Philippa Kaur

Steffen, W. Introducing the Anthropocene: The human epoch. Ambio 50, 1784–1787 (2021).Article 

Google Scholar 
Keys, P. W. et al. Anthropocene risk. Nat. Sustain. 2, 667–673 (2019).Article 

Google Scholar 
Bell, G. Evolutionary rescue and the limits of adaptation. Philos. Trans. R. Soc. B Biol. Sci. 368, 20120080 (2013).Article 

Google Scholar 
Byrne, M. & Przeslawski, R. Multistressor impacts of warming and acidification of the ocean on marine invertebrates’ life histories. Integr. Comp. Biol. 53, 582–596 (2013).Article 
CAS 

Google Scholar 
Feely, R. A. et al. Impact of anthropogenic CO2 on the CaCO3 system in the oceans. Science 305, 362–366 (2004).Article 
CAS 

Google Scholar 
Doney, S. C., Fabry, V. J., Feely, R. A. & Kleypas, J. A. Ocean acidification: the other CO2 problem. Ann. Rev. Mar. Sci. 1, 169–192 (2009).Article 

Google Scholar 
Hill, T. S. & Hoogenboom, M. O. The indirect effects of ocean acidification on corals and coral communities. Coral Reefs https://doi.org/10.1007/s00338-022-02286-z (2022).Biagi, E. et al. Patterns in microbiome composition differ with ocean acidification in anatomic compartments of the Mediterranean coral Astroides calycularis living at CO2 vents. Sci. Total Environ. 724, 138048 (2020).Article 
CAS 

Google Scholar 
Chen, B. et al. Microbiome community and complexity indicate environmental gradient acclimatisation and potential microbial interaction of endemic coral holobionts in the South China Sea. Sci. Total Environ. 765, 142690 (2021).Article 
CAS 

Google Scholar 
Palumbi, S. R., Barshis, D. J., Traylor-Knowles, N. & Bay, R. A. Mechanisms of reef coral resistance to future climate change. Science 344, 895–898 (2014).Article 
CAS 

Google Scholar 
Wood, R. The ecological evolution of reefs. Annu. Rev. Ecol. Syst. 29, 179–206 (1998).Article 

Google Scholar 
Drake, J. L. et al. How corals made rocks through the ages. Glob. Chang. Biol. 26, 31–53 (2020).Article 

Google Scholar 
Stanley, G. D. Photosymbiosis and the evolution of modern coral reefs. Science 312, 857–858 (2006).Article 
CAS 

Google Scholar 
Kitahara, M. V., Cairns, S. D., Stolarski, J., Blair, D. & Miller, D. J. A comprehensive phylogenetic analysis of the scleractinia (Cnidaria, Anthozoa) based on mitochondrial CO1 sequence data. PLoS One. 5, e11490 (2010).Article 

Google Scholar 
Dubinsky, Z. & Jokiel, P. Ratio of energy and nutrient fluxes regulates symbiosis between zooxanthellae and corals. Pac. Sci. 48, 313–324 (1994).
Google Scholar 
Falkowski, P. G., Dubinsky, Z., Muscatine, L. & Porter, J. W. Light and the bioenergetics of a symbiotic coral. Bioscience 34, 705–709 (1984).Article 
CAS 

Google Scholar 
Frankowiak, K., Roniewicz, E. & Stolarski, J. Photosymbiosis in Late Triassic scleractinian corals from the Italian Dolomites. PeerJ 9, e11062 (2021).Article 

Google Scholar 
Davy, S. K., Allemand, D. & Weis, V. M. Cell biology of cnidarian-dinoflagellate symbiosis. Microbiol. Mol. Biol. Rev. 76, 229–261 (2012).Article 
CAS 

Google Scholar 
Kremer, P. Ingestion and elemental budgets for Linuche unguiculata, a scyphomedusa with zooxanthellae. J. Mar. Biol. Assoc. UK. 85, 613–625 (2005).Article 

Google Scholar 
Welsh, D. T., Dunn, R. J. K. & Meziane, T. Oxygen and nutrient dynamics of the upside down jellyfish (Cassiopea sp.) and its influence on benthic nutrient exchanges and primary production. Hydrobiologia 635, 351–362 (2009).Article 
CAS 

Google Scholar 
Muscatine, L., McCloskey, L. R. & Marian, R. E. Estimating the daily contribution of carbon from zooxanthellae to coral animal respiration. Limnol. Oceanogr. 26, 601–611 (1981).Article 
CAS 

Google Scholar 
Ferrier‐Pagès, C. & Leal, M. C. Stable isotopes as tracers of trophic interactions in marine mutualistic symbioses. Ecol. Evol. 9, 723–740 (2019).Article 

Google Scholar 
Teixidó, N. et al. Ocean acidification causes variable trait shifts in a coral species. Glob. Chang. Biol. 26, 6813–6830 (2020).Article 

Google Scholar 
Fantazzini, P. et al. Gains and losses of coral skeletal porosity changes with ocean acidification acclimation. Nat. Commun. 6, 7785 (2015).Article 
CAS 

Google Scholar 
Prada, F. et al. Coral micro- and macro-morphological skeletal properties in response to life-long acclimatization at CO2 vents in Papua New Guinea. Sci. Rep. 11, 19927 (2021).Article 
CAS 

Google Scholar 
Kerrison, P., Hall-Spencer, J. M., Suggett, D. J., Hepburn, L. J. & Steinke, M. Assessment of pH variability at a coastal CO2 vent for ocean acidification studies. Estuar. Coast. Shelf Sci. 94, 129–137 (2011).Article 
CAS 

Google Scholar 
Johnson, V. R., Russell, B. D., Fabricius, K. E., Brownlee, C. & Hall-Spencer, J. M. Temperate and tropical brown macroalgae thrive, despite decalcification, along natural CO2 gradients. Glob. Chang. Biol. 18, 2792–2803 (2012).Article 

Google Scholar 
Caroselli, E. et al. Low and variable pH decreases recruitment efficiency in populations of a temperate coral naturally present at a CO2 vent. Limnol. Oceanogr. 64, 1059–1069 (2019).Article 
CAS 

Google Scholar 
González-Delgado, S. & Hernández, J. C. The importance of natural acidified systems in the study of ocean acidification: what have we learned? Adv. Mar. Biol. 80, 57–99 (2018).Article 

Google Scholar 
Capaccioni, B., Tassi, F., Vaselli, O., Tedesco, D. & Poreda, R. Submarine gas burst at Panarea Island (southern Italy) on 3 November 2002: A magmatic versus hydrothermal episode. J. Geophys. Res. 112, B05201 (2007).
Google Scholar 
Reggi, M. et al. Biomineralization in mediterranean corals: The role of the intraskeletal organic matrix. Cryst. Growth Des. 14, 4310–4320 (2014).Article 
CAS 

Google Scholar 
Prada, F. et al. Ocean warming and acidification synergistically increase coral mortality. Sci. Rep. 7, 1–10 (2017).Article 

Google Scholar 
Goffredo, S. et al. Biomineralization control related to population density under ocean acidification. Nat. Clim. Chang. 4, 593–597 (2014).Article 
CAS 

Google Scholar 
Wall, M. et al. Linking internal carbonate chemistry regulation and calcification in corals growing at a Mediterranean CO2 vent. Front. Mar. Sci. 6, 699 (2019).Article 

Google Scholar 
Zohary, T., Erez, J., Gophen, M., Berman-Frank, I. & Stiller, M. Seasonality of stable carbon isotopes within the pelagic food web of Lake Kinneret. Limnol. Oceanogr. 39, 1030–1043 (1994).Article 
CAS 

Google Scholar 
Xu, S. et al. Spatial variations in the trophic status of Favia palauensis corals in the South China Sea: Insights into their different adaptabilities under contrasting environmental conditions. Sci. China Earth Sci. 64, 839–852 (2021).Article 

Google Scholar 
Horwitz, R., Borell, E. M., Yam, R., Shemesh, A. & Fine, M. Natural high pCO2 increases autotrophy in Anemonia viridis (Anthozoa) as revealed from stable isotope (C, N) analysis. Sci. Rep. 5, 1–9 (2015).Article 

