Ecology

1.Berg, B. et al. Factors influencing limit values for pine needle litter decomposition: A synthesis for boreal and temperate pine forest systems. Biogeochemistry 100, 57–73. https://doi.org/10.1007/s10533-009-9404-y (2010).Article 
CAS 

Google Scholar 
2.Hobbie, S. E. et al. Response of decomposing litter and its microbial community to multiple forms of nitrogen enrichment. Ecol. Monogr. 82, 389–405 (2012).
Google Scholar 
3.Handa, I. T. et al. Consequences of biodiversity loss for litter decomposition across biomes. Nature 509, 218–221 (2014).PubMed 
ADS 
CAS 

Google Scholar 
4.Talbot, J. M., Yelle, D. J., Nowick, J. S. & Treseder, K. K. Litter decay rates are determined by lignin chemistry. Biogeochemistry 108, 279–295 (2012).CAS 

Google Scholar 
5.Pei, G. et al. Nitrogen, lignin, C/N as important regulators of gross nitrogen release and immobilization during litter decomposition in a temperate forest ecosystem. For. Ecol. Manage. 440, 61–69 (2019).
Google Scholar 
6.Couˆteaux, M., Bottner, P. & Berg, B. Litter decomposition, climate and liter quality. Trends Ecol. Evol. 10, 63–66 (1995).
Google Scholar 
7.Galloway, J. N. et al. Transformation of the nitrogen cycle: Recent trends, questions, and potential solutions. Science 320, 889. https://doi.org/10.1126/science.1136674 (2008).Article 
PubMed 
ADS 
CAS 

Google Scholar 
8.Kanakidou, M. et al. Past, present, and future atmospheric nitrogen deposition. J. Atmos. Sci. 73, 2039–2047. https://doi.org/10.1175/JAS-D-15-0278.1 (2016).Article 
PubMed 
PubMed Central 
ADS 
CAS 

Google Scholar 
9.Zhu, J. et al. The composition, spatial patterns, and influencing factors of atmospheric wet nitrogen deposition in Chinese terrestrial ecosystems. Sci. Total Environ. 511, 777–785 (2015).PubMed 
ADS 
CAS 

Google Scholar 
10.Liu, X. et al. Nitrogen deposition and its ecological impact in China: An overview. Environ. Pollut. 159, 2251–2264. https://doi.org/10.1016/j.envpol.2010.08.002 (2011).Article 
PubMed 
CAS 

Google Scholar 
11.Chen, H. Y. H. & Zhang, T. Data for: Responses of litter decomposition and nutrient release to N addition: A meta-analysis of terrestrial ecosystems. Appl. Soil. Ecol. 1, 35–42 (2018).
Google Scholar 
12.Knorr, M., Frey, S. & Curtis, P. Nitrogen additions and litter decomposition: A meta-analysis. Ecology 86, 3252–3257. https://doi.org/10.1890/05-0150 (2005).Article 

Google Scholar 
13.Hobbie, S. E. & Vitousek, P. M. Nutrient limitation of decomposition in Hawaiian forests. Ecology 81, 1867–1877 (2000).
Google Scholar 
14.Zhou, S. X. et al. Simulated nitrogen deposition significantly suppresses the decomposition of forest litter in a natural evergreen broad-leaved forest in the Rainy Area of Western China. Plant Soil 420(1–2), 135–145 (2017).CAS 

Google Scholar 
15.Wang, Q., Kwak, J., Choi, W. & Chang, S. X. Long-term N and S addition and changed litter chemistry do not affect trembling aspen leaf litter decomposition, elemental composition and enzyme activity in a boreal forest. Environ. Pollut. 250, 143–154 (2019).PubMed 
CAS 

Google Scholar 
16.Magill, A. H. & Aber, J. D. Long-term effects of experimental nitrogen additions on foliar litter decay and humus formation in forest ecosystems. Plant Soil 203, 301–311 (1998).CAS 

Google Scholar 
17.Janssens, I. A. et al. Reduction of forest soil respiration in response to nitrogen deposition. Nat. Geosci. 3, 315–322 (2010).ADS 
CAS 

Google Scholar 
18.Zhang, W. et al. Litter quality mediated nitrogen effect on plant litter decomposition regardless of soil fauna presence. Ecology 97, 2834–2843 (2016).PubMed 

Google Scholar 
19.Wang, M. et al. Effects of sediment-borne nutrient and litter quality on macrophyte decomposition and nutrient release. Hydrobiologia 787, 205–215. https://doi.org/10.1007/s10750-016-2961-x (2017).Article 
CAS 

Google Scholar 
20.Talbot, J. M. & Treseder, K. K. Interactions among lignin, cellulose, and nitrogen drive litter chemistry–decay relationships. Ecology 93, 345–354 (2012).PubMed 

Google Scholar 
21.Zhang, T. A., Luo, Y. & Ruan, H. Responses of litter decomposition and nutrient release to N addition: A meta-analysis of terrestrial ecosystems. Appl. Soil Ecol. 128, 35–42. https://doi.org/10.1016/j.apsoil.2018.04.004 (2018).Article 
ADS 

Google Scholar 
22.Kuperman, R. G. Litter decomposition and nutrient dynamics in oak–hickory forests along a historic gradient of nitrogen and sulfur deposition. Soil Biol. Biochem. 31, 237–244 (1999).CAS 

Google Scholar 
23.Cleveland, C. C. & Townsend, A. R. Nutrient additions to a tropical rain forest drive substantial soil carbon dioxide losses to the atmosphere. Proc. Natl. Acad. Sci. U.S.A. 103, 10316–10321 (2006).PubMed 
PubMed Central 
ADS 
CAS 

Google Scholar 
24.Chen, J. et al. Costimulation of soil glycosidase activity and soil respiration by nitrogen addition. Glob. Change Biol. 23, 1328–1337 (2017).ADS 

Google Scholar 
25.Lu, X., Mao, Q., Gilliam, F. S., Luo, Y. & Mo, J. Nitrogen deposition contributes to soil acidification in tropical ecosystems. Glob. Change Biol. 20, 3790–3801 (2014).ADS 

Google Scholar 
26.Yang, D., Song, L. & Jin, G. The soil C:N: P stoichiometry is more sensitive than the leaf C:N: P stoichiometry to nitrogen addition: A four-year nitrogen addition experiment in a Pinus koraiensis plantation. Plant Soil 442, 183–198. https://doi.org/10.1007/s11104-019-04165-z (2019).Article 
CAS 

Google Scholar 
27.Penuelas, J. et al. Human-induced nitrogen–phosphorus imbalances alter natural and managed ecosystems across the globe. Nat. Commun. 4, 2934 (2013).PubMed 
ADS 

Google Scholar 
28.Liu, X. et al. Enhanced nitrogen deposition over China. Nature 494, 459–462. https://doi.org/10.1038/nature11917 (2013).Article 
PubMed 
ADS 
CAS 

Google Scholar 
29.Kang, Y. et al. High-resolution ammonia emissions inventories in China from 1980 to 2012. Atmos. Chem. Phys. 16, 2043–2058 (2015).ADS 

Google Scholar 
30.Huo, Y. et al. Climate–growth relationships of Schrenk spruce (Picea schrenkiana) along an altitudinal gradient in the western Tianshan mountains. northwest China. Trees 31, 429–439 (2017).
Google Scholar 
31.Zhonglin, X. et al. Climatic and topographic variables control soil nitrogen, phosphorus, and nitrogen: Phosphorus ratios in a Picea schrenkiana forest of the Tianshan Mountains. PLoS ONE 13(11), e0204130 (2018).
Google Scholar 
32.Zhang, T. et al. The impacts of climatic factors on radial growth patterns at different stem heights in Schrenk spruce (Picea schrenkiana). Trees 34(1), 163–175 (2020).
Google Scholar 
33.Chen, X., Gong, L. & Liu, Y. The ecological stoichiometry and interrelationship between litter and soil under seasonal snowfall in Tianshan Mountain. Ecosphere 9(11), e02520 (2018).
Google Scholar 
34.Gong, L. & Zhao, J. The response of fine root morphological and physiological traits to added nitrogen in Schrenk’s spruce (Picea schrenkiana) of the Tianshan mountains, China. PeerJ 7, e8194 (2019).PubMed 
PubMed Central 

Google Scholar 
35.Zhu, H., Zhao, J. & Gong, L. The morphological and chemical properties of fine roots respond to nitrogen addition in a temperate Schrenk’s spruce (Picea schrenkiana) forest. Sci. Rep. 11(1), 3839. https://doi.org/10.1038/s41598-021-83151-x (2021).Article 
PubMed 
PubMed Central 
ADS 
CAS 

Google Scholar 
36.Mo, J. et al. Decomposition responses of pine (Pinus massoniana) needles with two different nutrient-status to N deposition in a tropical pine plantation in southern China. Ann. For. Sci. 65, 405–405 (2008).
Google Scholar 
37.Wen, Z. et al. Changes of nitrogen deposition in China from 1980 to 2018. Environ. Int. 144, 106022. https://doi.org/10.1016/j.envint.2020.106022 (2020).Article 
PubMed 
CAS 

Google Scholar 
38.Liu, W. et al. Critical transition of soil bacterial diversity and composition triggered by nitrogen enrichment. Ecology 101, e03053. https://doi.org/10.1002/ecy.3053 (2020).Article 
PubMed 

Google Scholar 
39.Yao, M. et al. Rate-specific responses of prokaryotic diversity and structure to nitrogen deposition in the Leymus chinensis steppe. Soil Biol. Biochem. 79, 81–90 (2014).CAS 

Google Scholar 
40.Berg, B. & Matzner, E. Effect of N deposition on decomposition of plant litter and soil organic matter in forest systems. Environ. Rev. 5, 1–25. https://doi.org/10.1139/a96-017 (1997).Article 
CAS 

Google Scholar 
41.Liu, W. et al. Nonlinear responses of the Vmax and Km of hydrolytic and polyphenol oxidative enzymes to nitrogen enrichment. Soil Biol. Biochem. 141, 107656. https://doi.org/10.1016/j.soilbio.2019.107656 (2020).Article 
CAS 

Google Scholar 
42.Vestgarden, L. S. Carbon and nitrogen turnover in the early stage of Scots pine (Pinus sylvestris L.) needle litter decomposition: Effects of internal and external nitrogen. Soil Biol. Biochem. 33, 465–474 (2001).CAS 

Google Scholar 
43.Brown, M. E. & Chang, M. C. Y. Exploring bacterial lignin degradation. Curr. Opin. Chem. Biol. 19, 1–7 (2014).PubMed 
CAS 

Google Scholar 
44.Sun, T., Dong, L., Wang, Z., Lu, X. & Mao, Z. Effects of long-term nitrogen deposition on fine root decomposition and its extracellular enzyme activities in temperate forests. Soil Biol. Biochem. 93, 50–59 (2016).CAS 

Google Scholar 
45.Sjoberg, G., Nilsson, S. I., Persson, T. & Karlsson, P. Degradation of hemicellulose, cellulose and lignin in decomposing spruce needle litter in relation to N. Soil Biol. Biochem. 36, 1761–1768 (2004).CAS 

Google Scholar 
46.Sinsabaugh, R. L. Phenol oxidase, peroxidase and organic matter dynamics of soil. Soil Biol. Biochem. 42, 391–404 (2010).CAS 

Google Scholar 
47.Carreiro, M. M., Sinsabaugh, R. L., Repert, D. A. & Parkhurst, D. F. Microbial enzyme shifts explain litter decay responses to simulated nitrogen deposition. Ecology 81, 2359–2365. https://doi.org/10.1890/0012-9658(2000)081[2359:meseld]2.0.co;2 (2000).Article 

Google Scholar 
48.Hobbie, S. E. Nitrogen effects on decomposition: A five-year experiment in eight temperate sites. Ecology 89, 2633–2644 (2008).PubMed 

Google Scholar 
49.Mo, J., Brown, S., Xue, J., Fang, Y. & Li, Z. Response of litter decomposition to simulated N deposition in disturbed, rehabilitated and mature forests in subtropical China. Plant Soil 282, 135–151 (2006).CAS 

Google Scholar 
50.Ajwa, H. A., Dell, C. J. & Rice, C. W. Changes in enzyme activities and microbial biomass of tallgrass prairie soil as related to burning and nitrogen fertilization. Soil Biol. Biochem. 31, 769–777. https://doi.org/10.1016/S0038-0717(98)00177-1 (1999).Article 
CAS 

Google Scholar 
51.Li, Q. et al. Biochar mitigates the effect of nitrogen deposition on soil bacterial community composition and enzyme activities in a Torreya grandis orchard. For. Ecol. Manage. 457, 117717 (2020).
Google Scholar 
52.Chen, J. et al. Long-term nitrogen loading alleviates phosphorus limitation in terrestrial ecosystems. Glob. Change Biol. 26, 5077–5086. https://doi.org/10.1111/gcb.15218 (2020).Article 
ADS 

Google Scholar 
53.Marklein, A. R. & Houlton, B. Z. Nitrogen inputs accelerate phosphorus cycling rates across a wide variety of terrestrial ecosystems. New Phytol. 193, 696–704 (2012).PubMed 
CAS 

Google Scholar 
54.Corrales, A., Turner, B. L., Tedersoo, L., Anslan, S. & Dalling, J. W. Nitrogen addition alters ectomycorrhizal fungal communities and soil enzyme activities in a tropical montane forest. Fungal Ecol. 27, 14–23 (2017).
Google Scholar 
55.Cusack, D. F. Soil nitrogen levels are linked to decomposition enzyme activities along an urban-remote tropical forest gradient. Soil Biol. Biochem. 57, 192–203 (2013).CAS 

Google Scholar 
56.Xiao, S. et al. Effects of one-year simulated nitrogen and acid deposition on soil respiration in a subtropical plantation in China. Forests 11, 235 (2020).
Google Scholar 
57.Liang, X. et al. Global response patterns of plant photosynthesis to nitrogen addition: A meta-analysis. Glob. Change Biol. 26, 3585–3600. https://doi.org/10.1111/gcb.15071 (2020).Article 
ADS 

