Most species of plants form underground associations with arbuscular mycorrhizal (AM) fungi, which provide plant roots with nutrients in exchange for carbon. AM fungi form networks of hyphae that act as tubes spreading carbon and connecting plants, but the global scale of these networks is unknown because of the difficulty of observing them underground. Stewart et al. compiled field and experimental data on hyphal density and used machine learning to predict how AM density varies across the globe. They then predicted hyphal biomass using high-resolution image analysis of hyphal network length from two globally distributed fungal species grown on transparent media in the lab. The authors predicted a large and spatially variable extent of AM fungi across the globe. —Bianca Lopez
Arbuscular mycorrhizal fungi form symbioses with ~70% of plant species, building hyphal networks that exchange nutrients for host-derived carbon. These tubular networks move ~1 billion metric tons of carbon per year into Earth’s soils. However, we have no quantitative understanding of the hyphal infrastructure required to carry out this resource transfer. We assembled data from 322 studies representing more than 16,000 soil cores across nine biomes and developed machine-learning models to predict hyphal densities globally. With robotic imaging of more than 300,000 hyphae, we calibrated a biomass model from our spatial predictions. We estimate that global topsoils contain 1.10 × 1017 ± 0.13 × 1017 SD kilometers of living hyphae, weighing ~300 ± 60 SD megatons, ~4- to 6-fold the biomass of humans. Our uncertainty analyses identified undersampled ecosystems that require additional empirical attention.
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Materials and Methods
Figs. S1 to S17
MDAR Reproducibility Checklist
1
S. E. Smith, D. Read, Mycorrhizal Symbiosis (Academic Press, ed. 3, 2008).
2
H. J. Hawkins, R. I. M. Cargill, M. E. Van Nuland, S. C. Hagen, K. J. Field, M. Sheldrake, N. A. Soudzilovskaia, E. T. Kiers, Mycorrhizal mycelium as a global carbon pool. Curr. Biol. 33, R560–R573 (2023).
3
A. Kakouridis, J. A. Hagen, M. P. Kan, S. Mambelli, L. J. Feldman, D. J. Herman, P. K. Weber, J. Pett-Ridge, M. K. Firestone, Routes to roots: Direct evidence of water transport by arbuscular mycorrhizal fungi to host plants. New Phytol. 236, 210–221 (2022).
4
N. Dotzler, M. Krings, T. N. Taylor, R. Agerer, Germination shields in Scutellospora (Glomeromycota: Diversisporales, Gigasporaceae) from the 400 million-year-old Rhynie chert. Mycol. Prog. 5, 178–184 (2006).
5
W. Remy, T. N. Taylor, H. Hass, H. Kerp, Four hundred-million-year-old vesicular arbuscular mycorrhizae. Proc. Natl. Acad. Sci. U.S.A. 91, 11841–11843 (1994).
6
C. I. Mora, S. G. Driese, L. A. Colarusso, Middle to Late Paleozoic atmospheric CO2 levels from soil carbonate and organic matter. Science 271, 1105–1107 (1996).
7
K. J. Field, D. D. Cameron, J. R. Leake, S. Tille, M. I. Bidartondo, D. J. Beerling, Contrasting arbuscular mycorrhizal responses of vascular and non-vascular plants to a simulated Palaeozoic CO2 decline. Nat. Commun. 3, 835 (2012).
8
E. M. Goltapeh, Y. R. Danesh, R. Prasad, A. Varma, “Mycorrhizal fungi: What we know and what should we know?” in Mycorrhiza, A. Varma, Eds. (Springer, ed. 3, 2008), pp. 3–27.
