage by herbivory (‘presence of browsed stems’) on each plot.In years not impacted by the SARS-Cov-2 pandemic MW volunteers attend an in-person 3-hour botanical and phenological training session taught by UW scientists at the beginning of each sampling season. Volunteers were also provided with detailed species-identification guides, including an extensive description of sampling methods and location of the plots. The trainings for the 2020 and 2021 seasons were held virtually via a series of online training videos. In these years, volunteers took a quiz on wildflower phenology, plant identification and data collection methods after viewing these videos and were required to ‘pass’ a certain threshold to volunteer (unlimited attempts were allowed). During these virtual trainings, volunteers were provided with digital copies of the species identification guides, with many returning volunteers using printed guides they had kept from previous years.At the end of their phenological hike, volunteers submit their data sheets either by depositing them in lockboxes located within the park, or by scanning and emailing them directly to [email protected]. Data are then entered manually and stored in the UW repositories after being checked for consistency at the end of each sampling season.The parallel data collection by members of UW’s Hille Ris Lambers group (including PI, postdoctoral researchers, graduate students, and trained interns) acted as the following: (i) a quality-control, i.e., allowing us to compare the consistency in phenology assessments between volunteers and scientists, and (ii) a way to increase the temporal resolution and scale of the data, e.g., by reducing early season gaps and ‘weekend bias’17. This parallel expert sampling was carried out around once a week between 2013 and 2020, showing great consistency between the two groups. For detailed comparisons between volunteers and scientists’ assessments see the data validation section (as well as Appendix E in16).Processed dataIn addition to the raw phenological data, we also provide here parameters to construct the year, species, and plot-specific flowering phenology based on the timing of snow disappearance (as in16). Models describe unimodal probability distributions that were fitted with maximum likelihood models to binomial flowering data from each species, year, and plot. These curves have been used to estimate peak flowering dates and diversity and link them to reported visitor experiences16. Here, we provide the 3 parameters defining the unimodal curve of flowering probability per species i, plot j and year k: the duration of flowering (𝛿ijk), the maximum probability of flowering (𝜇ijk), and peak flowering (in DOY – ρijk); following the equations described in16 and https://github.com/ajijohn/MeadoWatch).The parameters of these probability distribution curves are ready-to-use values that can be broadly and easily used to estimate floral compositional change over past seasons due to changing environmental conditions—for example, to inform plant-pollinator interaction networks if combined with pollinator behavioral data (e.g.21). More