Google Scholar 
58.Peng, Y. et al. Soil biochemical responses to nitrogen addition in a secondary evergreen broad-leaved forest ecosystem. Sci. Rep. 7, 2783–2783. https://doi.org/10.1038/s41598-017-03044-w (2017).Article 
PubMed 
PubMed Central 
ADS 
CAS 

Google Scholar 
59.Tian, D. et al. A global analysis of soil acidification caused by nitrogen addition. Environ. Res. Lett. 10, 024019 (2015).ADS 

Google Scholar 
60.Gill, A. L. et al. Experimental nitrogen fertilisation globally accelerates, then slows decomposition of leaf litter. Ecol. Lett. 24, 802–811 (2021).PubMed 

Google Scholar 
61.Cotrufo, M. F. et al. Formation of soil organic matter via biochemical and physical pathways of litter mass loss. Nat. Geosci. 8, 776–779 (2015).ADS 
CAS 

Google Scholar 
62.Lu, X. et al. Nitrogen deposition accelerates soil carbon sequestration in tropical forests. Proc. Natl. Acad. Sci. USA 118, e2020790118 (2021).PubMed 
PubMed Central 
CAS 

Google Scholar 
63.Kallenbach, C. M. et al. Direct evidence for microbial-derived soil organic matter formation and its ecophysiological controls. Nat. Commun. 7, 1–10 (2016).
Google Scholar 
64.Sun, S. et al. Soil warming and nitrogen deposition alter soil respiration, microbial community structure and organic carbon composition in a coniferous forest on eastern Tibetan Plateau. Geoderma 353, 283–292 (2019).ADS 
CAS 

Google Scholar 
65.Liu, G. Soil Physical and Chemical Analysis and Description of Soil Profiles (Elsevier, 1996).
Google Scholar 
66.Lotse, E. G. Chemical analysis of ecological materials. Soil Sci. 121, 373 (1976).ADS 

Google Scholar 
67.Anderson, J. M. & Ingram, J. Tropical soil biology and fertility: A handbook of methods. Soil Sci. 157, 265 (1994).ADS 

Google Scholar 
68.Roberts, J. D. & Rowland, A. P. Cellulose fractionation in decomposition studies using detergent fibre pre-treatment methods. Commun. Soil Plant Anal. 29, 11–14 (1998).
Google Scholar 
69.Kotroczó, Z. et al. Soil enzyme activity in response to long-term organic matter manipulation. Soil Biol. Biochem. 70, 237–243 (2014).
Google Scholar 
70.Paolo, N., Brunello, C., Stefano, C. & Emilio, M. Extraction of phosphatase, urease, proteases, organic carbon, and nitrogen from soil. Soil Sci. Soc. Am. J. https://doi.org/10.2136/SSSAJ1980.03615995004400050028X (1981).Article 

Google Scholar 
71.Schinner, F. & Mersi, W. V. Xylanase-, CM-cellulase- and invertase activity in soil: An improved method. Soil Biol. Biochem. 22, 511–515 (1990).CAS 

Google Scholar  More

1.Keenan, T. F. et al. Recent pause in the growth rate of atmospheric CO2 due to enhanced terrestrial carbon uptake. Nat. Commun. 7, 13428 (2016).CAS 
PubMed 
PubMed Central 

Google Scholar 
2.Fatichi, S. et al. Partitioning direct and indirect effects reveals the response of water-limited ecosystems to elevated CO2. Proc. Natl Acad. Sci. USA 113, 12757–12762 (2016).CAS 
PubMed 
PubMed Central 

Google Scholar 
3.Smith, W. K. et al. Large divergence of satellite and Earth system model estimates of global terrestrial CO2 fertilization. Nat. Clim. Change 6, 306–310 (2016).
Google Scholar 
4.Schimel, D., Stephens, B. B. & Fisher, J. B. Effect of increasing CO2 on the terrestrial carbon cycle. Proc. Natl Acad. Sci. USA 112, 436–441 (2015).CAS 
PubMed 

Google Scholar 
5.Norby, R. J. et al. Forest response to elevated CO2 is conserved across a broad range of productivity. Proc. Natl Acad. Sci. USA 102, 18052–18056 (2005).CAS 
PubMed 
PubMed Central 

Google Scholar 
6.Mooney, H. A., Drake, B. G., Luxmoore, R. J., Oechel, W. C. & Pitelka, L. F. Predicting ecosystem responses to elevated CO2 concentrations. Bioscience 41, 96–104 (1991).
Google Scholar 
7.Leakey, A. D. B. et al. Elevated CO2 effects on plant carbon, nitrogen, and water relations: six important lessons from FACE. J. Exp. Bot. 60, 2859–2876 (2009).CAS 
PubMed 

Google Scholar 
8.Jackson, R. B., Sala, O. E., Field, C. B. & Mooney, H. A. CO2 alters water use, carbon gain, and yield for the dominant species in a natural grassland. Oecologia 98, 257–262 (1994).CAS 
PubMed 

Google Scholar 
9.Morgan, J. A. et al. Water relations in grassland and desert ecosystems exposed to elevated atmospheric CO2. Oecologia 140, 11–25 (2004).CAS 
PubMed 

Google Scholar 
10.Keenan, T. F. et al. Increase in forest water-use efficiency as atmospheric carbon dioxide concentrations rise. Nature 499, 324–327 (2013).CAS 
PubMed 

Google Scholar 
11.Donohue, R. J., Roderick, M. L., McVicar, T. R. & Farquhar, G. D. Impact of CO2 fertilization on maximum foliage cover across the globe’s warm, arid environments. Geophys. Res. Lett. 40, 3031–3035 (2013).CAS 

Google Scholar 
12.Poulter, B. et al. Contribution of semi-arid ecosystems to interannual variability of the global carbon cycle. Nature 509, 600–603 (2014).CAS 
PubMed 

Google Scholar 
13.Ahlström, A. et al. The dominant role of semi-arid ecosystems in the trend and variability of the land CO2 sink. Science 348, 895–899 (2015).PubMed 

Google Scholar 
14.Karnosky, D. F. et al. Tropospheric O3 moderates responses of temperate hardwood forests to elevated CO2: a synthesis of molecular to ecosystem results from the Aspen FACE project. Funct. Ecol. 17, 289–304 (2003).
Google Scholar 
15.Norby, R. J. & Zak, D. R. Ecological lessons from free-air CO2 enrichment (FACE) experiments. Annu. Rev. Ecol. Syst. 42, 181–203 (2011).
Google Scholar 
16.Nowak, R. S., Ellsworth, D. S. & Smith, S. D. Functional responses of plants to elevated atmospheric CO2— do photosynthetic and productivity data from FACE experiments support early predictions? N. Phytol. 162, 253–280 (2004).
Google Scholar 
17.Ainsworth, E. A. & Long, S. P. What have we learned from fifteen years of free air carbon dioxide enrichment (FACE)? A meta-analytic review of the responses of photosynthesis, canopy properties and plant production to rising CO2. N. Phytol. 165, 351–372 (2004).
Google Scholar 
18.Lee, T. D., Tjoelker, M. G., Ellsworth, D. S. & Reich, P. B. Leaf gas exchange responses of 13 prairie grassland species to elevated CO2 and increased nitrogen supply. N. Phytol. 150, 405–418 (2001).CAS 

Google Scholar 
19.Warren, J. M. et al. Ecohydrological impact of reduced stomatal conductance in forests exposed to elevated CO2. Ecohydrology 4, 196–210 (2011).
Google Scholar 
20.Morgan, J. A. et al. CO2 enhances productivity, alters species composition, and reduces digestibility of shortgrass steppe vegetation. Ecol. Appl. 14, 208–219 (2004).
Google Scholar 
21.Dukes, J. S. et al. Responses of grassland production to single and multiple global environmental changes. PLoS Biol. 3, 1829–1839 (2005).CAS 

Google Scholar 
22.Hovenden, M. J., Newton, P. C. D. & Wills, K. E. Seasonal not annual rainfall determines grassland biomass response to carbon dioxide. Nature 511, 583–586 (2014).CAS 
PubMed 

Google Scholar 
23.Reich, P. B., Hobbie, S. E. & Lee, T. D. Plant growth enhancement by elevated CO2 eliminated by joint water and nitrogen limitation. Nat. Geosci. 7, 920–924 (2014).CAS 

Google Scholar 
24.Hebeisen, T. et al. Growth response of Trifolium repens L. and Lolium perenne L. as monocultures and bi-species mixture to free air CO2 enrichment and management. Glob. Change Biol. 3, 149–160 (1997).
Google Scholar 
25.Prentice, I. C., Dong, N., Gleason, S. M., Maire, V. & Wright, I. J. Balancing the cost of carbon gain and water transport: testing a new theoretical framework for plant functional ecology. Ecol. Lett. 17, 82–91 (2014).PubMed 

Google Scholar 
26.Ellsworth, D. S. et al. Elevated CO2 does not increase eucalypt forest productivity on a low-phosphorus soil. Nat. Clim. Change 7, 279–282 (2017).CAS 

Google Scholar 
27.Ponce Campos, G. E. et al. Ecosystem resilience despite large-scale altered hydroclimatic conditions. Nature 494, 350–352 (2014).
Google Scholar 
28.Oren, R., Ewers, B. E., Todd, P., Phillips, N. & Katul, G. Water balance delineates the soil layer in which moisture affects canopy conductance. Ecol. Appl. 8, 990–1002 (1998).
Google Scholar 
29.Stanton, N. L. The underground in grasslands. Annu. Rev. Ecol. Syst. 19, 573–589 (1988).
Google Scholar 
30.Owensby, C. E., Ham, J. M., Knapp, A. K. & Auen, L. M. Biomass production and species composition change in a tallgrass prairie ecosystem after long-term exposure to elevated atmospheric CO2. Glob. Change Biol. 5, 497–506 (1999).
Google Scholar 
31.McCarthy, H. R. et al. Temporal dynamics and spatial variability in the enhancement of canopy leaf area under elevated atmospheric CO2. Glob. Change Biol. 13, 2479–2497 (2007).
Google Scholar 
32.McCathy, H. R., Oren, R., Finzi, A. C. & Jonsen, K. H. Canopy leaf area constrains CO2-induced enhancement of productivity and partitioning among aboveground carbon pools. Proc. Natl Acad. Sci. USA 103, 19356–19361 (2006).
Google Scholar 
33.Tor-ngern, P. et al. Increases in atmospheric CO2 have little influence on transpiration of a temperate forest canopy. N. Phytol. 205, 518–525 (2015).CAS 

Google Scholar 
34.Naumburg, E. et al. Photosynthetic responses of Mojave Desert shrubs to free air CO2 enrichment are greatest during wet years. Glob. Change Biol. 9, 276–285 (2003).
Google Scholar 
35.Housman, D. C. et al. Increases in desert shrub productivity under elevated carbon dioxide vary with water availability. Ecosystems 9, 374–385 (2006).
Google Scholar 
36.Warren, J. M., Norby, R. J. & Wullschleger, S. D. Elevated CO2 enhances leaf senescence during extreme drought in a temperate forest. Tree Physiol. 31, 117–130 (2011).PubMed 

Google Scholar 
37.Ellsworth, D. S. et al. Elevated CO2 affects photosynthetic responses in canopy pine and subcanopy deciduous trees over 10 years: a synthesis from Duke Face. Glob. Change Biol. 18, 223–242 (2012).
Google Scholar 
38.Mueller, K. E. et al. Impacts of warming and elevated CO2 on a semi-arid grassland are non-additive, shift with precipitation, and reverse over time. Ecol. Lett. 19, 956–966 (2016).CAS 
PubMed 

Google Scholar 
39.Morgan, J. A., Milchunas, D. G., LeCain, D. R., West, M. & Mosier, A. R. Carbon dioxide enrichment alters plant community structure and accelerates shrub growth in the shortgrass steppe. Proc. Natl Acad. Sci. USA 104, 14724–14729 (2007).CAS 
PubMed 
PubMed Central 

Google Scholar 
40.Farquhar, G. D. et al. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149, 78–90 (1980).CAS 
PubMed 

Google Scholar 
41.De Graaff, M. A., Van Groenigen, K. J., Six, J., Hungate, B. & Van Kessel, C. Interactions between plant growth and soil nutrient cycling under elevated CO2: a meta-analysis. Glob. Change Biol. 12, 2077–2091 (2006).
Google Scholar 
42.Jiang, M. et al. The fate of carbon in a mature forest under carbon dioxide enrichment. Nature 580, 227–231 (2020).CAS 
PubMed 

Google Scholar 
43.Bader, M. K. F. et al. Central European hardwood trees in a high-CO2 future: synthesis of an 8-year forest canopy CO2 enrichment project. J. Ecol. 101, 1509–1519 (2013).CAS 

Google Scholar 
44.Klein, T. et al. Growth and carbon relations of mature Picea abies trees under 5 years of free-air CO2 enrichment. J. Ecol. 104, 1720–1733 (2016).CAS 

Google Scholar 
45.McCarthy, M. C. & Enquist, B. J. Consistency between an allometric approach and optimal partitioning theory in global patterns of plant biomass allocation. Funct. Ecol. 21, 713–720 (2007).
Google Scholar 
46.Palmroth, S. et al. Aboveground sink strength in forests controls the allocation of carbon below ground and its CO2-induced enhancement. Proc. Natl Acad. Sci. USA 103, 19362–19367 (2006).CAS 
PubMed 
PubMed Central 

Google Scholar 
47.Wolf, A., Field, C. B. & Berry, J. A. Allometric growth and allocation in forests: a perspective from FLUXNET. Ecol. Appl. 21, 1546–1556 (2011).PubMed 

Google Scholar 
48.Hovenden, M. J. et al. Globally consistent influences of seasonal precipitation limit grassland biomass response to elevated CO2. Nat. Plants 5, 167–173 (2019).CAS 
PubMed 

Google Scholar 
49.Graven, H. D. et al. Enhanced seasonal exchange of CO2 by northern ecosystems since 1960. Science 341, 1085–1089 (2013).CAS 
PubMed 

Google Scholar 
50.Phillips, O. L. et al. Increasing dominance of large lianas in Amazonian forests. Nature 418, 770–774 (2002).CAS 
PubMed 

Google Scholar 
51.Zotz, G., Cueni, N. & Körner, C. In situ growth stimulation of a temperate zone liana (Hedera helix) in elevated CO2. Funct. Ecol. 20, 763–769 (2006).
Google Scholar 
52.Smith, S. D. et al. Elevated CO2 increases productivity and invasive species success in an arid ecosystems. Nature 408, 79–81 (2000).CAS 
PubMed 

Google Scholar 
53.Saintilan, N. & Rogers, K. Woody plant encroachment of grasslands: a comparison of terrestrial and wetland settings. N. Phytol. 205, 1062–1070 (2015).
Google Scholar 
54.Pan, Y. et al. A large and persistent carbon sink in the world’s forests. Science 333, 988–003 (2011).CAS 
PubMed 

Google Scholar 
55.Hubau, W. et al. Asynchronous carbon sink saturation in African and Amazonian tropical forests. Nature 579, 80–87 (2020).CAS 
PubMed 

Google Scholar 
56.Flato G. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 741–866 (Cambridge Univ. Press, 2013).57.

