Philippa Kaur

Our findings highlight the critical role of polyP in Sodalinema stali-formed cyanobacterial mats, as it was dynamically accumulated and recycled during acclimation to P fluctuations.Cellular response to progressive P starvationAnalogous to planktonic cyanobacteria, growth under low P availability could be sustained by recycling polyP, which acted as a primary P source (Fig. 2a) [16, 23, 24]. We further attribute the rapid reduction of easily dispensable cellular P-containing compounds to the substitution of cellular phospholipids with S- or N-containing membrane lipids to maintain growth at the onset of P stress (Fig. 2a) [15, 23]. However, the exhaustion of this easily dispensable P pool limited proliferation in Phase 2, and the metabolic strategy switched from a focus on growth towards maintenance (Fig. 5). The interpretation of prevailing cellular processes based on our results is graphically summarized and explained in detail below (Fig. 5).Fig. 5: Schematic interpretation of cellular phosphorus (P) cycling in a cyanobacterial mat, based on significant changes of the monitored parameters (arbitrary units).a At low P availability, initially contained polyphosphate (polyP) was recycled simultaneously with phosphate uptake to sustain growth at constant C:N:P ratios. Further proliferation at the onset of P stress in Phase 1 was sustained by mobilization of cellular P, e.g. phospholipids, which led to rapidly increasing C:N:P ratios. Severe P stress in Phase 2, indicated by increasing APase activity, prevented proliferation and photosynthesis, indicated by a loss of green chlorophyll pigments. PolyP accumulation by deficiency response occurs with severely increasing P stress, whereby globular DNA accumulation indicates the allocation of P contained in DNA into polyP. P re-addition to the P-stressed cells in Phase 3 triggered overplus uptake and narrow C:N:P ratios, transitioning to luxury uptake at higher C:N:P ratios following polyP recycling. b At high P availability, polyP in Phase 1 was accumulated by overplus uptake at narrow C:N:P ratios, transitioning to luxury uptake at higher C:N:P ratios during polyP recycling in Phase 2. P-deprivation in Phase 3 did not affect the cells, which we attributed to a sufficient amount of phosphate in the residual medium or within the biofilm matrix. Arrows indicate phosphorus transformation processes, whereby arrows pointing towards DNA represent cell growth. Yellow granules = polyP, blue granules = globular DNA spheres, P = phospholipids, S = substitute lipids.Full size imageSevere P stress in Phase 2 was indicated by the colour change from green towards yellow-green (Fig. S1) and increasing APase activity (Fig. 2a). The colour change suggested the loss of photosynthetic pigments [40], but we could not clarify whether this occurred through active cellular pigment reduction or degradation of available chlorophyll e.g., by oxidation. The increasing APase activity (Fig. 2a) suggested that Sodalinema stali is capable of hydrolysing organic P [14]. Even though APase expression did not trigger proliferation, it likely hydrolysed a potentially available organic P pool, as increasing DIC, NH4 and decreasing pH indicated progressive decay and remineralisation of organic matter (Fig. 1a). This suggests that in analogous oligotrophic environments with often fluctuating conditions, the strategy has to be maximizing the utilization of external P sources contained in organic and inorganic sediment particles that get trapped in the EPS [41]. The sediment can contain large amounts of organic P [42] and the fluctuating physico-chemical gradients in the EPS matrix due to high daytime pH and low oxygen conditions at night, facilitate P desorption from metal oxides, leading to higher dissolved phosphate concentrations within the mat, compared to the overlying water body [3]. However, alternating redox conditions at the SWI could also trigger polyP release from benthic microorganisms to the sediments, where it could act as a P source for the benthic food-chain, or ultimately trigger the formation of mineral P phases [32], to sustainably remove P from the aquatic cycle. Either way, we suggest that polyP-containing cyanobacterial mats critically impact P fluxes at the SWI.With persisting severe P stress and increasing APase activity in Phase 2, polyP accumulation as a deficiency response was observed (Fig. 2a), which has been reported from planktonic cyanobacteria of different habitats [24, 29, 23], as well as stream periphyton [28]. However, the reasons causing this deficiency response remain unresolved. In marine phytoplankton of the oligotrophic Sargasso Sea, Martin et al. [23] excluded that polyP-rich cells were in a perpetual overplus state with ‘undetectable’ pulses driving this state and suggested that polyP accumulation occurred as a cellular stress response. In other studies, reduced biosynthesis of P-rich rRNA coincided with deficiency responses [26, 28] and led to the suggestion that polyP accumulation at P concentrations below a certain threshold required for growth occurs because of P allocation changes away from growth and towards storage. Further, APase can hydrolytically cleave phosphate groups from nucleic acids and convert DNA-lipid-P to DNA-lipids, which were shown to self-assemble into globular lipid-based DNA micelles [43]. These preferentially anchor on cell membranes [44], and indeed, such DNA spheres were found to accumulate at the cell’s polar membranes in our experiments adjacent to polyP during deficiency response (Fig. 4a: Phase 2,c). Therefore, we suggest that intracellular P recovery by cleavage from P-rich DNA and reallocation to polyP, and potentially reduced rRNA synthesis [31], is also a strategy in benthic mats of Sodalinema stali as a response to severe P stress when P availability is too low to sustain growth. This supports the theory of a reallocation of resources away from growth towards flexibly available P and energy storage. Such direct intracellular P cycling could be beneficial to help retain P within the cyanobacterial population; while external P moieties such as dissolved organic P within the matrix can act as an additional P source, they are also likely to be subject to nutrient competition between cyanobacteria and other organisms inhabiting the matrix.Such effects of potential interactions in terms of nutrient competition or provision between cyanobacteria and mutualistic microorganisms contained within the same EPS matrix are difficult to assess and we cannot exclude some potential effects on our results. However, mutualistic microorganisms that are naturally contained in many cyanobacterial or algal cultures are often critical for metacommunity functioning and hence, working with axenic mat-forming strains may even further falsify any obtained results. Furthermore, microscopic analyses revealed that Sodalinema always dominated the biomass and hence, it is here considered reasonable to work with a non-axenic culture.Cellular response to a simulated P pulseIn P-deficient cells, the affinity of the P uptake system is typically increased to maximize P uptake for future pulses [13, 45]. The simulated P pulse to the P-stressed cells in Phase 3 led to a rapid increase of the cellular P content by 1260% relative to C within 3 days (Fig. 2a), whereby P was accumulated to a significant part as polyP, which is characteristic for overplus uptake [25]. Many different types of oligotrophic aquatic habitats experience only temporal P pulses, e.g., from redox changes at the benthic interface leading to P release from the sediment [32], storm run-off [28], upwelling [46], or excretions of aquatic animals [47]. The capability of microorganisms to immediately take up, store, and efficiently re-use this P by overplus uptake is hence of critical importance for a population to sustain a potential subsequent period of low P availability. Overplus uptake is typically accompanied by the overall slow growth of the population and cellular recovery from P starvation, including ultrastructural organization and recovery of the photosynthetic apparatus [48]. This took one week after re-feeding of P-starved Nostoc sp. PCC 7118 cells [48]—a timeframe very similar to the delayed onset of photosynthesis observed in our study, indicated by the elevated pH at day 9 (Fig. 1a). Regarding overplus-triggering mechanisms following P pulses, Solovochenko et al. [48] suggested that overplus uptake occurs due to a delayed down-regulation of high-affinity Pi transporters, which are active during P starvation, and emphasized the simultaneous advantage of osmotically inert polyP accumulation as a response to dramatically high phosphate concentrations in the cells. Even though APase levels declined following our experimental P re-addition, they were significantly elevated for at least 9 days (Fig. 2a). As our experimental design involved replacing the medium with APase-free, BG11 + medium after Phase 2, we assume that the APase detected in Phase 3 was actively produced, and we conclude that previously relevant, low-P response mechanisms are slowly disengaged with some sort of lag, even when ambient P is repleted. Following cellular recovery, Sodalinema now recycled stored polyP instead of further accumulating it during the transition from overplus-to luxury uptake, which was reflected in the increasing C:N:P molar ratios and decreasing polyP levels without significant additional phosphate uptake (Figs. 1a, 2a, 5).Qualitative observations on polyP distributionMost methods applied to analyse polyP in microorganisms are quantitative and do not contain information on its spatial distribution within a population. The here observed variable distribution of polyP between the cells during luxury uptake and deficiency response, as well as the retention of polyP in few individual filaments during polyP recycling in Phase 1 of the low P experiment (Fig. 4) suggests strategies of either slow growth with a retention of polyP, or of high growth with polyP recycling. This was also suggested for cells of a unicellular Synechocystis sp. PCC 6803 population during overplus uptake [47]. In contrast, polyP in our experiment was distributed homogeneously between all cyanobacterial cells during overplus uptake (Fig. 4a: Phase 3, Fig. 4b: Phase 1). Yet, we are unaware of any polyP distribution study in multicellular or mat-forming cyanobacteria and hence, further mechanisms of interactions, e.g., cell-to-cell communication [49, 50], might also contribute to purposeful differentiation of cells or filaments within a common matrix.In summary, our study shows that the mat-forming Sodalinema stali (1) is capable of luxury uptake, overplus uptake and deficiency response with a heterogenous polyP distribution during polyP recycling, luxury uptake and deficiency response, while (2) dynamically adjusting cellular P content to changing phosphate concentrations. (3) Proliferation is sustained under the expense of polyP, followed by P acquisition from other easily dispensable cellular P-containing compounds under the onset of P stress. (4) Further, biosynthetic allocation changes away from growth towards maintenance with relative polyP accumulation at the expense of P-rich DNA are conducted under severe P stress. Our findings demonstrate the extraordinary capabilities of mat-forming cyanobacteria to adapt their P acquisition strategies to strong P fluctuations. While lasting proliferation under P limitation requires the mobilization of additional P sources through regeneration of P from particulate matter, the transition to net P accumulation under excess ambient P is rapid and effective. Since current projections of climate and land use change include intensified pulses of P load to aquatic ecosystems [50], e.g., through external input from surplus of agriculture fertilizer, inefficient wastewater treatment plants, and internal loads via the mobilization of legacy P, these P ‘bioaccumulators’ could form an important component in P remediation by temporarily accumulating P within the mat, and synthesizing polyP that could ultimately stimulate the formation of mineral P phases to sustainably remove P from the aquatic cycle. More

Pardo, J. D., Lennie, K. & Anderson, J. S. Can we reliably calibrate deep nodes in the tetrapod tree? Case studies in deep tetrapod divergences. Front. Genet. 11, 1159 (2020).Article 

Google Scholar 
Rage, J.-C. & Roček, Z. Redescription of Triadobatrachus massinoti (Piveteau, 1936) an anuran amphibian from the early Triassic. Palaeontographica A 206, 1–16 (1989).
Google Scholar 
Evans, S. E. & Borsuk-Białynicka, M. A stem-group frog from the Early Triassic of Poland. Acta Palaeontol. Pol. 43, 573–580 (1998).Article 

Google Scholar 
Heckert, A. B., Mitchell, J. S., Schneider, V. P. & Olsen, P. E. Diverse new microvertebrate assemblage from the Upper Triassic Cumnock Formation, Sanford Subbasin, North Carolina, USA. J. Paleontol. 86, 368–390 (2012).Article 

Google Scholar 
Stocker, M. R. et al. The earliest equatorial record of frogs from the Late Triassic of Arizona. Biol. Lett. 15, 20180922 (2019).Article 

Google Scholar 
Schoch, R. R., Werneburg, R. & Voigt, S. A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders. Proc. Natl Acad. Sci. USA 117, 11584–11588 (2020).Article 
ADS 
CAS 

Google Scholar 
Anderson, J. S., Reisz, R. R., Scott, D., Fröbisch, N. B. & Sumida, S. S. A stem batrachian from the Early Permian of Texas and the origin of frogs and salamanders. Nature 453, 515–518 (2008).Article 
ADS 
CAS 

Google Scholar 
Anderson, J. S. Focal review: the origin(s) of modern amphibians. Evol. Biol. 35, 231–247 (2008).Article 

Google Scholar 
Sigurdsen, T. & Bolt, J. R. The Lower Permian amphibamid Doleserpeton (Temnospondyli: Dissorophoidea), the interrelationships of amphibamids, and the origin of modern amphibians. J. Vertebr. Paleontol. 30, 1360–1377 (2010).Article 

Google Scholar 
Schoch, R. R. The putative lissamphibian stem-group: phylogeny and evolution of the dissorophoid temnospondyls. J. Paleontol. 93, 137–156 (2019).Article 

Google Scholar 
Jenkins, P. A. & Walsh, D. M. An Early Jurassic caecilian with limbs. Nature 365, 246–250 (1993).Article 
ADS 

Google Scholar 
Jenkins, F. A., Walsh, D. M. & Carroll, R. L. Anatomy of Eocaecilia micropodia, a limbed caecilian of the Early Jurassic. Bull. Mus. Comp. Zool. 158, 285–365 (2007).Article 

Google Scholar 
Maddin, H. C., Jenkins, F. A. Jr & Anderson, J. S. The braincase of Eocaecilia micropodia (Lissamphibia, Gymnophiona) and the origin of caecilians. PLoS ONE 7, e50743 (2012).Article 
ADS 
CAS 

Google Scholar 
Pardo, J. D., Small, B. J. & Huttenlocker, A. K. Stem caecilian from the Triassic of Colorado sheds light on the origins of Lissamphibia. Proc. Natl Acad. Sci. USA 114, E5389–E5395 (2017).Article 
ADS 
CAS 

Google Scholar 
Nussbaum, R. A. The evolution of a unique dual jaw‐closing mechanism in caecilians: (Amphibia: Gymnophiona) and its bearing on caecilian ancestry. J. Zool. 199, 545–554 (1983).Article 

Google Scholar 
Kleinteich, T., Haas, A. & Summers, A. P. Caecilian jaw-closing mechanics: integrating two muscle systems. J. R. Soc. Interface 5, 1491–1504 (2008).Article 

Google Scholar 
Sherratt, E., Gower, D. J., Klingenberg, C. P. & Wilkinson, M. Evolution of cranial shape in caecilians (Amphibia: Gymnophiona). Evol. Biol. 41, 528–545 (2014).Article 

Google Scholar 
Schmidt, A. & Wake, M. H. Olfactory and vomeronasal systems of caecilians (Amphibia: Gymnophiona). J. Morphol. 205, 255–268 (1990).Article 

Google Scholar 
Pincheira‐Donoso, D., Meiri, S., Jara, M., Olalla‐Tárraga, M. Á. & Hodgson, D. J. Global patterns of body size evolution are driven by precipitation in legless amphibians. Ecography 42, 1682–1690 (2019).Article 

Google Scholar 
San Mauro, D., Vences, M., Alcobendas, M., Zardoya, R. & Meyer, A. Initial diversification of living amphibians predated the breakup of Pangaea. Am. Nat. 165, 590–599 (2005).Article 