Google Scholar 
Chen, B., Zou, D., Zhu, M. & Yang, Y. Effects of CO2 levels and light intensities on growth and amino acid contents in red seaweed Gracilaria lemaneiformis. Aquac. Res. 48, 2683–2690 (2017).Article 
CAS 

Google Scholar 
Winters, G., Beer, S., Zvi, B., Brickner, I. & Loya, Y. Spatial and temporal photoacclimation of Stylophora pistillata: zooxanthella size, pigmentation, location and clade. Mar. Ecol. Prog. Ser. 384, 107–119 (2009).Article 

Google Scholar 
Fitt, W. K., McFarland, F. K., Warner, M. E. & Chilcoat, G. C. Seasonal patterns of tissue biomass and densities of symbiotic dinoflagellates in reef corals and relation to coral bleaching. Limnol. Oceanogr. 45, 677–685 (2000).Article 
CAS 

Google Scholar 
Wangpraseurt, D., Larkum, A. W. D., Ralph, P. J. & Kühl, M. Light gradients and optical microniches in coral tissues. Front. Microbiol. 3, 1–9 (2012).Article 

Google Scholar 
Krief, S. et al. Physiological and isotopic responses of scleractinian corals to ocean acidification. Geochim. Cosmochim. Acta. 74, 4988–5001 (2010).Article 
CAS 

Google Scholar 
Scucchia, F., Malik, A., Zaslansky, P., Putnam, H. M. & Mass, T. Combined responses of primary coral polyps and their algal endosymbionts to decreasing seawater pH. Proc. R. Soc. B Biol. Sci. 288, 20210328 (2021).Article 
CAS 

Google Scholar 
Anthony, K. R. N., Connolly, S. R. & Willis, B. L. Comparative analysis of energy allocation to tissue and skeletal growth in corals. Limnol. Oceanogr. 47, 1417–1429 (2002).Article 

Google Scholar 
LaJeunesse, T. C. et al. Systematic revision of Symbiodiniaceae highlights the antiquity and diversity of coral endosymbionts. Curr. Biol. 28, 2570–2580.e6 (2018).Article 
CAS 

Google Scholar 
Howells, E. J. et al. Coral thermal tolerance shaped by local adaptation of photosymbionts. Nat. Clim. Chang. 2, 116–120 (2012).Article 

Google Scholar 
Brading, P. et al. Differential effects of ocean acidification on growth and photosynthesis among phylotypes of Symbiodinium (Dinophyceae). Limnol. Oceanogr. 56, 927–938 (2011).Article 
CAS 

Google Scholar 
Takahashi, T., Broecker, W. S. & Langer, S. Redfield ratio based on chemical data from isopycnal surfaces. J. Geophys. Res. 90, 6907 (1985).Article 
CAS 

Google Scholar 
Xu, Z. et al. Changes of carbon to nitrogen ratio in particulate organic matter in the marine mesopelagic zone: A case from the South China Sea. Mar. Chem. 231, 103930 (2021).Article 
CAS 

Google Scholar 
Crawford, D. W. et al. Low particulate carbon to nitrogen ratios in marine surface waters of the Arctic. Glob. Biogeochem. Cycles. 29, 2021–2033 (2015).Article 
CAS 

Google Scholar 
Kikumoto, R. et al. Nitrogen isotope chemostratigraphy of the Ediacaran and Early Cambrian platform sequence at Three Gorges, South China. Gondwana Res. 25, 1057–1069 (2014).Article 
CAS 

Google Scholar 
DeNiro, M. J. & Epstein, S. Influence of diet on the distribution of carbon isotopes in animals. Geochim. Cosmochim. Acta 42, 495–506 (1978).Article 
CAS 

Google Scholar 
Benavides, M., Bednarz, V. N. & Ferrier-Pagès, C. Diazotrophs: Overlooked key players within the coral symbiosis and tropical reef ecosystems? Front. Mar. Sci. 4, 10 (2017).Article 

Google Scholar 
Wannicke, N., Frey, C., Law, C. S. & Voss, M. The response of the marine nitrogen cycle to ocean acidification. Glob. Chang. Biol. 24, 5031–5043 (2018).Article 

Google Scholar 
Bourne, D. G., Morrow, K. M. & Webster, N. S. Insights into the coral microbiome: underpinning the health and resilience of reef ecosystems. Annu. Rev. Microbiol. 70, 317–340 (2016).Article 
CAS 

Google Scholar 
Palladino, G. et al. Metagenomic shifts in mucus, tissue and skeleton of the coral Balanophyllia europaea living along a natural CO2 gradient. ISME Commun. 2, 65 (2022).Article 

Google Scholar 
Muscatine, L. et al. Stable isotopes (δ13C and δ15N) of organic matrix from coral skeleton. Proc. Natl Acad. Sci. 102, 1525–1530 (2005).Article 
CAS 

Google Scholar 
Lesser, M. P. et al. Nitrogen fixation by symbiotic cyanobacteria provides a source of nitrogen for the scleractinian coral Montastraea cavernosa. Mar. Ecol. Prog. Ser. 346, 143–152 (2007).Article 
CAS 

Google Scholar 
Alamaru, A., Loya, Y., Brokovich, E., Yam, R. & Shemesh, A. Carbon and nitrogen utilization in two species of Red Sea corals along a depth gradient: Insights from stable isotope analysis of total organic material and lipids. Geochim. Cosmochim. Acta. 73, 5333–5342 (2009).Article 
CAS 

Google Scholar 
Lesser, M. P., Mazel, C. H., Gorbunov, M. Y. & Falkowski, P. G. Discovery of symbiotic nitrogen-fixing cyanobacteria in corals. Science 305, 997–1000 (2004).Article 
CAS 

Google Scholar 
Lesser, M. P., Morrow, K. M., Pankey, S. M. & Noonan, S. H. C. Diazotroph diversity and nitrogen fixation in the coral Stylophora pistillata from the Great Barrier Reef. ISME J. 12, 813–824 (2018).Article 
CAS 

Google Scholar 
Marcelino, V. R., Morrow, K. M., Oppen, M. J. H., Bourne, D. G. & Verbruggen, H. Diversity and stability of coral endolithic microbial communities at a naturally high pCO2 reef. Mol. Ecol. 26, 5344–5357 (2017).Article 
CAS 

Google Scholar 
Rädecker, N., Pogoreutz, C., Voolstra, C. R., Wiedenmann, J. & Wild, C. Nitrogen cycling in corals: the key to understanding holobiont functioning? Trends Microbiol. 23, 490–497 (2015).Article 

Google Scholar 
Santos, H. F. et al. Climate change affects key nitrogen-fixing bacterial populations on coral reefs. ISME J. 8, 2272–2279 (2014).Article 

Google Scholar 
Olson, N. D., Ainsworth, T. D., Gates, R. D. & Takabayashi, M. Diazotrophic bacteria associated with Hawaiian Montipora corals: Diversity and abundance in correlation with symbiotic dinoflagellates. J. Exp. Mar. Bio. Ecol. 371, 140–146 (2009).Article 
CAS 

Google Scholar 
Zheng, X. et al. Effects of ocean acidification on carbon and nitrogen fixation in the hermatypic coral Galaxea fascicularis. Front. Mar. Sci. 8, 644965 (2021).Article 

Google Scholar 
Lewis, E. & Wallace, D. Program developed for CO2 system calculations. Ornl/Cdiac-105 1–21 (1998).Dickson, A. G. & Millero, F. J. A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media. Deep Sea Res. Part A. Oceanogr. Res. Pap. 34, 1733–1743 (1987).Article 
CAS 

Google Scholar 
Dickson, A. G. Thermodynamics of the dissociation of boric acid in potassium chloride solutions from 273.15 to 318.15 K. J. Chem. Eng. Data. 35, 253–257 (1990).Article 
CAS 

Google Scholar 
Mehrbach, C., Culberson, C. H., Hawley, J. E. & Pytkowicx, R. M. Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnol. Oceanogr. 18, 897–907 (1973).Article 
CAS 