58.
https://facedata.ornl.gov/ornl/
59.Hymus, G. J. et al. Effects of elevated atmospheric CO2 on net ecosystem CO2 exchange of a scrub-oak ecosystem. Glob. Change Biol. 9, 1802–1812 (2003).
Google Scholar 
60.Riley, R. D., Lambert, P. C. & Abo-Zaid, G. Meta-analysis of individual participant data: rationale, conduct, and reporting. Br. Med. J. 340, c221 (2010).
Google Scholar 
61.Millar, R. B. & Anderson, M. J. Remedies for pseudo-replication. Fish. Res. 70, 397–407 (2004).
Google Scholar 
62.Cashman, K. D. et al. Improved dietary guidelines for vitamin D: application of individual participant data (IPD)-level meta-regression analyses. Nutrients 9, 469 (2017).PubMed Central 

Google Scholar  More

1.Arrhenius, O. Species and area. J. Ecol. 9, 95–99 (1921).
Google Scholar 
2.MacArthur, R. H. & Wilson, E. O. The Theory of Island Biogeography (Princeton Univ. Press, 1967).3.Rosenzweig, M. L. Species Diversity in Space and Time (Cambridge Univ. Press, 1995).4.Smith, A. B., Sandel, B., Kraft, N. J. B. & Carey, S. Characterizing scale‐dependent community assembly using the functional‐diversity–area relationship. Ecology 94, 2392–2402 (2013).PubMed 

Google Scholar 
5.Mazel, F. et al. Multifaceted diversity–area relationships reveal global hotspots of mammalian species, trait and lineage diversity. Glob. Ecol. Biogeogr. 23, 836–847 (2014).PubMed 
PubMed Central 

Google Scholar 
6.Dias, R. A. et al. Species richness and patterns of overdispersion, clustering and randomness shape phylogenetic and functional diversity–area relationships in habitat islands. J. Biogeogr. 47, 1638–1648 (2020).
Google Scholar 
7.Pereira, H. M. et al. Scenarios for global biodiversity in the 21st century. Science 330, 1496–1501 (2010).CAS 
PubMed 

Google Scholar 
8.Pimm, S. L., Russell, G. J., Gittleman, J. L. & Brooks, T. M. The future of biodiversity. Science 269, 347–350 (1995).CAS 
PubMed 

Google Scholar 
9.Simberloff, D. in Tropical Deforestation and Species Extinction (eds Whitmore, T. C. & Sayer, J. A.) 75–89 (Chapman & Hall, 1992).10.Jordano, P. Chasing ecological interactions. PLoS Biol. 14, e1002559 (2016).PubMed 
PubMed Central 

Google Scholar 
11.Montoya, J. M., Woodward, G., Emmerson, M. C. & Solé, R. V. Press perturbations and indirect effects in real food webs. Ecology 90, 2426–2433 (2009).PubMed 

Google Scholar 
12.Lurgi, M., López, B. C., Montoya, J. M. & Lopez, B. C. Novel communities from climate change. Philos. Trans. R. Soc. Lond. B 367, 2913–2922 (2012).
Google Scholar 
13.Tylianakis, J. M., Tscharntke, T. & Lewis, O. T. Habitat modification alters the structure of tropical host–parasitoid food webs. Nature 445, 202–205 (2007).CAS 
PubMed 

Google Scholar 
14.Montoya, J. M., Rodriguez, M. Á. & Hawkins, B. A. Food web complexity and higher-level ecosystem services. Ecol. Lett. 6, 587–593 (2003).
Google Scholar 
15.Reiss, J., Bridle, J. R., Montoya, J. M. & Woodward, G. Emerging horizons in biodiversity and ecosystem functioning research. Trends Ecol. Evol. 24, 505–514 (2009).PubMed 

Google Scholar 
16.Thompson, R. M. et al. Food webs: reconciling the structure and function of biodiversity. Trends Ecol. Evol. 27, 689–697 (2012).PubMed 

Google Scholar 
17.Cohen, J. E. & Newman, C. M. Community area and food-chain length: theoretical predictions. Am. Nat. 138, 1542–1554 (1991).
Google Scholar 
18.Schoener, T. W. Food webs from the small to the large: the Robert H. MacArthur Award lecture. Ecology 70, 1559–1589 (1989).
Google Scholar 
19.Post, D. M., Pace, M. L. & Hairston, N. G. Ecosystem size determines food-chain length in lakes. Nature 405, 1047–1049 (2000).CAS 
PubMed 

Google Scholar 
20.Brose, U., Ostling, A., Harrison, K. & Martinez, N. D. Unified spatial scaling of species and their trophic interactions. Nature 428, 167–171 (2004).CAS 
PubMed 

Google Scholar 
21.Galiana, N. et al. The spatial scaling of species interaction networks. Nat. Ecol. Evol. 2, 782–790 (2018).PubMed 

Google Scholar 
22.Wood, S. A., Russell, R., Hanson, D., Williams, R. J. & Dunne, J. A. Effects of spatial scale of sampling on food web structure. Ecol. Evol. 5, 3769–3782 (2015).PubMed 
PubMed Central 

Google Scholar 
23.Pimm, S. L. et al. Food web patterns and their consequences. Nature 350, 669–674 (1991).
Google Scholar 
24.Martinez, N. D. Constant connectance in community food webs. Am. Nat. 139, 1208–1218 (1992).
Google Scholar 
25.Ings, T. C. et al. Ecological networks–beyond food webs. J. Anim. Ecol. 78, 253–69 (2009).PubMed 

Google Scholar 
26.Montoya, J. M. & Solé, R. V. Topological properties of food webs: from real data to community assembly models. Oikos 102, 614–622 (2003).
Google Scholar 
27.Drakare, S., Lennon, J. J. & Hillebrand, H. The imprint of the geographical, evolutionary and ecological context on species–area relationships. Ecol. Lett. 9, 215–227 (2006).PubMed 

Google Scholar 
28.Preston, F. W. Time and space and the variation of species. Ecology 41, 611–627 (1960).
Google Scholar 
29.Turner, W. R. & Tjørve, E. Scale-dependence in species–area relationships. Ecography 6, 721–730 (2005).
Google Scholar 
30.Bengtsson, J. Confounding variables and independent observations in comparative analyses of food webs. Ecology 75, 1282–1288 (1994).
Google Scholar 
31.Vermaat, J. E., Dunne, J. A. & Gilbert, A. J. Major dimensions in food-web structure properties. Ecology 90, 278–282 (2009).PubMed 

Google Scholar 
32.Dunne, J. A. et al. Parasites affect food web structure primarily through increased diversity and complexity. PLoS Biol. 11, e1001579 (2013).CAS 
PubMed 
PubMed Central 

Google Scholar 
33.Poisot, T. & Gravel, D. When is an ecological network complex? Connectance drives degree distribution and emerging network properties. PeerJ 2, e251 (2014).PubMed 
PubMed Central 

Google Scholar 
34.Cohen, J. E. & Briand, Fredeiri Trophic links of community food webs. Proc. Natl Acad. Sci. USA 81, 4105–4109 (1984).CAS 
PubMed 
PubMed Central 

Google Scholar 
35.Roslin, T., Várkonyi, G., Koponen, M., Vikberg, V. & Nieminen, M. Species–area relationships across four trophic levels—decreasing island size truncates food chains. Ecography 37, 443–453 (2014).
Google Scholar 
36.Holt, R. D., Lawton, J. H., Polis, G. A. & Martinez, N. D. Trophic rank and the species–area relationship. Ecology 80, 1495–1504 (1999).
Google Scholar 
37.Dunne, J. A., Williams, R. J. & Martinez, N. D. Food-web structure and network theory: the role of connectance and size. Proc. Natl Acad. Sci. USA 99, 12917–12922 (2002).CAS 
PubMed 
PubMed Central 

Google Scholar 
38.Montoya, J. M., Pimm, S. L. & Solé, R. V. Ecological networks and their fragility. Nature 442, 259–264 (2006).CAS 
PubMed 

Google Scholar 
39.James, A., Pitchford, J. W. & Plank, M. J. Disentangling nestedness from models of ecological complexity. Nature 487, 227–230 (2012).CAS 
PubMed 

Google Scholar 
40.Valverde, S. et al. The architecture of mutualistic networks as an evolutionary spandrel. Nat. Ecol. Evol. 2, 94–99 (2018).PubMed 

Google Scholar 
41.Valiente-Banuet, A. et al. Beyond species loss: the extinction of ecological interactions in a changing world. Funct. Ecol. 29, 299–307 (2015).
Google Scholar 
42.Janzen, D. H. The deflowering of central America. Nat. Hist. 83, 49–53 (1974).43.Mendoza, M. & Araújo, M. B. Climate shapes mammal community trophic structures and humans simplify them. Nat. Commun. 10, 5197 (2019).PubMed 
PubMed Central 

Google Scholar 
44.Emer, C. et al. Seed dispersal networks in tropical forest fragments: area effects, remnant species, and interaction diversity. Biotropica 52, 81–89 (2020).
Google Scholar 
45.McWilliams, C., Lurgi, M., Montoya, J. M., Sauve, A. & Montoya, D. The stability of multitrophic communities under habitat loss. Nat. Commun. 10, 2322 (2019).PubMed 
PubMed Central 

Google Scholar 
46.McCann, K. S. The diversity–stability debate. Nature 405, 228–233 (2000).CAS 
PubMed 

Google Scholar 
47.Fig, T., Mccann, K., Hastings, A. & Huxel, G. R. Weak trophic interactions and the balance of nature. Nature 395, 794–798 (1998).
Google Scholar 
48.Pimm, S. L. & Lawton, J. H. Are food webs divided into compartments? J. Anim. Ecol. 49, 879–898 (1980).
Google Scholar 
49.Macfadyen, S., Gibson, R. H., Symondson, W. O. C. & Memmott, J. Landscape structure influences modularity patterns in farm food webs: consequences for pest control. Ecol. Appl. 21, 516–524 (2011).PubMed 
PubMed Central 

Google Scholar 
50.Reverté, S. et al. Spatial variability in a plant–pollinator community across a continuous habitat: high heterogeneity in the face of apparent uniformity. Ecography 42, 1558–1568 (2019).
Google Scholar 
51.Torné‐Noguera, A., Arnan, X., Rodrigo, A. & Bosch, J. Spatial variability of hosts, parasitoids and their interactions across a homogeneous landscape. Ecol. Evol. 10, 3696–3705 (2020).PubMed 
PubMed Central 

Google Scholar 
52.Hernández‐Castellano, C. et al. A new native plant in the neighborhood: effects on plant–pollinator networks, pollination, and plant reproductive success. Ecology 101, e03046 (2020).PubMed 

Google Scholar 
53.Osorio, S., Arnan, X., Bassols, E., Vicens, N. & Bosch, J. Local and landscape effects in a host–parasitoid interaction network along a forest–cropland gradient. Ecol. Appl. 25, 1869–1879 (2015).PubMed 

Google Scholar 
54.Kaartinen, R. & Roslin, T. Shrinking by numbers: landscape context affects the species composition but not the quantitative structure of local food webs. J. Anim. Ecol. 80, 622–631 (2011).PubMed 

Google Scholar 
55.Vázquez, D. P. & Simberloff, D. Changes in interaction biodiversity induced by an introduced ungulate. Ecol. Lett. 6, 1077–1083 (2003).
Google Scholar 
56.Mulder, C., Den Hollander, H. A. & Hendriks, A. J. Aboveground herbivory shapes the biomass distribution and flux of soil invertebrates. PLoS ONE 3, e3573 (2008).PubMed 
PubMed Central 

Google Scholar 
57.Montoya, D., Yallop, M. L. & Memmott, J. Functional group diversity increases with modularity in complex food webs. Nat. Commun. 6, 7379 (2015).CAS 
PubMed 

Google Scholar 
58.Grass, I., Jauker, B., Steffan-Dewenter, I., Tscharntke, T. & Jauker, F. Past and potential future effects of habitat fragmentation on structure and stability of plant–pollinator and host–parasitoid networks. Nat. Ecol. Evol. https://doi.org/10.1038/s41559-018-0631-2 (2018).59.Cagnolo, L., Salvo, A. & Valladares, G. Network topology: patterns and mechanisms in plant–herbivore and host–parasitoid food webs. J. Anim. Ecol. 80, 342–351 (2011).PubMed 