Google Scholar 
Padian, K. & Sues, H.-D. in Great Transformations in Vertebrate Evolution (eds Dial, K. P., Shubin, N. & Brainerd, E. L.) 351–374 (Univ. Chicago Press, 2021).Santos, R. O., Laurin, M. & Zaher, H. A review of the fossil record of caecilians (Lissamphibia: Gymnophionomorpha) with comments on its use to calibrate molecular timetrees. Biol. J. Linn. Soc. 131, 737–755 (2020).Article 

Google Scholar 
Evans, S. E. & Sigogneau‐Russell, D. A stem‐group caecilian (Lissamphibia: Gymnophiona) from the Lower Cretaceous of North Africa. Palaeontology 44, 259–273 (2001).Article 

Google Scholar 
Ramezani, J. et al. High-precision U-Pb zircon geochronology of the Late Triassic Chinle Formation, Petrified Forest National Park (Arizona, USA): temporal constraints on the early evolution of dinosaurs. GSA Bull. 123, 2142–2159 (2011).Article 
CAS 

Google Scholar 
Rasmussen, C. et al. U-Pb zircon geochronology and depositional age models for the Upper Triassic Chinle Formation (Petrified Forest National Park, Arizona, USA): implications for Late Triassic paleoecological and paleoenvironmental change. GSA Bull. 133, 539–558 (2021).Article 
CAS 

Google Scholar 
Nordt, L., Atchley, S. & Dworkin, S. Collapse of the Late Triassic megamonsoon in western equatorial Pangea, present-day American Southwest. GSA Bull. 127, 1798–1815 (2015).Article 
CAS 

Google Scholar 
Martz, J. W. & Parker, W. G. in Terrestrial Depositional Systems (eds Zeigler, K. E. & Parker, W. G.) 39–125 (Elsevier, 2017).Daza, J. D. et al. Enigmatic amphibians in mid-Cretaceous amber were chameleon-like ballistic feeders. Science 370, 687–691 (2020).Article 
ADS 
CAS 

Google Scholar 
Gardner, J. D. Monophyly and affinities of albanerpetontid amphibians (Temnospondyli; Lissamphibia). Zool. J. Linn. Soc. 131, 309–352 (2001).Article 

Google Scholar 
Bolt, J. R. Lissamphibian origins: possible protolissamphibian from the Lower Permian of Oklahoma. Science 166, 888–891 (1969).Article 
ADS 
CAS 

Google Scholar 
Gardner, J. D. & Averianov, A. O. Albanerpetontid amphibians from the Upper Cretaceous of Middle Asia. Acta Palaeontol. Pol. 43, 453–476 (1998).
Google Scholar 
Carroll, R. L. The Palaeozoic ancestry of salamanders, frogs and caecilians. Zool. J. Linn. Soc. 150, 1–140 (2007).Article 

Google Scholar 
Müller, H., Oommen, O. V. & Bartsch, P. Skeletal development of the direct-developing caecilian Gegeneophis ramaswamii (Amphibia: Gymnophiona: Caeciliidae). Zoomorphology 124, 171–188 (2005).Article 

Google Scholar 
Ahlberg, P. E. & Clack, J. A. Lower jaws, lower tetrapods—a review based on the Devonian genus Acanthostega. Earth Environ. Sci. Trans. R. Soc. Edinb. 89, 11–46 (1998).Article 

Google Scholar 
Bolt, J. R. & Lombard, R. E. The mandible of the primitive tetrapod Greererpeton, and the early evolution of the tetrapod lower jaw. J. Paleontol. 75, 1016–1042 (2001).Article 

Google Scholar 
Shishkin, M. A. & Sulej, T. The Early Triassic temnospondyls of the Czatkowice 1 tetrapod assemblage. Acta Palaeontol. Pol. 65, 31–77 (2009).
Google Scholar 
Anderson, J. S., Scott, D. & Reisz, R. R. The anatomy of the dermatocranium and mandible of Cacops aspidephorus Williston, 1910 (Temnospondyli: Dissorophidae), from the Lower Permian of Texas. J. Vertebr. Paleontol. 40, e1776720 (2020).Article 

Google Scholar 
Wilkinson, M., San Mauro, D., Sherratt, E. & Gower, D. J. A nine-family classification of caecilians (Amphibia: Gymnophiona). Zootaxa 2874, 41–64 (2011).Article 

Google Scholar 
Jared, C. et al. Skin gland concentrations adapted to different evolutionary pressures in the head and posterior regions of the caecilian Siphonops annulatus. Sci. Rep. 8, 3576 (2018).Article 
ADS 

Google Scholar 
O’Reilly, J. C., Ritter, D. A. & Carrier, D. R. Hydrostatic locomotion in a limbless tetrapod. Nature 386, 269–272 (1997).Article 
ADS 

Google Scholar 
Muttoni, G. & Kent, D. V. Jurassic monster polar shift confirmed by sequential paleopoles from Adria, promontory of Africa. J. Geophys. Res. 124, 3288–3306 (2019).Article 
ADS 

Google Scholar 
Parsons, T. S. & Williams, E. E. The relationships of the modern Amphibia: a re-examination. Q. Rev. Biol. 38, 26–53 (1963).Article 

Google Scholar 
Marjanović, D. & Laurin, M. A reevaluation of the evidence supporting an unorthodox hypothesis on the origin of extant amphibians. Contrib. Zool. 77, 149–199 (2008).Article 

Google Scholar 
Jenkins, X. A. et al. Using manual ungual morphology to predict substrate use in the Drepanosauromorpha and the description of a new species. J. Vertebr. Paleontol. 40, e1810058 (2020).Article 

Google Scholar 
Kligman, B. T., Marsh, A. D., Nesbitt, S. J., Parker, W. G. & Stocker, M. R. New trilophosaurid species demonstrates a decline in allokotosaur diversity across the Adamanian–Revueltian boundary in the Late Triassic of western North America. Palaeodiversity 13, 25–37 (2020).Article 

Google Scholar 
Marsh, A. D., Smith, M. E., Parker, W. G., Irmis, R. B. & Kligman, B. T. Skeletal anatomy of Acaenasuchus geoffreyi Long and Murry, 1995 (Archosauria: Pseudosuchia) and its implications for the origin of the aetosaurian carapace. J. Vertebr. Paleontol. 40, e1794885 (2020).Article 

Google Scholar 
Marsh, A. D. & Parker, W. G. New dinosauromorph specimens from Petrified Forest National Park and a global biostratigraphic review of Triassic dinosauromorph body fossils. PaleoBios https://doi.org/10.5070/P9371050859 (2020).Kligman, B. T., Marsh, A. D., Sues, H.-D. & Sidor, C. A. A new non-mammalian eucynodont from the Chinle Formation (Triassic: Norian), and implications for the early Mesozoic equatorial cynodont record. Biol. Lett. 16, 20200631 (2020).Article 

Google Scholar 
Huttenlocker, A. K., Pardo, J. D., Small, B. J. & Anderson, J. S. Cranial morphology of recumbirostrans (Lepospondyli) from the Permian of Kansas and Nebraska, and early morphological evolution inferred by micro-computed tomography. J. Vertebr. Paleontol. 33, 540–552 (2013).Article 

Google Scholar 
Pardo, J. D., Szostakiwskyj, M., Ahlberg, P. E. & Anderson, J. S. Hidden morphological diversity among early tetrapods. Nature 546, 642–645 (2017).Article 
ADS 
CAS 

Google Scholar 
Marjanović, D. & Laurin, M. Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix. PeerJ 6, e5565 (2019).Article 

Google Scholar 
Goloboff, P. A. & Catalano, S. A. TNT version 1.5, including a full implementation of phylogenetic morphometrics. Cladistics 32, 221–238 (2016).Article 

Google Scholar 
Huelsenbeck, J. P. & Ronquist, F. MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics 17, 754–755 (2001).Article 
CAS 

Google Scholar 
Lewis, P. O. A likelihood approach to estimating phylogeny from discrete morphological character data. Syst. Biol. 50, 913–925 (2001).Article 
CAS 

Google Scholar 
Eltink, E., Schoch, R. R. & Langer, M. C. Interrelationships, palaeobiogeography and early evolution of Stereospondylomorpha (Tetrapoda: Temnospondyli). J. Iber. Geol. 45, 251–267 (2019).Article 

Google Scholar 
Bystrow, A. Dvinosaurus als neotenische Form der Stegocephalen. Acta Zool. 19, 209–295 (1938).Article 

Google Scholar 
Dutuit, J.-M. Introduction à l’étude paléontologique du Trias continental Marocain. Description des premiers stegocephales recueillis dans le couloir d’Argana (Atlas Occidental). Mémoires du Muséum National d’Histoire 36, 1–253 (1976).
Google Scholar 
Dias, E. V., Dias-da-Silva, S. & Schultz, C. L. A new short-snouted rhinesuchid from the Permian of southern Brazil. Revista Brasileira de Paleontologia 23, 98–122 (2020).Article 

Google Scholar 
Damiani, R. J. & Kitching, J. W. A new brachyopid temnospondyl from the Cynognathus Assemblage Zone, Upper Beaufort Group, South Africa. J. Vertebr. Paleontol. 23, 67–78 (2003).Article 

Google Scholar 
Schoch, R. R. & Witzmann, F. Cranial morphology of the plagiosaurid Gerrothorax pulcherrimus as an extreme example of evolutionary stasis. Lethaia 45, 371–385 (2012).Article 

Google Scholar 
Schoch, R. R. Studies on braincases of early tetrapods: Structure, morphological diversity, and phylogeny-1 Trimerorhacis and other prmitive temnospondyls. Neues Jahrbuch für Geologie und Paläontologie-Abhandlungen 213, 233–259 (1999).Article 

Google Scholar 
Ruta, M. & Bolt, J. R. The brachyopoid Hadrokkosaurus bradyi from the early Middle Triassic of Arizona, and a phylogenetic analysis of lower jaw characters in temnospondyl amphibians. Acta Palaeontol. Pol. 53, 579–592 (2008).Article 

Google Scholar 
Bystrow, A. & Efremov, J. Benthosuchus sushkini Efr.—a labyrinthodont from the Eotriassic of Sharzhenga River. Trudy Paleontol. Inst. 10, 1–152 (1940).
Google Scholar 
Warren, A. Karoo tupilakosaurid: a relict from Gondwana. Earth Environ. Sci. Trans. R. Soc. Edinb. 89, 145–160 (1998).Article 

Google Scholar 
Holmes, R. B., Carroll, R. L. & Reisz, R. R. The first articulated skeleton of Dendrerpeton acadianum (Temnospondyli, Dendrerpetontidae) from the Lower Pennsylvanian locality of Joggins, Nova Scotia, and a review of its relationships. J. Vertebr. Paleontol. 18, 64–79 (1998).Article 

Google Scholar 
Steyer, J. S. The first articulated trematosaur ‘amphibian’ from the Lower Triassic of Madagascar: implications for the phylogeny of the group. Palaeontol. 45, 771–793 (2002).Article 

Google Scholar 
Englehorn, J., Small, B. J. & Huttenlocker, A. A redescription of Acroplous vorax (Temnospondyli: Dvinosauria) based on new specimens from the Early Permian of Nebraska and Kansas, USA. J. Vertebr. Paleontol. 28, 291–305 (2008).Article 

Google Scholar 
Warren, A. Laidleria uncovered: a redescription of Laidleria gracilis Kitching (1957), a temnospondyl from the Cynognathus Zone of South Africa. Zool. J. Linn. Soc. 122, 167–185 (1998).Article 

Google Scholar 
Bolt, J. R. & Chatterjee, S. A new temnospondyl amphibian from the Late Triassic of Texas. J. Paleontol. 74, 670–683 (2000).Article 

Google Scholar 
Milner, A. & Sequeira, S. The temnospondyl amphibians from the Viséan of east Kirkton, West Lothian, Scotland. Earth Environ. Sci. Trans. R. Soc. Edinb. 84, 331–361 (1993).
Google Scholar 
Schoch, R. R. & Milner, A. R. Encyclopedia of Paleoherpetology, Part 3A. Temnospondyli (Verlag Dr. Friedrich Pfeil, 2014).Damiani, R., Schoch, R. R., Hellrung, H., Werneburg, R. & Gastou, S. The plagiosaurid temnospondyl Plagiosuchus pustuliferus (Amphibia: Temnospondyli) from the Middle Triassic of Germany: anatomy and functional morphology of the skull. Zool. J. Linn. Soc. 155, 348–373 (2009).Article 

Google Scholar 
Chernin, S. A new brachyopid, Batrachosuchus concordi sp. nov. from the Upper Luangwa Valley, Zambia with a redescription of Batrachosuchus browni Broom, 1903. Palaeontol. Afr. 20, 87–109 (1977).
Google Scholar 
Sulej, T. Osteology, variability, and evolution of Metoposaurus, a temnospondyl from the Late Triassic of Poland. Acta Palaeontol. Pol. 64, 29–139 (2007).
Google Scholar  More

