Ecology

The Asiatic cheetah (Acinonyx jubatus venaticus) once roamed throughout the Middle East and central India. Today there remain only an estimated 20 free-ranging individuals in central Iran and 5 in captivity. International economic sanctions against Iran have had devastating effects on its cheetah conservation and management (see go.nature.com/3suohzb; in Farsi). To help overcome these effects, we suggest that Iran work with the Indian government, which is conducting a rewilding programme for cheetahs.
Competing Interests
The authors declare no competing interests. More

Cline and colleagues analysed spatiotemporal datasets covering 5000 km of popular trout rivers from 1983 to 2017, finding that fishing pressure was four times higher in cold-water sections of rivers than adjacent cool-water sections of rivers, with fisher spending in cold-water sections generating US$500,000 km−1 year−1 and cool-water sections generating US$60,000 km−1 year−1. Overall, 17% and 35% of the current cold-water habitats are projected to be warmer than 18 °C (the threshold for trout thermal extremes) by 2040 and 2080, respectively, with some river sections possibly experiencing habitat losses in excess of 80% by 2080. The combined effects of cold-water habitat loss and increased frequency and severity of drought on fishing pressure could result in 64% declines in fishing river sections by 2040 and 76% declines by 2080. The cumulative impacts of these environmental changes in fishing spending across these rivers could put a total of US$103 million year−1 and US$192 million year−1 at risk by 2040 and 2080, respectively. More

Wurst, S., Sonnemann, I. & Zaller, J. G. Soil Macro-Invertebrates: Their Impact on Plants and Associated Aboveground Communities in Temperate Regions. in Aboveground-Belowground Community Ecology. Ecological Studies 234 (eds. Ohgushi, T., Wurst, S. & Johnson, S. N.) 175–200 (Springer International Publishing, 2018).Wagg, C., Bender, S. F., Widmer, F. & van der Heijden, M. G. A. Soil biodiversity and soil community composition determine ecosystem multifunctionality. PNAS 111, 5266–5270 (2014).ADS 
CAS 
Article 

Google Scholar 
Potapov, A. M. et al. Feeding habits and multifunctional classification of soil-associated consumers from protists to vertebrates. Biol. Rev. 97, 1057–1117 (2022).Article 

Google Scholar 
Potapov, A., Tiunov, A. V. & Scheu, S. Uncovering trophic positions and food resources of soil animals using bulk natural stable isotope composition. Biol. Rev. 94, 37–59 (2019).Article 

Google Scholar 
Voroney, R. P. & Heck, R. J. The Soil Habitat. Soil Microbiology, Ecology and Biochemistry (Elsevier Inc., 2015).Wardle, D. A. The influence of biotic interactions on soil biodiversity. Ecol. Lett. 9, 870–886 (2006).Article 

Google Scholar 
De Deyn, G. B. & Kooistra, L. The role of soils in habitat creation, maintenance and restoration. Philos. Trans. R. Soc. Lond., B, Biol. Sci. 376 (2021).Phillips, H. R. P. et al. Global distribution of earthworm diversity. Science 366, 480–485 (2019).ADS 
CAS 
Article 

Google Scholar 
Geitner, C. et al. Soil and Land Use in the Alps—Challenges and Examples of Soil-Survey and Soil-Data Use to Support Sustainable Development. In Soil Mapping and Process Modelling for Sustainable Land Use Management 221–292 (Elsevier, 2017).FAO. Understanding Mountain Soils: A contribution from mountain areas to the International Year of Soils 2015. (2015).Praeg, N. et al. The role of land management and elevation in shaping soil microbial communities: Insights from the Central European Alps. Soil Biol. Biochem. 150, 107951 (2020).CAS 
Article 

Google Scholar 
Somme, L. Adaptations of terrestrial arthropods to the alpine environment. Biol. Rev. 64, 367–407 (1989).Article 

Google Scholar 
Meyer, E. & Thaler, K. Animal Diversity at High Altitudes in the Austrian Central Alps. In Arctic and Alpine Biodiversity (eds. Chapin, F. S. & Körner, C.) (Springer Berlin Heidelberg, 1995).Guerra, C. A. et al. Blind spots in global soil biodiversity and ecosystem function research. Nat. Commun. 11, 1–13 (2020).Article 

Google Scholar 
Kempson, D., Lloyd, M. & Ghelardi, R. A new extractor for woodland litter. Pedobiologia 3, 1–30 (1963).
Google Scholar 
Tasser, E., Ruffini, F. V. & Tappeiner, U. An integrative approach for analysing landscape dynamics in diverse cultivated and natural mountain areas. Landsc. Ecol. 24, 611–628 (2009).Article 

Google Scholar 
European Environment Agency, (EAA). European Union, Copernicus Land Monitoring Service. https://land.copernicus.eu/pan-european/corine-land-cover/clc2018 (2018).IUSS Working Group WRB. World Reference Base for Soil Resources 2014, update 2015 International soil classification system for naming soils and creating legends for soil maps. World Soil Resources Reports No. 106 (2015).Christian, E. & Zicsi, A. A synoptic key to the earthworms of Austria (Oligochaeta: Lumbricidae). Die Bodenkultur 50, 121–131 (1999).Czusdi, C. & Zicsi, A. Earthworms of Hungary (Annelida, Oligochaeta, Lumbricidae). (Hungarian Natural History Museum, 2003).Schaefer, M. Brohmer – Fauna von Deutschland: Ein Bestimmungsbuch unserer heimischen Tierwelt. (Quelle & Meyer Verlag, 2009).Klausnitzer, B. Exkursionsfauna von Deutschland. (Springer Berlin Heidelberg, 2011).Ellis, D. Taxonomic sufficiency in pollution assessment. Mar. Pollut. Bull. 16, 459 (1985).Article 

Google Scholar 
Caruso, T. & Migliorini, M. Micro-arthropod communities under human disturbance: is taxonomic aggregation a valuable tool for detecting multivariate change? Evidence from Mediterranean soil oribatid coenoses. Acta Oecol. 30, 46–53 (2006).ADS 
Article 

Google Scholar 
Steinwandter, M., Schlick-Steiner, B. C., Seeber, G. U. H., Steiner, F. M. & Seeber, J. Effects of Alpine land-use changes: Soil macrofauna community revisited. Ecol. Evol. 7, 5389–5399 (2017).Article 

Google Scholar 
de Oliveira, S. S. et al. Higher taxa are sufficient to represent biodiversity patterns. Ecol. Indic. 111, 105994 (2020).Article 

Google Scholar 
Lavelle, P. et al. Soil macroinvertebrate communities: A world‐wide assessment. Glob. Ecol. Biogeogr. 31, 1261–1276 (2022).Article 

Google Scholar 
Pik, A. J., Oliver, I. & Beattie, A. J. Taxonomic sufficiency in ecological studies of terrestrial invertebrates. Austral. Ecol. 24, 555–562 (1999).Article 

Google Scholar 
Parisi, V., Menta, C., Gardi, C., Jacomini, C. & Mozzanica, E. Microarthropod communities as a tool to assess soil quality and biodiversity: A new approach in Italy. Agric. Ecosyst. Environ. 105, 323–333 (2005).Article 

Google Scholar 
Ruiz, N. et al. IBQS: A synthetic index of soil quality based on soil macro-invertebrate communities. Soil Biol. Biochem. 43, 2032–2045 (2011).
Google Scholar 
Seeber, J. et al. A 30-years collection of soil macro-invertebrate abundance data from the European Alps. PANGAEA https://doi.org/10.1594/PANGAEA.944405 (2022).de Jong, Y. et al. Fauna Europaea – All European animal species on the web. Biodivers. Data J. 2 (2014).Shannon, C. E. A Mathematical Theory of Communication. Bell Syst. Tech. J. 27, 379–423 (1948).MathSciNet 
Article 

Google Scholar 
Steinberger, K.-H. & Meyer, E. The Spider Fauna of the Nature Reserve Rheindelta (Vorarlberg, Western Austria) (Arachnida: Araneae). Ber. nat.-med. Verein Innsbruck 82, 195–215 (1995).
Google Scholar 
Kopeszki, H. & Meyer, E. Species Composition and Abundance of Collembola in Forest Soils in the Provinces of Bozen and Trient (Italy). Ber. nat.-med. Verein Innsbruck 83, 221–237 (1996).
Google Scholar 
Geitner, C., Mätzler, A., Bou-Vinals, A., Meyer, E. & Tusch, M. Soil characteristics and colonization by earthworms (Lumbricidae) on pastures and hay meadows in the Brixenbach Valley (Kitzbühel Alps, Tyrol). Die Bodenkultur 65, 39–51 (2014).
Google Scholar 
Meyer, E. & Steinberger, K.-H. Über die Bodenfauna in Wäldern Vorarlbergs (Österreich) Bestand und Auswirkungen von Gesteinsmehlapplikationen. Verhandlungen der Gesellschaft für Ökologie 23, 149–164 (1994).
Google Scholar 
Peham, T. & Meyer, E. Kommentierte Artenlisten ausgewählter Bodentiergruppen aus der Erhebung des SoilDiv-Projektes in Südtirol. Gredleriana 14, 227–262 (2014).
Google Scholar 
Steinwandter, M., Rief, A., Scheu, S., Traugott, M. & Seeber, J. Structural and functional characteristics of high alpine soil macro-invertebrate communities. Eur. J. Soil Biol. 86, 72–80 (2018).Article 