9
P. Friedlingstein, M. O’Sullivan, M. W. Jones, R. M. Andrew, D. C. E. Bakker, J. Hauck, P. Landschützer, C. Le Quéré, I. T. Luijkx, G. P. Peters, W. Peters, J. Pongratz, C. Schwingshackl, S. Sitch, J. G. Canadell, P. Ciais, R. B. Jackson, S. R. Alin, P. Anthoni, L. Barbero, N. R. Bates, M. Becker, N. Bellouin, B. Decharme, L. Bopp, I. B. M. Brasika, P. Cadule, M. A. Chamberlain, N. Chandra, T. T. T. Chau, F. Chevallier, L. P. Chini, M. Cronin, X. Dou, K. Enyo, W. Evans, S. Falk, R. A. Feely, L. Feng, D. J. Ford, T. Gasser, J. Ghattas, T. Gkritzalis, G. Grassi, L. Gregor, N. Gruber, Ö. Gürses, I. Harris, M. Hefner, J. Heinke, R. A. Houghton, G. C. Hurtt, Y. Iida, T. Ilyina, A. R. Jacobson, A. Jain, T. Jarníková, A. Jersild, F. Jiang, Z. Jin, F. Joos, E. Kato, R. F. Keeling, D. Kennedy, K. K. Goldewijk, J. Knauer, J. I. Korsbakken, A. Körtzinger, X. Lan, N. Lefèvre, H. Li, J. Liu, Z. Liu, L. Ma, G. Marland, N. Mayot, P. C. McGuire, G. A. McKinley, G. Meyer, E. J. Morgan, D. R. Munro, S. I. Nakaoka, Y. Niwa, K. M. O’Brien, A. Olsen, A. M. Omar, T. Ono, M. Paulsen, D. Pierrot, K. Pocock, B. Poulter, C. M. Powis, G. Rehder, L. Resplandy, E. Robertson, C. Rödenbeck, T. M. Rosan, J. Schwinger, R. Séférian, T. L. Smallman, S. M. Smith, R. Sospedra-Alfonso, Q. Sun, A. J. Sutton, C. Sweeney, S. Takao, P. P. Tans, H. Tian, B. Tilbrook, H. Tsujino, F. Tubiello, G. R. van der Werf, E. van Ooijen, R. Wanninkhof, M. Watanabe, C. Wimart-Rousseau, D. Yang, X. Yang, W. Yuan, X. Yue, S. Zaehle, J. Zeng, B. Zheng, Global carbon budget 2023. Earth Syst. Sci. Data 15, 5301–5369 (2023).
10
D. P. Janos, Plant responsiveness to mycorrhizas differs from dependence upon mycorrhizas. Mycorrhiza 17, 75–91 (2007).
11
L. Oyarte Galvez, C. Bisot, P. Bourrianne, R. Cargill, M. Klein, M. van Son, J. van Krugten, V. Caldas, T. Clerc, K. K. Lin, F. Kahane, S. van Staalduine, J. D. Stewart, V. Terry, B. Turcu, S. van Otterdijk, A. Babu, M. Kamp, M. Seynen, B. Steenbeek, J. Zomerdijk, E. Tutucci, M. Sheldrake, C. Godin, V. Kokkoris, H. A. Stone, E. T. Kiers, T. S. Shimizu, A travelling-wave strategy for plant-fungal trade. Nature 639, 172–180 (2025).
12
I. Sciascia, A. Crosino, A. Genre, Quantifying root colonization by a symbiotic fungus using automated image segmentation and machine learning approaches. Sci. Rep. 13, 14830 (2023).
13
E. Evangelisti, C. Turner, A. McDowell, L. Shenhav, T. Yunusov, A. Gavrin, E. K. Servante, C. Quan, S. Schornack, Deep learning-based quantification of arbuscular mycorrhizal fungi in plant roots. New Phytol. 232, 2207–2219 (2021).
14
J. R. Leake, D. J. Read, “Mycorrhizal symbioses and pedogenesis throughout Earth’s history” in Mycorrhizal Mediation of Soil: Fertility, Structure, and Carbon Storage, N. C. Johnson, C. Gehrig, J. Jansa, Eds. (Elsevier, 2017), pp. 9–33.
15
J. Leake, D. Johnson, D. Donnelly, G. Muckle, L. Boddy, D. Read, Networks of power and influence: The role of mycorrhizal mycelium in controlling plant communities and agroecosystem functioning. Can. J. Bot. 82, 1016–1045 (2011).
16
M. G. A. van der Heijden, R. Streitwolf-Engel, R. Riedl, S. Siegrist, A. Neudecker, K. Ineichen, T. Boller, A. Wiemken, I. R. Sanders, The mycorrhizal contribution to plant productivity, plant nutrition and soil structure in experimental grassland. New Phytol. 172, 739–752 (2006).