DatasetsImage acquisitionFor this study, we assembled three datasets: one for training of the RootDetector Convolutional Neural Network (Training-Set), one for a performance comparison between humans and RootDetector in segmenting roots in minirhizotron images (Comparison-Set), and one for the validation of the algorithm (Validation-Set). The Training-Set contained 129 images comprised of 17 randomly selected minirhizotron images sampled in a mesocosm experiment (see “Mesocosm sampling” Section), 47 randomly selected minirhizotron images sampled in a field study (see “Field sampling” Section) as well as the 65 minirhizotron images of soy roots published by Wang et al.15. The Comparison-Set contained 25 randomly selected minirhizotron images from the field-study which all were not part of the images included in the Training- and Validation-Sets. The Validation-Set contained 10 randomly selected minirhizotron images from the same field study, which had not been used in the Training-Set. All images were recorded with 2550 ✕ 2273 pixels at 300 dpi with a CI-600 In-Situ Root Imager (CID Bio-Science Inc., Camas, WA, USA) and stored as .tiff files to reduce compression loss. For all training and evaluation purposes we used raw, unprocessed output images from the CI-600.Mesocosm samplingThe mesocosm experiment was established in 2018 on the premises of the Institute for Botany and Landscape Ecology of the University of Greifswald (Fig. S1). It features 108 heavy duty plastic buckets of 100 l each, filled to two thirds of their height with moderately decomposed sedge fen peat. Each mesocosm contained one minirhizotron (inner diameter: 64 mm, outer diameter: 70 mm, length: 650 mm) installed at a 45°angle and capped in order to avoid penetration by light. The mesocosms were planted with varying compositions of plant species that typically occur in north-east German sedge fens (Carex rostrata, Carex acutiformis, Glyceria maxima, Equisetum fluviatile, Juncus inflexus, Mentha aquatica, Acorus calamus and Lycopus europaeus). The mesocosms were subjected to three different water table regimes: stable at soil surface level, stable at 20 cm below soil surface and fluctuating between the two levels every two weeks. The minirhizotrons were scanned weekly at two levels of soil depth (0–20 cm and 15–35 cm) between April 2019 and December 2021, resulting in roughly 9500 minirhizotron images of 216 × 196 mm. Manual quantification of root length would, based on own experience, take approximately three hours per image, resulting in approximately 28,500 h of manual processing for the complete dataset. Specimens planted were identified by author Dr. Blume-Werry, however no voucher specimen were deposited. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation.Field samplingThe field study was established as part of the Wetscapes project in 201716. The study sites were located in Mecklenburg-Vorpommern, Germany, in three of the most common wetland types of the region: alder forest, percolation fen and coastal fen (Fig. S2). For each wetland type, a pair of drained versus rewetted study sites was established. A detailed description of the study sites and the experimental setup can be found in Jurasinski et al.16. At each site, 15 minirhizotrons (same diameter as above, length: 1500 mm) were installed at 45° angle along a central boardwalk. The minirhizotrons have been scanned biweekly since April 2018, then monthly since January 2019 at two to four levels of soil depth (0–20 cm, 20–40 cm, 40–60 cm and 60–80 cm), resulting in roughly 12,000 minirhizotron images of 216 × 196 cm, i.e. an estimated 36,000 h of manual processing for the complete dataset. Permission for the study was obtained from the all field owners. Figure 1Overview of the RootDetector system. The main component is a semantic segmentation network based on the U-Net architecture. The root length is estimated by skeletonizing the segmentation output and applying the formula introduced by Kimura et al.17. During training only, a weight map puts more emphasis on fine roots.Full size imageThe CNN RootDetectorImage annotationFor the generation of training data for the CNN, human analysts manually masked all root pixels in the 74 images of the Training-Set using GIMP 2.10.12. The resulting ground truth data are binary, black-and-white images in Portable Network Graphics (.png) format, where white pixels represent root structures and black pixels represent non-root objects and soil (Fig. 2b). All training data were checked and, if required, corrected by an expert (see “Selection of participants” for definition). The Validation-Set was created in the same way but exclusively by experts.Figure 2Example of segmentation and result of skeletonization. A 1000 by 1000 pixel input image (a), the manually annotated ground truth image (b), the RootDetector estimation image (c), the combined representation image (error map, d with green indicating true positives, red indicating false positive, blue indicating false negatives), the skeletonized RootDetector estimation image (e), and the skeletonized ground truth image (f).Full size imageArchitectureRootDetector’s core consists of a Deep Neural Network (DNN) based on the U-Net image segmentation architecture[27]nd is implemented in TensorFlow and Keras frameworks18. Although U-Net was originally developed for biomedical applications, it has since been successfully applied to other domains due to its generic design.RootDetector is built up of four down-sampling blocks, four up-sampling blocks and a final output block (Fig. 1). Every block contains two 3 × 3 convolutional layers, each followed by rectified linear units (ReLU). The last output layer instead utilizes Sigmoid activation. Starting from initial 64 feature channels, this number is doubled in every down-block and the resolution is halved via 2 × 2 max-pooling. Every up-block again doubles the resolution via bilinear interpolation and a 1 × 1 convolution which halves the number of channels. Importantly, after each up-sampling step, the feature map is concatenated with the corresponding feature map from the down-sampling path. This is crucial to preserve fine spatial details.Our modifications from the original architecture include BatchNormalization19 after each convolutional layer which significantly helps to speed up the training process and zero-padding instead of cropping as suggested by Ronneberger, Fischer, & Brox20 to preserve the original image size.In addition to the root segmentation network, we trained a second network to detect foreign objects, specifically the adhesive tape that is used as a light barrier on the aboveground part of the minirhizotrons. We used the same network architecture as above and trained in a supervised fashion with the binary cross-entropy loss. During inference, the result is thresholded (predefined threshold value: 0.5) and used without post-processing.TrainingWe pre-trained RootDetector on the COCO dataset21 to generate a starting point. Although the COCO dataset contains a wide variety of image types and classes not specifically related to minirhizotron images, Majurski et al.22 showed, that for small annotation counts, transfer-learning even from unrelated datasets may improve a CNNs performance by up to 20%. We fine-tuned for our dataset with the Adam optimizer23 for 15 epochs and trained on a total of 129 images from the Training-Set (17 mesocosm images, 47 field-experiment images, 65 soy root images). To enhance the dataset size and reduce over-fitting effects, we performed a series of augmentation operations as described by Shorten & Khoshgoftaar24. In many images, relatively coarse roots ( > 3 mm) occupied a major part of the positive (white) pixel space, which might have caused RootDetector to underestimate fine root details overall. Similarly, negative space (black pixels) between tightly packed, parallel roots was often very small and might have impacted the training process to a lesser extent when compared to large areas with few or no roots (Fig. 2). To mitigate both effects, we multiplied the result of the cross-entropy loss map with a weight map which emphasizes positive–negative transitions. This weight map is generated by applying the following formula to the annotated ground truth images:$$omega left( x right) = 1 – left( {tanh left( {2tilde{x} – 1} right)} right)^{2}$$
(1)
where ω(x) is the average pixel value of the annotated weight map in a 5 × 5 neighborhood around pixel x. Ronneberger, Fischer, & Brox20 implemented a similar weight map, however with stronger emphasis on space between objects. As this requires computation of distances between two comparatively large sets of points, we adapted and simplified their formula to be computable in a single 5 × 5 convolution.For the loss function we applied a combination of cross-entropy and Dice loss 25:$${mathcal{L}} = {mathcal{L}}_{CE} + lambda {mathcal{L}}_{Dice} = – frac{1}{N}sumnolimits_{i} {wleft( {x_{i} } right)y_{i} log left( {x_{i} } right) + lambda frac{{2sumnolimits_{i} {x_{i} y_{i} } }}{{sumnolimits_{i} {x_{i}^{2} sumnolimits_{i} {y_{i}^{2} } } }}}$$
(2)

where x are the predicted pixels, y the corresponding ground truth labels, N the number of pixels in an image and λ a balancing factor which we set to 0.01. This value was derived empirically. The Dice loss is applied per-image to counteract the usually high positive-to-negative pixel imbalance. Since this may produce overly confident outputs and restrict the application of weight maps, we used a relatively low value for λ.Output and post-processingRootDetector generates two types of output. The first type of output are greyscale .png files in which white pixels represent pixels associated with root structures and black pixels represent non-root structures and soil (Fig. 2c). The advantage of .png images is their lossless ad artifact-free compression at relatively small file sizes. RootDetector further skeletonizes the output images and reduces root-structures to single-pixel representations using the skeletonize function of scikit-image v. 0.17.1 (26; Fig. 2e,f). This helps to reduce the impact of large diameter roots or root-like structures such as rhizomes in subsequent analyses and is directly comparable to estimations of root length. The second type of output is a Comma-separated values (.csv) file, with numerical values indicating the number of identified root pixels, the number of root pixels after skeletonization, the number of orthogonal and diagonal connections between pixels after skeletonization and an estimation of the physical combined length of all roots for each processed image. The latter is a metric commonly used in root research as in many species, fine roots provide most vital functions such as nutrient and water transport3. Therefore, the combined length of all roots in a given space puts an emphasis on fine roots as they typically occupy a relatively smaller fraction of the area in a 2D image compared to often much thicker coarse roots. To derive physical length estimates from skeletonized images, RootDetector counts orthogonal- and diagonal connections between pixels of skeletonized images and employs the formula proposed by Kimura et al.17 (Eq. 3).$$L = left[ {N_{d}^{2} + left( {N_{d} + N_{o} /2} right)^{2} } right]^{{1/2}} + N_{o} /2$$
(3)
where Nd is the number of diagonally connected and No the number of orthogonally connected skeleton pixels. To compute Nd we convolve the skeletonized image with two 2 × 2 binary kernels, one for top-left-to-bottom-right connections and another for bottom-left-to-top-right connections and count the number of pixels with maximum response in the convolution result. Similarly, No is computed with a 1 × 2 and a 2 × 1 convolutional kernels.Performance comparisonSelection of participantsFor the performance comparison, we selected 10 human analysts and divided them into three groups of different expertise levels in plant physiology and with the usage of digital root measuring tools. The novice group consisted of 3 ecology students (2 bachelor’s, 1 master’s) who had taken or were taking courses in plant physiology but had no prior experience with minirhizotron images or digital root measuring tools. This group represents undergraduate students producing data for a Bachelor thesis or student assistants employed to process data. The advanced group consisted of 3 ecology students (1 bachelor’s, 2 master’s) who had already taken courses in plant physiology and had at least 100 h of experience with minirhizotron images and digital root measuring tools. The expert group consisted of 4 scientists (2 PhD, 2 PhD candidates) who had extensive experience in root science and at least 250 h of experience with digital root measuring tools. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation and informed consent was obtained from all participants.Instruction and root tracingAll three groups were instructed by showing them a 60 min live demo of an expert tracing roots in minirhizotron images, during which commonly encountered challenges and pitfalls were thoroughly discussed. Additionally, all participants were provided with a previously generated, in-depth manual containing guidelines on the identification of root structures, the correct operation of the root tracing program and examples of often encountered challenges and suggested solutions. Before working on the Comparison-Set, all participants traced roots in one smaller-size sample image and received feedback from one expert.Image preparation and root tracingBecause the minirhizotron images acquired in the field covered a variety of different substrates, roots of different plant species, variance in image quality, and because tracing roots is very time consuming, we decided to maximize the number of images by tracing roots only in small sections, in order to cover the largest number of cases possible. To do this, we placed a box of 1000 × 1000 pixels (8.47 × 8.47 cm) at a random location in each of the images in the Comparison-Set and instructed participants to trace only roots within that box. Similarly, we provided RootDetector images where the parts of the image outside the rectangle were occluded. All groups used RootSnap! 1.3.2.25 (CID Bio-Science Inc., Camas, WA, USA;27), a vector based tool to manually trace roots in each of the 25 images in the comparison set. We decided on RootSnap! due to our previous good experience with the software and its’ relative ease of use. The combined length of all roots was then exported as a csv file for each person and image and compared to RootDetector’s output of the Kimura root length.ValidationWe tested the accuracy of RootDetector on a set of 10 image segments of 1000 by 1000 pixels cropped from random locations of the 10 images of the Validation-Set. These images were annotated by a human expert without knowledge of the estimations by the algorithm and were exempted from the training process. As commonly applied in binary classification, we use the F1 score as a metric to evaluate the performance RootDetector. F1 is calculated from precision (Eq. 4) and recall (Eq. 5) and represents their harmonic mean (Eq. 6). Ranging from 0 to 1, higher values indicate high classification (segmentation) performance. As one of the 10 image sections contained no roots and thus no F1 Score was calculable, it was excluded from the validation. We calculated the F1 score for each of the nine remaining image sections and averaged the values as a metric for overall segmentation performance.$$Precision;(P) = frac{{tp}}{{tp + fp}}$$
(4)
$$Recall;(R) = frac{{tp}}{{tp + fn}}$$
(5)
$$F1 = 2*frac{{P*R}}{{P + R}}$$
(6)
where P = precision, R = recall, tp = true positives; fp = false positives, fn = false negatives.Statistical analysisWe used R Version 4.1.2 (R Core Team, 2021) for all statistical analyses and R package ggplot2 Version 3.2.128 for visualizations. Pixel identification-performance comparisons were based on least-squares fit and the Pearson method. Root length estimation-performance comparisons between groups of human analysts (novice, advanced, expert) and RootDetector were based on the respective estimates of total root length plotted over the minirhizotron images in increasing order of total root length. Linear models were calculated using the lm function for each group of analysts. To determine significant differences between the groups and the algorithm, 95% CIs as well as 83% CIs were displayed and RootDetector root length outside the 95% CI were considered significantly different from the group estimate at α = 0.0529. The groups of human analysts were considered significantly different if their 83% CIs did not overlap, as the comparison of two 83% CIs approximates an alpha level of 5%30,31.This study is approved by Ethikkommission der Universitätsmedizin Greifswald, University of Greifswald, Germany. More

Speakman, J. R. The cost of living: Field metabolic rates of small mammals. Adv. Ecol. Res. 30, 177–297 (1999).Article 

Google Scholar 
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. Toward a metaboolic theory of ecology. Ecology 85(7), 1771–1789. https://doi.org/10.1890/03-9000 (2004).Article 

Google Scholar 
Larivée, M. L., Boutin, S., Speakman, J. R., McAdam, A. G. & Humphries, M. M. Associations between over-winter survival and resting metabolic rate in juvenile North American red squirrels. Funct. Ecol. 24(3), 597–607. https://doi.org/10.1111/j.1365-2435.2009.01680.x (2010).Article 

Google Scholar 
Corp, N., Gorman, M. L. & Speakman, J. R. Seasonal variation in the resting metabolic rate of male wood mice Apodemus sylvaticus from two contrasting habitats 15 km apart. J. Comp. Physiol. B 167(3), 229–239. https://doi.org/10.1007/s003600050069 (1997).Article 
CAS 

Google Scholar 
Lehto Hürlimann, M., Martin, J. G. A. & Bize, P. Evidence of phenotypic correlation between exploration activity and resting metabolic rate among populations across an elevation gradient in a small rodent species. Behav. Ecol. Sociobiol. 73(9), 131. https://doi.org/10.1007/s00265-019-2740-6 (2019).Article 

Google Scholar 
Reher, S., Rabarison, H., Montero, B. K., Turner, J. M. & Dausmann, K. H. Disparate roost sites drive intraspecific physiological variation in a Malagasy bat. Oecologia 198(1), 35–52. https://doi.org/10.1007/s00442-021-05088-2 (2022).Article 
ADS 

Google Scholar 
McDonald, R. I. et al. Research gaps in knowledge of the impact of urban growth on biodiversity. Nat. Sustain. https://doi.org/10.1038/s41893-019-0436-6 (2019).Article 

Google Scholar 
Shochat, E., Warren, P. S., Faeth, S. H., McIntyre, N. E. & Hope, D. From patterns to emerging processes in mechanistic urban ecology. Trends Ecol. Evol. 21(4), 186–191. https://doi.org/10.1016/j.tree.2005.11.019 (2006).Article 

Google Scholar 
United Nations, Department of Economic and Social Affairs, Population Division. World Urbanization Prospects 2018: Highlights. https://population.un.org/wup/Publications/ (2018).Alberti, M. et al. The complexity of urban eco-evolutionary dynamics. Bioscience 70(9), 772–793. https://doi.org/10.1093/biosci/biaa079 (2020).Article 

Google Scholar 
Birnie-Gauvin, K., Peiman, K. S., Gallagher, A. J., de Bruijn, R. & Cooke, S. J. Sublethal consequences of urban life for wild vertebrates. Environ. Rev. 24(4), 416–425. https://doi.org/10.1139/er-2016-0029 (2016).Article 

Google Scholar 
Diamond, S. E. & Martin, R. A. Physiological adaptation to cities as a proxy to forecast global-scale responses to climate change. J. Exp. Biol. 224((Suppl_1)), jeb22336. https://doi.org/10.1242/jeb.229336 (2021).Article 

Google Scholar 
Grimm, N. B. et al. Global change and the ecology of cities. Science 319(5864), 756–760. https://doi.org/10.1126/science.1150195 (2008).Article 
ADS 
CAS 