Google Scholar 
60.Maiorano, L., Montemaggiori, A., Ficetola, G. F., O’Connor, L. & Thuiller, W. TETRA‐EU 1.0: a species‐level trophic metaweb of European tetrapods. Glob. Ecol. Biogeogr. 29, 1452–1457 (2020).61.Kopelke, J. et al. Food‐web structure of willow‐galling sawflies and their natural enemies across Europe. Ecology 98, 1730 (2017).PubMed 

Google Scholar 
62.Sole, R. V. & Montoya, M. Complexity and fragility in ecological networks. Proc. R. Soc. Lond. B 268, 2039–2045 (2001).CAS 

Google Scholar 
63.Broido, A. D. & Clauset, A. Scale-free networks are rare. Nat. Commun. 10, 1017 (2019).PubMed 
PubMed Central 

Google Scholar 
64.Guilhaumon, F., Mouillot, D. & Gimenez, O. mmSAR: an R-package for multimodel species–area relationship inference. Ecography 33, 420–424 (2010).
Google Scholar 
65.Matthews, T. J., Triantis, K. A., Whittaker, R. J. & Guilhaumon, F. sars: an R package for fitting, evaluating and comparing species–area relationship models. Ecography https://doi.org/10.1111/ecog.04271 (2019).66.Galiana, N. Ecological network complexity scales with area. Dryad https://doi.org/10.5061/dryad.zcrjdfndg (2021). More

Hydrothermal vent rock and sediment sample collectionRock no. NA091-R045 (source of Ca. H. endolithica PR6, Ca. H. repetitus FW102 and Thorarchaeote FW25) and rock no. NA091-R008 (source of Heimdall group Gerdarchaeote AC18) were retrieved from the Auka hydrothermal vent site situated on the margin of the southern Pescadero Basin of the Gulf of California using remotely operated vehicle Hercules during research expedition NA091 on E/V Nautilus on 2 November 2017. Local venting fluids have a measured temperature approaching 300 °C, contain hydrocarbons and hydrogen and are precipitating minerals, such as calcite and barite15. R045 was collected during dive H1658 at coordinates 23.956987786° N, 108.86227922° W at a water depth of 3,674 m, near shimmering water, a sign of locally focused hydrothermal fluid discharge. R008 was collected during dive H1657 at coordinates 23° 57′ N, 108° 52′ W at a water depth of 3,651 m. After shipboard recovery, rock samples were placed in Mylar bags prefilled with 0.2 µm filtered bottom seawater collected during the same dive, flushed with N2 gas for 10 min, sealed and stored at 4 °C until preparation for incubations in the laboratory.Sediment sample no. FK181031-S0193-PC3 (source of Ca. H. aukensis) was collected during the research expedition FK181031 on R/V Falkor to the southern Pescadero Basin on 14 November 2018. The sample was collected during dive S193 at the Auka hydrothermal vent site (23.954822° N, 108.863009° W, water depth of 3,657 m), near the site where rocks nos. NA091-R045 and NA091-R008 were collected in 2017. The sediment push core was extruded upwards and sectioned into discrete 3 cm depth horizons on board immediately after recovery, transferred into sterile Whirl-Pak bags and sealed in a larger Mylar bag, flushed with argon gas, heat-sealed and stored at 4 °C until use in the laboratory.Sample collection permits for the expedition were granted by the Dirección General de Ordenamiento Pesquero y Acuícola, Comisión Nacional de Acuacultura y Pesca (Permiso de Pesca de Fomento no. PPFE/DGOPA-200/18) and the Dirección General de Geografía y Medio Ambiente, Instituto Nacional de Estadística y Geografía (authorization no. EG0122018), with the associated diplomatic note no. 18-2083 (CTC/07345/18) from the Secretaría de Relaciones Exteriores-Agencia Mexicana de Cooperación Internacional para el Desarrollo/Dirección General de Cooperación Técnica y Científica.Artificial seawater medium recipeArtificial seawater was prepared as described in Scheller et al.47 with minor modifications. Briefly, 1 l of artificial seawater (ASW) medium contained 46.6 mM MgCl2, 9.2 mM CaCl2, 485 mM NaCl, 7 mM KCl, 20 mM Na2SO4, 1 mM K2HPO4, 2 mM NH4Cl, 1 ml of 1,000× trace element solution, 1 ml of 1,000× vitamin solution and 0.5 mg of resazurin and was buffered by 25 mM HEPES buffer adjusted to pH 7.5. One litre of 1,000× trace element solution contained 50 mM nitrilotriacetic acid, 5 mM FeCl3, 2.5 mM MnCl2, 1.3 mM CoCl2, 1.5 mM ZnCl2, 0.32 mM H3BO3, 0.38 mM NiCl2, 0.03 mM Na2SeO3, 0.01 mM CuCl2, 0.21 mM Na2MoO4 and 0.02 mM Na2WO4. One litre of 1,000× vitamin solution contained 82 μM d-biotin, 45 μM folic acid, 490 μM pyridoxine, 150 μM thiamine, 410 μM nicotinic acid, 210 μM pantothenic acid, 310 μM para-aminobenzoic acid, 240 μM lipoic acid, 14 μM choline chloride and 7.4 μM vitamin B12.Enrichment cultivationRock no. NA091-R045 was anaerobically fragmented; then, approximately 5 g wet weight was crushed using a sterile agate mortar and pestle on 8 November 2018 and immediately immersed in anaerobic ASW medium in 25–125 ml of butyl rubber-stoppered serum bottles supplemented with different carbon/energy sources, including lactate, H2/CO2, hexane and decane and incubated in the dark at 40 °C (Extended Data Fig. 1a). The headspace for all cultures was flushed and overpressurized with N2 gas (2 atm). For the H2-containing cultures, the N2 gas headspace was replaced with H2/CO2 at an 80:20 mixture by flushing for 1 min and subsequent equilibration at 2 atm. After 33 d of incubation, the lactate-fed first-generation culture produced 5 mM sulphide, indicating active sulphate reduction. This enrichment was mixed by gentle shaking and diluted 1:100 vol/vol into fresh anaerobic ASW medium containing the same suite of carbon/energy sources as described above (Extended Data Fig. 1b). A transfer using the liquid fraction-lacking rock particles from the primary lactate enrichment was also included to enrich for members of the planktonic community alone with lactate as the carbon and energy source. This enrichment was later found to be devoid of the AAG (Heimdall) phylotype. Third- and fourth-generation cultures were set up in the following months through 1:100 dilution (Extended Data Fig. 1b). Further details of microbial community development in these enrichments are provided in Supplementary Note 1 and Supplementary Tables 1–3.R008 was prepared as above except using 2 atm of methane in the headspace as the sole carbon source and electron donor. The culture was passaged twice using a 1:100 dilution under the same culturing conditions; the cell fraction was collected by centrifugation after a total of 22 months for metagenomic sequencing (described below).For sediment enrichment cultivation, the top 3 cm section of the sediment core was mixed with anaerobic ASW at a 1:4 vol/vol ratio; a total of 60 ml volume each was dispensed into seven 125 ml glass serum bottles sealed with butyl rubber stoppers. The headspace was replaced by ethane (2 atm) in 2 bottles (Supplementary Table 5), while the headspace in 1 bottle was replaced by 100% N2 gas (2 atm). The cultures were incubated at 37 °C in the dark. Further details on microbial community development are provided in Supplementary Note 1 and Supplementary Table 4.Mineralogical analysesThe mineralogical composition of rocks NA091-R045 and R008 was characterized on a PANalytical X’Pert Pro X-Ray diffractometer. A dried rock aliquot was finely powdered using a clean agate mortar and pestle and scanned from 3 to 75° (2θ angle) at a 0.0167° step size. Mineral identification was performed with the X’Pert HighScore software v4.1 using the search and march algorithm.DNA extractionCombined cells with rock or sediment substrate were pelleted through centrifugation at 13,000 r.p.m. for 3 min. For amplicon sequencing, unless specified in Supplementary Table 6, DNA was extracted using the Qiagen DNeasy PowerSoil kit (catalogue no. 47014) according to the manufacturer’s instructions as described previously48 with a minor modification, where mechanical shearing was carried out using the MP Biomedicals FastPrep-24 system (catalogue no. 116004500) at level 5.5 for 45 s. For genomic sequencing, incubated rock and sediment cultures were extracted using multiple approaches, including the Qiagen DNeasy PowerSoil kit, ZymoBIOMICS 96 MagBead DNA Kit (catalogue no. D4302; Zymo Research Corporation), Quick-DNA 96 Kit (catalogue no. D3010; Zymo Research Corporation), ZymoBIOMICS DNA Microprep Kit (catalogue no. D4301; Zymo Research Corporation) and a standard phenol/chloroform-based protocol. The list of samples and their extraction methods are provided in Supplementary Table 6.16S rRNA gene amplicon sequencingFor amplicon (iTAG) sequencing of 16S rRNA genes, extracted DNA was amplified using primer pair 515f/806r GTGCCAGCMGCCGCGGTAA/ GGACTACHVGGGTWTCTAAT, barcoded and sequenced at Laragen using the Illumina MiSeq platform and analysed using Qiime v.1.8.0 (ref. 49) as described previously48. Taxonomic assignment was based on the SILVA 138 database (https://www.arb-silva.de)50.Full-length 16S archaeal rRNA gene sequences were amplified using the archaeal primer pair SSU1Arf/SSU1492Rngs TCCGGTTGATCCYGCBRG/ CGGNTACCTTGTKACGAC as described by Bahram et al.51, multiplexed as instructed by PacBio and sequenced using the PacBio Sequel II at the Brigham Young University DNA Sequencing Center and then analysed using the DADA2 package v1.9.1 in R v3.6.0 as described in Callahan et al.52 using the SILVA 138 database for taxonomic classification. Note that in the SILVA 138 database, all Asgard archaea clades are classified under Asgardarchaeota.Metagenomic sequencingA total of 11 metagenomic sequencing runs were performed using the Illumina and Oxford Nanopore platforms, with details listed in Supplementary Table 6. For Illumina short-read sequencing, libraries were constructed using the NEBNext Ultra and Nextera Flex Library kits as specified in the Supplementary Table 6. Sequencing was carried out using a HiSeq 2500 system (single-end, 100 bp) at the Caltech Genetics and Genomics Laboratory and HiSeq 4000 system at Novogene (paired-end, 150 bp). Only paired-end data were used for assembly, while all data were used for error correction. Due to the low DNA quantity obtained from the sediment incubation that yielded Ca. H. aukensis, we used multiple displacement amplification with the QIAGEN REPLI g Midi Kit before library preparation for Nanopore sequencing. Oxford Nanopore sequencing libraries were constructed using the PCR Barcoding Kit (catalogue no. SQK-PBK004) and were sequenced on MinION flow cells FLO-MIN106. Base calling was performed with the ONT Guppy software v.3.4.5.Genome assembly, error correction and read coverage mappingTwo different approaches were used to assemble contiguous genomes from metagenomes. For species of interest, if Nanopore sequencing yielded high read coverage and read lengths N50  > 2 kb, we obtained more contiguous genomes through de novo assembly purely based on Nanopore reads. If Nanopore sequencing did not yield a high number of reads or exhibited low read lengths, we obtained more contiguous genomes through de novo assembly first based on Illumina reads and then joined using Nanopore reads.For Ca. H. endolithica, Nanopore sequencing data were assembled de novo using Canu17 v.2.1, which yielded a 30 Mbp assembly, including a 3.4 Mbp contig. The approximate 40 kilobase (kb) regions at two ends of an approximate 3.4 Mbp contig were repetitive. This repeated region was deleted at one end and the two ends were joined to result in a circular genome. The resulting genome was mapped using BamM (http://ecogenomics.github.io/BamM/, based on Burrows–Wheeler Aligner53 mapping) with 150 bp Illumina paired-end reads (88× coverage on average) and 100 bp single-end reads (20× coverage). Mapped reads were then used for error correction through pilon54 v.1.22. To account for the reduced mapping at the edges (approximate 50 bp region), the two ends of the genomic sequence were joined, read-mapped and error-corrected again using the same methods. After the genome was annotated, it was rotated such that the genomic sequence ended with tRNA (GlyCCC), which was the integration site of the putative provirus HeimV1. All sequencing reads derived from incubations of the same rock were mapped onto the final genome using BamM, which was then used for coverage calculation through bedtools (https://bedtools.readthedocs.io/en/latest/).For Ca. H. aukensis, Illumina PE150 bp sequencing data were assembled using SPAdes18 v.3.14.1 with the ‘-meta’ option and k-mers 21,33,55,77,99. The assembly was then scaffolded using Nanopore reads through two iterations of LRScaf55 v.1.1.10. The Ca. H. aukensis genome was joined after trimming the identical sequences at the two ends. The end-joining region was verified through PCR amplification and Sanger sequencing using the primer pair CGCTTTCTTCAAACAATATTTCTGGTG/CTTACTTTCTCTCGGTCCATTTTTCAC. Finally, a 1 kbp stretch of unresolved genomic sequence at an approximate 2.9 Mbp position was resequenced through PCR amplification and Sanger sequencing using the primers GAGTTTTTTCAATCTTATAATGCCAAACTAAAAAATAG (forward), CAGTCAGATTTGACACAATTTTGGTC (reverse) and GCTGGACTCAACCTATAACTAATAGT (reverse). The final assembly was read-mapped, error-corrected through pilon v.1.24 using 346× coverage. It was rotated as described above to place the tRNA gene GlyCCC at the end.The metagenome containing the Lokiarchaeote Ca. H. repetitus FW102 was assembled using Canu v.2.1, as described for the Ca. H. endolithica genome, and then binned using metabat2 v.2.15 (ref. 56) with default parameters. The bin was then used to recruit long reads using minimap2 v.2.17 and reassembled and binned again. We then used LRScaf to scaffold the contigs and used ten iterations of pilon v.1.24 to achieve error correction and resolve ambiguous bases.The Thorarcheote FW25 MAG was assembled using the hybrid assembly of Illumina reads and Nanopore reads using SPAdes v.3.14.1 with k-mers 21,33,55,77,99, and then binned using metabat2 v.2.15 with default parameters. The MAG bin was then used to recruit reads through MIRAbait in the MIRA v.4 package (http://mira-assembler.sourceforge.net/docs/DefinitiveGuideToMIRA.html#chap_intro). These reads were then used for hybrid assembly with Nanopore long reads via SPAdes v.3.14.1 with k-mers 21,33,55,77,99. It was then binned again using metabat2 v.2.15 with default parameters to yield the final Thorarcheote FW25 MAG.The metagenome containing Gerdarchaeote AC18 was assembled from Illumina reads using SPAdes v.3.14.1 with k-mers 21,33,55,77,99 and then binned using metabat2 v.2.15 with default parameters. The MAG bin was then used to recruit reads through MIRAbait in the MIRA v.4 package and then reassembled and binned using SPAdes and metabat2 to yield the final Gerdarchaeote AC18 bin.Alignment fraction, ANI and AAIANI and alignment fraction values, independently calculated for rRNA, tRNA and coding gene sequences were obtained using ANIcalculator57 2014-127, v.1.0 (https://ani.jgi.doe.gov/html/download.php?). Note that Lokiarchaeote FW102 contains 2 copies of 16S rRNA genes at 99% identity with each other, and Thorarchaeote BC has a partial 16S rRNA gene. The alignment of 16S rRNA was carried out using SINA58 v.1.2.11. The AAI values of translated proteomes were obtained with the enveomics package v1.8.059. The final output is shown in Supplementary Table 7.Genome and mobilome annotationsGene calling was done using a combination of Prodigal v.2.6.3 and Glimmer v.3.0.2 using translation code 11 within the RASTtk60 pipeline, now under the PATRIC package v1.03261. Translated coding sequences were annotated and domain-assigned using eggNOG mapper39 v.2. The tRNA, 16S rRNA and 23S rRNA genes were identified using RNAmmer62 v.1.2 embedded in RASTtk. Thus far, 5S rRNA gene sequences could not be predicted through the existing HMM using various approaches. Long, non-tandem repeats were identified using RASTtk with the default cut-off of 95% identity and 100 bp. Tandem repeat sequences were identified using RASTtk, Prokka v1.14.6 and CRISPRCasTyper 1.1.463. Prokka and CRISPRCasTyper both employ MinCED (https://github.com/ctSkennerton/minced) to identify repeats and detect intragenic tandem repeats, which were manually removed from the CRISPR–Cas analyses. The Cas genes were annotated using CRISRCasTyper.All identified Heimdallarchaeum mobilomes were further analysed using PSI-BLAST 1.10.064, CDD search v3.1965 and PhANNs webserver (version March 2021)37.Genome evaluation and HMM constructionMarker coverage was carried out using a two-step process. First, we used the automated marker analyses via CheckM66 v.1.1.3 with the lineage_wf option and the default HMM E value cut-off, which included the 149 standard archaeal single-copy marker set. Next, each of the missing markers was examined with hmmer67 v.3.3.2 using the hmmsearch option with manual inspection of alignment regions and bitscores. This rescued markers unidentified through the default cut-offs by CheckM as well as divergent variants that most likely functionally replace the genuinely missing marker. The detailed description of markers missed by CheckM can be found in Supplementary Note 2 and the final evaluation of marker presence is displayed in Extended Data Fig. 4a and Supplementary Table 15. Next, we constructed an updated HMM set to replace the CheckM set by (1) updating all HMM to the most recent versions, (2) removing the six commonly missing or duplicated markers shown in Extended Data Fig. 4a from the list and (3) overcoming the pitfall of existing HMMs constructed using only a few sequences acquired from Euryarchaeota and Crenarchaeota. We manually constructed Asgard-specific versions based on the 282 Asgard archaea genomes. The HMMs constructed in this study are PF00832.ASG, PF00861.ASG, PF01194.ASG, PF01287.ASG, PF01667.ASG, PF03874.ASG, PF03876.ASG, PF13656.ASG, TIGR00270.ASG, TIGR00336.ASG, TIGR00442.ASG, TIGR02338.ASG and TIGR03677.ASG. The updated HMM file has been provided as a supplementary data file. The updated HMM was used to evaluate the 282 genomes reported in this study and in the literature3,6,7,8,9,10,11,12,16,23,26,68,69,70,71,72,73,74,75,76,77 through (1) CheckM, which uses Prodigal for gene calling, and (2) the more up to date HMMER3.2.2 on our gene calls described above. The latter generally produced slightly higher completeness and redundancy values (Supplementary Tables 8 and 9). For the expanded set of Asgard archaea genomes used for the phylogenomic analyses shown in Extended Data Fig. 4b, we applied the following filtering criteria: ≤100 contigs, >96% marker completeness and 20% sequence identity, >85% sequence alignment and 30% sequence identity, >90% sequence alignment and More