Google Scholar 
Steinwandter, M. et al. Does green manuring positively affect the soil macro-invertebrates in vineyards? A case study from Kaltern/Caldaro (South Tyrol, Italy). Gredleriana 18, 17–26 (2018).
Google Scholar 
Steinwandter, M. et al. Raw data from: Does green manuring positively affect the soil macro-invertebrates in vineyards? A case study from Kaltern/ Caldaro (South Tyrol, Italy). PANGAEA https://doi.org/10.1594/PANGAEA.900632 (2019).Damisch, K., Steinwandter, M., Tappeiner, U. & Seeber, J. Soil Macroinvertebrate Distribution along a Subalpine Land Use Transect. Mt. Res. Dev. 40, R1–R10 (2020).Article 

Google Scholar 
Damisch, K., Steinwandter, M., Tappeiner, U. & Seeber, J. Abundance data from soil macro-invertebrates along a subalpine land-use transect. PANGAEA https://doi.org/10.1594/PANGAEA.918958 (2020).Schneider, E., Steinwandter, M. & Seeber, J. A comparison of Alpine soil macro-invertebrate communities from European larch and Swiss pine forests in the LTSER area “Val Mazia/Matschertal”, South Tyrol. Gredleriana 19, 217–228 (2019).
Google Scholar 
Schneider, E., Steinwandter, M. & Seeber, J. Raw data from: A comparison of Alpine soil macro-invertebrate communities from European larch and Swiss pine forests in the LTSER area “Val Mazia/Matschertal”, South Tyrol. PANGAEA https://doi.org/10.1594/PANGAEA.910666 (2020).Seeber, J. et al. Soil invertebrate abundance, diversity, and community composition across steep high elevation snowmelt gradients in the European Alps. Arct. Antarct. Alp. Res. 53, 288–299 (2021).Article 

Google Scholar 
Seeber, J. et al. Abundance data from soil macro- and mesofauna of alpine snowbeds in the European Alps (summer 2017). PANGAEA https://doi.org/10.1594/PANGAEA.935737 (2021).Guariento, E. et al. Management intensification of hay meadows and fruit orchards alters soil macro-invertebrate communities differently. Agronomy 10, 767 (2020).CAS 
Article 

Google Scholar  More

Similar non-native and invasive flora, such as the fever tree (pictured) are found in regions previously occupied by the same European empire.Credit: Alamy

In 1860, a British expedition raided the highland forests of South America, looking for a hot commodity: Cinchona seeds. The bark of these ‘fever’ trees produces the anti-malarial compound quinine, and the British Empire sought a stable source of the drug for its soldiers and civil service in India. After cultivation in the United Kingdom, young Cinchona trees were planted across southern India and what is now Sri Lanka.The British quinine scheme failed — instead, a species introduced to Java, now part of Indonesia, by the Dutch Empire later dominated the global market — but Cinchona trees are still common in parts of India.Such botanical legacies of imperial rule are common, finds a study published on 17 October in Nature Ecology & Evolution1. Regions that were once occupied by the same European colonial power — such as India and Sri Lanka — tend to have similar species of non-native and invasive plants. The longer the regions were occupied, the more their populations of invasive species resemble each other, the research found.Alien floraThe link between European colonialism and invasive species is intuitive, and has been noted by other researchers, says Bernd Lenzner, a macro-ecologist at the University of Vienna who led the study. To test the association, his team turned to the Global Naturalized Alien Flora database, which maps the distribution of nearly 14,000 invasive plant species.
The imperial roots of climate science
Across more than 1,100 regions, including 404 islands, the researchers found that regions once occupied by the British Empire had more similarities in their invasive flora than did ‘artificial’ empires that the team assembled from random regions. This was also the case for regions once part of the Dutch Empire (former Spanish and Portuguese colonies had alien-plant compositions similar to those of the artificial empires).Climate and geography play an important part in explaining the overlap in the diversity of invasive species, modelling by Lenzner’s team found, but so does the length of time regions were occupied by an imperial power. Regions that were central to trade, such as southern India for the British Empire and Indonesia for the Dutch Empire, formed clusters with considerable overlap in invasive-plant composition.The analysis did not look at when individual plant species were introduced or why. But anecdotally, many of the plants that were commonly taken to former empires were once of economic value and their populations were probably established on purpose, says Lenzner.Global trade impactsThe study’s conclusions might be “super obvious”, but they have important implications for conservation, says Nussaïbah Raja, a palaeontologist at Friedrich-Alexander University of Erlangen–Nürnberg in Erlangen, Germany. “We should be taking this history into consideration when we think about management of species.” Appreciating the history of introduced plants — as well as their place in today’s ecosystems — could help conservationists to handle future changes in biodiversity, such as those driven by climate change, Raja adds.Global trade is beginning to overwrite the colonial legacy of introduced plants. For example, the analysis showed similarities between invasive plant populations in Fujian, China, and some parts of Australia. Although both places were once connected by the British Empire, more recent global trade might also be partly responsible for the overlap.“We are still seeing these imprints of the colonial-empire legacies from centuries ago,” Lenzner says. “So what we’re doing and the species we’re redistributing today will be visible far into the future.” More

Bardgett, R. D. & van der Putten, W. H. Belowground biodiversity and ecosystem functioning. Nature 515, 505–511 (2014).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Fierer, N. Embracing the unknown: Disentangling the complexities of the soil microbiome. Nat. Rev. Microbiol. https://doi.org/10.1038/nrmicro.2017.87 (2017).Article 
PubMed 

Google Scholar 
Frouz, J. Effects of soil macro- and mesofauna on litter decomposition and soil organic matter stabilization. Geoderma 332, 161–172 (2018).ADS 
CAS 
Article 

Google Scholar 
Hicks Pries, C. E., Castanha, C., Porras, R., Phillips, C. & Torn, M. S. Response to comment on “The whole-soil carbon flux in response to warming”. Science 359, 1420–1423 (2018).Article 

Google Scholar 
Lavelle, P. et al. Soil function in a changing world: The role of invertebrate ecosystem engineers. Eur. J. Soil Biol. 33, 159–193 (1997).CAS 

Google Scholar 
Frouz, J., Špaldoňová, A., Fričová, K. & Bartuška, M. The effect of earthworms (Lumbricus rubellus) and simulated tillage on soil organic carbon in a long-term microcosm experiment. Soil. Biol. Biochem. 78, 58–64 (2014).CAS 
Article 

Google Scholar 
Lavelle, P., Blanchart, E., Martin, A., Martin, S. & Schaefer, R. A hierarchical model for decomposition in terrestrial ecosystems: Application to soils of the humid tropics. Assoc. Trop. Biol. 25, 130–150 (2016).
Google Scholar 
Lavelle, P. et al. Earthworms as a resource in tropical agroecosystems. Nat. Res. 34, 26–41 (1998).
Google Scholar 
Lavelle, P. Diversity of soil fauna and ecosystem function. Biol. Int. J. 33, 3–16 (1996).
Google Scholar 
Ruiz, N., Lavelle, P. & Jiménez, J. Soil macrofauna field manual. Recherche 113 (2008).Xiong, W. et al. Soil protist communities form a dynamic hub in the soil microbiome. ISME J. 12, 634–638 (2018).PubMed 
Article 

Google Scholar 
Fierer, N., Strickland, M. S., Liptzin, D., Bradford, M. A. & Cleveland, C. C. Global patterns in belowground communities. Ecol. Lett. 12, 1238–1249 (2009).PubMed 
Article 

Google Scholar 
Nielsen, U. N. et al. Global-scale patterns of assemblage structure of soil nematodes in relation to climate and ecosystem properties. Glob. Ecol. Biogeogr. 23, 968–978 (2014).Article 

Google Scholar 
Špaldoňová, A. & Frouz, J. The role of Armadillidium vulgare (Isopoda: Oniscidea) in litter decomposition and soil organic matter stabilization. Appl. Soil. Ecol. https://doi.org/10.1016/j.apsoil.2014.04.012 (2014).Article 

Google Scholar 
McCay, T. S., Cardelus, C. L. & Neatrour, M. A. Rate of litter decay and litter macroinvertebrates in limed and unlimed forests of the Adirondack Mountains, USA. For. Ecol. Manag. 304, 254–260 (2013).Article 

Google Scholar 
Slade, E. M. & Riutta, T. Interacting effects of leaf litter species and macrofauna on decomposition in different litter environments. Basic Appl. Ecol. 13, 423–431 (2012).Article 

Google Scholar 
Joly, F.-X., Coq, S., Coulis, M., Nahmani, J. & Hättenschwiler, S. Litter conversion into detritivore faeces reshuffles the quality control over C and N dynamics during decomposition. Funct. Ecol. https://doi.org/10.1111/1365-2435.13178 (2018).Article 

Google Scholar 
Hättenschwiler, S. Isopod effects on decomposition of litter produced under elevated CO2, N deposition and different soil types Isopod effects on decomposition of litter produced under elevated CO2, N deposition and different soil types. Glob. Change Biol. https://doi.org/10.1046/j.1365-2486.2001.00402.x (2015).Article 

Google Scholar 
Wall, D. H. et al. Global decomposition experiment shows soil animal impacts on decomposition are climate-dependent. Glob. Change Biol. 14, 2661–2677 (2008).ADS 
Article 

Google Scholar 
Brussaard, L., Pulleman, M. M., Ouédraogo, É., Mando, A. & Six, J. Soil fauna and soil function in the fabric of the food web. Pedobiologia (Jena) 50, 447–462 (2007).Article 

Google Scholar 
Frouz, J., Elhottová, D., Kuráž, V. & Šourková, M. Effects of soil macrofauna on other soil biota and soil formation in reclaimed and unreclaimed post mining sites: Results of a field microcosm experiment. Appl. Soil Ecol. 33, 308–320 (2006).Article 

Google Scholar 
García-Palacios, P., Maestre, F. T., Kattge, J. & Wall, D. H. Climate and litter quality differently modulate the effects of soil fauna on litter decomposition across biomes. Ecol. Lett. 16, 1045–1053 (2013).PubMed 
PubMed Central 
Article 