Google Scholar 
McDonnell, M. J. & Pickett, S. T. Ecosystem structure and function along urban-rural gradients: An unexploited opportunity for ecology. Ecology 71(4), 1232–1237. https://doi.org/10.2307/1938259 (1990).Article 

Google Scholar 
Francis, R. A. & Chadwick, M. A. What makes a species synurbic?. Appl. Geogr. 32(2), 514–521. https://doi.org/10.1016/j.apgeog.2011.06.013 (2012).Article 

Google Scholar 
Luniak, M. Synurbization–adaptation of animal wildlife to urban development. In Proc. 4th Int. Symposium Urban Wildl. Conserv (Tucson, University of Arizona, 2004).Coogan, S. C. P., Raubenheimer, D., Zantis, S. P. & Machovsky-Capuska, G. E. Multidimensional nutritional ecology and urban birds. Ecosphere 9(4), e02177. https://doi.org/10.1002/ecs2.2177 (2018).Article 

Google Scholar 
Lowry, H., Lill, A. & Wong, B. B. Behavioural responses of wildlife to urban environments. Biol. Rev. Camb. Philos. Soc. 88(3), 537–549. https://doi.org/10.1111/brv.12012 (2013).Article 

Google Scholar 
Łopucki, R., Klich, D., Ścibior, A. & Gołębiowska, D. Hormonal adjustments to urban conditions: Stress hormone levels in urban and rural populations of Apodemus agrarius. Urban Ecosyst. 22(3), 435–442. https://doi.org/10.1007/s11252-019-0832-8 (2019).Article 

Google Scholar 
McCleery, R. in Urban mammals in Urban Ecosystem Ecology (eds. Aitkenhead-Peterson, J., Volder, A.) 87–102 (American Society of Agronomy, 2010). https://doi.org/10.2134/agronmonogr55.c52010Uchida, K., Suzuki, K., Shimamoto, T., Yanagawa, H. & Koizumi, I. Seasonal variation of flight initiation distance in Eurasian red squirrels in urban versus rural habitat. J. Zool. 298(3), 225–231. https://doi.org/10.1111/jzo.12306 (2016).Article 

Google Scholar 
Kleerekoper, L., van Esch, M. & Salcedo, T. B. How to make a city climate-proof, addressing the urban heat island effect. Resour. Conserv. Recyl. 64, 30–38. https://doi.org/10.1016/j.resconrec.2011.06.004 (2012).Article 

Google Scholar 
Pickett, S. T. et al. Urban ecological systems: Scientific foundations and a decade of progress. J. Environ. Manag. 92(3), 331–362. https://doi.org/10.1016/j.jenvman.2010.08.022 (2011).Article 
CAS 

Google Scholar 
Rizwan, A. M., Dennis, L. Y. & Chunho, L. A review on the generation, determination and mitigation of Urban Heat Island. J. Environ. Sci. 20(1), 120–128 (2008).Article 
CAS 

Google Scholar 
Isaksson, C. Urban ecophysiology: Beyond costs, stress and biomarkers. J. Exp. Biol. 223(22), jeb203794. https://doi.org/10.1242/jeb.203794 (2020).Article 

Google Scholar 
Miles, L. S., Carlen, E. J., Winchell, K. M. & Johnson, M. T. J. Urban evolution comes into its own: Emerging themes and future directions of a burgeoning field. Evol. Appl. 14(1), 3–11. https://doi.org/10.1111/eva.13165 (2020).Article 

Google Scholar 
Gavett, A. P. & Wakeley, J. S. Blood constituents and their relation to diet in urban and rural house sparrows. Condor 88(3), 279–284. https://doi.org/10.2307/1368873 (1986).Article 

Google Scholar 
Murray, M. et al. Greater consumption of protein-poor anthropogenic food by urban relative to rural coyotes increases diet breadth and potential for human-wildlife conflict. Ecography 38(12), 1235–1242. https://doi.org/10.1111/ecog.01128 (2015).Article 

Google Scholar 
Pollock, C. J., Capilla-Lasheras, P., McGill, R. A. R., Helm, B. & Dominoni, D. M. Integrated behavioural and stable isotope data reveal altered diet linked to low breeding success in urban-dwelling blue tits (Cyanistes caeruleus). Sci. Rep. 7(1), 5014. https://doi.org/10.1038/s41598-017-04575-y (2017).Article 
ADS 
CAS 

Google Scholar 
Schulte-Hostedde, A. I., Mazal, Z., Jardine, C. M. & Gagnon, J. Enhanced access to anthropogenic food waste is related to hyperglycemia in raccoons (Procyon lotor). Conserv. Physiol. 6(1), coy026. https://doi.org/10.1093/conphys/coy026 (2018).Article 
CAS 

Google Scholar 
Fingland, K., Ward, S. J., Bates, A. J. & Bremner-Harrison, S. A systematic review into the suitability of urban refugia for the Eurasian red squirrel Sciurus vulgaris. Mamm. Rev. 52(1), 26–38. https://doi.org/10.1111/mam.12264 (2021).Article 

Google Scholar 
Jokimäki, J., Selonen, V., Lehikoinen, A. & Kaisanlahti-Jokimäki, M.-L. The role of urban habitats in the abundance of red squirrels (Sciurus vulgaris, L.) in Finland. Urban For. Urban Green. 27, 100–108. https://doi.org/10.1016/j.ufug.2017.06.021 (2017).Article 

Google Scholar 
Dausmann, K. H., Wein, J., Turner, J. M. & Glos, J. Absence of heterothermy in the European red squirrel (Sciurus vulgaris). Mammal. Biol. 78(5), 332–335. https://doi.org/10.1016/j.mambio.2013.01.004 (2013).Article 

Google Scholar 
Turner, J. M., Reher, S., Warnecke, L. & Dausmann, K. H. Eurasian red squirrels show little seasonal variation in metabolism in food-enriched habitat. Physiol. Biochem. Zool. 90(6), 655–662. https://doi.org/10.1086/694847 (2017).Article 

Google Scholar 
McNab, B. K. On the comparative ecological and evolutionary significance of total and mass-specific rates of metabolism. Physiol. Biochem. Zool. 72(5), 642–644 (1999).Article 
CAS 

Google Scholar 
Menzies, A. K. et al. Body temperature, heart rate, and activity patterns of two boreal homeotherms in winter: Homeostasis, allostasis, and ecological coexistence. Funct. Ecol. 34(11), 2292–2301. https://doi.org/10.1111/1365-2435.13640 (2020).Article 

Google Scholar 
Wauters, L. & Dhondt, A. Activity budget and foraging behaviour of the red squirrel (Sciurus vulgaris Linnaeus, 1758) in a coniferous habitat. Z. Säugetierkd. 52(6), 341–353 (1987).
Google Scholar 
Wauters, L., Swinnen, C. & Dhondt, A. A. Activity budget and foraging behaviour of red squirrels (Sciurus vulgaris) in coniferous and deciduous habitats. J. Zool. 227(1), 71–86. https://doi.org/10.1111/j.1469-7998.1992.tb04345.x (1992).Article 

Google Scholar 
Reher, S., Dausmann, K. H., Warnecke, L. & Turner, J. M. Food availability affects habitat use of Eurasian red squirrels (Sciurus vulgaris) in a semi-urban environment. J. Mammal. 97(6), 1543–1554. https://doi.org/10.1093/jmammal/gyw105 (2016).Article 

Google Scholar 
Moller, H. Foods and foraging behavior of red (Sciurus vulgaris) and grey (Sciurus carolinensis) squirrels. Mammal. Rev. 13(2–4), 81–98. https://doi.org/10.1111/j.1365-2907.1983.tb00270.x (1983).Article 

Google Scholar 
Krauze-Gryz, D. & Gryz, J. in A review of the diet of the red squirrel (Sciurus vulgaris) in different types of habitats in Red squirrels: Ecology, conservation & management in Europe (eds. Shuttleworth, C. M., Lurz, P. W. W., Hayward, M. W.) 39–50 (European Squirrel Initiative, London, 2015)Shuttleworth, C. M. in The effect of supplemental feeding on the red squirrel (Sciurus vulgaris), Doctoral dissertation (University of London, London, 1996).Birnie-Gauvin, K., Peiman, K. S., Raubenheimer, D. & Cooke, S. J. Nutritional physiology and ecology of wildlife in a changing world. Conserv. Physiol. https://doi.org/10.1093/conphys/cox030 (2017).Article 

Google Scholar 
Wist, B., Stolter, C. & Dausmann, K. H. Sugar addicted in the city: Impact of urbanisation on food choice and diet composition of the Eurasian red squirrel (Sciurus vulgaris). J. Urban Ecol. 8(1), juac012. https://doi.org/10.1093/jue/juac012 (2022).Article 

Google Scholar 
Burton, T., Killen, S. S., Armstrong, J. D. & Metcalfe, N. B. What causes intraspecific variation in resting metabolic rate and what are its ecological consequences?. Proc. Biol. Sci. 278(1724), 3465–3473. https://doi.org/10.1098/rspb.2011.1778 (2011).Article 
CAS 

Google Scholar 
Clarke, A. Costs and consequences of evolutionary temperature adaptation. Trends Ecol. Evol. 18(11), 573–581. https://doi.org/10.1016/j.tree.2003.08.007 (2003).Article 

Google Scholar 
Lovegrove, B. G. The influence of climate on the basal metabolic rate of small mammals: A slow-fast metabolic continuum. J. Comp. Physiol. B 173(2), 87–112. https://doi.org/10.1007/s00360-002-0309-5 (2003).Article 
CAS 

Google Scholar 
McNab, B. K. The energetics of endotherms. Ohio J. Sci. 74(6), 370–380 (1974).
Google Scholar 
Tattersall, G. J. et al. Coping with thermal challenges: Physiological adaptations to environmental temperatures. Compr. Physiol. 2(3), 2151–2202 (2012).Article 

Google Scholar 
Broggi, J. et al. Sources of variation in winter basal metabolic rate in the great tit. Funct. Ecol. 21(3), 528–533. https://doi.org/10.1111/j.1365-2435.2007.01255.x (2007).Article 

Google Scholar 
Schlünzen, K. H., Hoffmann, P., Rosenhagen, G. & Riecke, W. Long-term changes and regional differences in temperature and precipitation in the metropolitan area of Hamburg. Int. J. Climatol. 30(8), 1121–1136. https://doi.org/10.1002/joc.1968 (2010).Article 

Google Scholar 
Reher, S. & Dausmann, K. H. Tropical bats counter heat by combining torpor with adaptive hyperthermia. Proc. R. Soc. B Biol. Sci. 288(1942), 20202059. https://doi.org/10.1098/rspb.2020.2059 (2021).Article 

Google Scholar 
Rezende, E. L. & Bacigalupe, L. D. Thermoregulation in endotherms: Physiological principles and ecological consequences. J. Comp. Physiol. B 185(7), 709–727. https://doi.org/10.1007/s00360-015-0909-5 (2015).Article 
CAS 

Google Scholar 
Scholander, P. F., Hock, R., Walters, V., Johnson, F. & Irving, L. Heat regulation in some arctic and tropical mammals and birds. Biol. Bull. 99(2), 237–258. https://doi.org/10.2307/1538741 (1950).Article 
CAS 

Google Scholar 
Terblanche, J. S., Clusella-Trullas, S., Deere, J. A., Van Vuuren, B. J. & Chown, S. L. Directional evolution of the slope of the metabolic rate-temperature relationship is correlated with climate. Physiol. Biochem. Zool. 82(5), 495–503. https://doi.org/10.1086/605361 (2009).Article 

Google Scholar 
Gallo, K. P., Easterling, D. R. & Peterson, T. C. The influence of land use/land cover on climatological values of the diurnal temperature range. J. Clim. 9(11), 2941–2944. https://doi.org/10.1175/1520-0442(1996)009%3c2941:TIOLUC%3e2.0.CO;2 (1996).Article 
ADS 

Google Scholar 
Wang, K. et al. Urbanization effect on the diurnal temperature range: Different roles under solar dimming and brightening. J. Clim. 25(3), 1022–1027. https://doi.org/10.1175/jcli-d-10-05030.1 (2012).Article 
ADS 

Google Scholar 
Fristoe, T. S. et al. Metabolic heat production and thermal conductance are mass-independent adaptations to thermal environment in birds and mammals. Proc. Natl. Acad. Sci. USA 112(52), 15934–15939. https://doi.org/10.1073/pnas.1521662112 (2015).Article 
ADS 
CAS 

Google Scholar 
Sándor, K. et al. Urban nestlings have reduced number of feathers in Great Tits (Parus major). Ibis 163(4), 1369–1378. https://doi.org/10.1111/ibi.12948 (2021).Article 

Google Scholar 
Beliniak, A., Krauze-Gryz, D., Jasińska, K., Jankowska, K. & Gryz, J. Contrast in daily activity patterns of red squirrels inhabiting urban park and urban forest. Hystrix https://doi.org/10.4404/hystrix-00476-2021 (2021).Article 

Google Scholar 
Thomas, L. S., Teich, E., Dausmann, K., Reher, S. & Turner, J. M. Degree of urbanisation affects Eurasian red squirrel activity patterns. Hystrix 29(2), 175–180. https://doi.org/10.4404/hystrix-00065-2018 (2018).Article 

Google Scholar 
Krauze-Gryz, D., Gryz, J. & Brach, M. Spatial organization, behaviour and feeding habits of red squirrels: Differences between an urban park and an urban forest. J. Zool. 315(1), 69–78. https://doi.org/10.1111/jzo.12905 (2021).Article 

Google Scholar 
Jarman, T. E., Gartrell, B. D. & Battley, P. F. Differences in body composition between urban and rural mallards Anas platyrhynchos. J. Urban Ecol. 6(1), juaa011. https://doi.org/10.1093/jue/juaa011 (2020).Article 

Google Scholar 
Cruz-Neto, A. P. & Bozinovic, F. The relationship between diet quality and basal metabolic rate in endotherms: Insights from intraspecific analysis. Physiol. Biochem. Zool. 77(6), 877–889 (2004).Article 

Google Scholar 
Geluso, K. & Hayes, J. P. Effects of dietary quality on basal metabolic rate and internal morphology of European starlings (Sturnus vulgaris). Physiol. Biochem. Zool. 72(2), 189–197 (1999).Article 
CAS 

Google Scholar 
Seebacher, F. Is endothermy an evolutionary by-product?. Trends Ecol. Evol. 35(6), 503–511. https://doi.org/10.1016/j.tree.2020.02.006 (2020).Article 

Google Scholar 
Perissinotti, P. P., Antenucci, C. D., Zenuto, R. & Luna, F. Effect of diet quality and soil hardness on metabolic rate in the subterranean rodent Ctenomys talarum. Comp. Biochem. Physiol. Mol. Integr. Physiol. 154(3), 298–307. https://doi.org/10.1016/j.cbpa.2009.05.013 (2009).Article 
CAS 

Google Scholar 
Thorp, C. R., Ram, P. K. & Florant, G. L. Diet alters metabolic rate in the yellow-bellied marmot (Marmota flaviventris) during hibernation. Physiol. Zool. 67(5), 1213–1229. https://doi.org/10.1086/physzool.67.5.30163890 (1994).Article 