17
I. Hiiesalu, M. Pärtel, J. Davison, P. Gerhold, M. Metsis, M. Moora, M. Öpik, M. Vasar, M. Zobel, S. D. Wilson, Species richness of arbuscular mycorrhizal fungi: Associations with grassland plant richness and biomass. New Phytol. 203, 233–244 (2014).
18
R. M. Miller, J. D. Jastrow, D. R. Reinhardt, External hyphal production of vesicular-arbuscular mycorrhizal fungi in pasture and tallgrass prairie communities. Oecologia 103, 17–23 (1995).
19
S. J. McNaughton, M. Oesterheld, Extramatrical mycorrhizal abundance and grass nutrition in a tropical grazing ecosystem, the Serengeti National Park, Tanzania. Oikos 59, 92 (1990).
20
T. Helgason, T. J. Daniell, R. Husband, A. H. Fitter, J. P. W. Young, Ploughing up the wood-wide web? Nature 394, 431 (1998).
21
Z. Kabir, Tillage or no-tillage: Impact on mycorrhizae. Can. J. Plant Sci. 85, 23–29 (2011).
22
J. Jansa, F. A. Smith, S. E. Smith, Are there benefits of simultaneous root colonization by different arbuscular mycorrhizal fungi? New Phytol. 177, 779–789 (2008).
23
J. van den Hoogen, N. Robmann, D. Routh, T. Lauber, N. van Tiel, O. Danylo, T. W. Crowther, A geospatial mapping pipeline for ecologists. bioRxiv 2021.07.07.451145 [Preprint] (2021); https://doi.org/10.1101/2021.07.07.451145.
24
N. Gorelick, M. Hancher, M. Dixon, S. Ilyushchenko, D. Thau, R. Moore, Google Earth Engine: Planetary-scale geospatial analysis for everyone. Remote Sens. Environ. 202, 18–27 (2017).
25
R. B. Jackson, H. A. Mooney, E. D. Schulze, A global budget for fine root biomass, surface area, and nutrient contents. Proc. Natl. Acad. Sci. U.S.A. 94, 7362–7366 (1997).
26
A. Shukla, D. Vyas, A. Jha, Soil depth: An overriding factor for distribution of arbuscular mycorrhizal fungi. J. Soil Sci. Plant Nutr. 13, 23–33 (2013).
27
F. Oehl, E. Sieverding, K. Ineichen, E. A. Ris, T. Boller, A. Wiemken, Community structure of arbuscular mycorrhizal fungi at different soil depths in extensively and intensively managed agroecosystems. New Phytol. 165, 273–283 (2005).
28
R. B. Jackson, J. Canadell, J. R. Ehleringer, H. A. Mooney, O. E. Sala, E. D. Schulze, A global analysis of root distributions for terrestrial biomes. Oecologia 108, 389–411 (1996).
29
J. C. Dodd, C. L. Boddington, A. Rodriguez, C. Gonzalez-Chavez, I. Mansur, Mycelium of arbuscular mycorrhizal fungi (AMF) from different genera: Form, function and detection. Plant Soil 226, 131–151 (2000).
30
C. Bisot, L. O. Galvez, F. Kahane, M. van Son, B. Turcu, R. Broekman, K.-K. Lin, P. Bontenbal, M. K. Winter, V. Kokkoris, S. A. West, C. Godin, E. T. Kiers, T. S. Shimizu, Carbon-phosphorus exchange rate constrains density-speed trade-off in arbuscular mycorrhizal fungal growth. Proc. Natl. Acad. Sci. U.S.A. 123, e2512182123 (2026).
31
Y. M. Bar-On, R. Phillips, R. Milo, The biomass distribution on Earth. Proc. Natl. Acad. Sci. U.S.A. 115, 6506–6511 (2018).
32
S. D. Allison, Rethinking microbial carbon use efficiency in soil models. Nat. Clim. Chang. 15, 10–12 (2025).
33
C. R. See, C. R. See, A. B. Keller, S. E. Hobbie, P. G. Kennedy, P. K. Weber, J. Pett-Ridge, Hyphae move matter and microbes to mineral microsites: Integrating the hyphosphere into conceptual models of soil organic matter stabilization. Glob. Change Biol. 28, 2527–2540 (2022).