Google Scholar 
Ivancic, I. & Degobbis, D. An optimal manual procedure for ammonia analysis in natural waters by the indophenol blue method. Water Res. 18, 1143–1147 (1984).Article 
CAS 

Google Scholar 
Parson, T. R., Maita, Y. & Llli, C. M. A manual of chemical & biological methods for seawater analysis. (Elsevier, 1984). https://doi.org/10.1016/C2009-0-07774-5Schreiber, U. Pulse-Amplitude-Modulation (PAM) fluorometry and saturation pulse method: an overview. in Chlorophyll a Fluorescence 1367, 279–319 (Springer Netherlands, 2004).Grover, R., Maguer, J. F., Reynaud-Vaganay, S. & Ferrier-Pagès, C. Uptake of ammonium by the scleractinian coral Stylophora pistillata: Effect of feeding, light, and ammonium concentrations. Limnol. Oceanogr. 47, 782–790 (2002).Article 

Google Scholar 
Tremblay, P., Grover, R., Maguer, J. F., Hoogenboom, M. & Ferrier-Pagès, C. Carbon translocation from symbiont to host depends on irradiance and food availability in the tropical coral Stylophora pistillata. Coral Reefs. 33, 1–13 (2014).Article 

Google Scholar 
Pupier, C. A. et al. Productivity and carbon fluxes depend on species and symbiont density in soft coral symbioses. Sci. Rep. 9, 17819 (2019).Article 

Google Scholar 
Ritchie, R. J. Universal chlorophyll equations for estimating chlorophylls a, b, c, and d and total chlorophylls in natural assemblages of photosynthetic organisms using acetone, methanol, or ethanol solvents. Photosynthetica 46, 115–126 (2008).Article 
CAS 

Google Scholar 
Goffredo, S., Arnone, S. & Zaccanti, F. Sexual reproduction in the Mediterranean solitary coral Balanophyllia europaea (Scleractinia, Dendrophylliidae). Mar. Ecol. Prog. Ser. 229, 83–94 (2002).Article 

Google Scholar 
Barshis, D. J. et al. Genomic basis for coral resilience to climate change. Proc. Natl Acad. Sci. 110, 1387–1392 (2013).Article 
CAS 

Google Scholar 
Moore, R. B. Highly organized structure in the non-coding region of the psbA minicircle from clade C Symbiodinium. Int. J. Syst. Evol. Microbiol. 53, 1725–1734 (2003).Article 
CAS 

Google Scholar 
LaJeunesse, T. C. & Thornhill, D. J. Improved resolution of reef-coral endosymbiont (Symbiodinium) species diversity, ecology, and evolution through psbA non-coding region genotyping. PLoS One. 6, e29013 (2011).Article 
CAS 

Google Scholar 
LaJeunesse, T. C. et al. Revival of Philozoon Geddes for host-specialized dinoflagellates, ‘zooxanthellae’, in animals from coastal temperate zones of northern and southern hemispheres. Eur. J. Phycol. 57, 166–180 (2022).Article 

Google Scholar 
Anderson, M. J. PERMANOVA: a FORTRAN computer program for permutational multivariate analysis of variance. Wiley StatsRef: Statistics Reference Online (2005). More

Battin, T. J. et al. The boundless carbon cycle. Nat. Geosci. 2, 598–600 (2009).Article 
CAS 

Google Scholar 
Raymond, P. A. et al. Global carbon dioxide emissions from inland waters. Nature 503, 355–359 (2013).Article 
CAS 

Google Scholar 
Hotchkiss, E. R. et al. Sources of and processes controlling CO2 emissions change with the size of streams and rivers. Nat. Geosci. 8, 696–699 (2015). Important study conceptualizing (on the basis of a data synthesis) how the sources and magnitude of CO2 evasion flux change along a stream–river continuum.Ciais, P. et al. in Climate Change 2013 The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al.) Ch. 6 (Cambridge Univ. Press, 2013).Friedlingstein, P. et al. Global carbon budget 2021. Earth Syst. Sci. Data 14, 1917–2005 (2022).Article 

Google Scholar 
Cole, J. J. et al. Plumbing the global carbon cycle: integrating inland waters into the terrestrial carbon budget. Ecosystems 10, 172–185 (2007). A pioneering study showing the role of inland waters for large-scale carbon fluxes and highlighting them as ‘reactors’ rather than ‘passive pipes’.Article 

Google Scholar 
Drake, T. W., Raymond, P. A. & Spencer, R. G. M. Terrestrial carbon inputs to inland waters: a current synthesis of estimates and uncertainty. Limnol. Oceanogr. Lett. 3, 132–142 (2018).Article 
CAS 

Google Scholar 
Odum, H. T. Primary production in flowing waters. Limnol. Oceanogr. 1, 102–117 (1956).Article 

Google Scholar 
Bernhardt, E. S. et al. The metabolic regimes of flowing waters. Limnol. Oceanogr. 63, 99–118 (2018). A synthesis of the predominant drivers and constraints on metabolic regimes of stream and river ecosystems.Article 

Google Scholar 
Barnes, A. D. et al. Energy flux: the link between multitrophic biodiversity and ecosystem functioning. Trends Ecol. Evol. 33, 186–197 (2018).Article 

Google Scholar 
Costanza, R. & Mageau, M. What is a healthy ecosystem? Aquat. Ecol. 33, 105–115 (1999).Article 

Google Scholar 
Blöschl, G. et al. Changing climate both increases and decreases European river floods. Nature 573, 108–111 (2019).Article 

Google Scholar 
Gudmundsson, L. et al. Globally observed trends in mean and extreme river flow attributed to climate change. Science 371, 1159–1162 (2021).Article 
CAS 

Google Scholar 
Yang, X., Pavelsky, T. M. & Allen, G. H. The past and future of global river ice. Nature 577, 69–73 (2020).Article 
CAS 

Google Scholar 
Grill, G. et al. Mapping the world’s free-flowing rivers. Nature 569, 215–221 (2019).Article 
CAS 

Google Scholar 
Belletti, B. et al. More than one million barriers fragment Europe’s rivers. Nature 588, 436–441 (2020).Article 
CAS 

Google Scholar 
Pekel, J.-F., Cottam, A., Gorelick, N. & Belward, A. S. High-resolution mapping of global surface water and its long-term changes. Nature 540, 418–422 (2016).Article 
CAS 

Google Scholar 
Cooley, S. W., Ryan, J. C. & Smith, L. C. Human alteration of global surface water storage variability. Nature 591, 78–81 (2021).Article 
CAS 

Google Scholar 
Jaramillo, F. & Destouni, G. Local flow regulation and irrigation raise global human water consumption and footprint. Science 350, 1248–1251 (2015).Article 
CAS 

Google Scholar 
Quinton, J. N., Govers, G., Oost, K. V. & Bardgett, R. D. The impact of agricultural soil erosion on biogeochemical cycling. Nat. Geosci. 3, 311–314 (2010).Article 
CAS 

Google Scholar 
Mekonnen, M. M. & Hoekstra, A. Y. Global anthropogenic phosphorus loads to freshwater and associated grey water footprints and water pollution levels: a high‐resolution global study. Water Resour. Res. 54, 345–358 (2018).Article 
CAS 

Google Scholar 
Regnier, P. et al. Anthropogenic perturbation of the carbon fluxes from land to ocean. Nat. Geosci. 6, 597–607 (2013). The first study showing the extent to which human activities have altered the magnitude of contemporary lateral carbon fluxes from land to ocean.Article 
CAS 

Google Scholar 
Rüegg, J. et al. Thinking like a consumer: linking aquatic basal metabolism and consumer dynamics. Limnol. Oceanogr. Lett. 6, 1–17 (2021).Article 

Google Scholar 
Fernández-Martínez, M. et al. Global trends in carbon sinks and their relationships with CO2 and temperature. Nat. Clim. Change 9, 73–79 (2019).Article 

Google Scholar 
Behrenfeld, M. J. et al. Climate-driven trends in contemporary ocean productivity. Nature 444, 752–755 (2006).Article 
CAS 

Google Scholar 
Phillips, J. S. Time‐varying responses of lake metabolism to light and temperature. Limnol. Oceanogr. 65, 652–666 (2020).Article 
CAS 