Google Scholar 
Silva, S. I., Jaksic, F. M. & Bozinovic, F. Interplay between metabolic rate and diet quality in the South American fox Pseudalopex culpaeus. Comp. Biochem. Physiol. Mol Integr. Physiol. 137(1), 33–38. https://doi.org/10.1016/j.cbpb.2003.09.022 (2004).Article 
CAS 

Google Scholar 
Rewkiewicz-Dziarska, A., Wielopolska, A. & Gill, J. Hematological indices of Apodemus agrarius (Pallas, 1771) from different urban environments. Bull. Acad. Polon. Sci. Ser. Sci. Biol. 25(4), 261–268 (1977).CAS 

Google Scholar 
Ohrnberger, S. A., Hambly, C., Speakman, J. R. & Valencak, T. G. Limits to sustained energy intake XXXII: Hot again: Dorsal shaving increases energy intake and milk output in golden hamsters (Mesocricetus auratus). J Exp. Biol. https://doi.org/10.1242/jeb.230383 (2020).Article 

Google Scholar 
Speakman, J. R. & Król, E. The heat dissipation limit theory and evolution of life histories in endotherms—Time to dispose of the disposable soma theory?. Integr. Comp. Biol. 50(5), 793–807. https://doi.org/10.1093/icb/icq049 (2010).Article 

Google Scholar 
Diamond, S. E., Chick, L. D., Perez, A., Strickler, S. A. & Martin, R. A. Evolution of thermal tolerance and its fitness consequences: Parallel and non-parallel responses to urban heat islands across three cities. Proc. R. Soc. B Biol. Sci. 285(1882), 20180036. https://doi.org/10.1098/rspb.2018.0036 (2018).Article 

Google Scholar 
Isaksson, C. & Hahs, A. Urbanization, oxidative stress and inflammation: A question of evolving, acclimatizing or coping with urban environmental stress. Funct. Ecol. 29(7), 913–923. https://doi.org/10.1111/1365-2435.12477 (2015).Article 

Google Scholar 
Sokolova, I. M. & Lannig, G. Interactive effects of metal pollution and temperature on metabolism in aquatic ectotherms: Implications of global climate change. Clim. Res. 37(2–3), 181–201 (2008).Article 

Google Scholar 
Carey, H. V., Andrews, M. T. & Martin, S. L. Mammalian hibernation: Cellular and molecular responses to depressed metabolism and low temperature. Physiol. Rev. 83(4), 1153–1181 (2003).Article 
CAS 

Google Scholar 
Pereira, M. E., Aines, J. & Scheckter, J. L. Tactics of heterothermy in eastern gray squirrels (Sciurus carolinensis). J. Mammal. 83(2), 467–477 (2002).Article 

Google Scholar 
Breuner, C. W., Wingfield, J. C. & Romero, L. M. Diel rhythms of basal and stress-induced corticosterone in a wild, seasonal vertebrate. Gambel’s white-crowned sparrow. J Exp. Zool. 284(3), 334–342. https://doi.org/10.1002/(SICI)1097-010X(19990801)284:3%3c334::AID-JEZ11%3e3.0.CO;2-# (1999).Article 
CAS 

Google Scholar 
Careau, V., Thomas, D., Humphries, M. M. & Réale, D. Energy metabolism and animal personality. Oikos 117(5), 641–653. https://doi.org/10.1111/j.0030-1299.2008.16513.x (2008).Article 

Google Scholar 
Fletcher, Q. E. et al. Seasonal stage differences overwhelm environmental and individual factors as determinants of energy expenditure in free-ranging red squirrels. Funct. Ecol. 26(3), 677–687. https://doi.org/10.1111/j.1365-2435.2012.01975.x (2012).Article 

Google Scholar 
Barthel, L. & Berger, A. Unexpected gene-flow in urban environments: The example of the European Hedgehog. Animals 10(12), 2315. https://doi.org/10.3390/ani10122315 (2020).Article 

Google Scholar 
Fusco, N. A., Carlen, E. J. & Munshi-South, J. Urban landscape genetics: are biologists keeping up with the pace of urbanization?. Current Landsc. Ecol. Rep. 6(2), 35–45. https://doi.org/10.1007/s40823-021-00062-3 (2021).Article 

Google Scholar 
Ziege, M. et al. Population genetics of the European rabbit along a rural-to-urban gradient. Sci. Rep. 10(1), 2448. https://doi.org/10.1038/s41598-020-57962-3 (2020).Article 
ADS 
CAS 

Google Scholar 
Morash, A. J., Neufeld, C., MacCormack, T. J. & Currie, S. The importance of incorporating natural thermal variation when evaluating physiological performance in wild species. J. Exp. Biol. 221(14), jeb164673. https://doi.org/10.1242/jeb.164673 (2018).Article 

Google Scholar 
Pörtner, H.-O., et al. Climate change 2022: Impacts, adaptation and vulnerability. IPCC Sixth Assessment Report (2022).Anderies, J. M., Katti, M. & Shochat, E. Living in the city: Resource availability, predation, and bird population dynamics in urban areas. J. Theor. Biol. 247(1), 36–49. https://doi.org/10.1016/j.jtbi.2007.01.030 (2007).Article 
ADS 
MATH 

Google Scholar 
Shochat, E. Credit or debit? Resource input changes population dynamics of city-slicker birds. Oikos 106(3), 622–626. https://doi.org/10.1111/j.0030-1299.2004.13159.x (2004).Article 

Google Scholar 
Koprowski, J. L. Handling tree squirrels with a safe and efficient restraint. Wildl. Soc. B 30(1), 101–103. https://doi.org/10.2307/3784642 (2002).Article 

Google Scholar 
Magris, L. & Gurnell, J. Population ecology of the red squirrel (Sciurus vulgaris) in a fragmented woodland ecosystem on the Island of Jersey Channel Islands. J. Zool. 256(1), 99–112. https://doi.org/10.1017/s0952836902000134 (2002).Article 

Google Scholar 
Bethge, J., Wist, B., Stalenberg, E. & Dausmann, K. Seasonal adaptations in energy budgeting in the primate Lepilemur leucopus. J Comp. Physiol. B 187(5–6), 827–834. https://doi.org/10.1007/s00360-017-1082-9 (2017).Article 

Google Scholar 
Dausmann, K. H., Glos, J. & Heldmaier, G. Energetics of tropical hibernation. J Comp. Physiol. B 179(3), 345–357. https://doi.org/10.1007/s00360-008-0318-0 (2009).Article 
CAS 

Google Scholar 
Kobbe, S., Nowack, J. & Dausmann, K. H. Torpor is not the only option: Seasonal variations of the thermoneutral zone in a small primate. J. Comp. Physiol. B 184(6), 789–797. https://doi.org/10.1007/s00360-014-0834-z (2014).Article 

Google Scholar 
Lighton, J. R. Measuring Metabolic Rates: A Manual for Scientists (Oxford University Press, 2018).Book 

Google Scholar 
Bethge, J., Razafimampiandra, J. C., Wulff, A. & Dausmann, K. H. Sportive lemurs elevate their metabolic rate during challenging seasons and do not enter regular heterothermy. Conserv. Physiol. 9(1), coab075. https://doi.org/10.1093/conphys/coab075 (2021).Article 

Google Scholar 
Reher, S., Ehlers, J., Rabarison, H. & Dausmann, K. H. Short and hyperthermic torpor responses in the Malagasy bat Macronycteris commersoni reveal a broader hypometabolic scope in heterotherms. J. Comp. Physiol. B 188(6), 1015–1027. https://doi.org/10.1007/s00360-018-1171-4 (2018).Article 
CAS 

Google Scholar 
Grolemund, G. & Wickham, H. Dates and times made easy with lubridate. J Stat. Softw. 40(3), 1–25 (2011).Article 

Google Scholar 
Wickham, H., François, R., Henry, L. & Müller, K. RStudio. dplyr: A Grammar of Data Manipulation (1.0. 7) (2021).Zeileis, A. & Grothendieck, G. zoo: S3 infrastructure for regular and irregular time series. J. Stat. Softw. 14(6), 1–27. https://doi.org/10.18637/jss.v014.i06 (2005).Article 

Google Scholar 
Sarkar, D. Lattice: Multivariate Data Visualization with R (Springer Science & Business Media, New York, 2008).Book 
MATH 

Google Scholar 
Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effects models using lme4. J. Stat. Softw. https://doi.org/10.18637/jss.v067.i01 (2015).Article 

Google Scholar 
Kuznetsova, A., Brockhoff, P. B. & Christensen, R. H. lmerTest package: Tests in linear mixed effects models. J. Stat. Softw. 82(13), 1–26 (2017).Article 

Google Scholar 
Wickham, H. ggplot2: Elegant graphics for data analysis (Springer, 2016).Book 
MATH 

Google Scholar 
Fox, J. Effect displays in R for generalised linear models. J. Stat. Softw. 8(15), 1–27 (2003).Article 

Google Scholar 
Garamszegi, L. Z. et al. Changing philosophies and tools for statistical inferences in behavioral ecology. Behav. Ecol. 20(6), 1363–1375. https://doi.org/10.1093/beheco/arp137 (2009).Article 

Google Scholar 
Symonds, M. R. E. & Moussalli, A. A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike’s information criterion. Behav. Ecol. Sociobiol. 65(1), 13–21. https://doi.org/10.1007/s00265-010-1037-6 (2010).Article 

Google Scholar 
Whittingham, M. J., Stephens, P. A., Bradbury, R. B. & Freckleton, R. P. Why do we still use stepwise modelling in ecology and behaviour?. J. Anim. Ecol. 75(5), 1182–1189. https://doi.org/10.1111/j.1365-2656.2006.01141.x (2006).Article 

Google Scholar 
Barton, K. & Barton, M. K. MuMIn: Multi-Model Inference. R package version 1.43.17; https://CRAN.R-project.org/package=MuMIn (2020).Zuur, A., Ieno, E. N., Walker, N., Saveliev, A. A. & Smith, G. M. Mixed effects models and extensions in ecology with R ( Springer Science & Business Media 2009).Burnham, K. P. & Anderson, D. R. Multimodel inference: Understanding AIC and BIC in model selection. Soc. Method. Res. 33(2), 261–304 (2004).Article 

Google Scholar 
Johnson, J. B. & Omland, K. S. Model selection in ecology and evolution. Trends Ecol. Evol. 19(2), 101–108. https://doi.org/10.1016/j.tree.2003.10.013 (2004).Article 

Google Scholar 
Lorah, J. Effect size measures for multilevel models: Definition, interpretation, and TIMSS example. Large-scale Assess. Educ. 6(1), 8. https://doi.org/10.1186/s40536-018-0061-2 (2018).Article 

Google Scholar 
Selya, A. S., Rose, J. S., Dierker, L. C., Hedeker, D. & Mermelstein, R. J. A practical guide to calculating cohen’s f2, a measure of local effect size, from PROC MIXED. Front. Psychol. 3, 111–111. https://doi.org/10.3389/fpsyg.2012.00111 (2012).Article 

Google Scholar 
Lüdecke, D. sjPlot: Data visualization for statistics in social science. R package version 2.8.5 2020; https://CRAN.R-project.org/package=sjPlot (2020).Nakagawa, S., Johnson, P. C. & Schielzeth, H. The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. J. R. Soc. Interface 14(134), 20170213 (2017).Article 

Google Scholar 
Nakagawa, S. & Schielzeth, H. Repeatability for Gaussian and non-Gaussian data: A practical guide for biologists. Biol. Rev. Camb. Philos. Soc. 85(4), 935–956. https://doi.org/10.1111/j.1469-185X.2010.00141.x (2010).Article 

Google Scholar 
Stoffel, M. A., Nakagawa, S. & Schielzeth, H. rptR: Repeatability estimation and variance decomposition by generalized linear mixed-effects models. Methods Ecol. Evol. 8(11), 1639–1644. https://doi.org/10.1111/2041-210X.12797 (2017).Article 