Google Scholar 
Melguizo-Ruiz, N. et al. Field exclusion of large soil predators impacts lower trophic levels and decreases leaf-litter decomposition in dry forests. J. Anim. Ecol. 89, 334–346 (2020).PubMed 
Article 

Google Scholar 
Lavelle, P. et al. Soil macroinvertebrate communities: A world-wide assessment. Glob. Ecol. Biogeogr. https://doi.org/10.1111/geb.13492 (2022).Article 

Google Scholar 
Coq, S. et al. Faeces traits as unifying predictors of detritivore effects on organic matter turnover. Geoderma 422, 115940 (2022).ADS 
CAS 
Article 

Google Scholar 
Lavelle, P. et al. Soil aggregation, ecosystem engineers and the C cycle. Act Oecol. 105, 103561 (2020).Article 

Google Scholar 
Filser, J. et al. Soil fauna: Key to new carbon models. Soil 2, 565–582 (2016).ADS 
CAS 
Article 

Google Scholar 
Wardle, D. A. et al. Ecological linkages between aboveground and belowground biota. Science 304, 1629–1633 (2004).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Joly, F. X. et al. Detritivore conversion of litter into faeces accelerates organic matter turnover. Commun. Biol. 3, 1–9 (2020).MathSciNet 
Article 

Google Scholar 
Frouz, J., Roubíčková, A., Heděnec, P. & Tajovský, K. Do soil fauna really hasten litter decomposition? A meta-analysis of enclosure studies. Eur. J. Soil Biol. 68, 18 (2015).CAS 
Article 

Google Scholar 
Lavelle, P., Blanchart, E., Martin, A., Martin, S. & Spain, A. A hierarchical model for decomposition in terrestrial ecosystems: Application to soils of the humid tropics. Biotropica 25, 130–150 (1993).Article 

Google Scholar 
Crowther, T. W. & A’Bear, A. D. Impacts of grazing soil fauna on decomposer fungi are species-specific and density-dependent. Fungal Ecol. 5, 277–281 (2012).Article 

Google Scholar 
Decaëns, T. Macroecological patterns in soil communities. Glob. Ecol. Biogeogr. 19, 287–302 (2010).Article 

Google Scholar 
Tordoff, G. M., Boddy, L. & Jones, T. H. Species-specific impacts of collembola grazing on fungal foraging ecology. Soil. Biol. Biochem. 40, 434–442 (2008).CAS 
Article 

Google Scholar 
Meysman, F. J. R., Middelburg, J. J. & Heip, C. H. R. Bioturbation: A fresh look at Darwin’s last idea. Trends Ecol. Evol. 21, 688–695 (2006).PubMed 
Article 

Google Scholar 
Frouz, J. et al. Soil food web changes during spontaneous succession at post mining sites: A possible ecosystem engineering effect on food web organization? PLoS ONE 8, e79694 (2013).ADS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Frouz, J., Moradi, J., Püschel, D. & Rydlová, J. Earthworms affect growth and competition between ectomycorrhizal and arbuscular mycorrhizal plants. Ecosphere 10, e02736 (2019).Article 

Google Scholar 
Marichal, R. et al. Soil macroinvertebrate communities and ecosystem services in deforested landscapes of Amazonia. Appl. Soil. Ecol. 83, 177–185 (2014).Article 

Google Scholar 
Prescott, C. E. & Vesterdal, L. Forest ecology and management decomposition and transformations along the continuum from litter to soil organic matter in forest soils. For. Ecol. Manag. 498, 119522 (2021).Article 

Google Scholar 
Kampichler, C. & Bruckner, A. The role of microarthropods in terrestrial decomposition: A meta-analysis of 40 years of litterbag studies. Biol. Rev. Camb. Philos. Soc. 84, 375–389 (2009).PubMed 
Article 

Google Scholar 
Brennan, K. E. C., Christie, F. J. & York, A. Global climate change and litter decomposition: More frequent fire slows decomposition and increases the functional importance of invertebrates. Glob. Change. Biol. 15, 2958–2971 (2009).ADS 
Article 

Google Scholar 
Birkhofer, K. et al. General relationships between abiotic soil properties and soil biota across spatial scales and different land-use types. PLoS ONE 7, e43292 (2012).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wu, T., Ayres, E., Bardgett, R. D., Wall, D. H. & Garey, J. R. Molecular study of worldwide distribution and diversity of soil animals. PNAS 108, 17720–17725 (2011).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
James, S. W. et al. Comment on Global distribution of earthworm diversity. Science 371, 4629 (2021).Article 

Google Scholar 
Cesarz, S. et al. Tree species diversity versus tree species identity: Driving forces in structuring forest food webs as indicated by soil nematodes. Soil. Biol. Biochem. 62, 36–45 (2013).CAS 
Article 

Google Scholar 
Eppinga, M. B., Kaproth, M. A., Collins, A. R. & Molofsky, J. Litter feedbacks, evolutionary change and exotic plant invasion. J. Ecol. 99, 503–514 (2011).
Google Scholar 
Harrison, K. A., Bol, R. & Bardgett, R. D. Do plant species with different growth strategies vary in their ability to compete with soil microbes for chemical forms of nitrogen? Soil. Biol. Biochem. 40, 228–237 (2008).CAS 
Article 

Google Scholar 
Wardle, D. A., Yeates, G. W., Barker, G. M. & Bonner, K. I. The influence of plant litter diversity on decomposer abundance and diversity. Soil Biol. Biochem. 38, 1052–1062 (2006).CAS 
Article 

Google Scholar 
Zhang, D., Hui, D., Luo, Y. & Zhou, G. Rates of litter decomposition in terrestrial ecosystems: Global patterns and controlling factors. J. Plant Ecol. 1, 85–93 (2008).Article 

Google Scholar 
Preston, C. M. & Trofymow, J. A. Variability in litter quality and its relationship to litter decay in Canadian forests. Botany 78, 1269–1287 (2000).Article 

Google Scholar 
Bar-On, Y. M., Phillips, R. & Milo, R. The biomass distribution on Earth. PNAS 115, 6506–6511 (2018).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Phillips, H. R. P. et al. Global distribution of earthworm diversity. Science 366, 480–485 (2019).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Andersen, D. C. Below-ground herbivory in natural communities: A review emphasizing fossorial animals. Q. Rev. Biol. 62, 261–286 (1987).Article 

Google Scholar 
Cepáková, S. & Frouz, J. Changes in chemical composition of litter during decomposition: A review of published 13C NMR spectra. Plant Nutr. Soil Sci. 15, 805–815 (2015).
Google Scholar 
Pietsch, K. A. et al. Global relationship of wood and leaf litter decomposability: The role of functional traits within and across plant organs. Glob. Ecol. Biogeogr. 23, 1046–1057 (2014).Article 

Google Scholar 
Cornwell, W. K. et al. Plant species traits are the predominant control on litter decomposition rates within biomes worldwide. Ecol. Lett. 11, 1065–1071 (2008).PubMed 
Article 

Google Scholar 
Ponge, J.-F. Plant–soil feedbacks mediated by humus forms: A review. Soil. Biol. Biochem. 57, 1048–1060 (2013).CAS 
Article 

Google Scholar 
Salmon, S., Mantel, J., Frizzera, L. & Zanella, A. Changes in humus forms and soil animal communities in two developmental phases of Norway spruce on an acidic substrate. For. Ecol. Manag. 237, 47–56 (2006).Article 

Google Scholar 
Desie, E. et al. Positive feedback loop between earthworms, humus form and soil pH reinforces earthworm abundance in European forests. Funct. Ecol. 34, 2598–2610 (2020).Article 

Google Scholar 
Samson, F. B. & Knopf, F. L. (eds) Organisms as Ecosystem Engineers BT—Ecosystem Management: Selected Readings 130–147 (Springer, 1996).
Google Scholar 
Araujo, P. I., Yahdjian, L. & Austin, A. T. Do soil organisms affect aboveground litter decomposition in the semiarid Patagonian steppe, Argentina? Oecologia 168, 221–230 (2012).ADS 
PubMed 
Article 

Google Scholar 
Frouz, J. et al. Soil biota in post-mining sites along a climatic gradient in the USA: Simple communities in shortgrass prairie recover faster than complex communities in tallgrass prairie and forest. Soil. Biol. Biochem. 67, 212–225 (2013).CAS 
Article 

Google Scholar 
Hattenschwiler, S., Tiunov, A. V. & Scheu, S. Biodiversity and litter decomposition interrestrial ecosystems. Annu. Rev. Ecol. Evol. Syst. 36, 191–218 (2005).Article 

Google Scholar 
Deckmyn, G. et al. KEYLINK: Towards a more integrative soil representation for inclusion in ecosystem scale models I. Review and model concept. PeerJ 8, 1–69 (2020).Article 

Google Scholar 
Héry, M. et al. Effect of earthworms on the community structure of active methanotrophic bacteria in a landfill cover soil. SME J. 2, 92–104 (2008).
Google Scholar 
Roubickova, A., Mudrak, O. & Frouz, J. Effect of earthworm on growth of late succession plant species in postmining sites under laboratory and field conditions. Biol. Fert. Soils 45, 769–774 (2009).Article 

Google Scholar 
Bodine, M. C. & Ueckert, D. N. Effect litter in west of desert termites on herbage and in a shortgrass Texas. J. Range. Manag. 28, 353–358 (1975).Article 

Google Scholar 
Cebrian, J. Patterns in the fate of production in plant communities. Am. Nat. 154, 449–468 (1999).PubMed 
Article 