Google Scholar 
Uehlinger, U. Annual cycle and inter‐annual variability of gross primary production and ecosystem respiration in a floodprone river during a 15‐year period. Freshw. Biol. 51, 938–950 (2006).Article 
CAS 

Google Scholar 
Uehlinger, U. & Naegeli, M. W. Ecosystem metabolism, disturbance, and stability in a prealpine gravel bed river. J. North Am. Benthol. Soc. 17, 165–178 (1998).Article 

Google Scholar 
Mulholland, P. J. et al. Inter-biome comparison of factors controlling stream metabolism. Freshw. Biol. 46, 1503–1517 (2001).Article 
CAS 

Google Scholar 
Roberts, B. J., Mulholland, P. J. & Hill, W. R. Multiple scales of temporal variability in ecosystem metabolism rates: results from 2 years of continuous monitoring in a forested headwater stream. Ecosystems 10, 588–606 (2007).Article 
CAS 

Google Scholar 
Appling, A. P., Hall, R. O., Yackulic, C. B. & Arroita, M. Overcoming equifinality: leveraging long time series for stream metabolism estimation. J. Geophys. Res. Biogeosci. 123, 624–645 (2018).Article 
CAS 

Google Scholar 
Appling, A. P. et al. The metabolic regimes of 356 rivers in the United States. Sci. Data 5, 180292 (2018).Article 
CAS 

Google Scholar 
Canadell, M. B. et al. Regimes of primary production and their drivers in Alpine streams. Freshw. Biol. 66, 1449–1463 (2021).Article 

Google Scholar 
Myrstener, M., Gómez‐Gener, L., Rocher‐Ros, G., Giesler, R. & Sponseller, R. A. Nutrients influence seasonal metabolic patterns and total productivity of Arctic streams. Limnol. Oceanogr. 66, S182–S196 (2021).Article 
CAS 

Google Scholar 
Savoy, P. et al. Metabolic rhythms in flowing waters: an approach for classifying river productivity regimes. Limnol. Oceanogr. 64, 1835–1851 (2019).Article 

Google Scholar 
Kirk, L., Hensley, R. T., Savoy, P., Heffernan, J. B. & Cohen, M. J. Estimating benthic light regimes improves predictions of primary production and constrains light-use efficiency in streams and rivers. Ecosystems 24, 825–839 (2021).Article 

Google Scholar 
Bernhardt, E. S. et al. Light and flow regimes regulate the metabolism of rivers. Proc. Natl Acad. Sci. USA 119, e2121976119 (2022).Article 
CAS 

Google Scholar 
Savoy, P. & Harvey, J. W. Predicting light regime controls on primary productivity across CONUS river networks. Geophys. Res. Lett. 48, e2020GL092149 (2021).Article 

Google Scholar 
Julian, J. P., Stanley, E. H. & Doyle, M. W. Basin-scale consequences of agricultural land use on benthic light availability and primary production along a sixth-order temperate river. Ecosystems 11, 1091–1105 (2008).Article 

Google Scholar 
Hall, R. O. et al. Turbidity, light, temperature, and hydropeaking control primary productivity in the Colorado River, Grand Canyon. Limnol. Oceanogr. 60, 512–526 (2015).Article 

Google Scholar 
Hosen, J. D. et al. Enhancement of primary production during drought in a temperate watershed is greater in larger rivers than headwater streams. Limnol. Oceanogr. 64, 1458–1472 (2019).Article 

Google Scholar 
Allen, A. P., Gillooly, J. F. & Brown, J. H. Linking the global carbon cycle to individual metabolism. Funct. Ecol. 19, 202–213 (2005).Article 

Google Scholar 
Demars, B. O. L. et al. Temperature and the metabolic balance of streams. Freshw. Biol. 56, 1106–1121 (2011).Article 

Google Scholar 
Song, C. et al. Continental-scale decrease in net primary productivity in streams due to climate warming. Nat. Geosci. 11, 415–420 (2018).Article 
CAS 

Google Scholar 
Hood, J. M. et al. Increased resource use efficiency amplifies positive response of aquatic primary production to experimental warming. Glob. Change Biol. 24, 1069–1084 (2018).Article 

Google Scholar 
Schindler, D. E., Carpenter, S. R., Cole, J. J., Kitchell, J. F. & Pace, M. L. Influence of food web structure on carbon exchange between lakes and the atmosphere. Science 277, 248–251 (1997).Article 
CAS 

Google Scholar 
Iannucci, F. M., Beneš, J., Medvedeff, A. & Bowden, W. B. Biogeochemical responses over 37 years to manipulation of phosphorus concentrations in an Arctic river: The Upper Kuparuk River Experiment. Hydrol. Process. 35, e14075 (2021).Article 
CAS 

Google Scholar 
Rosemond, A. D. et al. Experimental nutrient additions accelerate terrestrial carbon loss from stream ecosystems. Science 347, 1142–1145 (2015). A key study explaining how nutrient excess can accelerate terrestrial carbon loss from stream ecosystems.Article 
CAS 

Google Scholar 
Arroita, M., Elosegi, A. & Hall, R. O. Jr Twenty years of daily metabolism show riverine recovery following sewage abatement. Limnol. Oceanogr. 64, 77–92 (2019).Article 

Google Scholar 
Battin, T. J. et al. Biophysical controls on organic carbon fluxes in fluvial networks. Nat. Geosci. 1, 95–100 (2008). An important article conceptualizing how physical and biological processes combine to shape metabolic dynamics and carbon fluxes in fluvial networks.Article 
CAS 

Google Scholar 
Hoellein, T. J., Bruesewitz, D. A. & Richardson, D. C. Revisiting Odum (1956): a synthesis of aquatic ecosystem metabolism. Limnol. Oceanogr. 58, 2089–2100 (2013).Article 
CAS 

Google Scholar 
Marzolf, N. S. & Ardón, M. Ecosystem metabolism in tropical streams and rivers: a review and synthesis. Limnol. Oceanogr. 66, 1627–1638 (2021).Article 

Google Scholar 
Gounand, I., Little, C. J., Harvey, E. & Altermatt, F. Cross-ecosystem carbon flows connecting ecosystems worldwide. Nat. Commun. 9, 4825 (2018).Article 

Google Scholar 
Ciais, P. et al. Empirical estimates of regional carbon budgets imply reduced global soil heterotrophic respiration. Natl Sci. Rev. 8, nwaa145 (2020).Article 

Google Scholar 
Bauer, J. E. et al. The changing carbon cycle of the coastal ocean. Nature 504, 61–70 (2013). Important review on the sources, exchange and fates of carbon in the coastal ocean and how human activities have altered the coastal carbon cycle.Article 
CAS 

Google Scholar 
Reichert, P., Uehlinger, U. & Acuña, V. Estimating stream metabolism from oxygen concentrations: effect of spatial heterogeneity. J. Geophys. Res. Biogeosci. 114, G03016 (2009).Article 

Google Scholar 
Koenig, L. E. et al. Emergent productivity regimes of river networks. Limnol. Oceanogr. Lett. 4, 173–181 (2019).Article 

Google Scholar 
Rodríguez-Castillo, T., Estévez, E., González-Ferreras, A. M. & Barquín, J. Estimating ecosystem metabolism to entire river networks. Ecosystems 22, 892–911 (2019).Article 

Google Scholar 
Segatto, P. L., Battin, T. J. & Bertuzzo, E. The metabolic regimes at the scale of an entire stream network unveiled through sensor data and machine learning. Ecosystems 24, 1792–1809 (2021).Article 
CAS 

Google Scholar 
Loreau, M., Mouquet, N. & Holt, R. D. Meta‐ecosystems: a theoretical framework for a spatial ecosystem ecology. Ecol. Lett. 6, 673–679 (2003).Article 

Google Scholar 
Mastrandrea, M. D. et al. Guidance Note for Lead Authors of the IPCC Fifth Assessment Report on Consistent Treatment of Uncertainties (Intergovernmental Panel on Climate Change (IPCC), 2010).Tank, S. E., Fellman, J. B., Hood, E. & Kritzberg, E. S. Beyond respiration: controls on lateral carbon fluxes across the terrestrial‐aquatic interface. Limnol. Oceanogr. Lett. 3, 76–88 (2018). Important synthesis on the mechanisms and controls of organic and inorganic carbon flows across terrestrial–aquatic interfaces.Article 