Environmental isotopic baseline of the Yingpan cemeteryMultiple body tissues of Yingpan Man, including his serial dentine, bone collagen, hair keratin and muscle, were isotopically analyzed. The δ13C measurements show a mix of C3 and C4 dietary inputs with values that range from − 17.3‰ to − 13.7‰, while the δ15N results are remarkably elevated and range from 14.9‰ to 19.9‰. According to the isotopic literature, plant δ15N values above 20‰ are relatively rare in terrestrial environments22,26,27,28. However, the δ15N values of the plants, animals and Yingpan Man are remarkably elevated (up to 23.3‰) compared to isotopic results from other parts of China and Europe (Fig. 3)12. This suggests that the entire ecosystem of this portion of Xinjiang is 15N-enriched. In addition, seeds of Nitraria pamirica having elevated δ15N results (up to 27.9‰) were found in the western region of the Pamir Plateau near the Afghanistan border23. Grains of wheat and barley from Shichengzi (ca. 202 BC–220 AD; ~ 400 km from Yingpan) yielded δ15N values that range from 14.6‰ to 19.8‰ (mean ± SD = 17.2 ± 1.5‰; n = 10) and 13.4‰ to 19.8‰ (mean ± SD = 17.3 ± 1.9‰; n = 12), respectively29. This evidence suggests that the entire Tarim Basin and greater Xinjiang has some of the most elevated terrestrial δ15N values in Eurasia. This is also supported by past isotopic work in China, which demonstrated a correlation between human δ15N values and annual mean precipitation, with individuals from Xinjiang having the highest δ15N values of all regions studied12. The cause of this 15N-enrichment must be at least partially environmental based on past isotopic studies27,30. The extreme aridity of the Yingpan cemetery site, which is located in the Taklamakan Desert, the driest region of China and characterized by little rainfall of 0 to 100 mm/yr and high evapotranspiration rates  > 2500 mm/year (Fig. 1)31, results in a large plant 15N-enrichment by intensive evaporation of 15N-depleted ammonia (NH4+) from the soil. These elevated δ15N results are then translated up the food chain to the domestic animals and humans. This is compelling evidence that Yingpan man was born and raised in a 15N-enriched environment that was extremely arid, and that he consumed wheat/barley, broomcorn millet and grape that were grown locally.Breastfeeding, weaning and childhood dietary patterns of Yingpan ManIsotopic analysis of dentine serial sections in human teeth permit an investigation of individual dietary patterns over the time period when the teeth were developing24. For Yingpan Man, his first molar (M1), represents the period of his life from birth to approximately 10 years old32. The first five 1 mm dentine sections from the M1 crown, corresponding to the first ~ 2.2 years of his life, show a steady decrease in δ15N of 2.5‰ (Fig. 4). This is evidence that Yingpan Man was fully weaned off breastmilk at or before the age of ~ 2.2 years old (Fig. 4)33,34, and is similar to findings of the Zhou Dynasty (1122–771 BC) sites of Boyangcheng35, Xiyasi and Changxinyuan36.Archaeological evidence for infant feeding practices is rarely preserved in Xinjiang. However, two extraordinary feeding vessels (one made of goat breast skin, the other made from an ox horn) were previously discovered with the burial of a 10-month old infant mummy in the southern Tarim Basin4,7. This infant dates to ~ 1000 BC and was found at the Zhagunluke site which is ~ 460 km from the Yingpan cemetery (Fig. 1). In addition, historical documents also provide supporting evidence that children were fed with animal milk in ancient Xinjiang. For example, the Kharosthī scripts (written in a version of the north Indian Prakrit language) are a collection of contracts, letters and other documents (e.g. wood tablets, leather, silk, paper, etc.) that detail life, events, trading, taxes and agricultural practices during the third to fifth century AD of the Shanshan Kingdom (~ 250 km from Yingpan, see Fig. 6)37. It is recorded in these documents that a “milk fee” of cattle or camel was paid to the adoptee when children were adopted in ancient Shanshan, and this exchange was not only protected by the law but also needed to be ensured by witnesses37,38. Thus, there may have been a common tradition of feeding infants with milk from domestic animals (e.g. goat, cattle, camel, etc.) during the weaning process in ancient Xinjiang.Figure 6Yingpan Man’s grave goods mirroring the cultural contact across the Eurasian continent (~ 300 AD). (a) Decorative patterns of vase and flowers on the sideboards of Yingpan Man’s coffin. (b) Decorative patterns of nude putties, goats, bulls and pomegranate trees on Yingpan Man’s woolen caftan. (c) Yingpan Man’s white hemp mask with golden diadem (possibly related to the death masks from Tashtyk culture). (d) Woolen trousers with decorative patterns of double quatrefoil florals surrounded by lozenges made up of solid circles and flowers. (e) Miniature funerary summer coat. (f) Miniature funerary winter robe. (g) Embroidered armband. (h) Yellow painted wood coffin with decorative patterns. (i) A broken brocade that was decorated with Chinese characters of “Shou” and “You”. (j) Silk fish. (k) Crowing cockerel pillow. (l) Perfume sachet. (m) A tufted carpet with decorative patterns of a male lion. (Map was generated using GMT 5.2.1. The original pictures of artifacts were previously published14 and provided by Wenying Li. Pictures were modified using Adobe Photoshop CC 2015 V.1.2. The final layout was created in Adobe Illustrator CC 2019 V.23.1.1).Full size imageIn contrast, the δ13C results of the first four dentine sections show little variability, which indicates that Yingpan Man consumed other foods/liquids from an early age and was not exclusively breastfed for a significant amount of time after birth (Fig. 4; Fig. S4)34. Between 4 and 9 mm, there is an increase in the δ13C values of 1.7‰, which corresponds to a late weaning and childhood diet from approximately 1.8 to 4.2 years old, where more millet was consumed (Fig. 4; Fig. S4). This millet possibly took the form of a gruel as there is little evidence that Yingpan Man consumed increased amounts of animal protein during this period. Similar isotopic patterns in dentine representing individuals that consumed increasing amounts of millet during weaning and early childhood were found at the Late Neolithic (4500 BP) Gaoshan site in Sichuan Province39. This suggests that millet may have had a long history of being used as a weaning or childhood food in China. From 9 to 14 mm, the dentine serial sections show a decline in δ13C values of 1.4‰ which indicates a period of increasing C3 foods in the diet from approximately 4.2 to 6.6 years old (Fig. 4; Fig. S4). Then from 14 to 21 mm the δ13C values increase again by 1.3‰, evidence of a change back to millet consumption from approximately 6.6 to 10 years old. Thus, over the first 10 years of life, Yingpan Man had frequent dietary shifts between C3-based and C4-based foods (Fig. 4; Fig. S4).Seasonal diet of Yingpan ManIn agreement with his dentine serial sections, the δ13C results of Yingpan Man’s hair display fluctuations between C3-based (e.g. wheat, barley) and C4-based (millet) foods (Fig. 5a). These hair δ13C results appear to follow a periodic trend, and suggest that his diet changed during different seasons of the year. In contrast, apart from the last 6–7 months of life, Yingpan Man’s hair δ15N values show little variation (Fig. 5b). However, a strong correlation was found between the variability of both the hair δ13C and δ15N values (Sperman’s r = − 0.534; sig = 0; n = 46; Fig. S5a), but not between the δ13C and δ34S values (Sperman’s r = 0.100; sig = 0.539; n = 40; Fig. 5; Fig. S5b). The lack of significant changes in the δ15N values is evidence that Yingpan Man’s protein consumption was relatively constant for approximately the last 4 years before death. This constant protein consumption, but variable intake of C3 and C4 plants, could suggest that in addition to directly consuming different amounts of wheat/barley and millet, Yingpan Man may have actually consumed domestic animals (goats, sheep, cattle) that were foddered on these crops at different times of the year. This possibility could explain the periodic variability in the δ13C values as well as the lack of variability in the δ15N values. In addition, the δ34S hair results also show little variation in the serial sections (~ 1.5‰). Yingpan Man’s δ34S results have a terrestrial range between 10.4‰ and 11.9‰40,41,42 and are similar to past δ34S values from the Proto-Shang site of Nancheng in Hebei Province43. While few δ34S studies have been reported for China for comparison, this lack of isotopic variability in sulfur suggests that Yingpan Man was likely not a Silk Road traveler, but stayed close to the local area during the last years of his life42. Future research involving strontium analysis on Yingpan Man’s hair serial sections and teeth will hopefully support or refute these findings44.Regional evidence in support of seasonal dietary changes comes from apatite δ13C and δ18O results of serial sections of tooth enamel of domesticates from the pastoral sites of Dali, Begash and Tasbas in Kazakhstan (~ 750 km from Yingpan)45. Specifically, data from early and middle Bronze Age sheep, goats and cattle displayed periodic patterns in their δ13Capa and δ18Oapa results that reflect the consumption of more millet during winter and more C3 plants during summer months, based on environmental inputs of body water45. A combination of radiocarbon dates and the application of the dietary mixing model (MixSIAR) identified early sheep and goats from this region (e.g. Dali, 2705–2545 cal BC) to be winter foddered with up to 44–50% of millet intake45. During later periods, this reliance on millet fodder during the winter months increased with some goats from Begash having 50–60% millet in their diets. Further, the relative contribution of millet to the diet of sheep and goats from the early phase (2345–2080 cal BC) of Begash reached up to 68–74% of the whole diet during winter months, especially from November to December45. This key study indicates that there is a long history and precedent for seasonal C3 and C4 feeding of domestic animals in Central Asia, and supports the isotopic findings of a seasonal diet in the hair of Yingpan Man.In addition, isotopic analysis of sequential hair samples from mummies recovered from the Oglakhty cemetery in the Minusinsk Basin of southern Siberia, Russia (~ 900 km north of Yingpan) also show seasonal dietary variation with millet and fish consumed during the late summer and autumn46. These mummies of the Tashtyk culture date to the same period as Yingpan Man (third to fourth centuries AD), and interestingly were also buried with white painted gypsum funerary masks that are similar to the one that Yingpan Man was wearing46,47. This unique burial tradition could suggest links such as trade or an association between Yingpan Man and the Tashtyk culture and additional research is necessary to explore this possibility in more detail (Fig. 6).Historical documents such as the Kharosthī scripts provide additional valuable information about seasonal diets and the foods consumed by the inhabitants of ancient Xinjiang37. These texts describe how the people of the Tarim Basin cultivated mainly wheat, millet and barley as their main cereal crops and that grapes were carefully managed for the production of wine37. Autumn (around the 10th month of the year), was mentioned as the time for harvesting crops and trading crops as well as wine and animals, and paying debts37. Thus, autumn would have been the time of the year with the most abundant amount of food resources, especially C3 foods like fruit, vegetables and wine. This is still true today, as the harvesting of agricultural products in the Tarim Basin mainly occurs in the month of October48. In contrast, during the winter months food resources would have been scarce with only non-perishable crops like millets and wheat available to guarantee the food supply “in the harsh winters of Inner Asia”45. Thus, more C4 foods were likely consumed during the winter and spring months while more C3 foods were consumed during the summer and autumn months.If this information is applied to Yingpan Man’s hair δ13C results, it would suggest that the δ13C values decreased during the summer and autumn months (June to October) and likely reach a nadir during the middle of autumn or October. Therefore, Yingpan Man’s hair sections which are 8 to 10 cm, 18 to 25 cm and 36 to 43 cm from his scalp reflect the period of middle autumn (between August to October) while the hair sections which are 4 to 6 cm, 13 to 15 cm and 29 to 33 cm from his scalp represent late winter (December to February). This would suggest that Yingpan Man died ~ 4 months after the last drop in his δ13C hair values or in spring, possibly March or April (Fig. 5). In addition, the clothes in which Yingpan Man was buried, as well as his associated wardrobe, also provide information about the timing of his death14,15. The miniature robe placed on his chest was designed for winter, as it was long, double layered and the interior was lined with sheep’s wool (Fig. 2f). Whereas the miniature coat placed near his wrist was designed for summer as it was shorter and made only of a single layer of silk (Fig. 2p). Yingpan Man’s caftan, in which he was buried, was double layered with the outer layer made of wool and the inner lining made of silk, and this was likely designed either for the spring or autumn (Fig. 2k)14. Thus, Yingpan Man’s burial clothes combined with the isotopic and historical evidence indicate that Yingpan Man died sometime during the spring months14,15.To better illustrate Yingpan Man’s seasonal dietary variation, two hair sections respectively representing the highest (Sample A: − 14.0 ± 0.1‰, 15.2 ± 0.1‰) and lowest δ13C values (Sample B: − 17.3 ± 0.2‰, 15.8 ± 0.1‰) were analyzed by a Bayesian mixing model with the application of FRUITS (Food Reconstruction Using Isotopic Transferred signals)49,50. As displayed in Fig. S6, isotopic data for millet, wheat/barley, grape and sheep/goat from the Yingpan cemetery were incorporated into the mixing model as feasible dietary sources for Yingpan Man in both scenarios (Sample A and Sample B). The isotopic fractionation between human hair and diet is corrected with an offset of 4.0 ± 0.5‰ for δ13C values51,52,53 and 4.5 ± 0.5‰ for δ15N values51,54. The relative contribution of different macronutrients is defined in the mixing model according to published records with 74 ± 4% of the carbon originating from protein and 26 ± 4% originating from carbohydrates and lipids and all of the nitrogen originating from protein55,56. The high hair δ13C value of − 14.0‰ (Sample A) represents a heavy reliance on millet consumption (39–67%; median = 53%) and a low amount of dietary input from wheat/barley (0–51%; median = 12%), grape (1–46%; median = 25%) and sheep/goat (0–30%; median = 4%), which likely reflects Yingpan Man’s diet during the winter and spring months (Fig. S6 and Table S13). In contrast, the low hair δ13C value of − 17.3‰ (Sample B) likely represents a summer/autumn diet with a decline in C4 foods, like millet (8–44%; median = 28%), as well as increased reliance on C3 foods like wheat/barley (1–71%; median = 21%) and sheep/goat (0–81%; median = 9%) (Fig. S6 and Table S13). However, the importance of sheep/goat and wheat/barley is likely under-estimated here given their small sample size and highly elevated δ15N values. Nonetheless, the FRUITS mixing model indicates that the varying consumption of plant foods, especially millet, is clearly responsible for the δ13C shifts of Yingpan Man’s diet.The last months of Yingpan ManThe hair δ13C results provide an estimate for the time of year Yingpan Man likely died. In addition, the hair δ15N and δ34S values can provide evidence for how Yingpan Man may have died. The last ~ 6 cm (closest to the scalp) of Yingpan Man’s hair show a general rise in δ15N by ~ 1‰ (Fig. 5b). This pattern is uncharacteristic compared to the other hair δ15N results that display little variation. This unique 15N-enrichment could represent a period of catabolic wasting due to the recycling of tissue proteins as a result of a prolonged illness25,57,58. Additional support for some sort of disease or period of illness comes from the fact that there is little change in the δ13C values but a slight decrease in the δ34S values during the last ~ 6 cm of Yingpan Man’s hair. Tissue catabolism is known to cause an increase in δ15N but little change in δ13C values in human hair25. Further, δ34S results are known to decrease in the red blood cells and serum (by ~ 1.5‰) of patients suffering from liver cancer59. As the last ~ 6 cm of hair displayed a slight decrease in δ34S by ~ 1‰, with the largest decline during the last month of life, this evidence in conjunction with the δ13C and δ15N values suggests that Yingpan Man did not die suddenly but likely suffered some type of debilitating sickness over the last months of his life before he succumbed. However, as most wasting diseases or illnesses leave no traces on human skeletons, it is difficult to define the specific disease that caused Yingpan Man’s death, and a detailed paleo-pathological study of Yingpan Man is needed in the future.The grave goods buried with Yingpan Man also suggest he may have suffered a compromised health status before death. In particular, a piece of tattered yellow brocade decorated with brown and blue images of vines, animals, birds, flowers, as well as the Chinese characters of “Shou” and “You” was found placed at a prominent position on the right side of Yingpan Man’s head (Fig. 7)14. According to Chinese historical literature sources, “You” means “blessing” or “blessed”. While, “Shou” means “long live” or “healthy” (Fig. 7)60. Similar grave goods with Chinese characters e.g. “Yan Nian Yi Shou Da Yi Zi Sun” (meaning “live longer and benefit the descendants”), “Chang Le Ming Guang Cheng Fu Shou You” (meaning “always be happy, be bright, be lucky and be blessed”), “Yong Chang” (meaning “always be