34
M. Kleber, K. Eusterhues, M. Keiluweit, C. Mikutta, R. Mikutta, P. S. Nico, Mineral–organic associations: Formation, properties, and relevance in soil environments. Adv. Agron. 130, 1–140 (2015).
35
A. Kakouridis, M. Yuan, E. E. Nuccio, J. A. Hagen, C. A. Fossum, M. L. Moore, K. Y. Estera-Molina, P. S. Nico, P. K. Weber, J. Pett-Ridge, M. K. Firestone, Arbuscular mycorrhiza convey significant plant carbon to a diverse hyphosphere microbial food web and mineral-associated organic matter. New Phytol. 242, 1661–1675 (2024).
36
P. L. Staddon, C. B. Ramsey, N. Ostle, P. Ineson, A. H. Fitter, Rapid turnover of hyphae of mycorrhizal fungi determined by AMS microanalysis of 14C. Science 300, 1138–1140 (2003).
37
A. Schnepf, T. Roose, P. Schweiger, Growth model for arbuscular mycorrhizal fungi. J. R. Soc. Interface 5, 773–784 (2008).
38
N. A. Soudzilovskaia, P. M. van Bodegom, C. Terrer, M. V. Zelfde, I. McCallum, M. Luke McCormack, J. B. Fisher, M. C. Brundrett, N. C. de Sá, L. Tedersoo, Global mycorrhizal plant distribution linked to terrestrial carbon stocks. Nat. Commun. 10, 5077 (2019).
39
P. Dass, B. Z. Houlton, Y. Wang, D. Warlind, Grasslands may be more reliable carbon sinks than forests in California. Environ. Res. Lett. 13, 074027 (2018).
40
R. D. Bardgett, J. M. Bullock, S. Lavorel, P. Manning, U. Schaffner, N. Ostle, M. Chomel, G. Durigan, E. L. Fry, D. Johnson, J. M. Lavallee, G. Le Provost, S. Luo, K. Png, M. Sankaran, X. Hou, H. Zhou, L. Ma, W. Ren, X. Li, Y. Ding, Y. Li, H. Shi, Combatting global grassland degradation. Nat. Rev. Earth Environ. 2, 720–735 (2021).
41
M. E. Van Nuland, C. Averill, J. D. Stewart, O. Prylutskyi, A. Corrales, L. G. van Galen, B. F. Manley, C. Qin, T. Lauber, V. Mikryukov, O. Dulia, G. Furci, C. Marín, M. Sheldrake, J. T. Weedon, K. G. Peay, C. K. Cornwallis, T. Větrovský, P. Kohout, P. Baldrian, L. Tedersoo, S. A. West, T. W. Crowther, E. T. Kiers, J. van den Hoogen; SPUN Mapping Consortium, Global hotspots of mycorrhizal fungal richness are poorly protected. Nature 645, 414–422 (2025).