Google Scholar 
Aitkenhead, J. A. & McDowell, W. H. Soil C:N ratio as a predictor of annual riverine DOC flux at local and global scales. Global Biogeochem. Cycles 14, 127–138 (2000).Article 
CAS 

Google Scholar 
Regnier, P., Resplandy, L., Najjar, R. G. & Ciais, P. The land-to-ocean loops of the global carbon cycle. Nature 603, 401–410 (2022).Article 
CAS 

Google Scholar 
van Hoek, W. J. et al. Exploring spatially explicit changes in carbon budgets of global river basins during the 20th century. Environ. Sci. Technol. 55, 16757–16769 (2021). A global quantitative assessment of river carbon fluxes in the twentieth century, highlighting the combined influence of environmental and anthropogenic controls on the long-term patterns of global carbon export.Article 

Google Scholar 
Abril, G. & Borges, A. V. Ideas and perspectives: carbon leaks from flooded land: do we need to replumb the inland water active pipe? Biogeosciences 16, 769–784 (2019). Important review emphasizing the role of flooding for inland water carbon cycling at the global scale.Article 
CAS 

Google Scholar 
Lauerwald, R., Regnier, P., Guenet, B., Friedlingstein, P. & Ciais, P. How simulations of the land carbon sink are biased by ignoring fluvial carbon transfers: a case study for the Amazon Basin. One Earth 3, 226–236 (2020).Article 

Google Scholar 
Raymond, P. A., Saiers, J. E. & Sobczak, W. V. Hydrological and biogeochemical controls on watershed dissolved organic matter transport: pulse‐shunt concept. Ecology 97, 5–16 (2016).Article 

Google Scholar 
Catalán, N., Marcé, R., Kothawala, D. N. & Tranvik, L. J. Organic carbon decomposition rates controlled by water retention time across inland waters. Nat. Geosci. 9, 501–504 (2016).Article 

Google Scholar 
Maavara, T., Lauerwald, R., Regnier, P. & Cappellen, P. V. Global perturbation of organic carbon cycling by river damming. Nat. Commun. 8, 15347 (2017).Article 
CAS 

Google Scholar 
Mendonça, R. et al. Organic carbon burial in global lakes and reservoirs. Nat. Commun. 8, 1694–1697 (2017).Article 

Google Scholar 
Downing, J. A. et al. Sediment organic carbon burial in agriculturally eutrophic impoundments over the last century. Global Biogeochem. Cycles 22, GB1018 (2008).Article 

Google Scholar 
Deemer, B. R. et al. Greenhouse gas emissions from reservoir water surfaces: a new global synthesis. Bioscience 66, 949–964 (2016).Article 

Google Scholar 
Abril, G. et al. Amazon River carbon dioxide outgassing fuelled by wetlands. Nature 505, 395–398 (2014).Article 
CAS 

Google Scholar 
Dodds, W. K. et al. Abiotic controls and temporal variability of river metabolism: multiyear analyses of Mississippi and Chattahoochee River data. Freshw. Sci. 32, 1073–1087 (2013).Article 

Google Scholar 
Ros, G. R., Sponseller, R. A., Bergström, A. K., Myrstener, M. & Giesler, R. Stream metabolism controls diel patterns and evasion of CO2 in Arctic streams. Glob. Change Biol. 26, 1400–1413 (2020).Article 

Google Scholar 
Rasilo, T., Hutchins, R. H. S., Ruiz-González, C. & Del Giorgio, P. A. Transport and transformation of soil-derived CO2, CH4 and DOC sustain CO2 supersaturation in small boreal streams. Sci. Total Environ. 579, 902–912 (2017).Article 
CAS 

Google Scholar 
Aho, K. S., Hosen, J. D., Logozzo, L. A., McGillis, W. R. & Raymond, P. A. Highest rates of gross primary productivity maintained despite CO2 depletion in a temperate river network. Limnol. Oceanogr. Lett. 6, 200–206 (2021).Article 
CAS 

Google Scholar 
Wehrli, B. Conduits of the carbon cycle. Nature 503, 346–347 (2013).Article 
CAS 

Google Scholar 
Sarmiento, J. L. & Sundquist, E. T. Revised budget for the oceanic uptake of anthropogenic carbon dioxide. Nature 356, 589–593 (1992).Article 
CAS 

Google Scholar 
Lacroix, F., Ilyina, T., Laruelle, G. G. & Regnier, P. Reconstructing the preindustrial coastal carbon cycle through a global ocean circulation model: was the global continental shelf already both autotrophic and a CO2 sink? Glob. Biogeochem. Cycles 35, e2020GB006603 (2021).Article 
CAS 

Google Scholar 
Jacobson, A. R., Fletcher, S. E. M., Gruber, N., Sarmiento, J. L. & Gloor, M. A joint atmosphere‐ocean inversion for surface fluxes of carbon dioxide: 1. Methods and global‐scale fluxes. Global Biogeochem. Cycles 21, GB1019 (2007).
Google Scholar 
Resplandy, L. et al. Revision of global carbon fluxes based on a reassessment of oceanic and riverine carbon transport. Nat. Geosci. 11, 504–509 (2018).Article 
CAS 

Google Scholar 
Lee, L.-C. et al. Unusual roles of discharge, slope and SOC in DOC transport in small mountainous rivers, Taiwan. Sci. Rep. 9, 1574 (2019).Article 

Google Scholar 
Reddy, S. K. K. et al. Export of particulate organic carbon by the mountainous tropical rivers of Western Ghats, India: variations and controls. Sci. Total Environ. 751, 142115 (2021).Article 
CAS 

Google Scholar 
Zhang, X., Tarpley, D. & Sullivan, J. T. Diverse responses of vegetation phenology to a warming climate. Geophys. Res. Lett. 34, L19405 (2007).Article 

Google Scholar 
Pan, Y. et al. A large and persistent carbon sink in the world’s forests. Science 333, 988–993 (2011).Article 
CAS 

Google Scholar 
Heathcote, A. J., Anderson, N. J., Prairie, Y. T., Engstrom, D. R. & del Giorgio, P. A. Large increases in carbon burial in northern lakes during the Anthropocene. Nat. Commun. 6, 10016 (2015).Article 
CAS 

Google Scholar 
Guillemette, F., Berggren, M., Giorgio, P. Adel. & Lapierre, J.-F. Increases in terrestrially derived carbon stimulate organic carbon processing and CO2 emissions in boreal aquatic ecosystems. Nat. Commun. 4, 2972 (2013).Article 

Google Scholar 
Hastie, A., Lauerwald, R., Ciais, P., Papa, F. & Regnier, P. Historical and future contributions of inland waters to the Congo Basin carbon balance. Earth Syst. Dyn. 12, 37–62 (2020).Article 

Google Scholar 
Nakhavali, M. et al. Leaching of dissolved organic carbon from mineral soils plays a significant role in the terrestrial carbon balance. Glob. Change Biol. 27, 1083–1096 (2021).Article 
CAS 

Google Scholar 
Tian, H. et al. Global patterns and controls of soil organic carbon dynamics as simulated by multiple terrestrial biosphere models: current status and future directions. Global Biogeochem. Cycles 29, 775–792 (2015).Article 
CAS 

Google Scholar 
Öquist, M. G. et al. The full annual carbon balance of boreal forests is highly sensitive to precipitation. Environ. Sci. Technol. Lett. 1, 315–319 (2014).Article 

Google Scholar 
Jones, J. B.Jr, Stanley, E. H. & Mulholland, P. J. Long‐term decline in carbon dioxide supersaturation in rivers across the contiguous United States. Geophys. Res. Lett. 30, 1495 (2003).Article 

Google Scholar 
Raymond, P. A. & Oh, N.-H. Long term changes of chemical weathering products in rivers heavily impacted from acid mine drainage: insights on the impact of coal mining on regional and global carbon and sulfur budgets. Earth Planet. Sci. Lett. 284, 50–56 (2009).Article 
CAS 