Google Scholar  More

Figure 1 presents the average monthly energy expenditure at the household level based on USD across the 37 surveyed nations. The households in Singapore expend the most amount of energy, that is, 748 USD each month on average. The energy consumption appears positively associated with the economic development level; for example, households from high-income countries, including France, Italy, Japan and the US, tend to consume more energy than those from low-income countries (e.g., Kazakhstan, Myanmar, and Mongolia). In India, Indonesia, and Vietnam, households with higher income expend more on energy than rural/slum households. For the energy expenditure to household income ratio, strong trends were not found between developing and developed countries. Notably, middle-income countries (e.g., Greece, Chile, Brazil, Egypt) spend a relatively higher share of total income on energy.Figure 1Average monthly energy expenditure at the household level across the 37 surveyed nations. Data source: Original survey.Full size imageThe relationship between subjective well-being and energy consumption expenditure based on the ordered logit, ordered probit, and OLS models is shown in Table 2, panel A. The LR Chi-Square test and Pseudo R-squared for the ordered logistic regression model and the ordered probit model were applied to measure the goodness of the fit, whereas F-statistics and adjusted R-squared were used for the OLS model. For the validation of the measurement of subjective well-being, life satisfaction and happiness measures were used. Importantly, the results from variated regression models are consistent, indicating a positive relationship between household energy consumption expenditure and the improvement of individuals’ subjective well-being. Regarding the model’s goodness of fit, the LR Chi-Square test with ordered logit and probit models, and the F-statistic in the OLS model are all statistically significant at 0.1%, which validates the regression model. As the consistency of the robustness results is derived from different models, the ordered logit model is applied in Table 2 (Panel B).Table 2 Association between energy consumption expenditure and subjective well-being in high- and non-high-income countries.Full size tableWith the control variables being constant, energy consumption expenditure improves subjective well-being, including life satisfaction and happiness. The coefficients for the relationship of energy consumption with life satisfaction and with happiness are 0.018 and 0.008, respectively, and they are statistically significant at the 1% level; in other words, there is increased energy consumption for people who are satisfied with their lives and are happier. This is because electricity, water, gas, or gasoline are indispensable consumption goods in daily life. The results suggest that when policies lead to a reduction in the consumption of these goods at the household level, the life satisfaction of citizens is likely to decrease. When reducing energy consumption at the household level to reduce the emission of greenhouse gases, the conflicts of interest of individuals in these households (given that they derive life satisfaction from energy consumption) pose a challenge to policymakers; therefore, policymakers should devise strategies to improve both citizens’ living standards and environmental preservation.Referring to the criteria developed by the World Bank, the standard classification of high-income nations and non-high-income nations is as follows. Based on the 2017 gross national income (GNI) per capita, the World Bank List of Economies (June 2018) presented the following criteria for nations to be classified as high-income and non-high-income nations, respectively: a GNI per capita of $12,056 or higher, and less than $12,056. According to this standard of classification, in this study, high-income nations comprise Japan, Singapore, Chile, Australia, the United States, Germany, the United Kingdom, France, Spain, Italy, Sweden, Canada, Netherlands, Greece, Hungary, Poland, and the Czech Republic, whereas non-high-income nations comprise Thailand, Malaysia, Indonesia, Vietnam, Philippines, Mexico, Venezuela, Brazil, Colombia, South Africa, India, Myanmar, Kazakhstan, Mongolia, Egypt, Russia, China, Turkey, Romania, and Sri Lanka.Regarding the comparison of high- and non-high-income countries, energy consumption at the household level is more likely to lead to life satisfaction in non-high-income than in high-income countries. In high-income countries, the coefficients for the relationship of energy consumption with life satisfaction and with happiness are 0.010 and 0.003, respectively; these coefficients are 0.035 and 0.015, respectively, among non-high-income countries. Hence, in both high-income and non-high-income countries, an increase in energy consumption leads to an increase in life satisfaction; nonetheless, energy consumption is more crucial for households in non-high-income countries. Compared to the effect of energy consumption on satisfaction in high-income countries and non-high-income countries, individuals living in less urbanized countries appear more satisfied with energy consumption.Table 3 presents the association between life satisfaction and energy consumption expenditure at the household level in each country by estimating Eq. (2) based on the ordered logit model for each country. There is a positive relationship between energy consumption expenditure and life satisfaction in 27 out of the 37 nations. For example, the coefficient of this relationship is 0.062 in Brazil, and is statistically significant at the 1% level. An increase in energy consumption expenditure positively impacts the life satisfaction of households in Brazil, meaning that individuals with greater energy expenditure tend to be satisfied with their lives. Similar results are found in other countries: Canada, Chile, China, Egypt, France, Germany, Greece, India, Indonesia, Italy, and Japan. As life satisfaction is a proxy of well-being, energy consumption is expected to increase when households can afford more energy to obtain higher life satisfaction. These results indicate that most of the developed and developing countries analyzed face a conflict of interest in addressing individuals’ life satisfaction and environment conservation goals; these countries include China and India that are home to large populations that have a positive desire for energy consumption.Table 3 Relationship between energy expenditure and life satisfaction for each country.Full size tableHowever, the association between life satisfaction and energy consumption expenditure at the household level was non-significant across some countries. In Australia, the coefficient of this association is positive but not statistically significant; hence, an increase in energy expenditure is not completely associated with life satisfaction at the household level here. Similar results are found in the Netherlands, Hungary, Sweden, Singapore, Poland, the Czech Republic, and Colombia. In these countries, energy consumption is at an adequate level, and additional energy consumption does not lead to higher life satisfaction. It may be that households consume an adequate amount of energy with their income and energy price.Tables 4, 5, 6, and 7 display the determinant factors of household energy consumption in 37 nations by estimating the energy demand equation for each country using Eq. (3). The key energy consumption metric is the quantity of energy consumed (e.g., kWh) across the targeted households. Since price information is limited, transforming consumption expenditure into a quantity (e.g., kWh) is problematic. As explained earlier, this study adopted the energy demand equation.Table 4 Household socioeconomic and demographic determinants of household energy consumption expenditure I.Full size tableTable 5 Household socioeconomic and demographic determinants of household energy consumption expenditure II.Full size tableTable 6 Household socioeconomic and demographic determinants of household energy consumption expenditure III.Full size tableTable 7 Household socioeconomic and demographic determinants of household energy consumption expenditure IV.Full size tableThere are positive relationships between energy consumption expenditure at the household level and household income across countries. If the coefficients for household income are positive and statistically significant, this means that energy consumption expenditure at the household level would increase with an increase in household income ensuing from economic development in the country, ceteris paribus. The positive coefficients for the association between energy consumption expenditure and household income range from 0.756 (Japan) to 3.613 (the Philippines) in our sample, indicating that an additional 10,000 USD would lead to an additional energy consumption expenditure at the household level of approximately 17.3% (Japan) – 445% (Mongolia). The number is calculated using the magnitude of the coefficient/energy consumption expenditure. The results also show that homeowners tend to consume more energy than renters in Australia, Brazil, Canada, Chile, China, Colombia, Germany, India, Italy, Japan, Malaysia, Mexico, Russia, the United States, and Vietnam. This indicates that if individuals live in their own houses, the household energy consumption expenditure tends to be higher owing to the wealth effect, as energy is a normal consumption good. Overall, the wealth effect on energy consumption expenditure at the household level is increasing in our sample, and with economic development, energy consumption may increase.The following factors are confirmed to reduce energy consumption at the household level: (1) energy-curtailment behavior regarding electricity, (2) higher education, and (3) age. The energy-saving effect is confirmed in households. In Canada, the coefficient of energy-saving behaviors is -0.642, indicating that households consume 12.5% less energy when they adopt both energy curtailment behavior and non-saving groups (64.2/513). The Canadian household average energy consumption is 513 USD. Similar results are seen in Colombia, Germany, India, Indonesia, Italy, Japan, the Netherlands, Poland, Russia, Turkey, the United Kingdom, and the United States. The magnitude of the effect of energy curtailment behavior ranged from 6.4% (Russia) to 32% (India) less energy consumption expenditure. Hence, energy-saving behaviors have a favorable effect on environmentally preferable outcomes. By contrast, households in Indonesia save electricity as they tend to spend more on purchasing energy.Individuals with higher education tend to save energy in 23 out of the 37 nations. For instance, the coefficient for individuals with university-level education is -2.292 and statistically significant at the 1% level. This suggests that households with individuals who have university-level education have less energy consumption expenditure than households with individuals with junior high school or lower levels of education. Similar results are seen in Brazil, Canada, Chile, Colombia, the Czech Republic, France, Germany, Hungary, India, Indonesia, Japan, Malaysia, the Netherlands, the Philippines, Poland, Russia, Singapore, South Africa, Spain, Sweden, Turkey, the United Kingdom, and the United States. Encouraging households to engage in energy curtailment behaviors and higher educational attainment may lead to environment-friendly outcomes.Surprisingly, purchasing energy-saving household products has a limited effect on reducing energy consumption expenditure at the household level. The coefficients for purchasing energy-saving household products are negative, ranging between -0.044 and -0.763, and are statistically significant in Australia, Canada, the Czech Republic, Italy, and Kazakhstan. Hence, the purchase of these products in these five countries decreases energy expenditure from 2.9% (China) to 14% (Australia). However, the relationship between energy consumption expenditure at the household level and purchasing energy-saving household products is non-significant in the other countries. Moreover, in Poland and Turkey, households that purchase these products consume more energy than those that do not. Therefore, purchasing energy-saving household products has a limited contribution to energy saving at the household level.The findings also show that older individuals tend to have lower energy consumption. The coefficients for the age variable are negative and statistically significant in 30 countries (out of 37). The effect of age on energy consumption expenditure ranges between -0.003 and -0.148, indicating that as the average age of individuals increases by one year, their monthly energy consumption expenditure reduces from 0.3–14.8 USD. This may be because older individuals are more likely to live frugally. More

Game theory is a framework for analysing the outcome of the strategic interaction between decision makers1. The fundamental concept is that of a Nash equilibrium where no player can improve her payoff by a unilateral strategy change. Typically, the Nash equilibrium is considered to be the optimal outcome of a game, however in social dilemmas the individual optimal outcome is at odds with the collective optimal outcome2. This means that one player can improve her payoff at the expense of the other by unilaterally deviating, but if both deviate, they end up with lower payoffs. In this type of games, the mutually beneficial, but non-Nash equilibrium strategy is called cooperation. However, in this context cooperation should not be interpreted as an interest in the welfare of others, as players only aim to secure a high payoff for themselves.In this framework, payoff maximisation is considered to be rational, but when such rational players then seize every opportunity to gain at the opponent’s expense, they may counterintuitively both end up with low payoffs. A game that clearly exhibits this contradiction is the Traveler’s Dilemma. Since its formulation in 1994 by the economist Kaushik Basu3, the game has become one of the most studied in the economics literature. Additionally, it has been discussed in theoretical biology in the context of evolutionary game theory.In general, the dilemma relies on the individuals’ incentive to undercut the opponent. To be more specific, players are motivated to claim a lower value than their opponent to reach a higher payoff at the opponent’s expense. Such incentive leads players to a systematic mutual undercutting until the lowest possible payoff is reached, which is the unique Nash equilibrium. It seems paradoxical that players defined as rational in a game theoretical sense end up with such a poor outcome. Therefore, the question that naturally arises is how can this poor outcome be prevented and how cooperation can be achieved.To address these questions, it can be helpful to better understand price wars, which consist in the mutual undercutting of prices to gain market share. In addition, it can provide information about human behaviour, because economic experiments have shown that individuals prefer to choose the cooperative high payoff action, instead of the Nash equilibrium4.Our analysis focuses on showing that the Traveler’s Dilemma can be decomposed into a local and a global game. If the payoff optimisation is constrained to the local game, then players will inevitably end up in the Nash equilibrium. However, if players escape the local maximisation and optimise their payoff for the global game, they can reach the cooperative high payoff equilibrium.Here, we show that the cooperative equilibrium can be reached in a game like the Traveler’s Dilemma due to diversity, which we define as the presence of suboptimal strategies. The appearance of strategies far from those of the residents allows for the local maximisation process to be escaped, such that an optimisation at a global level takes place. Overall this can lead to cooperation because by considering “suboptimal strategies” that play against each other it is possible to reach higher payoffs, both collectively and individually.GameThe Traveler’s Dilemma is a two-player game. Player i has to choose a claim, (n_i), from the action space, consisting of all integers on the interval [L, U], where (0 le L < U). The payoffs are determined as follows: If both players, i and j, choose the same value ((n_i = n_j)), both get paid that value. There is a reward parameter (R >1), such that if (n_i < n_j), then i receives (n_i + R) and j gets (n_i- R) Thus, the payoff of player i playing against player j is$$begin{aligned} pi _{ij} = {left{ begin{array}{ll} n_i& text { if } n_i = n_j\ n_i + R& text { if } n_i < n_j\ n_j - R& text { if } n_i > n_j end{array}right. } end{aligned}$$
(1)
Thus, a player is better off by choosing a slightly lower value than the opponent: when j plays (n_j), then it is best for i to play (n_j-1). The iteration of this reasoning, which we will call the stairway to hell, leads to the only Nash equilibrium of the game, ({L,L}), where both players choose the lowest possible claim. The classical game theory method to arrive to this equilibrium is called iterative elimination of dominated strategies5.The game can be visualised through its payoff matrix (Fig. 1). For simplicity, we use the values from the original formulation: (L=2), (U=100) and (R=2). The payoff matrix shows that the Traveler’s Dilemma can be decomposed into a local and a global game. Let us begin with the local game. When the action space of the game is reduced to two adjacent actions n and (n+1) (black boxes in Fig. 1), the Traveler’s Dilemma with (R=2) is equivalent to the Prisoner’s Dilemma6. In general, for any value of R, the Traveler’s Dilemma becomes a Prisoner’s Dilemma for any pair of actions n and (n+s), where ( 1 le s le R-1 ). For example, for (R=4) the pair of actions n and (n+1), n and (n+2), n and (n+3) follow the same game structure as the Prisoner’s Dilemma. Therefore, the Traveler’s Dilemma consists of many embedded Prisoners’ Dilemmas. This means that at a local level the game is a Prisoner’s Dilemma.If we now consider actions that are distant from each other in the action space, e.g. 2 and 100, we can observe a coordination game structure (gray boxes in Fig. 1), where ({100,100}) is payoff and risk dominant7,8. In general, any pair of actions n and (n+s), where ( R le s le U-n), construct a coordination game. As a result, the Traveler’s Dilemma becomes a coordination game at a global level, which has different equilibria than the local game.Figure 1Payoff matrix of the Traveler’s Dilemma. Visualisation of the payoff scheme described by Eq. (1). For simplicity, the action space is ( {n_i in {mathbb {N}} mid 2 le n_i le 100}) and the reward parameter is (R=2). The Traveler’s Dilemma can be decomposed into a local and a global game. At a local level the game is a Prisoner’s Dilemma (black boxes). This happens when the action space is reduced to any pair of actions n and (n+s), where ( 1 le s le R-1 ). While at the global level, we can observe a coordination game (gray boxes). This level is defined as any pair of actions n and (n+s), where ( R le s le U-n).Full size imageParadoxSocial dilemmas appear paradoxical in the sense that self-interested competing players, when rationally playing the Nash equilibrium, end up with a payoff that clearly goes against their self-interest. But with the Traveler’s Dilemma, the paradox goes further, as suggested in its original formulation3. Classical game theory proposes ({L,L}) as the Nash equilibrium of the game. However, it seems unlikely and implausible that, with R being moderately low, say (R=2), for individuals to play the Nash equilibrium. This has been confirmed in economic experiments where individuals rather choose values close to the upper bound of the interval. Such experiments have also shown that the chosen value depends on the reward parameter (R), where an increasing value of R shifts players’ decision towards ({L,L})4. Nonetheless, classical game theory states that the Nash equilibrium of the game is independent of R.Consequently, the aim of this paper is to seek and explore simple mechanisms through which the apparent non-rational cooperative behaviour can come about. We also examine the effect of the reward parameter on the game’s outcome. Given that the Traveler’s Dilemma paradox emerges in the classical game theory framework, we analyse the game using evolutionary game theory tools5,9,10. This dynamical approach allows us to explore adaptive behaviour outside of the stationary classical game theory framework. To be more precise, for this approach individuals dynamically adjust their actions according to their payoffs.The key point of course is to understand how the system can converge to high claims. We show that this behaviour is possible because the Traveler’s Dilemma can be decomposed into a local and a global game. If the payoff maximisation is constrained to the local level, then the stairway to hell leads the system to the Nash equilibrium; given that locally the game is a Prisoner’s Dilemma. On the other hand, at a global level the game follows a coordination game structure, where the high claim actions are payoff dominant. Thus, for the system to reach a high claim equilibrium the maximisation process needs to jump from the local to the global level.Our analysis led us to identify the mechanism of diversity as responsible for enabling this jump and preventing players from going down the stairway to hell. This mechanism works on the idea that to reach a high claim equilibrium, players have to benefit from playing a high claim. For a population setting, it means that players need to have the chance to encounter opponents also playing high. From a learning model point of view, it refers to the belief that the opponent will also play high, at least with a certain probability. If the belief is shared by both players, they should both play high and reach the cooperative equilibrium. Here, we explore these two types of models to unveil the mechanism leading to cooperation.Population based models unveil diversity as the cooperative mechanism via the effect of mutations on the game’s outcome. This is shown for the replicator-mutator equation and the Wright–Fisher model. Similarly, a two-player learning model approach, more in line with human reasoning, shows that if players are free to adopt a higher payoff action from a diverse action set during their introspection process, they can reach the cooperative equilibrium. This result is obtained using introspection dynamics.Finally, we explain how diversity is the underlying mechanism that enables the convergence to high claims in previously proposed models. To be more precise, we show that diversity is required because it allows for the maximisation process to jump from the local to the global level. More

Bradford, M. A. et al. Soil carbon science for policy and practice. Nat. Sustain. 2, 1070–1072 (2019).Article 

Google Scholar 
Lehmann, J. & Kleber, M. The contentious nature of soil organic matter. Nature 528, 60–68 (2015).Article 