Google Scholar 
Petersen, H. & Luxton, M. A comparative analysis of soil fauna populations and their role in decomposition processes. Oikos 39, 288 (1982).Article 

Google Scholar 
Gongalsky, K. B., Persson, T. & Pokarzhevskii, A. D. Effects of soil temperature and moisture on the feeding activity of soil animals as determined by the bait-lamina test. Appl. Soil Ecol. 39, 84–90 (2008).Article 

Google Scholar 
Simpson, J. E., Slade, E., Riutta, T. & Taylor, M. E. Factors affecting soil fauna feeding activity in a fragmented lowland temperate deciduous woodland. PLoS ONE 7, 0029616 (2012).ADS 
Article 

Google Scholar 
Clarke, A. Is there a universal temperature dependence of metabolism? Funct. Ecol. 18, 252–256 (2004).Article 

Google Scholar 
Coq, S. & Ibanez, S. Soil fauna contribution to winter decomposition in subalpine grasslands. Soil Org. https://doi.org/10.25674/so91iss3pp107 (2019).Article 

Google Scholar 
Frouz, J., Špaldoňová, A., Lhotáková, Z. & Cajthaml, T. Major mechanisms contributing to the macrofauna-mediated slow down of litter decomposition. Soil. Biol. Biochem. 91, 23–31 (2015).CAS 
Article 

Google Scholar 
Frouz, J., Šustr, V. & Kalčík, J. Energetic budget of three species of bibionid larvae. In Contributions to Soil Zoology in Central Europe I. ISB AS CR, České Budějovice, 15–18 (2005).Frouz, J., Jedlička, P., Šimáčková, H. & Lhotáková, Z. The life cycle, population dynamics, and contribution to litter decomposition of Penthetria holosericea (Diptera: Bibionidae) in an alder forest. Eur. J. Soil Biol. 71, 21–27 (2015).Article 

Google Scholar 
Brovkin, V. et al. Plant-driven variation in decomposition rates improves projections of global litter stock distribution. Biogeosciences 9, 565–576 (2012).ADS 
CAS 
Article 

Google Scholar 
Buis, G. M. et al. Controls of aboveground net primary production in mesic savanna grasslands: An inter-hemispheric comparison. Ecosystems 12, 982–995 (2009).CAS 
Article 

Google Scholar 
O’Neill, D. W. & Abson, D. J. To settle or protect? A global analysis of net primary production in parks and urban areas. Ecol. Econ. 69, 319–327 (2009).Article 

Google Scholar 
Pan, S. et al. Impacts of climate variability and extremes on global net primary production in the first decade of the 21st century. J. Geogr. Sci. 25, 1027–1044 (2015).Article 

Google Scholar 
Yanai, R. D. et al. Litterfall and litter chemistry change over time in an old-growth temperate forest, northeastern China. For. Ecol. Manag. 43, 279–287 (1999).
Google Scholar 
Shchelchkova, M., Davydov, S., Fyodorov-Davydov, D., Davydova, A. & Boeskorov, G. The characteristics of a relic steppe of Northeast Asia: Refuges of the Pleistocene Mammoth steppe (an example from the Lower Kolyma area). IOP Conf. Ser. Earth Environ. Sci. 438, 012025 (2020).Article 

Google Scholar 
Ayuke, F. O. et al. Soil fertility management: Impacts on soil macrofauna, soil aggregation and soil organic matter allocation. Appl. Soil Ecol. 48, 53–62 (2011).Article 

Google Scholar 
Blanchart, E. et al. Effect of direct seeding mulch-based systems on soil carbon storage and macrofauna in Central Brazil. Agric. Conspec. Sci. 72, 81–87 (2007).
Google Scholar 
Korboulewsky, N., Perez, G. & Chauvat, M. How tree diversity affects soil fauna diversity: A review. Soil Biol. Biochem. 94, 94–106 (2016).CAS 
Article 

Google Scholar 
Frouz, J., Pizl, V., Cienciala, E. & Kalcik, J. Carbon storage in post-mining forest soil, the role of tree biomass and soil bioturbation. Biogeochemistry 94, 111–121 (2009).CAS 
Article 

Google Scholar 
Milton, Y. & Kaspari, M. Bottom-up and top-down regulation of decomposition in a tropical forest. Oecologia 153, 163–172 (2007).ADS 
PubMed 
Article 

Google Scholar 
Öpik, M., Moora, M., Liira, J. & Zobel, M. Composition of root-colonizing arbuscular mycorrhizal fungal communities in different ecosystems around the globe. J. Ecol. 94, 778–790 (2006).Article 

Google Scholar 
Portela, M. B. et al. Do ecological corridors increase the abundance of soil fauna? Écoscience 27, 45–57 (2020).Article 

Google Scholar 
Prieto, I., Almagro, M., Bastida, F. & Querejeta, J. I. Altered leaf litter quality exacerbates the negative impact of climate change on decomposition. J. Ecol. 107, 2364–2382 (2019).CAS 
Article 

Google Scholar 
Van der Putten, W. H. et al. Plant-soil feedbacks: The past, the present and future challenges. J. Ecol. 101, 265–276 (2013).Article 

Google Scholar 
Artz, R. et al. European atlas of soil. Biodiversity. https://doi.org/10.13140/RG.2.1.3178.2880 (2010).Article 

Google Scholar 
Orgiazzi, A. et al. Global Soil Biodiversity Atlas (European Soil Data Centre, 2016).
Google Scholar 
Peng, Y. et al. Litter quality, mycorrhizal association, and soil properties regulate effects of tree species on the soil fauna community. Geoderma 407, 115570 (2022).ADS 
CAS 
Article 

Google Scholar 
Bardgett, R. D. The Biology of Soil: A Community and Ecosystem Approach 255 (Oxford University Press, 2005).Book 

Google Scholar 
Jackson, R. B. et al. A global analysis of root distributions for terrestrial biomes. Oecologia 108, 389–411 (1996).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Jackson, R. B., Mooney, H. A. & Schulze, E.-D. A global budget for fine root biomass, surface area, and nutrient contents. PNAS 94, 7362–7366 (1997).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Sanchez, G. PLS Path Modeling with R, 235 (2013).Holland, E. A. et al. A global database of litterfall mass and litter pool carbon and nutrients. 10.3334/ORNLDAAC/1244 (2014).Palpurina, S. et al. The type of nutrient limitation affects the plant species richness–productivity relationship: Evidence from dry grasslands across Eurasia. J. Ecol. 107, 1038–1050 (2019).CAS 
Article 

Google Scholar 
Green, C. & Byrne, K. A. Biomass: Impact on carbon cycle and greenhouse gas emissions. In Encyclopedia of Energy (ed. Cleveland, C. J.) 223–236 (Elsevier, 2004).Chapter 

Google Scholar 
Liang, W. et al. Analysis of spatial and temporal patterns of net primary production and their climate controls in China from 1982 to 2010. Agric. For. Meteorol. 204, 22–36 (2015).ADS 
Article 

Google Scholar 
Ise, T., Litton, C. M., Giardina, C. P. & Ito, A. Comparison of modeling approaches for carbon partitioning: Impact on estimates of global net primary production and equilibrium biomass of woody vegetation from MODIS GPP. J. Geo. Res. Biogeosci. 115, 1–11 (2010).
Google Scholar 
Ni, J. Net primary production, carbon storage and climate change in Chinese biomes. Nord. J. Bot. 20, 415–426 (2000).Article 

Google Scholar 
Jandl, R. et al. How strongly can forest management influence soil carbon sequestration? Geoderma 137, 253–268 (2007).ADS 
CAS 
Article 

Google Scholar 
Reeves, M. C., Moreno, A. L., Bagne, K. E. & Running, S. W. Estimating climate change effects on net primary production of rangelands in the United States. Clim. Change 126, 429–442 (2014).ADS 
Article 

Google Scholar 
Cappai, C. et al. Small-scale spatial variation of soil organic matter pools generated by cork oak trees in Mediterranean agro-silvo-pastoral systems. Geoderma 304, 59–67 (2017).ADS 
CAS 
Article 

Google Scholar 
Clark, D. A. et al. Net primary production in tropical forests: An evaluation and synthesis of existing field data. Ecol. Appl. 11, 371–384 (2001).Article 

Google Scholar 
Yanai, R. D., Arthur, M. A., Acker, M., Levine, C. R. & Park, B. B. Variation in mass and nutrient concentration of leaf litter across years and sites in a northern hardwood forest. Can. J. For. Res. 42, 1597–1610 (2012).CAS 
Article 

Google Scholar  More

Richardson, D. M. et al. Naturalization and invasion of alien plants: concepts and definitions. Divers. Distrib. 6, 93–107 (2000).
Google Scholar 
Winter, M. et al. Plant extinctions and introductions lead to phylogenetic and taxonomic homogenization of the European flora. Proc. Natl Acad. Sci. USA 106, 21721–21725 (2009).CAS 
PubMed 
PubMed Central 

Google Scholar 
Pyšek, P. et al. Naturalized alien flora of the world: species diversity, taxonomic and phylogenetic patterns, geographic distribution and global hotspots of plant invasion. Preslia 89, 203–274 (2017).
Google Scholar 
Daru, B. H. et al. Widespread homogenization of plant communities in the Anthropocene. Nat. Commun. 12, 6983 (2021).Yang, Q. et al. The global loss of floristic uniqueness. Nat. Commun. 12, 7290 (2021).van Kleunen, M. et al. Global exchange and accumulation of non-native plants. Nature 525, 100–103 (2015).PubMed 