Google Scholar 
Ran, L. et al. Substantial decrease in CO2 emissions from Chinese inland waters due to global change. Nat. Commun. 12, 1730 (2021).Article 
CAS 

Google Scholar 
Zarnetske, J. P., Bouda, M., Geophysical, B. A., Saiers, J. & Raymond, P. Generality of hydrologic transport limitation of watershed organic carbon flux across ecoregions of the United States. Geophys. Res. Lett. 45, 11,702–11,711 (2018).Article 
CAS 

Google Scholar 
Liu, S. et al. The importance of hydrology in routing terrestrial carbon to the atmosphere via global streams and rivers. Proc. Natl Acad. Sci. USA 119, e2106322119 (2022).Article 
CAS 

Google Scholar 
Nydahl, A. C., Wallin, M. B. & Weyhenmeyer, G. A. No long‐term trends in pCO2 despite increasing organic carbon concentrations in boreal lakes, streams, and rivers. Global Biogeochem. Cycles 31, 985–995 (2017).Article 
CAS 

Google Scholar 
Raymond, P. A. & Hamilton, S. K. Anthropogenic influences on riverine fluxes of dissolved inorganic carbon to the oceans. Limnol. Oceanogr. Lett. 3, 143–155 (2018).Article 
CAS 

Google Scholar 
Ulseth, A. J., Bertuzzo, E., Singer, G. A., Schelker, J. & Battin, T. J. Climate-induced changes in spring snowmelt impact ecosystem metabolism and carbon fluxes in an Alpine stream network. Ecosystems 21, 373–390 (2018).Article 
CAS 

Google Scholar 
Berghuijs, W. R., Woods, R. A. & Hrachowitz, M. A precipitation shift from snow towards rain leads to a decrease in streamflow. Nat. Clim. Change 4, 583–586 (2014).Article 

Google Scholar 
Drake, T. W. et al. Mobilization of aged and biolabile soil carbon by tropical deforestation. Nat. Geosci. 12, 541–546 (2019).Article 
CAS 

Google Scholar 
Wit, F. et al. The impact of disturbed peatlands on river outgassing in Southeast Asia. Nat. Commun. 6, 10155 (2015).Article 
CAS 

Google Scholar 
Moore, S., Gauci, V., Evans, C. D. & Page, S. E. Fluvial organic carbon losses from a Bornean blackwater river. Biogeosciences 8, 901–909 (2011).Article 
CAS 

Google Scholar 
Masese, F. O., Salcedo-Borda, J. S., Gettel, G. M., Irvine, K. & McClain, M. E. Influence of catchment land use and seasonality on dissolved organic matter composition and ecosystem metabolism in headwater streams of a Kenyan river. Biogeochemistry 132, 1–22 (2017).Article 
CAS 

Google Scholar 
Bernot, M. J. et al. Inter‐regional comparison of land‐use effects on stream metabolism. Freshw. Biol. 55, 1874–1890 (2010). Among the first studies showing how land use alters ecosystem metabolism across geographic regions.Article 

Google Scholar 
Griffiths, N. A. et al. Agricultural land use alters the seasonality and magnitude of stream metabolism. Limnol. Oceanogr. 58, 1513–1529 (2013).Article 
CAS 

Google Scholar 
Sweeney, B. W. et al. Riparian deforestation, stream narrowing, and loss of stream ecosystem services. Proc. Natl Acad. Sci. 101, 14132–14137 (2004).Article 
CAS 

Google Scholar 
Roley, S. S., Tank, J. L., Griffiths, N. A., Hall, R. O. Jr & Davis, R. T. The influence of floodplain restoration on whole-stream metabolism in an agricultural stream: insights from a 5-year continuous data set. Freshw. Sci. 33, 1043–1059 (2014).Article 

Google Scholar 
Crawford, J. T., Stanley, E. H., Dornblaser, M. M. & Striegl, R. G. CO2 time series patterns in contrasting headwater streams of North America. Aquat. Sci. 79, 473–486 (2016).Article 

Google Scholar 
Blackburn, S. R. & Stanley, E. H. Floods increase carbon dioxide and methane fluxes in agricultural streams. Freshw. Biol. 66, 62–77 (2021).Article 
CAS 

Google Scholar 
Robertson, G. P., Paul, E. A. & Harwood, R. R. Greenhouse gases in intensive agriculture: contributions of individual gases to the radiative forcing of the atmosphere. Science 289, 1922–1925 (2000).Article 
CAS 

Google Scholar 
Min, S.-K., Zhang, X., Zwiers, F. W. & Hegerl, G. C. Human contribution to more-intense precipitation extremes. Nature 470, 378–381 (2011).Article 
CAS 

Google Scholar 
Yin, J. et al. Large increase in global storm runoff extremes driven by climate and anthropogenic changes. Nat. Commun. 9, 4389 (2018).Article 
CAS 

Google Scholar 
Myhre, G. et al. Sensible heat has significantly affected the global hydrological cycle over the historical period. Nat. Commun. 9, 1922 (2018).Article 
CAS 

Google Scholar 
Messager, M. L. et al. Global prevalence of non-perennial rivers and streams. Nature 594, 391–397 (2021).Article 
CAS 

Google Scholar 
Ward, A. S., Wondzell, S. M., Schmadel, N. M. & Herzog, S. P. Climate change causes river network contraction and disconnection in the H.J. Andrews Experimental Forest, Oregon, USA. Front. Water 2, 7 (2020).Article 

Google Scholar 
Sabater, S., Timoner, X., Borrego, C. & Acuña, V. Stream biofilm responses to flow intermittency: from cells to ecosystems. Front. Environ. Sci. 4, 14 (2016).Article 

Google Scholar 
Gómez-Gener, L., Lupon, A., Laudon, H. & Sponseller, R. A. Drought alters the biogeochemistry of boreal stream networks. Nat. Commun. 11, 1795 (2020).Article 

Google Scholar 
Marcé, R. et al. Emissions from dry inland waters are a blind spot in the global carbon cycle. Earth Sci. Rev. 188, 240–248 (2019).Article 

Google Scholar 
Blaszczak, J. R., Delesantro, J. M., Urban, D. L., Doyle, M. W. & Bernhardt, E. S. Scoured or suffocated: urban stream ecosystems oscillate between hydrologic and dissolved oxygen extremes. Limnol. Oceanogr. 64, 877–894 (2019).Article 
CAS 

Google Scholar 
Reisinger, A. J. et al. Recovery and resilience of urban stream metabolism following Superstorm Sandy and other floods. Ecosphere 8, e01776 (2017).Article 

Google Scholar 
O’Donnell, B. & Hotchkiss, E. R. Coupling concentration‐ and process‐discharge relationships integrates water chemistry and metabolism in streams. Water Resour. Res. 55, 10179–10190 (2019).Article 

Google Scholar 
Thellman, A. et al. The ecology of river ice. J. Geophys. Res. Biogeosci. 126, e2021JG006275 (2021).Article 

Google Scholar 
Maavara, T. et al. River dam impacts on biogeochemical cycling. Nat. Rev. Earth Environ. 1, 103–116 (2020).Article 

Google Scholar 
Rosentreter, J. A. et al. Half of global methane emissions come from highly variable aquatic ecosystem sources. Nat. Geosci. 14, 225–230 (2021).Article 
CAS 

Google Scholar 
Barros, N. et al. Carbon emission from hydroelectric reservoirs linked to reservoir age and latitude. Nat. Geosci. 4, 593–596 (2011).Article 
CAS 

Google Scholar 
Keller, P. S., Marcé, R., Obrador, B. & Koschorreck, M. Global carbon budget of reservoirs is overturned by the quantification of drawdown areas. Nat. Geosci. 14, 402–408 (2021).Article 
CAS 

Google Scholar 
Calamita, E. et al. Unaccounted CO2 leaks downstream of a large tropical hydroelectric reservoir. Proc. Natl Acad. Sci. USA 118, e2026004118 (2021).Article 
CAS 