prosperous”), were also frequently unearthed from contemporary and later cemeteries of the Tarim Basin, especially the nearby sites of the Loulan culture (third century BC to 448 AD, renamed as Shanshan in 77 BC, ~ 250 km from Yingpan), as grave goods that carry good wishes for the dead15. However, Yingpan Man’s brocade shows significant traces of wear or “rubbing” (Fig. 7). This is interesting as this brocade was not complete or new but well-worn to the point of being tattered and frayed, yet it was still placed at a very important position in Yingpan Man burial—just beside his head14. This suggests that this brocade may have been an important “lucky” health charm for Yingpan Man that was frequently used either by himself or by those who cared for him before burial. Thus, both isotopic and archaeological evidence suggest Yingpan Man suffered some type of illness during the last ~ 6 months of his life, likely in winter, and that he succumbed to this illness in the following spring.Figure 7Photo and sketch showing details of the embroidered brocade that was found with Yingpan Man burial. (The original picture and sketch were previously published14 and provided by Wenying Li. Pictures were modified using Adobe Photoshop CC 2015 V.1.2. The final layout was created in Adobe Illustrator CC 2019 V.23.1.1).Full size imageWho was Yingpan Man?The social identity and status of Yingpan Man is enigmatic given the various cultural components of his grave goods and since the collection of his funerary objects are unique compared to all of the other burials found in the same cemetery14. This has created much controversy and debate about the social identity of Yingpan Man7,14,15,16. Thus, “Who was Yingpan Man?” and “Why was he buried here, in a normal unmarked grave with such lavish and exotic grave goods?” is an active topic of debate.The physical anthropology of Yingpan Man was investigated but not formally published. According to which, the metric and nonmetric index of traits of his skeletal remains suggest a mix of both European and Mongolian features (Dong Wei, personal communication). However, facial reconstruction conducted by Dong Wei (personal communication) indicates that Yingpan Man’s facial structure is more characteristic of the features from Western Eurasia. This is consistent with the image of the face painted on his death mask and the fact that he wears a golden diadem across his forehead, which is more traditionally associated with Greece4,7. However, Yingpan Man’s white hemp mask is similar in style to the white painted gypsum masks of the Tashtyk culture from the Minusinsk Basin of Russia46. In addition, Yingpan Man and the mummies of the Oglakhty cemetery of Tashtyk date to nearly the same period (third to fourth centuries AD), and the polychrome silk cloth from the Tarim Basin has also been discovered in Oglakhty46. This evidence, while circumstantial, could suggest some form of association or that links with the Tashtyk may have taken place during the lifetime of Yingpan Man, possibly through trade or familial relationships (Fig. 6).Other components of Yingpan Man’s burial provide important clues about his social identity and cultural affiliations in life61. The styles and types of grave goods of Yingpan Man display an unique mix of both Eastern and Western cultures and traditions that were likely common to inhabitants of Silk Road trading towns in Xinjiang during the third to fourth centuries AD (Fig. 6)14,15,16. However, there appears to be a strong eastern component in some of his funerary arrangements. For example, the burial practices associated with Yingpan Man: covering his face, filling his nose, burying his body fully clothed, covering it with a silken burial shroud, as well as using miniature funeral objects as grave goods are in accordance with the suggested burial rites of “Yan” (meaning “covering”), “Zhen” (meaning “filling”), “She Min Mu” (meaning “covering the eyes”), “Qin” (meaning “quilt” or “burial shroud”) mentioned in the Confucian literature of Yili (meaning “Rites”, formed during the Zhou Dynasties (1046 BC to 256 BC))15,62. In addition, the styles and designs of some of his grave goods are indicative of Chinese spiritual beliefs. For instance, the diamond and circle-shaped designs of decorative patterns on the cover and sideboards of Yingpan Man’s coffin are argued by some scholars to be the traditional “Lianbi” pattern (meaning “linked jades”) which symbolizes the jade burial suits (“Jinlü Yuyi”) that were popular in Han Dynasty burials of high status nobles in central and southern China (e.g. Nanyuewang tomb, Mancheng tomb)15. In particular, as jades are believed to be the ideal material for embalming in ancient China63, the “Lianbi” pattern on Yingpan Man’s coffin carries the symbolic meaning of preserving his body forever so that his soul and spirt will reach heaven (Fig. 6; Fig. S1)15.The brocade “health charm” found to the right side of Yingpan Man also shows a clear affiliation with China, as it was decorated with the Chinese characters of “Shou” and “You”. This is important as some historical documents suggest that Kharosthī was the common language in the Tarim Basin at this time37,38, but Yingpan Man was likely more accustomed to Chinese spiritual beliefs according to this brocade (Figs. 6, 7). Moreover, the crowing cockerel pillow is also interesting as it was recorded in the Han Dynasty literature of Lunheng (meaning “On Balance”, compiled by Chong Wang during the Eastern Han Dynasty in 88 AD), that the dead “turns into ghosts” and “hurt the living ones”64, and that a crowing cockerel was believed to be able to expel evil spirts and ghosts65. Thus, a crowing cockerel pillow was frequently used in funerary practices in China since the Han Dynasty66, and it is still a common grave good today in some areas of modern China (e.g. Shandong and Guizhou Provinces)65.The eight decorative pearls attached to the crowing cockerel pillow are also important status markers regarding the identity of Yingpan Man (Fig. 8). In Xinjiang, pearls would have been long distance imported products from the coastal regions which are  > 3000 km from the Yingpan cemetery. Ancient China, Egypt, Persia, Greece and India were known to have produced and prized pearls67. However, according to Chinese historic literature sources: Shangshu (meaning “the Book of Documents”; written by pre-Qin philosophers during the Zhou Dynasty ~ 1000 BC)68, Hanshu (meaning “the Book of Han”; written by Gu Ban during the Eastern Han Dynasty in 105 AD)69 and Hou Hanshu (meaning “the Book of Later Han”; written by Ye Fan during the Southern Dynasties from 432 to 445 AD)70, pearls were known as royal tributes in China since the Xia Dynasty (~ 2000 BC), and were mainly produced in the coastal cities of southern China, such as Panyu (modern Guangzhou City in Guangdong Province), Hepu (modern Hainan Province), Zhuya (modern Guangxi and Guangdong Province), etc.67 These coastal regions of China were connected to the Tarim Basin area via the Silk Road trading routes and were possibly the source for the pearls found on Yingpan Man’s pillow (Fig. 6). In particular, a silk pillow fully covered with unpolished natural pearls (placed beneath the tomb owner’s head, weighing ~ 470 g) and a lacquer box of pearls (weighing 4,117 g) were unearthed from the tomb of the King of the Nanyue Kingdom (a vassal state of Han) in modern Guangzhou71. This demonstrates a similar preference for pearls as decorations on pillows or as grave goods for high status individuals.Figure 8Crowing cockerel pillow. (a–d) Photo and sketch of the crowing cockerel pillow from Yingpan Man burial. (e–h) Decorative patterns of the four mythical beasts on Han Dynasty eaves tiles. (The original pictures and sketches were previously published14 and provided by Wenying Li. Pictures were modified using Adobe Photoshop CC 2015 V.1.2. The final layout was created in Adobe Illustrator CC 2019 V.23.1.1).Full size imageMoreover, the decorative patterns found on Yingpan Man’s crowing cockerel pillow are remarkable. These include the images of: a monkey-shaped face, a griffin-shaped beast and a net-shaped pattern as well as the images of the mythical beasts of the “blue dragon”, “red sparrow” and “white tiger” (Fig. 8d)17,47,61,72. Together with another mythical beast known as the “black turtle-snake”, these four mythical beasts were believed to be the guardians of the four cardinal directions and also represents four different colors and elements according to traditional Chinese cosmology (Fig. 8e–h). The dragon guarding the East and representing the color blue and the element of wood, the sparrow guarding the South and representing the color red as well as the element of fire, the tiger guarding the West and representing the color white and the element of metal, and the turtle-snake guarding the North and representing the color black and the element of water62,73. Thus, the images of these four mythical beasts were frequently integrated into the designs of cities, buildings, cemeteries and objects of ancient China for their symbolic function of protection63. In this context, the net-shaped pattern on Yingpan Man’s crowing cockerel pillow is likely a symbol of the four cardinal directions, while the monkey shaped face possibly symbolizes a human, that is to be protected. Notably, here, in the design of Yingpan Man’s crowing cockerel pillow, the image of the northern guardian of the turtle-snake is replaced by the Greek mythical beast known as Griffin (Fig. 8d)16,47,74. This change in imagery and symbolism could suggest that contact between the East and the West was via a northern route and that this was associated with some type of Greek influence or the Griffin. According to historical literature sources, a large number of Greeks migrated into Central Asia with Alexander the Great’s eastward expedition3,5,6. Hellenistic kingdoms such as Bactria (a.k.a. Daxia in the Chinese literature, located in the area of Pamir Plateau in modern Afghanistan, ~ 1900 km from Yingpan) subsequently became centers of Greek influence in this area and exported elements of Hellenistic culture to surrounding kingdoms that were located along the main routes of the Silk Road, such as Dayuan (located in the Fergana Valley, ~ 1300 km from Yingpan)2,6,75. Some ancient cities in the Tarim Basin area, such as Yingpan, Maideke and Yuansha, are also argued to have been influenced by Hellenistic elements as their city walls were circular in shape and this was clearly a unique architecture compared to the square-shaped traditional Chinese city walls63,76. It is highly probably that these Hellenistic elements were transported to the ancient city of Yingpan by the Silk Road trading routes which followed a north–south direction in this region, and therefore would support that Greek elements would be associated with the northern direction in this region of Xinjiang. In conclusion, Yingpan Man’s crowing cockerel pillow displays an unprecedented combination of Chinese spiritual beliefs incorporated with western motifs, and symbolizes the intertwining of Eastern and Western cultures in this part of Central Asia (Figs. 6, 8).Even more significant uses of western components in Yingpan Man’s burial is also visualized in other grave goods, e.g. his: carpet, coffin, caftan. The decorative pattern of the male lion on Yingpan Man’s tufted woolen carpet is clearly an imported element as the lion was originally from Africa, Southern Europe, West Asia and India. Lions were not introduced into China until 87 AD, being sent to Emperor Zhang of the Eastern Han Dynasty as a gift from Pacorus II, the King of the Anxi Empire (a.k.a. Parthian Empire (247 BC to 224 AD, replaced by the Persian in 226 AD, located in modern Iran))70. In particular, this exquisite lion-decorated carpet suggests a very high social status for Yingpan Man as lions were deified in ancient China since the Han Dynasty and were used as symbols of power, authority and royalty as it was in other areas of the Eurasia (Fig. 2a)15,61. Moreover, it is also argued by some scholars that the motif of the lion on this carpet is from the Buddhist art of India, as lions are frequently mentioned in Buddhist stories and a Buddhist temple was also found at the site of Yingpan (Fig. 6)17,77.In addition, though the main decorative patterns on Yingpan Man’s coffin are the “Lianbi” pattern, images of vines, leaves, pomegranate flowers and vases were also depicted inside of the diamond patterns (Fig. S1)15. Among which, the image of pomegranate flowers is clearly an imported element from the West as pomegranates were originally domesticated in the middle East ~ 5000 years ago and were not introduced into China until the Han to Jin Dynasties, or with the flow of goods along the Silk Road78. In particular, the pomegranate was used as a symbol of health, fertility and rebirth as mentioned in many ancient cultures, especially in Greek and Turkish myths78. Thus, this is particularly interesting as the image of pomegranate appears not only on Yingpan Man’s coffin as flowers on the headboard and footboard (Fig. 6; Fig. S1), but also on his caftan as decorative patterns of fruited-trees (Figs. 6, 9). Specifically, the decorative patterns on Yingpan Man’s woolen caftan consists of six sets of nude puttis and animals with fruited pomegranate trees standing in between (Fig. 9)14. In particular, each of these six sets of images is composed of a symmetrical pair of confronting muscular puttis or animals (goats or bulls) that are either leaning away from or toward each other14. The nude puttis are holding either a spear, sword or a shield with capes swirling from their shoulders, while the animals of goats and bulls are in the pose of jumping and the bulls have laurel wreaths around their waists (Fig. 9)14. A similar design of stance and composition of figures was also discovered in a mosaic floor from the Villa of Good Fortune at Olynthos, Greece (paired female figures with weapons, fourth century BC)79 as well as another mosaic floor from Pella, the Macedonian capital (two nude youths with capes flying on their shoulder and weapons held in their hand, about to attack an animal in between of them, 325 to 300 BC)79. Thus, it is suggested that this caftan was the work of a weaver familiar with both Western and Eastern motifs as the character and poses of the nude puttis are clearly Western in style and appearance, the fruited pomegranate tree is believed to be a Persian motif, while the paired facing animals of goats and bulls are similar to the animal art of Central Asia8. However, this caftan was completed using the technique of double-weaving, the lining and belt were made of silk14, while the design of the side slits are indicative of a localized adaptation for horse-riding15. Moreover, analysis using high performance liquid chromatography (HPLC) on the red and yellow threads of this caftan suggest that they were dyed in a local workshop with indigenous materials of Rubia Tinctorum and Populus Pruinosa Schrenk, respectively80,81. In conclusion, the design and style of Yingpan Man’s caftan is unprecedented, and it is a masterpiece that combines both Greek/Roman, Persian, Central Asian, Chinese and local elements (Fig. 6).Figure 9Photo and sketch of the decorative patterns on Yingpan Man’s caftan. (The original pictures and sketches were previously published14 and provided by Wenying Li. Pictures were modified using Adobe Photoshop CC 2015 V.1.2. The final layout was created in Adobe Illustrator CC 2019 V.23.1.1).Full size imageThe opulence and fine quality of the objects buried with Yingpan Man indicate that he must have had a high social status before death14,47. Given the importance of the town of Yingpan as a trading center on the Silk Road, the excavators who discovered Yingpan Man suggested that he was a wealthy merchant from the West14. Others have proposed that Yingpan Man might have been a Sogdian merchant since the Sogdians (an Iranian-speaking people whose homeland lay near Samarkand in what is now Uzbekistan) were the richest traders along the route7. However, given the relatively young age of Yingpan Man before his death (~ 30 years old), it is unlikely that he amassed all his fortune and high social status only through trade, and possibly by inheritance or military feats. The government of the Jin Dynasty established the administrative organization of “Xiyu Zhangshi Fu” (meaning “Chief Governor of the Western Regions”) in ancient Xinjiang, and the capital city of “Xiyu Zhangshi Fu” was located nearby Lop Nur and is very close to the ancient city of Yingpan (~ 185 km away)15,16. In addition, comparison of Yingpan Man’s burial to other contemporary burials from Gansu also suggest that Yingpan Man was possibly a military official from the government of Central China16. More supporting evidence comes from the embroidered armband that was buried with Yingpan Man as colorful armbands were suggested to be used by soldiers for the protection from evil forces in ancient Xinjiang (Fig. 6)15. An additional explanation is that Yingpan Man was a noble or even a king of the nearby state named Shan (a.k.a. Moshan)76, and the ancient city of Yingpan was suggested to be the capital city of this state15. An alternative explanation is that Yingpan Man belonged to a local noble family who were displaced from Bactria to the southern Tarim Basin after civil strife in the Kushan Empire at the end of the second century AD, given the popularity of Kushan arts in this area during the Han to Jin Dynasties82,83. The isotopic evidence presented here, in particular the hair δ34S results, add additional information to Yingpan Man’s identity. The lack of δ34S isotopic variability (10.4‰ to 11.9‰) over the last ~ 3–4 years of life indicates that Yingpan Man was not a Silk Road traveler or merchant, at least during this period of his life. Thus, Yingpan Man appears to have been a local, possibly a governmental official or royal to this region of the Tarim Basin, perhaps from the nearby state of Shan. This might suggest why he was buried in the Yingpan cemetery as it was purported to be capital of this ancient state. More