Google Scholar 
Liang, C., Schimel, J. P. & Jastrow, J. D. The importance of anabolism in microbial control over soil carbon storage. Nat. Microbiol. 2, 17105 (2017).Article 

Google Scholar 
Liang, C., Amelung, W., Lehmann, J. & Kästner, M. Quantitative assessment of microbial necromass contribution to soil organic matter. Glob. Change Biol. 25, 3578–3590 (2019).Article 

Google Scholar 
Wang, B. R., An, S. S., Liang, C., Liu, Y. & Kuzyakov, Y. Microbial necromass as the source of soil organic carbon in global ecosystems. Soil Biol. Biochem. 162, 108422 (2021).Article 

Google Scholar 
Kästner, M. & Miltner, A. in The Future of Soil Carbon (eds Garcia, C. et al.) Ch. 5 (Academic Press, 2018).Buckeridge, K. M. et al. Sticky dead microbes: rapid abiotic retention of microbial necromass in soil. Soil Biol. Biochem. 149, 107929 (2020).Article 

Google Scholar 
Kallenbach, C. M., Grandy, A. S., Frey, S. D. & Diefendorf, A. F. Microbial physiology and necromass regulate agricultural soil carbon accumulation. Soil Biol. Biochem. 91, 279–290 (2015).Article 

Google Scholar 
Kallenbach, C. M., Frey, S. D. & Grandy, A. S. Direct evidence for microbial-derived soil organic matter formation and its ecophysiological controls. Nat. Commun. 7, 13630 (2016).Article 

Google Scholar 
Emerson, J. B. et al. Schrödinger’s microbes: tools for distinguishing the living from the dead in microbial ecosystems. Microbiome 5, 86 (2017).Article 

Google Scholar 
Zhang, Y. et al. Simulating measurable ecosystem carbon and nitrogen dynamics with the mechanistically defined MEMS 2.0 model. Biogeosciences 18, 3147–3171 (2021).Article 

Google Scholar 
Ackermann, M., Stearns Stephen, C. & Jenal, U. Senescence in a bacterium with asymmetric division. Science 300, 1920–1920 (2003).Article 

Google Scholar 
Aguilaniu, H., Gustafsson, L., Rigoulet, M. & Nyström, T. Asymmetric inheritance of oxidatively damaged proteins during cytokinesis. Science 299, 1751–1753 (2003).Article 

Google Scholar 
Maheshwari, R. & Navaraj, A. Senescence in fungi: the view from Neurospora. FEMS Microbiol. Lett. 280, 135–143 (2008).Article 

Google Scholar 
See, C. R. et al. 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).Article 

Google Scholar 
Pusztahelyi, T. et al. Comparative studies of differential expression of chitinolytic enzymes encoded by chiA, chiB, chiC and nagA genes in Aspergillus nidulans. Folia Microbiologica 51, 547–554 (2006).Article 

Google Scholar 
Bartoszewska, M. & Kiel, J. A. The role of macroautophagy in development of filamentous fungi. Antioxid. Redox Signal. 14, 2271–2287 (2011).Article 

Google Scholar 
Josefsen, L. et al. Autophagy provides nutrients for nonassimilating fungal structures and is necessary for plant colonization but not for infection in the necrotrophic plant pathogen Fusarium graminearum. Autophagy 8, 326–337 (2012).Article 

Google Scholar 
Heaton, L. L., Jones, N. S. & Fricker, M. D. Energetic constraints on fungal growth. Am. Nat. 187, E27–E40 (2016).Article 

Google Scholar 
Taiz, L. & Zeiger, E. Plant Physiology 4th edn (Spektrum Akademischer Verlag, 2008).Bowman, E. J. & Bowman, B. J. in Cellular and Molecular Biology of Filamentous Fungi (eds Borkovich, K. & Ebbole, D.) 179–190 (ASM Press, 2010).Voigt, O. & Pöggeler, S. Self-eating to grow and kill: autophagy in filamentous ascomycetes. Appl. Microbiol. Biotechnol. 97, 9277–9290 (2013).Article 

Google Scholar 
Grimmett, I. J., Shipp, K. N., Macneil, A. & Barlocher, F. Does the growth rate hypothesis apply to aquatic hyphomycetes? Fungal Ecol. 6, 493–500 (2013).Article 

Google Scholar 
Camenzind, T., Philipp Grenz, K., Lehmann, J. & Rillig, M. C. Soil fungal mycelia have unexpectedly flexible stoichiometric C:N and C:P ratios. Ecol. Lett. 24, 208–218 (2021).Article 

Google Scholar 
Mason-Jones, K., Robinson, S. L., Veen, G. F., Manzoni, S. & van der Putten, W. H. Microbial storage and its implications for soil ecology. ISME J. 16, 617–629 (2022).Article 

Google Scholar 
Gow, N. A. R., Latge, J. P. & Munro, C. A. The fungal cell wall: structure, biosynthesis, and function. Microbiol. Spectr. 5, FUNK-0035–2016 (2017).Article 

Google Scholar 
Steiner, U. K. Senescence in bacteria and its underlying mechanisms. Front. Cell Dev. Biol. 9, 668915 (2021).Article 

Google Scholar 
Allocati, N., Masulli, M., Di Ilio, C. & De Laurenzi, V. Die for the community: an overview of programmed cell death in bacteria. Cell Death Dis. 6, e1609 (2015).Article 

Google Scholar 
Peeters, S. H. & de Jonge, M. I. For the greater good: programmed cell death in bacterial communities. Microbiol. Res. 207, 161–169 (2018).Article 

Google Scholar 
Wang, J. & Bayles, K. W. Programmed cell death in plants: lessons from bacteria? Trends Plant Sci. 18, 133–139 (2013).Article 

Google Scholar 
Nagamalleswari, E., Rao, S., Vasu, K. & Nagaraja, V. Restriction endonuclease triggered bacterial apoptosis as a mechanism for long time survival. Nucleic Acids Res. 45, 8423–8434 (2017).Article 

Google Scholar 
Kysela, D. T., Brown, P. J. B., Huang, K. C. & Brun, Y. V. Biological consequences and advantages of asymmetric bacterial growth. Annu. Rev. Microbiol. 67, 417–435 (2013).Article 

Google Scholar 
Bayles, K. W. Bacterial programmed cell death: making sense of a paradox. Nat. Rev. Microbiol. 12, 63–69 (2014).Article 

Google Scholar 
Flemming, H.-C. & Wuertz, S. Bacteria and archaea on Earth and their abundance in biofilms. Nat. Rev. Microbiol. 17, 247–260 (2019).Article 

Google Scholar 
Coleman, D. C. & Wall, D. H. in Soil Microbiology, Ecology and Biochemistry 4th edn (ed. Paul, E. A.) Ch. 5 (Academic Press, 2015).Hungate, B. A. et al. The functional significance of bacterial predators. mBio 12, e00466-21 (2021).Article 

Google Scholar 
Kuzyakov, Y. & Mason-Jones, K. Viruses in soil: nano-scale undead drivers of microbial life, biogeochemical turnover and ecosystem functions. Soil Biol. Biochem. 127, 305–317 (2018).Article 

Google Scholar 
Williamson, K. E., Fuhrmann, J. J., Wommack, K. E. & Radosevich, M. Viruses in soil ecosystems: an unknown quantity within an unexplored territory. Annu. Rev. Virol. 4, 201–219 (2017).Article 

Google Scholar 
Sokol, N. W. et al. Life and death in the soil microbiome: how ecological processes influence biogeochemistry. Nat. Rev. Microbiol. 20, 415–430 (2022).Article 

Google Scholar 
Bonkowski, M. & Clarholm, M. J. A. P. Stimulation of plant growth through interactions of bacteria and protozoa: testing the auxiliary microbial loop hypothesis. Acta Protozool. 51, 237–247 (2012).
Google Scholar 
Potapov, A. M., Pollierer, M. M., Salmon, S., Šustr, V. & Chen, T.-W. Multidimensional trophic niche revealed by complementary approaches: gut content, digestive enzymes, fatty acids and stable isotopes in Collembola. J. Anim. Ecol. 90, 1919–1933 (2021).Article 

Google Scholar 
Esteban, G. F. & Fenchel, T. M. in Ecology of Protozoa: The Biology of Free-living Phagotrophic Protists (eds Esteban, G. F. & Fenchel, T. M.) 33–54 (Springer, 2020).Koksharova, O. A. Bacteria and phenoptosis. Biochemistry 78, 963–970 (2013).
Google Scholar 
Tilman, D. Resource Competition and Community Structure (Princeton Univ. Press, 1982).Boddy, L. Interspecific combative interactions between wood-decaying basidiomycetes. FEMS Microbiol. Ecol. 31, 185–194 (2000).Article 

Google Scholar 
Hibbing, M. E., Fuqua, C., Parsek, M. R. & Peterson, S. B. Bacterial competition: surviving and thriving in the microbial jungle. Nat. Rev. Microbiol. 8, 15–25 (2010).Article 

Google Scholar 
Müller, S. et al. Predation by Myxococcus xanthus induces Bacillus subtilis to form spore-filled megastructures. Appl. Environ. Microbiol. 81, 203–210 (2015).Article 

Google Scholar 
Laskowska, E. & Kuczynska-Wisnik, D. New insight into the mechanisms protecting bacteria during desiccation. Curr. Genet. 66, 313–318 (2020).Article 

Google Scholar 
Rillig, M. C., Ryo, M. & Lehmann, A. Classifying human influences on terrestrial ecosystems. Glob. Change Biol. 27, 2273–2278 (2021).Article 

Google Scholar 
Dörr, T., Moynihan, P. J. & Mayer, C. Bacterial cell wall structure and dynamics. Front. Microbiol. 10, 02051 (2019).Article 

Google Scholar 
Corredor, B., Lang, B. & Russell, D. Effects of nitrogen fertilization on soil fauna in a global meta-analysis. Preprint at Res. Sq. https://doi.org/10.21203/rs.3.rs-1438491/v1 (2022).Blankinship, J. C., Niklaus, P. A. & Hungate, B. A. A meta-analysis of responses of soil biota to global change. Oecologia 165, 553–565 (2011).Article 

Google Scholar 
Manzoni, S., Chakrawal, A., Spohn, M. & Lindahl, B. D. Modeling microbial adaptations to nutrient limitation during litter decomposition. Front. For. Glob. Change 4, 686945 (2021).Article 

Google Scholar 
Frank, D. et al. Effects of climate extremes on the terrestrial carbon cycle: concepts, processes and potential future impacts. Glob. Change Biol. 21, 2861–2880 (2015).Article 

Google Scholar 
Gunina, A. & Kuzyakov, Y. From energy to (soil organic) matter. Glob. Change Biol. 28, 2169–2182 (2022).Article 

Google Scholar 
Fernandez, C. W. & Koide, R. T. Initial melanin and nitrogen concentrations control the decomposition of ectomycorrhizal fungal litter. Soil Biol. Biochem. 77, 150–157 (2014).Article 

Google Scholar 
Kästner, M., Miltner, A., Thiele-Bruhn, S. & Liang, C. Microbial necromass in soils—linking microbes to soil processes and carbon turnover. Front. Environ. Sci. 9, 756378 (2021).Article 

Google Scholar 
Buckeridge, K. M., Creamer, C. & Whitaker, J. Deconstructing the microbial necromass continuum to inform soil carbon sequestration. Funct. Ecol. 36, 1396–1410 (2022).Article 

Google Scholar 
Lehmann, J. et al. Persistence of soil organic carbon caused by functional complexity. Nat. Geosci. 13, 529–534 (2020).Article 

Google Scholar 
Blazewicz, S. J. et al. Taxon-specific microbial growth and mortality patterns reveal distinct temporal population responses to rewetting in a California grassland soil. ISME J. 14, 1520–1532 (2020).Article 

Google Scholar 
Kallenbach, C. M., Wallenstein, M. D., Schipanksi, M. E. & Grandy, A. S. Managing agroecosystems for soil microbial carbon use efficiency: ecological unknowns, potential outcomes, and a path forward. Front. Microbiol. 10, 1146 (2019).Article 

Google Scholar 
Liang, C. Soil microbial carbon pump: mechanism and appraisal. Soil Ecol. Lett. 2, 241–254 (2020).Article 

Google Scholar 
Sinsabaugh, R. L., Manzoni, S., Moorhead, D. L. & Richter, A. Carbon use efficiency of microbial communities: stoichiometry, methodology and modelling. Ecol. Lett. 16, 930–939 (2013).Article 

Google Scholar 
van Groenigen, J. W. et al. Sequestering soil organic carbon: a nitrogen dilemma. Environ. Sci. Technol. 51, 4738–4739 (2017).Article 

Google Scholar 
Greenlon, A. et al. Quantitative stable-isotope probing (qSIP) with metagenomics links microbial physiology and activity to soil moisture in Mediterranean-climate grassland ecosystems (in the press).Mafla-Endara, P. M. et al. Microfluidic chips provide visual access to in situ soil ecology. Commun. Biol. 4, 889 (2021).Article 

Google Scholar 
Schaible, G. A., Kohtz, A. J., Cliff, J. & Hatzenpichler, R. Correlative SIP-FISH-Raman-SEM-NanoSIMS links identity, morphology, biochemistry, and physiology of environmental microbes. ISME Commun. 2, 52 (2022).Article 

Google Scholar 
See, C. R. et al. Distinct carbon fractions drive a generalisable two-pool model of fungal necromass decomposition. Funct. Ecol. 35, 796–806 (2021).Article 

Google Scholar 
Wang, C. et al. Stabilization of microbial residues in soil organic matter after two years of decomposition. Soil Biol. Biochem. 141, 107687 (2020).Article 

Google Scholar 
Veresoglou, S. D., Halley, J. M. & Rillig, M. C. Extinction risk of soil biota. Nat. Commun. 6, 8862 (2015).Article 

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

Google Scholar 
Trap, J., Bonkowski, M., Plassard, C., Villenave, C. & Blanchart, E. Ecological importance of soil bacterivores for ecosystem functions. Plant Soil 398, 1–24 (2016).Article 

Google Scholar 
Dooley, S. R. & Treseder, K. K. The effect of fire on microbial biomass: a meta-analysis of field studies. Biogeochemistry 109, 49–61 (2012).Article 

Google Scholar 
Muñoz-Leoz, B., Ruiz-Romera, E., Antigüedad, I. & Garbisu, C. Tebuconazole application decreases soil microbial biomass and activity. Soil Biol. Biochem. 43, 2176–2183 (2011).Article 

Google Scholar 
Meyer, M., Diehl, D., Schaumann, G. E. & Muñoz, K. Agricultural mulching and fungicides—impacts on fungal biomass, mycotoxin occurrence, and soil organic matter decomposition. Environ. Sci. Pollut. Res. 28, 36535–36550 (2021).Article 

Google Scholar 
Thiery, S. & Kaimer, C. The predation strategy of Myxococcus xanthus. Front. Microbiol. 11, 2 (2020).Article 

Google Scholar 
Laloux, G. Shedding light on the cell biology of the predatory bacterium Bdellovibrio bacteriovorus. Front. Microbiol. 10, 3136 (2020).Article 