Google Scholar 
Park, J.-H. et al. Reviews and syntheses: anthropogenic perturbations to carbon fluxes in Asian river systems – concepts, emerging trends, and research challenges. Biogeosciences 15, 3049–3069 (2018).Article 
CAS 

Google Scholar 
Rosamond, M. S., Thuss, S. J. & Schiff, S. L. Dependence of riverine nitrous oxide emissions on dissolved oxygen levels. Nat. Geosci. 5, 715–718 (2012).Article 
CAS 

Google Scholar 
Stanley, E. H. et al. The ecology of methane in streams and rivers: patterns, controls, and global significance. Ecol. Monogr. 86, 146–171 (2016). Key paper highlighting the role of streams and rivers for methane production and emissions and developing a conceptual framework on the environmental drivers of methane dynamics in fluvial ecosystems.Article 

Google Scholar 
Breitburg, D. et al. Declining oxygen in the global ocean and coastal waters. Science 359, eaam7240 (2018).Article 

Google Scholar 
Jane, S. F. et al. Widespread deoxygenation of temperate lakes. Nature 594, 66–70 (2021).Article 
CAS 

Google Scholar 
Triska, F. J., Kennedy, V. C., Avanzino, R. J., Zellweger, G. W. & Bencala, K. E. Retention and transport of nutrients in a third‐order stream in northwestern California: hyporheic processes. Ecology 70, 1893–1905 (1989).Article 

Google Scholar 
Carter, A. M., Blaszczak, J. R., Heffernan, J. B. & Bernhardt, E. S. Hypoxia dynamics and spatial distribution in a low gradient river. Limnol. Oceanogr. 66, 2251–2265 (2021).Article 

Google Scholar 
Kadygrov, N. et al. On the potential of the ICOS atmospheric CO2 measurement network for estimating the biogenic CO2 budget of Europe. Atmos. Chem. Phys. 15, 12765–12787 (2015).Article 
CAS 

Google Scholar 
Hanson, P. C., Weathers, K. C. & Kratz, T. K. Networked lake science: how the Global Lake Ecological Observatory Network (GLEON) works to understand, predict, and communicate lake ecosystem response to global change. Inland Waters 6, 543–554 (2018).Article 

Google Scholar 
Claustre, H., Johnson, K. S. & Takeshita, Y. Observing the global ocean with biogeochemical-Argo. Annu. Rev. Mar. Sci. 12, 23–48 (2019).Article 

Google Scholar 
Jankowski, K. J., Mejia, F. H., Blaszczak, J. R. & Holtgrieve, G. W. Aquatic ecosystem metabolism as a tool in environmental management. Wiley Interdiscip. Rev. Water 8, e1521 (2021).Article 

Google Scholar 
Mao, F. et al. Moving beyond the technology: a socio-technical roadmap for low-cost water sensor network applications. Environ. Sci. Technol. 54, 9145–9158 (2020).Article 
CAS 

Google Scholar 
Park, J., Kim, K. T. & Lee, W. H. Recent advances in information and communications technology (ICT) and sensor technology for monitoring water quality. Water 12, 510 (2020).Article 
CAS 

Google Scholar 
Yamazaki, D. et al. MERIT Hydro: a high‐resolution global hydrography map based on latest topography dataset. Water Resour. Res. 55, 5053–5073 (2019).Article 

Google Scholar 
Lin, P., Pan, M., Wood, E. F., Yamazaki, D. & Allen, G. H. A new vector-based global river network dataset accounting for variable drainage density. Sci. Data 8, 28 (2021).Article 

Google Scholar 
Allen, G. H. & Pavelsky, T. M. Global extent of rivers and streams. Science 361, 585–587 (2018).Article 
CAS 
MATH 

Google Scholar 
Durand, M. et al. An intercomparison of remote sensing river discharge estimation algorithms from measurements of river height, width, and slope. Water Resour. Res. 52, 4527–4549 (2016).Article 

Google Scholar 
Frasson, R. P. M. et al. Exploring the factors controlling the error characteristics of the surface water and ocean topography mission discharge estimates. Water Resour. Res. 57, e2020WR028519 (2021).Article 

Google Scholar 
Dethier, E. N., Renshaw, C. E. & Magilligan, F. J. Rapid changes to global river suspended sediment flux by humans. Science 376, 1447–1452 (2022).Article 
CAS 

Google Scholar 
Campbell, A. D. et al. A review of carbon monitoring in wet carbon systems using remote sensing. Environ. Res. Lett. 17, 025009 (2022).Article 

Google Scholar 
Allen, G. H. et al. Similarity of stream width distributions across headwater systems. Nat. Commun. 9, 610 (2018).Article 

Google Scholar 
Rodriguez-Iturbe, I. & Rinaldo, A. Fractal River Basins: Chance and Self-organization (Cambridge Univ. Press, 2001). Game-changing oeuvre formalizing the structure and function of river networks.Bertuzzo, E., Helton, A. M., Hall, Robert, O. & Battin, T. J. Scaling of dissolved organic carbon removal in river networks. Adv. Water Resour. 110, 136–146 (2017).Article 
CAS 

Google Scholar 
Marzadri, A., Dee, M. M., Tonina, D., Bellin, A. & Tank, J. L. Role of surface and subsurface processes in scaling N2O emissions along riverine networks. Proc. Natl Acad. Sci. USA 114, 4330–4335 (2017).Article 
CAS 

Google Scholar 
Marzadri, A. et al. Global riverine nitrous oxide emissions: the role of small streams and large rivers. Sci. Total Environ. 776, 145148 (2021).Article 
CAS 

Google Scholar 
Botter, G. & Durighetto, N. The stream length duration curve: a tool for characterizing the time variability of the flowing stream length. Water Resour. Res. 56, e2020WR027282 (2020).Article 
CAS 

Google Scholar 
Wollheim, W. M. et al. River network saturation concept: factors influencing the balance of biogeochemical supply and demand of river networks. Biogeochemistry 141, 503–521 (2018).Article 
CAS 

Google Scholar 
Durighetto, N., Vingiani, F., Bertassello, L. E., Camporese, M. & Botter, G. Intraseasonal drainage network dynamics in a headwater catchment of the Italian Alps. Water Resour. Res. 56, e2019WR02556 (2020).Article 

Google Scholar 
Montgomery, D. R. & Dietrich, W. E. Source areas, drainage density, and channel initiation. Water Resour. Res. 25, 1907–1918 (1989).Article 

Google Scholar 
Fatichi, S., Ivanov, V. Y. & Caporali, E. A mechanistic ecohydrological model to investigate complex interactions in cold and warm water‐controlled environments: 1. Theoretical framework and plot‐scale analysis. J. Adv. Model. Earth. Syst. 4, M05002 (2012).
Google Scholar 
Ulseth, A. J. et al. Distinct air–water gas exchange regimes in low- and high-energy streams. Nat. Geosci. 12, 259–263 (2019).Article 
CAS 

Google Scholar 
Hall, R. O. in Streams and Ecosystems in a Changing Environment (eds. Jones, J. J. & Stanley, E. H.) 151–180 (Academic, 2016).Butman, D. & Raymond, P. A. Significant efflux of carbon dioxide from streams and rivers in the United States. Nat. Geosci. 4, 839–842 (2011).Article 
CAS 

Google Scholar 
Duvert, C., Butman, D. E., Marx, A., Ribolzi, O. & Hutley, L. B. CO2 evasion along streams driven by groundwater inputs and geomorphic controls. Nat. Geosci. 11, 813–818 (2018).Article 
CAS 

Google Scholar 
Zhang, L. et al. Significant methane ebullition from alpine permafrost rivers on the East Qinghai–Tibet Plateau. Nat. Geosci. 13, 349–354 (2020).Article 

Google Scholar  More

Stroeve, J. & Notz, D. Changing state of Arctic sea ice across all seasons. Environ. Res. Lett. 13, 103001 (2018).Article 
ADS 

Google Scholar 
Polyakov, I. V. et al. Borealization of the Arctic Ocean in response to anomalous advection from sub-Arctic seas. Front. Mar. Sci. 7, 983–992 (2020).Article 