Google Scholar 
Dawson, W. et al. Global hotspots and correlates of alien species richness across taxonomic groups. Nat. Ecol. Evol. 1, 0186 (2017).Essl, F. et al. Drivers of the relative richness of naturalized and invasive plant species on Earth. AoB Plants 11, plz051 (2019).Pyšek, P. & Richardson, D. M. The biogeography of naturalization in alien plants. J. Biogeogr. 33, 2040–2050 (2006).
Google Scholar 
Moser, D. et al. Remoteness promotes biological invasions on islands worldwide. Proc. Natl Acad. Sci. USA 115, 9270–9275 (2018).CAS 
PubMed 
PubMed Central 

Google Scholar 
Guo, Q. et al. Latitudinal patterns of alien plant invasions. J. Biogeogr. 48, 253–262 (2021).
Google Scholar 
Pyšek, P. et al. Disentangling the role of environmental and human pressures on biological invasions across Europe. Proc. Natl Acad. Sci. USA 107, 12157–12162 (2010).PubMed 
PubMed Central 

Google Scholar 
Essl, F. et al. Socioeconomic legacy yields an invasion debt. Proc. Natl Acad. Sci. USA 108, 203–207 (2011).CAS 
PubMed 

Google Scholar 
Helmus, M. R., Mahler, D. L. & Losos, J. B. Island biogeography of the Anthropocene. Nature 513, 543–546 (2014).CAS 
PubMed 

Google Scholar 
di Castri, F. in Biological Invasions: A Global Perspective (ed. Drake, J. et al.), Ch. 1 (Wiley, 1989).Crosby, A. W. Ecological Imperialism: The Biological Expansion of Europe, 900–1900 2nd edn (Cambridge Univ. Press, 2004).Diamond, J. M. Guns, Germs, and Steel: The Fates of Human Societies (Norton, 2005).Nunn, N. & Qian, N. The Columbian exchange: a history of disease, food, and ideas. J. Econ. Perspect. 24, 163–188 (2010).
Google Scholar 
Beinart, W. & Middleton, K. Plant transfers in historical perspective: a review article. Environ. Hist. Camb. 10, 3–29 (2004).
Google Scholar 
Mrozowski, S. A. in Historical Archaeology (eds Hall, M. & Silliman, S. W.) Ch. 2 (Blackwell, 2006).Brockway, L. H. Science and colonial expansion: the role of the British Royal Botanic Gardens. Am. Ethnol. 6, 449–465 (1979).
Google Scholar 
Hulme, P. E. Addressing the threat to biodiversity from botanic gardens. Trends Ecol. Evol. 26, 168–174 (2011).PubMed 

Google Scholar 
Baas, P. The golden age of Dutch colonial botany and its impact on garden and herbarium collections. In Proc. Int. Symp. held by The Royal Danish Academy of Sciences and Letters in Copenhagen (eds Friis, I. & Balselv, H.), 53–62 (2017).Anderson, W. Climates of opinion: acclimatization in nineteenth-century France and England. Vic. Stud. 35, 135–157 (1992).CAS 
PubMed 

Google Scholar 
Osborne, M. A. Acclimatizing the world: a history of the paradigmatic colonial science. Osiris 15, 135–151 (2000).CAS 
PubMed 

Google Scholar 
Musgrave, T., Gardner, C. & Musgrave, W. The Plant Hunters Two Hundred Years of Adventure and Discovery (Seven Dials, 1999).Stoner, A. & Hummer, K. 19th and 20th century plant hunters. HortScience 42, 197–199 (2007).
Google Scholar 
Williams, K. A. An overview of the U.S. National Plant Germplasm System’s Exploration Program. HortScience 40, 297–301 (2005).
Google Scholar 
McCracken, D. P. Gardens of Empire: Botanical Institutions of the Victorian British Empire Garden History Vol. 26 (Leicester Univ. Press, 1997).Mitchener, K. J. & Weidenmier, M. Trade and empire. Econ. J. 118, 1805–1834 (2008).
Google Scholar 
World Trade Report 2007: Six Decades of Multilateral Trade Cooperation: What Have We Learnt? (World Trade Organization, 2007).Seebens, H. et al. No saturation in the accumulation of alien species worldwide. Nat. Commun. 8, 14435 (2017).Seebens, H. et al. Global rise in emerging alien species results from increased accessibility of new source pools. Proc. Natl Acad. Sci. USA 115, E2264–E2273 (2018).CAS 
PubMed 
PubMed Central 

Google Scholar 
Essl, F. et al. Historical legacies accumulate to shape future biodiversity in an era of rapid global change. Divers. Distrib. 21, 534–547 (2015).
Google Scholar 
van Kleunen, M. et al. The Global Naturalized Alien Flora (GloNAF) database. Ecology 100, e02542 (2019).PubMed 

Google Scholar 
Soininen, J., McDonald, R. & Hillebrand, H. The distance decay of similarity in ecological communities. Ecography 30, 3–12 (2007).
Google Scholar 
Blackburn, T. M. et al. A proposed unified framework for biological invasions. Trends Ecol. Evol. 26, 333–339 (2011).PubMed 

Google Scholar 
Colautti, R. I., Grigorovich, I. A. & MacIsaac, H. J. Propagule pressure: a null model for biological invasions. Biol. Invasions 8, 1023–1037 (2006).
Google Scholar 
Cassey, P., Delean, S., Lockwood, J. L., Sadowski, J. S. & Blackburn, T. M. Dissecting the null model for biological invasions: a meta-analysis of the propagule pressure effect. PLoS Biol. 16, e2005987 (2018).PubMed 
PubMed Central 

Google Scholar 
Blackburn, T. M., Cassey, P. & Duncan, R. P. Colonization pressure: a second null model for invasion biology. Biol. Invasions 22, 1221–1233 (2020).
Google Scholar 
Nekola, J. C. & White, P. S. The distance decay of similarity in biogeography and ecology. J. Biogeogr. 26, 867–878 (1999).
Google Scholar 
Liu, C., Wolter, C., Xian, W. & Jeschke, J. M. Most invasive species largely conserve their climatic niche. Proc. Natl Acad. Sci. USA 117, 23643–23651 (2020).CAS 
PubMed 
PubMed Central 

Google Scholar 
Panton, K. J. Historical Dictionary of the British Empire (Rowman & Littlefield, 2015).Brendon, P. The Decline and Fall of the British Empire, 1781–1997 (Cape, 2007).Hulme, P. E. Unwelcome exchange: international trade as a direct and indirect driver of biological invasions worldwide. One Earth 4, 666–679 (2021).
Google Scholar 
Levinson, M. The Box: How the Shipping Container Made the World Smaller and the World Economy Bigger (Princeton Univ. Press, 2010).Liebhold, A. M., Brockerhoff, E. G. & Kimberley, M. Depletion of heterogeneous source species pools predicts future invasion rates. J. Appl. Ecol. 54, 1968–1977 (2017).
Google Scholar 
Theoharides, K. A. & Dukes, J. S. Plant invasion across space and time: factors affecting nonindigenous species success during four stages of invasion. New Phytol. 176, 256–273 (2007).PubMed 

Google Scholar 
Maltby, W. S. The Rise and Fall of the Spanish Empire (Palgrave Macmillan, 2008).Disdier, A. C. & Head, K. The puzzling persistence of the distance effect on bilateral trade. Rev. Econ. Stat. 90, 37–48 (2008).
Google Scholar 
Jiménez, A., Pauchard, A., Cavieres, L. A., Marticorena, A. & Bustamante, R. O. Do climatically similar regions contain similar alien floras? A comparison between the Mediterranean areas of central Chile and California. J. Biogeogr. 35, 614–624 (2008).
Google Scholar 
Epanchin-Niell, R., McAusland, C., Liebhold, A., Mwebaze, P. & Springborn, M. R. Biological invasions and international trade: managing a moving target. Rev. Environ. Econ. Policy 15, 180–190 (2021).
Google Scholar 
Bakewell, P. A History of Latin America (Wiley-Blackwell, 2003).Disney, A. R. A History of Portugal and the Portuguese Empire (Cambridge Univ. Press, 2009).De Zwart, P. Globalization in the early modern era: new evidence from the Dutch-Asiatic Trade, c. 1600–1800. J. Econ. Hist. 76, 520–558 (2016).
Google Scholar 
Emmer, P. C. & Gommans, J. J. L. The Dutch Overseas Empire, 1600–1800 (Cambridge Univ. Press, 2021).Melitz, J. & Toubal, F. Native language, spoken language, translation and trade. J. Int. Econ. 93, 351–363 (2014).
Google Scholar 
Becker, B. Introducing COLDAT: the colonial dates dataset. Preprint at OSF https://doi.org/10.31219/osf.io/apvqm (2019).Pyšek, P., Richardson, D. M. & Williamson, M. Predicting and explaining plant invasions through analysis of source area floras: some critical considerations. Divers. Distrib. 10, 179–187 (2004).
Google Scholar 
R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2021).Hui, C. & McGeoch, M. A. Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. Am. Nat. 184, 684–694 (2014).PubMed 

Google Scholar 
McGeoch, M. A. et al. Measuring continuous compositional change using decline and decay in zeta diversity. Ecology 100, e02832 (2019).Latombe, G., Richardson, D. M., Pyšek, P., Kučera, T. & Hui, C. Drivers of species turnover vary with species commonness for native and alien plants with different residence times. Ecology 99, 2763–2775 (2018).PubMed 