42
J. S. Kotiaho, B. ten Brink, J. Harris, Land use: A global baseline for ecosystem recovery. Nature 532, 37 (2016).
43
A. S. MacDougall, B. Vanzant, J. Sulik, S. Bagchi, D. Naidu, T. O. Muraina, E. W. Seabloom, E. T. Borer, P. Wilfahrt, I. Slette, J. L. Hierro, D. E. Pearson, M. Abedi, M. Akasaka, J. Alberti, A. Aleksanyan, A. A. Amisu, T. M. Anderson, C. A. Arnillas, M. Ayer, J. D. Bakker, S. Basant, S. Basto, L. Biederman, K. J. Bloodworth, F. Boscutti, E. H. Boughton, C. M. Bruschetti, H. L. Buckley, Y. M. Buckley, M. N. Bugalho, M. C. Caldeira, G. Campetella, N. Cannone, M. Carbognani, C. Carbutt, M. A. Carniello, M. Cervellini, T. Chaudhary, Q. Chen, A. T. Clark, S. Cousins, M. Dalle Fratte, N. J. Day, B. Deák, J. Dietrich, A. Dixon, N. Eisenhauer, K. J. Elgersma, O. Eren, A. Eskelinen, C. Estrada, P. A. Fay, G. Fayvush, K. C. Flynn, D. García Meza, D. Gargano, L. Gherardi, N. T. Girkin, L. González, P. Graff, L. W. C. Hagenberg, A. H. Halbritter, N. A. Havrilchak, N. Herdoiza, E. Hersch-Green, K. Hopping, A. Jentsch, S. O. Jimoh, J. Kerby, K. Kirkman, J. M. H. Knops, S. E. Koerner, A. Koltz, K. J. Komatsu, B. I. Koura, S. Kruse, L. Laanisto, L. S. Lannes, W. Li, M. Liang, A. Lkhagva, L. López-Olmedo, P. Lorenzo, C. J. Lortie, A. Loydi, W. Luo, P. Macek, F. Malfasi, P. Mariotte, J. P. Martina, A. Martínez-Blancas, H. Martinson, C. Martorell, J. A. Meave, S. Medina-Villar, K. Z. Mganga, J. Monsimet, A. N. Nerlekar, S. Niu, T. Ohlert, I. Oliveras Menor, G. R. Oñatibia, Y. K. Ortega, B. Osborne, S. Palpurina, J. Pascual, S. C. Pennings, E. Pérez-García, P. L. Peri, M. Petit Bon, A. Petraglia, F. Pijcke, S. M. Prober, R. E. Quiroga, J. I. Ramirez, S. Reed, B. H. P. Rosado, C. Roscher, D. W. Rowley, I. Sereda, D. M. Small, N. G. Smith, Y. Song, C. Stevens, L. E. Suarez Jimenez, M. Te Beest, M. Tedder, R. S. Terry, K. S. Thornton, D. Tian, G. Titcomb, O. Valkó, G. F. ‘Ciska’ Veen, R. Virtanen, E. A. R. Welti, G. R. Wheeler, A. A. Wolf, P. Wolff, A. L. Young, H. S. Young, L. H. Zeglin, K. Zhu, S. Zong, M. B. Siewert, The global extent of the grassland biome and implications for the terrestrial carbon sink. Nat. Ecol. Evol. 10, 246–257 (2026).
44
J. Köninger, M. Labouyrie, C. Ballabio, O. Dulya, V. Mikryukov, F. Romero, A. Franco, M. Bahram, P. Panagos, A. Jones, L. Tedersoo, A. Orgiazzi, M. J. I. Briones, M. G. A. van der Heijden, Pesticide residues alter taxonomic and functional biodiversity in soils. Nature 650, 367–373 (2026).
45
L. K. Abbott, A. D. Robson, G. De Boer, The effect of phosphorus on the formation of hyphae in soil by the vesicular-arbuscular mycorrhizal fungus, glomus fasciculatum. New Phytol. 97, 437–446 (1984).
46
E. K. Durant, K. J. Field, J. B. Sallach, S. Moeskjær, A. Williams, L. J. Carter, Azole antifungal contaminants disrupt mycorrhizal function and risk agricultural sustainability. Plants People Planet 8, 952–964 (2025).
47
K. Georgiou, R. B. Jackson, O. Vindušková, R. Z. Abramoff, A. Ahlström, W. Feng, J. W. Harden, A. F. A. Pellegrini, H. W. Polley, J. L. Soong, W. J. Riley, M. S. Torn, Global stocks and capacity of mineral-associated soil organic carbon. Nat. Commun. 13, 3797 (2022).
48
S. M. Lundberg, G. Erion, H. Chen, A. DeGrave, J. M. Prutkin, B. Nair, R. Katz, J. Himmelfarb, N. Bansal, S. I. Lee, From local explanations to global understanding with explainable AI for trees. Nat. Mach. Intell. 2, 56–67 (2020).