The prevalence of S. aureus isolation from the different examined samplesStaphylococcal infections represent a public health issue in hospitals and health care settings as well as a major economical and welfare problem in dairy animal farming25. The prevalence of S. aureus isolation from the farm under the study (Table 2) showed that 63 (33.1%) out of 190 different samples were bacteriologically positive. Moreover, the isolation was mainly obtained from manager swabs followed by milk machine swabs, nasal swabs and hand swabs (60.0, 53.3, 40.0 and 28.0%, respectively), and to a lesser extent in milk samples (24.0%). Meanwhile it was not isolated at any percent from water trough swabs, at X2 = 48.8, P  More

Generation timeDuring the infectious period, an infected individual may produce a secondary infection. However, the individual’s infectiousness is not constant during the infectious period, but it can be approximated by the probability distribution of the generation time (GT), which accounts for the time between the infection of a primary case and the infection of a secondary case. Unfortunately, such distribution is not as easy to estimate as that of the serial interval, which accounts for the time between the onset of symptoms in a primary case to the onset of symptoms of a secondary case. This is because the time of infection is more difficult to detect than the time of symptoms onset. Ganyani et al.27 developed a methodology to estimate the distribution of the GT from the distributions of the incubation period and the serial interval. Assuming an incubation period following a gamma distribution with a mean of 5.2 days and a standard deviation (SD) of 2.8 days, they estimated the serial interval from 91 and 135 pairs of documented infector-infectee in Singapore and Tianjin (China). Then, they found that the GT followed a gamma distribution with mean = 5.20 (95% CI = [3.78, 6.78]) days and SD = 1.72 (95% CI = [0.91, 3.93]) for Singapore (hereafter GT1), and with mean = 3.95 (95% CI = [3.01, 4.91]) days and SD = 1.51 (95% CI = [0.74, 2.97]) for Tianjin (hereafter GT2). Ng et al.28 applied the same methodology to 209 pairs of infector-infectee in Singapore and determined a gamma distribution with mean = 3.44 (95% CI = [2.79, 4.11]) days and SD 2.39 (95% CI = [1.27, 3.45]; hereafter GT3). Figure 3 shows the probability density functions (PDF) of such distributions, fGT. The differences between them are remarkable. For example, the 54.5%, 81.0%, and 80.7% of the contagions are produced in a pre-symptomatic stage (in the first 5.2 days after primary infection) assuming GT1, GT2, and GT3, respectively.Figure 3Probability density function of the generation time distribution, fGT(t), of GT1 (blue line; Singapore27), GT2 (yellow line; Tianjin27), GT3 (red line; Singapore28), and GTth (black line; theoretical distribution). Bars are the discretized version, (widetilde{{f_{GT} }}left( n right)), of the PDF of GTth.Full size imageTheoretically, assuming that the incubation periods of two individuals are independent and identically distributed, which is quite plausible, the expected/mean values of the GT and the serial interval should be equal29,30. The mean of the serial interval is easier to estimate than that of the GT. For that reason, we assume a mean serial interval as estimated from a meta-analysis of 13 studies involving a total of 964 pairs of infector-infectee, which is 4.99 days (95% CI = [4.17, 5.82])31, is more reliable than the aforementioned means of the GT. This value is within the error estimates of the means of GT1 and GT2, but not for GT3. Then, we construct a theoretical distribution for the GT that follows a gamma distribution (hereafter GTth) with mean = 4.99 days and SD = 1.88 days. This theoretical distribution can be seen in Fig. 3 and approximates the average PDF of three gamma distributions with mean = 4.99 and the SD of GT1, GT2, and GT3. We assume a conservative CI = [1.51, 2.39] for the theoretical SD, defined with the minimum and maximum SD values of GT1, GT2, and GT3. GTth shows 63.1% of pre-symptomatic contagions.
R