Google Scholar 
Latombe, G., McGeoch, M. A., Nipperess, D. A. & Hui, C. zetadiv: an R package for computing compositional change across multiple sites, assemblages or cases. Preprint at bioRxiv https://doi.org/10.1101/324897 (2018).Latombe, G., McGeoch, M. A., Nipperess, D. A. & Hui, C. zetadiv: Functions to compute compositional turnover using zeta diversity. R package version 1.2.0 (2020).Baselga, A. Partitioning the turnover and nestedness components of beta diversity. Glob. Ecol. Biogeogr. 19, 134–143 (2010).
Google Scholar 
Latombe, G., Hui, C. & McGeoch, M. A. Multi-site generalised dissimilarity modelling: using zeta diversity to differentiate drivers of turnover in rare and widespread species. Methods Ecol. Evol. 8, 431–442 (2017).
Google Scholar 
Newman, M. E. J. & Girvan, M. Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004).Clauset, A., Newman, M. E. J. & Moore, C. Finding community structure in very large networks. Phys. Rev. E 70, 066111 (2004).
Google Scholar 
Csardi, G. & Nepusz, T. The igraph software package for complex network research. InterJournal, Complex Systems, 1695 (2006).Bonacich, P. Power and centrality: a family of neasures. Am. J. Sociol. 92, 1170–1182 (1987).
Google Scholar 
Delmas, E. et al. Analysing ecological networks of species interactions. Biol. Rev. 94, 16–36 (2019).
Google Scholar  More

Bowman, D. M. J. S. et al. Fire in the Earth system. Science 324, 481–484 (2009).Article 

Google Scholar 
Bowman, D. M. J. S. et al. Human exposure and sensitivity to globally extreme wildfire events. Nat. Ecol. Evol. 1, 0058 (2017).Article 

Google Scholar 
Hamilton, D. S. et al. Earth, wind, fire, and pollution: aerosol nutrient sources and impacts on ocean biogeochemistry. Ann. Rev. Mar. Sci. 14, 303–330 (2022).Article 

Google Scholar 
Barkley, A. E. et al. African biomass burning is a substantial source of phosphorus deposition to the Amazon, tropical Atlantic Ocean, and Southern Ocean. Proc. Natl Acad. Sci. USA 116, 16216–16221 (2019).Article 

Google Scholar 
Schlosser, J. S. et al. Analysis of aerosol composition data for western United States wildfires between 2005 and 2015: dust emissions, chloride depletion, and most enhanced aerosol constituents. J. Geophys. Res. Atmos. 122, 8951–8966 (2017).Article 

Google Scholar 
Wagner, R., Schepanski, K. & Klose, M. The dust emission potential of agricultural-like fires—theoretical estimates from two conceptually different dust emission parameterizations. J. Geophys. Res. Atmos. 126, e2020JD034355 (2017).
Google Scholar 
Ichoku, C. et al. Biomass burning, land-cover change, and the hydrological cycle in northern sub-Saharan Africa. Environ. Res. Lett. 11, 095005 (2016).Article 

Google Scholar 
Bowman, D. M. J. S. et al. Vegetation fires in the Anthropocene. Nat. Rev. Earth Environ. 1, 500–515 (2020).Article 

Google Scholar 
Duniway, M. C. et al. Wind erosion and dust from US drylands: a review of causes, consequences, and solutions in a changing world. Ecosphere 10, e02650 (2019).Article 

Google Scholar 
Okin, G. S., Gillette, D. A. & Herrick, J. E. Multi-scale controls on and consequences of aeolian processes in landscape change in arid and semi-arid environments. J. Arid. Environ. 65, 253–275 (2006).Article 

Google Scholar 
Raupach, M. R. Drag and drag partition on rough surfaces. Boundary Layer Meteorol. 60, 375–395 (1992).Article 

Google Scholar 
Webb, N. P. et al. Vegetation canopy gap size and height: critical indicators for wind erosion monitoring and management. Rangel. Ecol. Manag. 76, 78–83 (2021).Article 

Google Scholar 
Ellis, T. M., Bowman, D. M. J. S., Jain, P., Flannigan, M. D. & Williamson, G. J. Global increase in wildfire risk due to climate-driven declines in fuel moisture. Glob. Change Biol. 28, 1544–1559 (2022).Article 

Google Scholar 
Ravi, S. et al. Aeolian processes and the biosphere. Rev. Geophys. 49, RG3001 (2011).Article 

Google Scholar 
Wagenbrenner, N. S., Germino, M. J., Lamb, B. K., Robichaud, P. R. & Foltz, R. B. Wind erosion from a sagebrush steppe burned by wildfire: Measurements of PM10 and total horizontal sediment flux. Aeolian Res. 10, 25–36 (2013).Article 

Google Scholar 
Wagenbrenner, N. S. A large source of dust missing in Particulate Matter emission inventories? Wind erosion of post-fire landscapes. Elementa 5, 2 (2017).
Google Scholar 
Jeanneau, A. C., Ostendorf, B. & Herrmann, T. Relative spatial differences in sediment transport in fire-affected agricultural landscapes: a field study. Aeolian Res. 39, 13–22 (2019).Article 

Google Scholar 
Deb, P. et al. Causes of the widespread 2019–2020 Australian bushfire season. Earths Future 8, e2020EF001671 (2020).Article 

Google Scholar 
Nogrady, B. & Nicky, B. The climate link to Australia’s fires. Nature 577, 610–612 (2020).Yu, Y. & Ginoux, P. Assessing the contribution of the ENSO and MJO to Australian dust activity based on satellite- and ground-based observations. Atmos. Chem. Phys. 21, 8511–8530 (2021).Article 

Google Scholar 
Ginoux, P., Prospero, J. M., Gill, T. E., Hsu, N. C. & Zhao, M. Global-scale attribution of anthropogenic and natural dust sources and their emission rates based on MODIS Deep Blue aerosol products. Rev. Geophys. 50, RG3005 (2012).Article 

Google Scholar 
Yu, Y., Kalashnikova, O. V., Garay, M. J., Lee, H. & Notaro, M. Identification and characterization of dust source regions across North Africa and the Middle East using MISR satellite observations. Geophys. Res. Lett. 45, 6690–6701 (2018).Article 

Google Scholar 
Brianne, P., Rebecca, H. & David, L. The fate of biological soil crusts after fire: a meta-analysis. Glob. Ecol. Conserv. 24, e01380 (2020).Article 

Google Scholar 
Rodriguez-Caballero, E. et al. Global cycling and climate effects of aeolian dust controlled by biological soil crusts. Nat. Geosci. 15, 458–463 (2022).Article 

Google Scholar 
Goudie, A. S. & Middleton, N. J. Desert Dust in the Global System (Springer, 2006).Ginoux, P. Atmospheric chemistry: warming or cooling dust? Nat. Geosci. 10, 246–247 (2017).Article 

Google Scholar 
DeMott, P. J. et al. Predicting global atmospheric ice nuclei distributions and their impacts on climate. Proc. Natl Acad. Sci. USA 107, 11217–11222 (2010).Article 

Google Scholar 
Yu, H. et al. The fertilizing role of African dust in the Amazon rainforest: a first multiyear assessment based on data from cloud–aerosol lidar and infrared Pathfinder satellite observations. Geophys. Res. Lett. 42, 1984–1991 (2015).Article 

Google Scholar 
Tang, W. et al. Widespread phytoplankton blooms triggered by 2019–2020 Australian wildfires. Nature 597, 370–375 (2021).Article 

Google Scholar 
Sarangi, C. et al. Dust dominates high-altitude snow darkening and melt over high-mountain Asia. Nat. Clim. Change 10, 1045–1051 (2020).Article 

Google Scholar 
Cook, B. I. et al. Twenty-first century drought projections in the CMIP6 forcing scenarios. Earths Future 8, e2019EF001461 (2020).Article 

Google Scholar 
Zheng, B. et al. Increasing forest fire emissions despite the decline in global burned area. Sci. Adv. 7, eabh2646 (2021).Article 

Google Scholar 
Abatzoglou, J. T. & Williams, A. P. Impact of anthropogenic climate change on wildfire across western US forests. Proc. Natl Acad. Sci. USA 113, 11770–11775 (2016).Article 

Google Scholar 
Abram, N. J. et al. Connections of climate change and variability to large and extreme forest fires in southeast Australia. Commun. Earth Environ. 2, 1–17 (2021).Article 

Google Scholar 
Yu, Y. et al. Machine learning–based observation-constrained projections reveal elevated global socioeconomic risks from wildfire. Nat. Commun. 13, 1250 (2022).Article 

Google Scholar 
Pu, B. & Ginoux, P. How reliable are CMIP5 models in simulating dust optical depth? Atmos. Chem. Phys. 18, 12491–12510 (2018).Article 

Google Scholar 
Pu, B. & Ginoux, P. Climatic factors contributing to long-term variations in surface fine dust concentration in the United States. Atmos. Chem. Phys. 18, 4201–4215 (2018).Article 

Google Scholar 
Bodí, M. B. et al. Wildland fire ash: production, composition and eco-hydro-geomorphic effects. Earth Sci. Rev. 130, 103–127 (2014).Article 

Google Scholar 
NCAR Command Language v.6.6.2 (NCAR, 2019); https://doi.org/10.5065/D6WD3XH5Giglio, L., Schroeder, W. & Justice, C. O. The collection 6 MODIS active fire detection algorithm and fire products. Remote Sens. Environ. 178, 31–41 (2016).Article 

Google Scholar 
Ramo, R. et al. African burned area and fire carbon emissions are strongly impacted by small fires undetected by coarse resolution satellite data. Proc. Natl Acad. Sci. USA 118, 1–7 (2021).Article 

Google Scholar 
Diner, D. J. et al. Multi-angle imaging spectroradiometer (MISR) instrument description and experiment overview. IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).Article 

Google Scholar 
Pu, B. et al. Retrieving the global distribution of the threshold of wind erosion from satellite data and implementing it into the Geophysical Fluid Dynamics Laboratory land–atmosphere model (GFDL AM4.0/LM4.0). Atmos. Chem. Phys. 20, 55–81 (2020).Article 