49
J. van den Hoogen, S. Geisen, D. Routh, H. Ferris, W. Traunspurger, D. A. Wardle, R. G. M. de Goede, B. J. Adams, W. Ahmad, W. S. Andriuzzi, R. D. Bardgett, M. Bonkowski, R. Campos-Herrera, J. E. Cares, T. Caruso, L. de Brito Caixeta, X. Chen, S. R. Costa, R. Creamer, J. Mauro da Cunha Castro, M. Dam, D. Djigal, M. Escuer, B. S. Griffiths, C. Gutiérrez, K. Hohberg, D. Kalinkina, P. Kardol, A. Kergunteuil, G. Korthals, V. Krashevska, A. A. Kudrin, Q. Li, W. Liang, M. Magilton, M. Marais, J. A. R. Martín, E. Matveeva, E. H. Mayad, C. Mulder, P. Mullin, R. Neilson, T. A. D. Nguyen, U. N. Nielsen, H. Okada, J. E. P. Rius, K. Pan, V. Peneva, L. Pellissier, J. Carlos Pereira da Silva, C. Pitteloud, T. O. Powers, K. Powers, C. W. Quist, S. Rasmann, S. S. Moreno, S. Scheu, H. Setälä, A. Sushchuk, A. V. Tiunov, J. Trap, W. van der Putten, M. Vestergård, C. Villenave, L. Waeyenberge, D. H. Wall, R. Wilschut, D. G. Wright, J. I. Yang, T. W. Crowther, Soil nematode abundance and functional group composition at a global scale. Nature 572, 194–198 (2019).
50
N. Cools, B. De Vos, “Part X: Sampling and analysis of soil. Version 2025-1” in Manual on Methods and Criteria for Harmonized Sampling, Assessment, Monitoring and Analysis of the Effects of Air Pollution on Forests, UNECE ICP Forests Programme Co-ordinating Centre, Ed. (Thünen Institute of Forest Ecosystems, 2010).
51
52
Y. Lekberg, E. Bååth, Å. Frostegård, E. Hammer, K. Hedlund, J. Jansa, C. Kaiser, P. W. Ramsey, T. Řezanka, J. Rousk, H. Wallander, M. Welc, P. A. Olsson, Fatty acid 16:1ω5 as a proxy for arbuscular mycorrhizal fungal biomass: current challenges and ways forward. Biol. Fertil. Soils 58, 835–842 (2022).
53
J. F. Hanssen, T. F. Thingstad, J. Goksøyr, Evaluation of hyphal lengths and fungal biomass in soil by a membrane filter technique. Oikos 25, 102 (1974).
54
J. D. Stewart, A. Corrales, C. Canteiro, C. Qin, M. M. Gupta, B. Otgonsuren, C. P. Peña-Venegas, M. E. Van Nuland, P. Kohout, T. Větrovský, V. Kokkoris, B. F. Manley, Advancing knowledge on the biogeography of arbuscular mycorrhizal fungi to support Sustainable Development Goal 15: Life on Land. FEMS Microbiol. Lett. 372, fnaf055 (2025).
55
L. Poggio, L. M. De Sousa, N. H. Batjes, G. B. M. Heuvelink, B. Kempen, E. Ribeiro, D. Rossiter, SoilGrids 2.0: Producing soil information for the globe with quantified spatial uncertainty. Soil 7, 217–240 (2021).
56
57
S. Pironon, I. Ondo, M. Diazgranados, R. Allkin, A. C. Baquero, R. Cámara-Leret, C. Canteiro, Z. Dennehy-Carr, R. Govaerts, S. Hargreaves, A. J. Hudson, R. Lemmens, W. Milliken, M. Nesbitt, K. Patmore, G. Schmelzer, R. M. Turner, T. R. van Andel, T. Ulian, A. Antonelli, K. J. Willis, The global distribution of plants used by humans. Science 383, 293–297 (2024).
58
D. Bates, M. Mächler, E. Zurich, B. M. Bolker, S. C. Walker, Fitting linear mixed-effects models using lme4. J. Stat. Softw. 67, 1–48 (2015).
59
L. Breiman, Random forests. Mach. Learn. 45, 5–32 (2001).
60
61
J. M. Kass, B. Guénard, K. L. Dudley, C. N. Jenkins, F. Azuma, B. L. Fisher, C. L. Parr, H. Gibb, J. T. Longino, P. S. Ward, A. Chao, D. Lubertazzi, M. Weiser, W. Jetz, R. Guralnick, R. Blatrix, J. D. Lauriers, D. A. Donoso, C. Georgiadis, K. Gomez, P. G. Hawkes, R. A. Johnson, J. E. Lattke, J. A. MacGown, W. Mackay, S. Robson, N. J. Sanders, R. R. Dunn, E. P. Economo, The global distribution of known and undiscovered ant biodiversity. Sci. Adv. 8, eabp9908 (2022).