0

from r
In theory, the basic reproduction number R0 can be estimated as far as the intrinsic growth rate r, and the distributions of both the latent and infectious periods are known26,32,33,34. The latent period accounts for the period during which an infected individual cannot infect other individuals. It is observed in diseases for which the infectious period starts around the end of the incubation period, as happened with influenza35 and SARS36. However, from Fig. 3 it is inferred that COVID-19 is transmissible from the moment of infection, and we will assume a null latent period. Then, if the GT follows a gamma distribution, R0 can be estimated from the formulation of Anderson and Watson32, which was adapted to null latent periods by Yan26 as$$ R_{0} = frac{{mean_{GT} }}{{1 – left( {1 + mean_{GT} cdot r cdot frac{1}{{shape_{GT} }}} right)^{{ – shape_{GT} }} }} cdot r, $$
(4)
where meanGT is the mean GT and shapeGT is one of the two parameters defining the gamma distribution, which can be estimated as$$ shape_{GT} = frac{{left( {mean_{GT} } right)^{2} }}{{left( {SD_{GT} } right)^{2} }}. $$
(5)
For GTth, we get R0 = 1.50 (CI = [1.41, 1.61]) for REMEDID I(n) and R0 = 1.76 (CI = [1.60, 1.94]) for official I(n). For the other three GT distributions, R0 ranges from 1.39 (CI = [1.27, 1.58]) to 1.51 (CI = [1.34, 1.80]) for REMEDID I(n) and from 1.59 (CI = [1.40, 1.88]) to 1.78 (CI = [1.51, 2.23]) for official I(n) (Table 1). In all cases, R0 from GTth are within those from the three known GT distributions and indistinguishable from them within the error estimates. The lower (upper) bound of the CI is estimated as the minimum (maximum) R0 obtained from all the possible combinations of 100 evenly spaced values covering the CI of r, meanGT and SDGT. Then, following the Bonferroni correction, the reported CI present at least a 85% of confidence level for GT1, GT2, and GT3, but it cannot be assured for GTth since the CI of its SD is unknown. In general, all these R0 estimates are lower than those summarised by Park et al.20.Table 1 R0 and HIT values of the ancestral SARS-CoV-2 variant estimated from GT1, GT2, GT3, and GTth, and REMEDID and official infections. For date0, “Dec.” means December 2019, and “Jan.” means January 2020.Full size tableAlternatively, R0 can be estimated by applying the Euler–Lotka equation29,33,$$ R_{0} = frac{1}{{mathop smallint nolimits_{0}^{ + infty } e^{ – rt} cdot f_{GT} left( t right)dt}}. $$
(6)
In this case, we get values closer to previous estimates20. In particular, for GTth, we get R0 = 2.12 (CI = [1.81, 2.48]) for REMEDID I(n) and R0 = 2.92 (CI = [2.28, 3.75]) for official I(n). For the other three GT distributions, R0 ranges from 1.63 (CI = [1.43, 1.90]) to 2.21 (CI = [1.59, 2.95]) for REMEDID I(n) and from 1.97 (CI = [1.59, 2.54]) to 3.11 (CI = [1.84, 4.90]) for official I(n) (Table 1). The CI are estimated as in Eq. (4).R0 from a dynamical modelWe designed a dynamic model with Susceptible-Infected-Recovered (SIR) as stocks that accounts for the infectiousness of the infectors. Such a model is a generalisation of the Susceptible-Exposed-Infected-Recovered (SEIR) model37. Births, deaths, immigration and emigration are ignored, which seems reasonable since the timescale of the outbreak is too short to produce significant demographic changes. For the sake of simplicity, the recovered stock includes recoveries and fatalities, and it is denoted as R(t). A random mixing population is assumed, that is a population where contacts between any two people are equally probable. Time is discretized in days, so the real time variable t is replaced by the integer variable n. As a consequence, the derivatives in the differential equations defining the dynamic model explained below are discrete derivatives.The size of the population is fixed at N = 100,000, and then, for any day n we get$$ tilde{S}left( n right) + left( {mathop sum limits_{k = 0}^{20} tilde{I}left( n-k right)} right) + tilde{R}left( n right) = N, $$
(7)
where (tilde{S}left( n right)), (tilde{I}left( n right)), and (tilde{R}left( n right)) are the discretized versions of S(t), I(t), and R(t) and (tilde{I}) is assumed to be null for negative integers. The summation is a consequence of the infectiousness, which is approximated according to the GT, whose PDF is discretized as$$ widetilde{{f_{GT} }}left( n right) = mathop smallint limits_{n – 1}^{n} f_{GT} left( t right) dt, $$
(8)
from n = 1 to 20. Figure 3 shows (widetilde{{f_{GT} }}left( n right)) for GTth. Truncating at n = 20 accounts for 99.99% of the area below the PDF of all the GT. Then, an infected individual at day n0 is expected to produce on average$$ widetilde{{R_{e} }}left( {n_{0} + n} right) cdot widetilde{{f_{GT} }}left( n right) $$
(9)
infections n days later, where (widetilde{{R_{e} }}left( n right)) is the discretized version of Re(t). From this expression, it is obvious that values of (widetilde{{R_{e} }}left( n right) < 1) will produce a decline of infections. Conversely, infections at day n0 are produced by all individuals infected during the previous 20 days as$$ tilde{I}(n_{0} ) = tilde{R}_{e} left( {n_{0} } right) cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{f_{GT} }}left( n right)} right), $$ (10) whose continuous version has been reported in previous studies29,38. The expression in brackets is called total infectiousness of infected individuals at day n039. According to Eq. (1), Eq. (10) can be expressed in terms of R0 as$$ tilde{I}(n_{0} ) = R_{0} cdot frac{{tilde{S}left( {n_{0} } right)}}{N} cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{f_{GT} }}left( n right)} right). $$ (11) As we want a dynamic model capable of providing (tilde{I}left( {n_{0} } right)) from the stocks at time step n0 − 1, we replaced (tilde{S}left( {n_{0} } right)) by (tilde{S}left( {n_{0} - 1} right)) in Eq. (11). This assumption makes sense in a discrete domain since the infections at time n0 take place in the susceptible population at time n0 − 1. Then, assuming that all stocks are set to zero for negative integers, our dynamic model can be expressed in terms of Eq. (7) and the following differential equations:$$ delta tilde{I}(n_{0} ) = R_{0} cdot frac{{tilde{S}left( {n_{0} - 1} right)}}{N} cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{{text{f}}_{GT} }}left( n right)} right) - tilde{I}(n_{0} - 1), $$ (12) $$ delta tilde{S}left( {n_{0} } right) = {-}tilde{I}left( {n_{0} } right), $$ (13) $$ delta tilde{R}left( {n_{0} } right) = tilde{I}left( {n_{0} - 21} right), $$ (14) where (delta tilde{I}), (delta tilde{S}), and (delta tilde{R}) are the (discrete) derivatives of (tilde{I}), (tilde{S}), and (tilde{R}), respectively. Applying the initial conditions (tilde{S}left( 0 right) = N - 1), (tilde{I}left( 0 right) = 1), and (tilde{R}left( 0 right) = 0), it is assumed that the outbreak was produced by only one infector. The latter is not true in Spain, since several independent introductions of SARS-CoV-2 were detected40. However, for modelling purposes it is equivalent to introducing a single infection at day 0 or M infections produced by the single infection n days later. Then, the date of the initial time n = 0 is accounted as a parameter date0, which is optimised, as well as R0, to minimise the root-mean square of the residual between the model simulated (tilde{I}left( n right)) and the REMEDID and official I(n) for the period from date0 to n0.The model was implemented in Stella Architect software v2.1.1 (www.iseesystems.com) and exported to R software v4.1.1 with the help of deSolve (v1.28) and stats (v4.1.1) packages, and the Brent optimisation algorithm was implemented. For REMEDID I(n) and GTth, we obtained date0 = 13 December 2019 and R0 = 2.71 (CI = [2.33, 3.15]). Optimal solutions combine lower/higher R0 and earlier/later date0 (Fig. 4), which highlights the importance of providing an accurate first infection date to estimate R0. When the other three GT distributions were considered, we obtained similar date0, ranging from 12 to 17 December 2019, and R0 values ranging from 2.08 (CI = [1.86, 2.42]) to 2.85 (CI = [2.05, 3.25]; see Table 1). For official infections, date0 was set to 1 January 2020 for all cases, and R0 ranged from 1.81 (CI = [1.64, 2.07]) to 2.41 (CI = [1.80, 2.91]). The CI are estimated as in Eq. (4).Figure 4Root-mean square (RMS) of the residuals between infections from the model, which depends on date0 (x-axis) and R0 (y-axis), and REMEDID (from MoMo ED) and official infections. Parameters optimizing the model are highlighted in purple. RMS larger than 1275 (left panel) and 103 (right panel) are saturated in white.Full size image More

1.Federal Office for the Environment (FOEN). Action Plan for the Swiss Biodiversity Strategy (FOEN, Bern, 2017).2.Geldmann, J. & González-Varo, J. P. Conserving honey bees does not help wildlife. Science 359, 392–393 (2018).Article 

Google Scholar 
3.Egerer, M. & Kowarik, I. Confronting the modern gordian knot of urban beekeeping. Trends Ecol. Evol. 35, 956–959 (2020).Article 

Google Scholar 
4.Herrera, C. M. Gradual replacement of wild bees by honeybees in flowers of the Mediterranean Basin over the last 50 years. Proc. R. Soc. B Biol. Sci. 287, 16–20 (2020).
Google Scholar 
5.Torné-Noguera, A., Rodrigo, A., Osorio, S. & Bosch, J. Collateral effects of beekeeping: impacts on pollen-nectar resources and wild bee communities. Basic Appl. Ecol. 17, 199–209 (2016).Article 

Google Scholar 
6.Magrach, A., González-Varo, J. P., Boiffier, M., Vilà, M. & Bartomeus, I. Honeybee spillover reshuffles pollinator diets and affects plant reproductive success. Nat. Ecol. Evol. 1, 1299–1307 (2017).Article 

Google Scholar 
7.Prendergast, K. S., DIxon, K. W. & Bateman, P. W. Interactions between the introduced European honey bee and native bees in urban areas varies by year, habitat type and native bee guild. Biol. J. Linn. Soc. 133, 725–743 (2021).Article 

Google Scholar 
8.Herbertsson, L., Lindström, S. A. M., Rundlöf, M., Bommarco, R. & Smith, H. G. Competition between managed honeybees and wild bumblebees depends on landscape context. Basic Appl. Ecol. 17, 609–616 (2016).Article 

Google Scholar 
9.Stevenson, P. C. et al. The state of the world’s urban ecosystems: what can we learn from trees, fungi, and bees? Plants People Planet 2, 482–498 (2020).Article 

Google Scholar 
10.Ropars, L., Dajoz, I., Fontaine, C., Muratet, A. & Geslin, B. Wild pollinator activity negatively related to honey bee colony densities in urban context. PLoS ONE 14, e0222316 (2019).CAS 
Article 

Google Scholar 
11.Venter, Z. S. & Sydenham, M. A. K. Continental-scale land cover mapping at 10 m resolution over Europe (ELC10). Remote Sens. 13, 2301 (2021).Article 

Google Scholar 
12.Hardin, G. The tragedy of the commons. Science 162, 1243–1248 (1968).CAS 
Article 

Google Scholar 
13.Tew, N. E. et al. Quantifying nectar production by flowering plants in urban and rural landscapes. J. Ecol. 109, 1747–1757 (2021).Article 

Google Scholar 
14.Baldock, K. C. R. et al. A systems approach reveals urban pollinator hotspots and conservation opportunities. Nat. Ecol. Evol. 3, 363–373 (2019).Article 

Google Scholar 
15.Casanelles-Abella, J. et al. Applying predictive models to study the ecological properties of urban ecosystems: A case study in Zürich, Switzerland. Landsc. Urban Plan. 214, 104137 (2021).Article 

Google Scholar 
16.IPBES. Summary for policymakers of the global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES, 2019).17.IUCN. IUCN’s Key Messages. First Draft of the Post-2020 Global Biodiversity Framework. In Convention on Biological Diversity Third meeting of the Open-Ended Working Group on the Post-2020 Global Biodiversity Framework (OEWG3) 15 (IUCN, 2021).18.Baldock, K. C. R. Opportunities and threats for pollinator conservation in global towns and cities. Curr. Opin. Insect Sci. 38, 63–71 (2020).Article 

Google Scholar 
19.Henry, M. & Rodet, G. The apiary influence range: a new paradigm for managing the cohabitation of honey bees and wild bee communities. Acta Oecologica 105, 103555 (2020).Article 

Google Scholar 
20.Ignatieva, M. & Hedblom, M. An alternative urban green carpet. Science 362, 148–149 (2018).CAS 
Article 

Google Scholar 
21.Vega, K. A. & Küffer, C. Promoting wildflower biodiversity in dense and green cities: The important role of small vegetation patches. Urban For. Urban Green. 62, 127165 (2021).Article 

Google Scholar 
22.Fabián, D., González, E., Sánchez Domínguez, M. V., Salvo, A. & Fenoglio, M. S. Towards the design of biodiverse green roofs in Argentina: assessing key elements for different functional groups of arthropods. Urban For. Urban Green. 61 (2021).23.Vega, K. A., Schläpfer-Miller, J. & Kueffer, C. Discovering the wild side of urban plants through public engagement. Plants People Planet 3, 389–401 (2021).Article 

Google Scholar 
24.Von Büren, R. S., Oehen, B., Kuhn, N. J. & Erler, S. High-resolution maps of Swiss apiaries and their applicability to study spatial distribution of bacterial honey bee brood diseases. PeerJ 2019, 1–21 (2019).
Google Scholar 
25.QGIS Development Team. QGIS Geographic Information System (Open Source Geospatial Foundation Project, 2020).26.R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2019).27.R Studio Team. R studio: Integrated Development for R (RStudio, Boston, 2020).28.Casanelles-Abella, J. & Moretti M. Challenging the sustainability of urban beekeeping: evidence from Swiss cities. Envidat. https://doi.org/10.16904/envidat.239 (2021).29.Casanelles-Abella, J. Code for the paper: Challenging the sustainability of urban beekeeping: evidence from Swiss cities (v. 1.0). Zenodo https://doi.org/10.5281/zenodo.5618254 (2021).30.Swiss Fedearl Office of Topography Swisstopo. SWISSIMAGE 25. https://www.swisstopo.admin.ch/en/geodata/images/ortho/swissimage25.html#links (Swisstopo, 2021). More