Google Scholar 
Sayer, A. M., Hsu, N. C., Bettenhausen, C. & Jeong, M. J. Validation and uncertainty estimates for MODIS collection 6 ‘Deep Blue’ aerosol data. J. Geophys. Res. Atmos. 118, 7864–7872 (2013).Article 

Google Scholar 
Hsu, N. C. et al. Enhanced Deep Blue aerosol retrieval algorithm: the second generation. J. Geophys. Res. Atmos. 118, 9296–9315 (2013).Article 

Google Scholar 
Ginoux, P., Garbuzov, D. & Hsu, N. C. Identification of anthropogenic and natural dust sources using moderate resolution imaging spectroradiometer (MODIS) Deep Blue level 2 data. J. Geophys. Res. 115, D05204 (2010).Article 

Google Scholar 
Eck, T. F. et al. Wavelength dependence of the optical depth of biomass burning, urban, and desert dust aerosols. J. Geophys. Res. Atmos. 104, 31333–31349 (1999).Article 

Google Scholar 
Anderson, T. L. et al. Testing the MODIS satellite retrieval of aerosol fine-mode fraction. J. Geophys. Res. 110, 1–16 (2005).Article 

Google Scholar 
Baddock, M. C., Bullard, J. E. & Bryant, R. G. Dust source identification using MODIS: a comparison of techniques applied to the Lake Eyre Basin, Australia. Remote Sens. Environ. 113, 1511–1528 (2009).Article 

Google Scholar 
Baddock, M. C., Ginoux, P., Bullard, J. E. & Gill, T. E. Do MODIS-defined dust sources have a geomorphological signature? Geophys. Res. Lett. 43, 2606–2613 (2016).Article 

Google Scholar 
Pu, B. & Ginoux, P. Projection of American dustiness in the late 21st century due to climate change. Sci. Rep. 7, 5553 (2017).Article 

Google Scholar 
Pu, B., Ginoux, P., Kapnick, S. B. & Yang, X. Seasonal prediction potential for springtime dustiness in the United States. Geophys. Res. Lett. 46, 9163–9173 (2019).Article 

Google Scholar 
Garay, M. J. et al. Introducing the 4.4 km spatial resolution multi-angle imaging spectroradiometer (MISR) aerosol product. Atmos. Meas. Tech. 13, 593–628 (2020).Article 

Google Scholar 
Kalashnikova, O. V., Kahn, R., Sokolik, I. N. & Li, W.-H. Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes. J. Geophys. Res. 110, D18S14 (2005).Article 

Google Scholar 
Yu, Y. et al. Assessing temporal and spatial variations in atmospheric dust over Saudi Arabia through satellite, radiometric, and station data. J. Geophys. Res. Atmos. 118, 13253–13264 (2013).Article 

Google Scholar 
Yu, Y., Notaro, M., Kalashnikova, O. V. & Garay, M. J. Climatology of summer Shamal wind in the Middle East. J. Geophys. Res. Atmos. 121, 289–305 (2016).Article 

Google Scholar 
Yu, Y. et al. Disproving the Bodélé depression as the primary source of dust fertilizing the Amazon rainforest. Geophys. Res. Lett. 47, e2020GL088020 (2020).Article 

Google Scholar 
Giles, D. M. et al. Advancements in the Aerosol Robotic Network (AERONET) version 3 database—automated near-real-time quality control algorithm with improved cloud screening for Sun photometer aerosol optical depth (AOD) measurements. Atmos. Meas. Tech. 12, 169–209 (2019).Article 

Google Scholar 
O’Neill, N. T., Eck, T. F., Smirnov, A., Holben, B. N. & Thulasiraman, S. Spectral discrimination of coarse and fine mode optical depth. J. Geophys. Res. Atmos. 108, 1–15 (2003).
Google Scholar 
Winker, D. M. et al. Overview of the CALIPSO mission and CALIOP data processing algorithms. J. Atmos. Ocean. Technol. 26, 2310–2323 (2009).Article 

Google Scholar 
Esselborn, M. et al. Spatial distribution and optical properties of Saharan dust observed by airborne high spectral resolution lidar during SAMUM 2006. Tellus B 61, 131–143 (2009).Article 

Google Scholar 
Kim, M. H. et al. The CALIPSO version 4 automated aerosol classification and lidar ratio selection algorithm. Atmos. Meas. Tech. 11, 6107–6135 (2018).Article 

Google Scholar 
Didan, K., Munoz, A. B., Solano, R. & Huete, A. MODIS Vegetation Index User’s Guide (Collection 6) (Univ. Arizona, 2015).Seddon, A. W. R., Macias-Fauria, M., Long, P. R., Benz, D. & Willis, K. J. Sensitivity of global terrestrial ecosystems to climate variability. Nature 531, 229–232 (2016).Article 

Google Scholar 
Saleska, S. R. et al. Dry-season greening of Amazon forests. Nature 531, E4–E5 (2016).Article 

Google Scholar 
Remer, L. A., Kaufman, Y. J., Holben, B. N., Thompson, A. M. & McNamara, D. Biomass burning aerosol size distribution and modeled optical properties. J. Geophys. Res. Atmos. 103, 31879–31891 (1998).Article 

Google Scholar 
Tegen, I. & Lacis, A. A. Modeling of particle size distribution and its influence on the radiative properties of mineral dust aerosol. J. Geophys. Res. Atmos. 101, 19237–19244 (1996).Article 

Google Scholar 
Friedl, M. A. & Sulla-Menashe, D. User Guide to Collection 6 MODIS Land Cover (MCD12Q1 and MCD12C1) Product 6 (USGS, 2018).Sulla-Menashe, D., Gray, J. M., Abercrombie, S. P. & Friedl, M. A. Hierarchical mapping of annual global land cover 2001 to present: the MODIS collection 6 land cover product. Remote Sens. Environ. 222, 183–194 (2019).Article 

Google Scholar 
Dorigo, W. et al. ESA CCI Soil Moisture for improved Earth system understanding: state-of-the art and future directions. Remote Sens. Environ. 203, 185–215 (2017).Article 

Google Scholar 
Hersbach, H. et al. The ERA5 global reanalysis. Q. J. R. Meteorol. Soc. 146, 1999–2049 (2020).Article 

Google Scholar 
Preimesberger, W., Scanlon, T., Su, C.-H., Gruber, A. & Dorigo, W. Homogenization of structural breaks in the global ESA CCI Soil Moisture multisatellite climate data record. IEEE Trans. Geosci. Remote Sens. 59, 2845–2862 (2021).Article 

Google Scholar 
Minola, L. et al. Near-surface mean and gust wind speeds in ERA5 across Sweden: towards an improved gust parametrization. Clim. Dyn. 55, 887–907 (2020).Article 

Google Scholar 
Molina, M. O., Gutiérrez, C. & Sánchez, E. Comparison of ERA5 surface wind speed climatologies over Europe with observations from the HadISD dataset. Int. J. Climatol. 41, 4864–4878 (2021).Article 

Google Scholar 
Klose, M. et al. Mineral dust cycle in the Multiscale Online Nonhydrostatic Atmosphere Chemistry model (MONARCH) version 2.0. Geosci. Model Dev. 14, 6403–6444 (2021).Article 

Google Scholar 
Mondal, A., Kundu, S. & Mukhopadhyay, A. Rainfall trend analysis by Mann–Kendall test: a case study of north-eastern part of Cuttack District, Orissa. Int. J. Geol. Earth Environ. Sci. 2, 2277–208170 (2012).
Google Scholar 
Yu, Y. & Ginoux, P. Dust emission following large wildfires. figshare. 2022. https://doi.org/10.6084/m9.figshare.20648055.v2 More