62
A. Shrikumar, P. Greenside, A. Kundaje, “ Learning important features through propagating activation differences” in ICML’17: Proceedings of the 34th International Conference on Machine Learning, ICML 2017, vol. 70 (ACM, 2017), pp. 4844–4866.
63
64
N. Jethani, M. Sudarshan, I. C. Covert, S.-I. Lee, R. Ranganath, FastSHAP: Real-time Shapley value estimation (2025); https://git.io/JCqbP.
65
P. Ploton, F. Mortier, M. Réjou-Méchain, N. Barbier, N. Picard, V. Rossi, C. Dormann, G. Cornu, G. Viennois, N. Bayol, A. Lyapustin, S. Gourlet-Fleury, R. Pélissier, Spatial validation reveals poor predictive performance of large-scale ecological mapping models. Nat. Commun. 11, 4540 (2020).
66
H. Meyer, E. Pebesma, Machine learning-based global maps of ecological variables and the challenge of assessing them. Nat. Commun. 13, 2208 (2022).
67
C. Milà, J. Mateu, E. Pebesma, H. Meyer, Nearest neighbour distance matching Leave-One-Out Cross-Validation for map validation. Methods Ecol. Evol. 13, 1304–1316 (2022).
68
A. M. Potapov, C. A. Guerra, J. van den Hoogen, A. Babenko, B. C. Bellini, M. P. Berg, S. L. Chown, L. Deharveng, Ľ. Kováč, N. A. Kuznetsova, J. F. Ponge, M. B. Potapov, D. J. Russell, D. Alexandre, J. M. Alatalo, J. I. Arbea, I. Bandyopadhyaya, V. Bernava, S. Bokhorst, T. Bolger, G. Castaño-Meneses, M. Chauvat, T. W. Chen, M. Chomel, A. T. Classen, J. Cortet, P. Čuchta, A. Manuela de la Pedrosa, S. S. D. Ferreira, C. Fiera, J. Filser, O. Franken, S. Fujii, E. G. Koudji, M. Gao, B. Gendreau-Berthiaume, D. F. Gomez-Pamies, M. Greve, I. Tanya Handa, C. Heiniger, M. Holmstrup, P. Homet, M. Ivask, C. Janion-Scheepers, M. Jochum, S. Joimel, B. Claudia S Jorge, E. Jucevica, O. Ferlian, L. C. Iuñes de Oliveira Filho, O. Klauberg-Filho, D. Baretta, E. J. Krab, A. Kuu, E. C. A. de Lima, D. Lin, Z. Lindo, A. Liu, J. Z. Lu, M. J. Luciañez, M. T. Marx, M. A. McCary, M. A. Minor, T. Nakamori, I. Negri, R. Ochoa-Hueso, J. G. Palacios-Vargas, M. M. Pollierer, P. Querner, N. Raschmanová, M. I. Rashid, L. J. Raymond-Léonard, L. Rousseau, R. A. Saifutdinov, S. Salmon, E. J. Sayer, N. Scheunemann, C. Scholz, J. Seeber, Y. B. Shveenkova, S. K. Stebaeva, M. Sterzynska, X. Sun, W. I. Susanti, A. A. Taskaeva, M. P. Thakur, M. A. Tsiafouli, M. S. Turnbull, M. N. Twala, A. V. Uvarov, L. A. Venier, L. A. Widenfalk, B. R. Winck, D. Winkler, D. Wu, Z. Xie, R. Yin, D. Zeppelini, T. W. Crowther, N. Eisenhauer, S. Scheu, Globally invariant metabolism but density-diversity mismatch in springtails. Nat. Commun. 14, 674 (2023).
69
A. M. J.-C. Wadoux, G. B. M. Heuvelink, Uncertainty of spatial averages and totals of natural resource maps. Methods Ecol. Evol. 14, 1320–1332 (2023).