Google Scholar  More

To calculate total root biomass C colonized by AM and EcM fungi, we developed a workflow that combines multiple publicly available datasets to ultimately link fine root stocks to mycorrhizal colonization estimates (Fig. 1). These estimates were individually derived for 881 different spatial units that were constructed by combining 28 different ecoregions, 15 land cover types and six continents. In a given spatial unit, the relationship between the proportion of AM- and EcM-plants aboveground biomass and the proportion of AM- and EcM-associated root biomass depends on the prevalence of distinct growth forms. Therefore, to increase the accuracy of our estimates, calculations were made separately for woody and herbaceous vegetation and combined in the final step and subsequently mapped. Below we detail the specific methodologies we followed within the workflow and the main assumptions and uncertainties associated.Fig. 1Workflow used to create maps of mycorrhizal fine root biomass carbon. The workflow consists of two main steps: (1) Estimation of total fine root stock capable to form mycorrhizal associations with AM and EcM fungi and (2) estimation of the proportion of fine roots colonized by AM and EcM fungi.Full size imageDefinition of spatial unitsAs a basis for mapping mycorrhizal root abundances at a global scale, we defined spatial units based on a coarse division of Bailey’s ecoregions23 After removing regions of permanent ice and water bodies, we included 28 ecoregions defined according to differences in climatic regimes and elevation (deposited at Dryad-Table S1). A map of Bailey’s ecoregions was provided by the Oak Ridge National Laboratory Distributed Active Archive Center24 at 10 arcmin spatial resolution. Due to potential considerable differences in plant species identities, ecoregions that extended across multiple continents were split for each continent. The continent division was based upon the FAO Global Administrative Unit Layers (http://www.fao.org/geonetwork/srv/en/). Finally, each ecoregion-continent combination was further divided according to differences in land cover types using the 2015 Land Cover Initiative map developed by the European Space Agency at 300 m spatial resolution (https://www.esa-landcover-cci.org/). To ensure reliability, non-natural areas (croplands and urban areas), bare areas and water bodies were discarded (Table 1). In summary, a combination of 28 ecoregions, 15 land cover types and six continents were combined to define a total of 881 different spatial units (deposited at Dryad-Table S2). The use of ecoregion/land cover/continent combination provided a much greater resolution than using a traditional biome classification and allowed to account for human-driven transformations of vegetation, the latter based on the land cover data.Table 1 List of land cover categories within the ESA CCI Land Cover dataset, used to assemble maps of mycorrhizal root biomass.Full size tableMycorrhizal fine root stocksTotal root C stocksEstimation of the total root C stock in each of the spatial units was obtained from the harmonized belowground biomass C density maps of Spawn et al.20. These maps are based on continental-to-global scale remote sensing data of aboveground biomass C density and land cover-specific root-to-shoot relationships to generate matching belowground biomass C maps. This product is the best up-to-date estimation of live root stock available. For subsequent steps in our workflow, we distinguished woody and herbaceous belowground biomass C as provided by Spawn et al.20. As the tundra belowground biomass C map was provided without growth form distinction, it was assessed following a slightly different workflow (see Section 2.2.3 for more details). To match the resolution of other input maps in the workflow, all three belowground biomass C maps were scaled up from the original spatial resolution of 10-arc seconds (approximately 300 m at the equator) to 10 arc‐minutes resolution (approximately 18.5 km at the equator) using the mean location of the raster cells as aggregation criterion.As the root biomass C maps do not distinguish between fine and coarse roots and mycorrhizal fungi colonize only the fine fractions of the roots, we considered the fine root fraction to be 88,5% and 14,1% of the total root biomass for herbaceous and woody plants, respectively. These constants represent the mean value of coarse/fine root mass ratios of herbaceous and woody plants provided by the Fine-Root Ecology Database (FRED) (https://roots.ornl.gov/)25 (deposited at Dryad-Table S3). Due to the non-normality of coarse/fine root mass ratios, mean values were obtained from log-transformed data and then back-transformed for inclusion into the workflow.Finally, the belowground biomass C maps consider the whole root system, but mycorrhizal colonization occurs mainly in the upper 30 cm of the soil18. Therefore, we estimated the total fine root stocks in the upper 30 cm by applying the asymptotic equation of vertical root distribution developed by Gale & Grigal26:$$y=1-{beta }^{d}$$where y is the cumulative root fraction from the soil surface to depth d (cm), and β is the fitted coefficient of extension. β values of trees (β = 0.970), shrubs (β = 0.978) and herbs (β = 0.952) were obtained from Jackson et al.27. A mean value was then calculated for trees and shrubs to obtain a woody vegetation β value of 0.974. As a result, we estimated that 54.6% of the total live root of woody vegetation and 77.1% of herbaceous vegetation is stored in the upper 30 cm of the soil. In combination, this allowed deriving fine root C stocks in the upper 30 cm of woody and herbaceous vegetation.The proportion of root stocks colonized by AM and EcMThe proportion of root stock that forms associations with AM or EcM fungi was obtained from the global maps of aboveground biomass distribution of dominant mycorrhizal types published by Soudzilovskaia et al.14. These maps provide the relative abundance of EcM and AM plants based on information about the biomass of grass, shrub and tree vegetation at 10arcmin resolution. To match with belowground root woody plants biomass data, proportions of AM trees and shrubs underlying the maps of Soudzilovskaia et al.14 were summed up to obtain the proportion of AM woody vegetation. The same was done for EcM trees and shrubs.Our calculations are subjected to the main assumption that, within each growth form, the proportion of aboveground biomass associated with AM and EcM fungi reflects the proportional association of AM and EM fungi to belowground biomass. We tested whether root:shoot ratios were significantly different between AM and EcM woody plants (the number of EcM herbaceous plants is extremely small17). Genera were linked to growth form based on the TRY database (https://www.try-db.org/)19 and the mycorrhizal type association based on the FungalRoots database17. Subsequently, it was tested whether root:shoot ratios of genera from the TRY database (https://www.try-db.org/)19 were significantly different for AM vs EcM woody plants. No statistically significant differences (ANOVA-tests p-value = 0.595) were found (Fig. 2).Fig. 2Mean and standar error of root to shoot ratios of AM and EcM woody plant species.Full size imageEstimation of mycorrhizal fine root stocksWe calculated the total biomass C of fine roots that can potentially be colonized by AM or EcM fungi by multiplying the total woody and herbaceous fine root C biomass in the upper 30 cm of the soil by the proportion of AM and EcM of woody and herbaceous vegetation. In the case of tundra vegetation, fine root C stocks were multiplied by the relative abundance of AM and EcM vegetation without distinction of growth forms (for simplicity, this path was not included in Fig. 1, but can be seen in Fig. 3. As tundra vegetation consists mainly of herbs and small shrubs, the distinction between woody and herbaceous vegetation is not essential in this case.Fig. 3Workflow used to create mycorrhizal fine root biomass C maps specific for tundra areas.Full size imageFinally, we obtained the mean value of mycorrhiza growth form fine root C stocks in each of the defined spatial units. These resulted in six independent estimations: AM woody, AM herbaceous, EcM woody, EcM herbaceous, AM tundra and EcM tundra total fine root biomass C (Fig. 4).Fig. 4Fine root biomass stocks capable to form association with AM (a) and EcM (b) fungi for woody, herbaceous and tundra vegetation. Final AM and EcM stock result from the sum of the growth form individual maps. There were no records of fine root biomass of EcM herbaceous vegetation.Full size imageThe intensity of root colonization by mycorrhizal fungiColonization databaseThe FungalRoot database is the largest up-to-date compilation of intensity of root colonization data, providing 36303 species observations for 14870 plant species. Colonization data was filtered to remove occurrences from non-natural conditions (i.e., from plantations, nurseries, greenhouses, pots, etc.) and data collected outside growing seasons. Records without explicit information about habitat naturalness and growing season were maintained as colonization intensity is generally recorded in the growing season of natural habitats. When the intensity of colonization occurrences was expressed in categorical levels, they were converted to percentages following the transformation methods stated in the original publications. Finally, plant species were distinguished between woody and herbaceous species using the publicly available data from TRY (https://www.trydb.org/)19. As a result, 9905 AM colonization observations of 4494 species and 521 EcM colonization observations of 201 species were used for the final calculations (Fig. 5).Fig. 5Number of AM (a) and EcM (b) herbaceous and woody plant species and total observations obtained from FungalRoot database.Full size imageThe use of the mean of mycorrhizal colonization intensity per plant species is based on two main assumptions:

1)

The intensity of root colonization is a plant trait: It is known that the intensity of mycorrhizal infections of a given plant species varies under different climatic and soil conditions28,29, plant age30 and the identity of colonizing fungal species31. However, Soudzilovskaia et al.9 showed that under natural growth conditions the intraspecific variation of root mycorrhizal colonization is lower than interspecific variation, and is within the range of variations in other plant eco-physiological traits. Moreover, recent literature reported a positive correlation between root morphological traits and mycorrhizal colonization, with a strong phylogenetic signature of these correlations32,33. These findings provide support for the use of mycorrhizal root colonization of plants grown in natural conditions as a species-specific trait.

2)

The percentage of root length or root tips colonized can be translated to the percentage of biomass colonized: intensity of root colonization is generally expressed as the proportion of root length colonized by AM fungi or proportion of root tips colonized by EcM fungi (as EcM infection is restricted to fine root tips). Coupling this data with total root biomass C stocks requires assuming that the proportion of root length or proportion of root tips colonized is equivalent to the proportion of root biomass colonized. While for AM colonization this equivalence can be straightforward, EcM colonization can be more problematic as the number of root tips varies between tree species. However, given that root tips represent the terminal ends of a root network34, the proportion of root tips colonized by EcM fungi can be seen as a measurement of mycorrhizal infection of the root system and translated to biomass independently of the number of root tips of each individual. Yet, it is important to stress that estimations of fine root biomass colonized by AM and EcM as provided in this paper might not be directly comparable.

sPlot databaseThe sPlotOpen database21 holds information about the relative abundance of vascular plant species in 95104 different vegetation plots spanning 114 countries. In addition, sPlotOpen provides three partially overlapping resampled subset of 50000 plots each that has been geographically and environmentally balanced to cover the highest plant species variability while avoiding rare communities. From these three available subsets, we selected the one that maximizes the number of spatial units that have at least one vegetation plot. We further checked if any empty spatial unit could be filled by including sPlot data from other resampling subsets.Plant species in the selected subset were classified as AM and EcM according to genus-based mycorrhizal types assignments, provided in the FungalRoot database17. Plant species that could not be assigned to any mycorrhizal type were excluded. Facultative AM species were not distinguished from obligated AM species, and all were considered AM species. The relative abundance of species with dual colonization was treated as 50% AM and 50% ECM. Plant species were further classified into woody and herbaceous species using the TRY database.Estimation of the intensity of mycorrhizal colonizationThe percentage of AM and EcM root biomass colonized per plant species was spatially upscaled by inferring the relative abundance of AM and EcM plant species in each plot. For each mycorrhizal-growth form and each vegetation plot, the relative abundance of plant species was determined to include only the plant species for which information on the intensity of root colonization was available. Then, a weighted mean intensity of colonization per mycorrhizal-growth form was calculated according to the relative abundance of the species featuring that mycorrhizal-growth form in the vegetation plot. Lastly, the final intensity of colonization per spatial unit was calculated by taking the mean value of colonization across all plots within that spatial unit. These calculations are based on 38127 vegetation plots that hold colonization information, spanning 384 spatial units.The use of vegetation plots as the main entity to estimate the relative abundance of AM and EcM plant species in each spatial unit assumes that the plant species occurrences and their relative abundances in the selected plots are representative of the total spatial unit. This is likely to be true for spatial units that are represented by a high number of plots. However, in those spatial units where the number of plots is low, certain vegetation types or plant species may be misrepresented. We addressed this issue in our uncertainty analysis. Details are provided in the Quality index maps section.Final calculation and maps assemblyThe fraction of total fine root C stocks that is colonized by AM and EcM fungi was estimated by multiplying fine root C stocks by the mean root colonization intensity in each spatial unit. This calculation was made separately for tundra, woody and herbaceous vegetation.To generate raster maps based on the resulting AM and EcM fine root biomass C data, we first created a 10 arcmin raster map of the spatial units. To do this, we overlaid the raster map of Bailey ecoregions (10 arcmin resolution)24, the raster of ESA CCI land cover data at 300 m resolution aggregated to 10 arcmin using a nearest neighbour approach (https://www.esa-landcover-cci.org/) and the FAO polygon map of continents (http://www.fao.org/geonetwork/srv/en/), rasterized at 10 arcmin. Finally, we assigned to each pixel the corresponding biomass of fine root colonized by mycorrhiza, considering the prevailing spatial unit. Those spatial units that remained empty due to lack of vegetation plots or colonization data were filled with the mean value of the ecoregion x continent combination.Quality index mapsAs our workflow comprises many different data sources and the extracted data acts in distinct hierarchical levels (i.e plant species, plots or spatial unit level), providing a unified uncertainty estimation for our maps is particularly challenging. Estimates of mycorrhizal fine root C stocks are related mainly to belowground biomass C density maps and mycorrhizal aboveground biomass maps, which have associated uncertainties maps provided by the original publications. In contrast, estimates of the intensity of root colonization in each spatial unit have been associated with three main sources of uncertainties:

1)

The number of observations in the FungalRoot database. The mean species-level intensity of mycorrhizal colonization in the vegetation plots has been associated with a number of independent observations of root colonization for each plant species. We calculated the mean number of observations of each plant species for each of the vegetation plots and, subsequently the mean number of observations (per plant species) from all vegetation plots in each spatial unit. These spatial unit averaged number of observations ranged from 1 to 14 in AM and from 1 to 26 in EcM. A higher number of observations would indicate that the intraspecific variation in the intensity of colonization is better captured and, therefore, the species-specific colonization estimates are more robust.

2)

The relative plant coverage that was associated with colonization data. From the selected vegetation plots, only a certain proportion of plant species could be associated with the intensity of colonization data in FungalRoot database. The relative abundance of the plant species with colonization data was summed up in each vegetation plot. Then, we calculated the average values for each spatial unit. Mean abundance values ranged from 0.3 to 100% in both AM and EcM spatial units. A high number indicates that the dominant plant species of the vegetation plots have colonization data associated and, consequently, the community-averaged intensity of colonization estimates are more robust.

3)

The number of vegetation plots in each spatial unit. Each of the spatial units differs in the number of plots used to calculate the mean intensity of colonization, ranging from 1 to 1583 and from 1 to 768 plots in AM and EcM estimations, respectively. A higher number of plots is associated with a better representation of the vegetation variability in the spatial units, although this will ultimately depend on plot size and intrinsic heterogeneity (i.e., a big but homogeneous spatial unit may need fewer vegetation plots for a good representation than a small but very heterogeneous spatial unit).

We provide independent quality index maps of the spatial unit average of these three sources of uncertainty. These quality index maps can be used to locate areas where our estimates have higher or lower robustness. More