Our experimental data reveals a scaling law between the mass of a layer along the vertical coordinate, M(z), and the weight that it supports, W(z), namely: (W(z) sim M(z)^a) with (a approx 1.5). To better understand the physical mechanism that yields this scaling law, we derive the force balance equation of a layer of the swarm and solve for W(z). We then equate the analytical expression for W(z) with the experimentally determined scaling law, (W(z) sim M(z)^a), to connect the swarm mass distribution to the exponent a and formulate the expressions for M(z) and W(z) in terms of a. We then consider a dimensional analysis of the strength of each layer of the swarm, S, or the maximum weight that it can support before the grip of the bees on one another breaks. As will be described in detail below, we find that (S sim M^{1.5}), which is close to the experimentally determined (a = 1.53). Deviation from this value increases the fraction of maximum strength exerted by different parts of the swarm.Force balance model of the weight distribution in the swarmWe assume that the swarm is at quasi-equilibrium (the shape does not change although individual bees may move), that all of the bees in each layer contribute equally to supporting the weight of the bees underneath that layer, that the layer thickness is very small, and that the swarm is radially symmetrical about the z-axis. We use a cylindrical coordinate system with a vertical coordinate z, as shown in Fig. 1e, and we consider layers of the swarm along the z-axis of thickness dz. Variables labeled with a tilde, as in (tilde{W}(z)), represent analytically derived expressions; variables without a tilde, as in W(z), represent values determined with power law fits to experimental data.We begin our analysis by applying the force balance principle to each layer of a swarm. As shown by the free body diagram in Fig. 1f, the force with which each layer of bees has to grasp the layer above it is equal to the weight of that layer and all of the layers underneath it: (tilde{F} = tilde{W}(z)). We express (tilde{W}(z)) using the force balance equation (a continuous version of the discrete definition in Eq. (5).):$$begin{aligned} tilde{W}(z) = g int _z^L tilde{M}(z) dz, end{aligned}$$
(8)
where the mass of bees per layer is (tilde{M}(z)), the swarm length is L, and g is the gravitational constant. Inspired by our experimental observation that the mass of the layers near the base is highest and the mass of the layers at the tip of the swarm is lowest in Fig. 3a, we model (tilde{M}(z)) as a monotonically decreasing function of z. To keep the units consistent, we normalize the z coordiante by the length of the swarm:$$begin{aligned} tilde{M}(z) = c left( 1-frac{z}{L}right) ^{tilde{b}}, end{aligned}$$
(9)
where the c factor in this expression ensures that the units of the mass per layer are mass/length, and (tilde{b}) is an unknown exponent. Choosing this function form allows us to easily integrate the expression for (tilde{W}(z)) when we substitute (tilde{M}(z)) into it, set this force balance derivation for (tilde{W}(z)) equal to the experimentally determined expression (W(z) = C M(z)^a), and compare the exponents a and (tilde{b}).To solve the expression for (tilde{W}(z)), we substitute the expression for (tilde{M}(z)), Eq. (9), into Eq. (8) and integrate. We then express (tilde{b}) in terms of the experimentally determined a by equating this expression for (tilde{W}(z)) to the scaling law we observe in our experiments, Eq. (7), (W(z) = C tilde{M}(z)^a). The exponent in the expression for (tilde{M(z)}), Eq. (9), is$$begin{aligned} tilde{b} = frac{1}{a-1}. end{aligned}$$
(10)
The weight supported by each layer is then:$$begin{aligned} tilde{W}(z) = cLg left( 1 – frac{1}{a}right) left( 1-frac{z}{L}right) ^{frac{a}{a-1}}. end{aligned}$$
(11)
Next, we test how well our force balance model predicts the data by comparing the predicted value of (tilde{b}) using the force balance to the value of b calculated using experimental fits. We first separate the expression for the layer mass, Eq. (9) into the product of the layer area, (tilde{A}(z)) and the layer density, (tilde{rho }(z)):$$begin{aligned} tilde{M}(z) sim tilde{A}(z) tilde{rho }(z). end{aligned}$$
(12)
To simplify our analysis, we model (tilde{A}(z)) and (tilde{rho }(z)) with a similar monotonically decreasing function to that in Eq. (9):$$begin{aligned} tilde{A}(z) = c_1 left( 1-frac{z}{L}right) ^{tilde{b}_1}, end{aligned}$$
(13)
and$$begin{aligned} tilde{rho }(z) =c_2 left( 1-frac{z}{L}right) ^{tilde{b}_2} end{aligned}$$
(14)
we can then separately measure the effect of the changes in area and density on the exponent in the mass per layer expression in Eq. (9), (tilde{b} = tilde{b}_1 + tilde{b}_2).We first calculate (tilde{b}) using the expression derived from the force balance, Eq. (10), and our experimental result for a, which yields (tilde{b} = 2 pm 0.47). Second, we calculate b by separately calculating power law fits to the data for A(z) in Fig. 2e according to Eq. (13) and (rho (z)) in Fig. 2d according to Eq. (14), which yields (b_1 = 1.38 pm 0.2) and (b_2 = 0.51 pm 0.09). Thus, (b = b_1 + b_2 = 1.89 pm 0.25). See Supplementary Fig. S5(a–c) for log-log plots of M(z), A(z) and (rho (z)), and Supplementary Fig. S5(d–f) for plots of the resulting b, (b_1), and (b_2).We calculate the deviation of (tilde{b}) from b, (frac{tilde{b} – b}{tilde{b}} = 0.03 pm 0.11), and plot the deviation of b from (tilde{b}) in Supplementary Fig. S5(g) as a comparison for the individual CT scans. The values of b and (tilde{b}) being on the same order of magnitude validates the model and allows us to compare (tilde{W}(z)) to a maximum strength of each layer, which we find with dimensional analysis in the following section.Strength of a swarm layer and individual beesThe strength of the layer, (tilde{S}(z)), or the maximum weight that it could support, can be greater than or equal to (tilde{W}(z)): (tilde{S}(z) ge tilde{W}(z)). If the weight of the bees underneath a layer were to exceed its strength (tilde{S}(z)), the layer would not be able to support the weight of those bees, and the swarm would break apart. We perform a dimensional analysis on the strength of each layer to find the relationship between the mass of a layer and its maximum strength, (tilde{S}(z) sim tilde{M}(z)^{alpha }). Force is proportional to mass, which is proprtional to volume, or a length cubed, so a layer’s strength scales with length cubed, (tilde{S}(z) propto L^3). The mass of each layer, with units of mass/length, is proportional to an area, or a length squared, so (tilde{M}(z)) scales with length squared, (tilde{M}(z) propto L^2). Thus, (alpha) must be 1.5 for (tilde{S}(z) sim tilde{M}(z)^{alpha }) to be dimensionally correct. This is similar to the relationship between weightifting capacity and body weight in Ref.16.Estimating (tilde{W}(z)/tilde{S}(z)) gives a measure of how much of its maximum strength each layer uses to hold up the rest of the swarm:$$begin{aligned} frac{tilde{W}(z)}{tilde{S}(z)} sim left( 1-frac{1}{a}right) left( 1-frac{z}{L}right) ^frac{2a-3}{2a-2} end{aligned}$$
(15)
The average number of bees that a bee in a swarm layer supports, (tilde{F}_{bee}(z)), is equal to the mass of bees supported by a layer divided by the sum of the mass of bees in a layer of bees that has the thickness of the length of a bee, (l approx 1.5), as a continuous version of the discrete equation in Eq. (6):$$begin{aligned} tilde{F}_{bee}(z) =frac{int _z^L tilde{M}(z) dz}{int _z^{z+l} tilde{M}(z) dz}. end{aligned}$$
(16)
After integrating, we get an expression for (tilde{F}_{bee} (z)):$$begin{aligned} tilde{F}_{bee}(z)= frac{left( 1-frac{z}{L}right) ^{frac{a}{a-1}}}{left( 1-frac{z}{L}right) ^{frac{a}{a-1}} – left( 1-frac{z + l}{L}right) ^{frac{a}{a-1}}}. end{aligned}$$
(17)
We use the expression for (frac{tilde{W}(z)}{tilde{S}(z)}), Eq. (15), and (tilde{F}_{bee}(z)), Eq. (17), in the next section to evaluate how the force distribution in the swarm would change for swarms with different values of a.Effect of a on the mass of each layer, the fraction of its maximum stregnth it uses, and the average force per beeWe now consider the effect of varying a on the mass and force distribution inside the swarm. To visualize the effect of a on the distribution of bees, we plot the mass per layer of a 1000-g, 12.5 cm long swarm, (tilde{M}(z)) vs. z/L, with (a = 1.5, 1.01, 1000), and (-0.2) in Fig. 3c and the corresponding average force per bee, (F_{bee}(z)) vs. z/L in Fig. 3d. These values of a are example values for the four possible cases of mass distribution in the swarm. We then evaluate how these values of a affect the fraction of maximum strength each layer uses to support the layers underneath it using Eq. (15).If (a approx alpha), as we found in our experiments, layers with higher mass near the attachment surface support the less massive layers under them, as in the solid black line in Fig. 3c. Correspondingly, Fig. 3d shows (tilde{F}_{bee}(z=0) approx 3) at the top of the swarm, and decreases towards the tip. The strength of each layer and the weight it supports are proportional to one another, (tilde{W}(z)/tilde{S}(z) sim 1/3), meaning that the fraction of maximum strength used by a layer is the same for all z. If (1< a < alpha), the swarm approaches one massive layer of bees, as in the dashed purple line in Fig. 3c. The dimensional analysis results in a very small fraction of the total strength used by this layer, (tilde{W}(z)/tilde{S}(z) rightarrow 0 (1-frac{z}{L})^{-infty }). The force supported by each bee in Fig. 3d shows (tilde{F}_{bee}(z) = 1) for the entire swarm, meaning that each bee only supports its own weight. This configuration would either require packing a large number of bees into one very dense or one very wide layer. A swarm with one very dense layer at the top would compress all of the bees; a swarm with one very wide layer would require a large surface area, which would put the swarm in danger from predators and changes in weather. Thus, despite a potentially lower fraction of strength used by the largest layer of bees, this configuration would put the swarm in danger by requiring a large surface area.For values of (a > alpha), as (a rightarrow infty), all the layers of the swarm have the same mass, as in the dash-dot red line in Fig. 3c. The force per bee in Fig. 3d shows (tilde{F}_{bee}(z=0) approx 8) at the top of the swarm, 2.5 times that of the (a = alpha) configuration. In this configuration, the top layers use a higher percentage of their available strength than the lower layers, (tilde{W}(z)/tilde{S}(z) rightarrow (1-frac{z}{L})). Thus, for large swarms, the bees that support the swarm would be under more strain, and the swarm would be more likely to break under external perturbation.Finally, (a < 0) ((0 le a le 1) results in negative values for (tilde{W}(z))) would suggest that the top layers of the swarm have a lower mass than the bottom layers, as in the dotted orange line in Fig. 3c. This is not a realistic range of values for a, but we include it here as a demonstration of a potential mass distribution with the largest layers being on the bottom of the swarm. This configuration would put even more strain on the layers of bees at the top of the swarm, as smaller layers near the attachment surface have a smaller maximum strength. As (a rightarrow 0) on the (a < 0) side, (tilde{W}(z)/tilde{S}(z) rightarrow infty (1-z/L)^{1.5}), and bees in the top layers use a much greater fraction of their strength than bees in the bottom layers. Accordingly, the mean force per bee in Fig. 3d exceeds the maximum bee grip strength of 35 bee weights, and the swarm could not support itself in this configuration.The swarm configuration with (a approx 1.5) uses the full strength of each layer and puts a lower strain on the bees than most other values of a, and avoids weight distributions that could expose a large number of bees to external danger. More