70
S. L. Maes, J. Dietrich, G. Midolo, S. Schwieger, M. Kummu, V. Vandvik, R. Aerts, I. H. J. Althuizen, C. Biasi, R. G. Björk, H. Böhner, M. Carbognani, G. Chiari, C. T. Christiansen, K. E. Clemmensen, E. J. Cooper, J. H. C. Cornelissen, B. Elberling, P. Faubert, N. Fetcher, T. G. W. Forte, J. Gaudard, K. Gavazov, Z. Guan, J. Guðmundsson, R. Gya, S. Hallin, B. B. Hansen, S. V. Haugum, J. S. He, C. Hicks Pries, M. J. Hovenden, M. Jalava, I. S. Jónsdóttir, J. Juhanson, J. Y. Jung, E. Kaarlejärvi, M. J. Kwon, R. E. Lamprecht, M. Le Moullec, H. Lee, M. E. Marushchak, A. Michelsen, T. M. Munir, E. M. Myrsky, C. S. Nielsen, M. Nyberg, J. Olofsson, H. Óskarsson, T. C. Parker, E. P. Pedersen, M. Petit Bon, A. Petraglia, K. Raundrup, N. M. R. Ravn, R. Rinnan, H. Rodenhizer, I. Ryde, N. M. Schmidt, E. A. G. Schuur, S. Sjögersten, S. Stark, M. Strack, J. Tang, A. Tolvanen, J. P. Töpper, M. K. Väisänen, R. S. P. van Logtestijn, C. Voigt, J. Walz, J. T. Weedon, Y. Yang, H. Ylänne, M. P. Björkman, J. M. Sarneel, E. Dorrepaal, Environmental drivers of increased ecosystem respiration in a warming tundra. Nature 629, 105–113 (2024).
71
72
G. T. Freschet, L. Pagès, C. M. Iversen, L. H. Comas, B. Rewald, C. Roumet, J. Klimešová, M. Zadworny, H. Poorter, J. A. Postma, T. S. Adams, A. Bagniewska-Zadworna, A. G. Bengough, E. B. Blancaflor, I. Brunner, J. H. C. Cornelissen, E. Garnier, A. Gessler, S. E. Hobbie, I. C. Meier, L. Mommer, C. Picon-Cochard, L. Rose, P. Ryser, M. Scherer-Lorenzen, N. A. Soudzilovskaia, A. Stokes, T. Sun, O. J. Valverde-Barrantes, M. Weemstra, A. Weigelt, N. Wurzburger, L. M. York, S. A. Batterman, M. Gomes de Moraes, Š. Janeček, H. Lambers, V. Salmon, N. Tharayil, M. L. McCormack, A starting guide to root ecology: Strengthening ecological concepts and standardising root classification, sampling, processing and trait measurements. New Phytol. 232, 973–1122 (2021).
73
L. R. Bakken, R. A. Olsen, Buoyant densities and dry-matter contents of microorganisms: Conversion of a measured biovolume into biomass. Appl. Environ. Microbiol. 45, 1188–1195 (1983).
74
K. K. Treseder, A. Cross, Global distributions of arbuscular mycorrhizal fungi. Ecosystems 9, 305–316 (2006).
75
L. Paré, C. Banchini, C. Hamel, L. Bernier, F. Stefani, A simple and low-cost technique to initiate single-spore cultures of arbuscular mycorrhizal fungi using a superabsorbent polymer. Symbiosis 88, 61–73 (2022).
76
K. A. Pirozynski, Y. Dalpé, Geological history of the Glomaceae with particular reference to mycorrhizal symbiosis. Symbiosis 7, 1–36 (1989).
77
D. Zanaga, R. Van De Kerchove, D. Daems, W. De Keersmaecker, C. Brockmann, G. Kirches, J. Wevers, O. Cartus, M. Santoro, S. Fritz, M. Lesiv, M. Herold, N.-E. Tsendbazar, P. Xu, F. Ramoino, O. Arino, ESA WorldCover 10 m 2021 v200. Zenodo (2022); https://doi.org/10.5281/zenodo.7254221.
78
S. R. Searle, F. M. Speed, G. A. Milliken, Population marginal means in the linear model: An alternative to least squares means. Am. Stat. 34, 216–221 (1980).