Google Scholar 
Lannuzel, D. et al. The future of Arctic sea-ice biogeochemistry and ice-associated ecosystems. Nat. Clim. Change. 10, 983–992 (2020).Article 
ADS 

Google Scholar 
Macias-Fauria, M. & Post, E. Effects of sea ice on Arctic biota: An emerging crisis discipline. Biol. Lett. 14, 20170702 (2018).Article 

Google Scholar 
Kohlbach, D. et al. The importance of ice algae-produced carbon in the central Arctic Ocean ecosystem: Food web relationships revealed by lipid and stable isotope analyses. Limnol. Oceanogr. 61, 2027–2044 (2016).Article 
ADS 

Google Scholar 
Søreide, J. E. et al. Sympagic-pelagic-benthic coupling in Arctic and Atlantic waters around Svalbard revealed by stable isotopic and fatty acid tracers. Mar. Biol. Res. 9, 831–850 (2013).Article 

Google Scholar 
Slagstad, D., Wassmann, P. F. J. & Ellingsen, I. Physical constrains and productivity in the future Arctic Ocean. Front. Mar. Sci. 2015, 2 (2015).
Google Scholar 
FISCAO. Final Report of the Fifth Meeting of Scientific Experts on Fish Stocks in the Central Arctic Ocean. https://apps-afsc.fisheries.noaa.gov/documents/Arctic_fish_stocks_fifth_meeting/508_Documents/508_Final_report_of_the_505th_FiSCAO_meeting.pdf (2018).David, C. et al. Under-ice distribution of polar cod Boreogadus saida in the central Arctic Ocean and their association with sea-ice habitat properties. Polar Biol. 39, 981–994 (2016).Article 

Google Scholar 
Gradinger, R. Vertical fine structure of the biomass and composition of algal communities in Arctic pack ice. Mar. Biol. 133, 745–754 (1999).Article 

Google Scholar 
Kosobokova, K. N., Hopcroft, R. R. & Hirche, H.-J. Patterns of zooplankton diversity through the depths of the Arctic’s central basins. Mar Biodivers. 41, 29–50 (2011).Article 

Google Scholar 
Mumm, N. et al. Breaking the ice: Large-scale distribution of mesozooplankton after a decade of Arctic and transpolar cruises. Polar Biol. 20, 189–197 (1998).Article 

Google Scholar 
Snoeijs-Leijonmalm, P. et al. Unexpected fish and squid in the central Arctic deep scattering layer. Sci. Adv. 8, 7536 (2022).Article 

Google Scholar 
David, C., Lange, B., Rabe, B. & Flores, H. Community structure of under-ice fauna in the Eurasian central Arctic Ocean in relation to environmental properties of sea-ice habitats. Mar. Ecol. Prog. Ser. 522, 15–32 (2015).Article 
ADS 

Google Scholar 
Gosselin, M., Levasseur, M., Wheeler, P. A., Horner, R. A. & Booth, B. C. New measurements of phytoplankton and ice algal production in the Arctic Ocean. Deep-Sea Res. Part II(44), 1623–1644 (1997).Article 
ADS 

Google Scholar 
Ardyna, M. & Arrigo, K. R. Phytoplankton dynamics in a changing Arctic Ocean. Nat. Clim. Change. 10, 892–903 (2020).Article 
ADS 
CAS 

Google Scholar 
Hays, G. C. In Migrations and Dispersal of Marine Organisms. (eds Jones, M. B. et al.) 163–170 (Springer).Irigoien, X. et al. Large mesopelagic fishes biomass and trophic efficiency in the open ocean. Nat. Commun. 5, 3271 (2014).Article 
ADS 

Google Scholar 
Geoffroy, M. et al. Mesopelagic sound scattering layers of the high arctic: Seasonal variations in biomass, species assemblage, and trophic relationships. Front. Mar. Sci. 2019, 6 (2019).
Google Scholar 
Gjøsæter, H., Wiebe, P. H., Knutsen, T. & Ingvaldsen, R. B. Evidence of Diel vertical migration of mesopelagic sound-scattering organisms in the Arctic. Front. Mar. Sci. 2017, 4 (2017).
Google Scholar 
Knutsen, T., Wiebe, P. H., Gjøsæter, H., Ingvaldsen, R. B. & Lien, G. High latitude epipelagic and mesopelagic scattering layers—a reference for future arctic ecosystem change. Front. Mar. Sci. 2017, 4 (2017).
Google Scholar 
Priou, P. et al. Dense mesopelagic sound scattering layer and vertical segregation of pelagic organisms at the Arctic-Atlantic gateway during the midnight sun. Prog. Oceanogr. 196, 102611 (2021).Article 

Google Scholar 
Snoeijs-Leijonmalm, P. et al. A deep scattering layer under the North Pole pack ice. Prog. Oceanogr. 194, 102560 (2021).Article 

Google Scholar 
St-John, M. A. et al. A dark hole in our understanding of marine ecosystems and their services: Perspectives from the mesopelagic community. Front. Mar. Sci. 2016, 3 (2016).
Google Scholar 
Fransson, A. et al. Joint cruise 2-2 2021: Cruise report. The Nansen Legacy Report Series, 30/2022. https://doi.org/10.7557/nlrs.6413 (2022).Rudels, B. et al. Observations of water masses and circulation with focus on the Eurasian Basin of the Arctic Ocean from the 1990s to the late 2000s. Ocean Sci. 9, 147–169 (2013).Article 
ADS 

Google Scholar 
Krumpen, T. et al. Arctic warming interrupts the Transpolar Drift and affects long-range transport of sea ice and ice-rafted matter. Sci. Rep. 9, 5459 (2019).Article 
ADS 

Google Scholar 
Aagaard, K. A synthesis of the Arctic Ocean circulation. Rapp. P.-V. Rcun. Cons. int. Explor. Mer. 188, 11–22 (1989).
Google Scholar 
Perez-Hernandez, M. D. et al. The Atlantic Water boundary current north of Svalbard in late summer. J. Geophys. Res. 122, 2269–2290 (2017).Article 
ADS 

Google Scholar 
Våge, K. et al. The Atlantic Water boundary current in the Nansen Basin: Transport and mechanisms of lateral exchange. J. Geophys. Res. 121, 6946–6960 (2016).Article 
ADS 

Google Scholar 
Crews, L., Sundfjord, A., Albretsen, J. & Hattermann, T. Mesoscale Eddy Activity and Transport in the Atlantic Water Inflow Region North of Svalbard. J. Geophys. Res. 123, 201–215 (2018).Article 
ADS 

Google Scholar 
Kolås, E. H., Koenig, Z., Fer, I., Nilsen, F. & Marnela, M. Structure and Transport of Atlantic Water North of Svalbard From Observations in Summer and Fall 2018. J. Geophys. Res. 125, 6174 (2020).Article 

Google Scholar 
Basedow, S. L. et al. Seasonal variation in transport of zooplankton into the arctic basin through the atlantic gateway. Fram Strait. Front. Mar. Sci. 2018, 5 (2018).
Google Scholar 
Vernet, M., Carstensen, J., Reigstad, M. & Svensen, C. Editorial: Carbon bridge to the Arctic. Front. Mar. Sci. 2020, 7 (2020).
Google Scholar 
Wassmann, P. et al. The contiguous domains of Arctic Ocean advection: Trails of life and death. Prog. Oceanogr. 139, 42–65 (2015).Article 
ADS 

Google Scholar 
Wassmann, P., Slagstad, D. & Ellingsen, I. Advection of mesozooplankton into the northern svalbard shelf region. Front. Mar. Sci. 2019, 6 (2019).
Google Scholar 
Auel, H. Egg size and reproductive adaptations among Arctic deep-sea copepods (Calanoida, Paraeuchaeta). Helgol. Mar. Res. 58, 147–153 (2004).Article 
ADS 

Google Scholar 
Gluchowska, M. et al. Zooplankton in Svalbard fjords on the Atlantic-Arctic boundary. Polar Biol. 39, 1785–1802 (2016).Article 

Google Scholar 
Wang, Y.-G., Tseng, L.-C., Lin, M. & Hwang, J.-S. Vertical and geographic distribution of copepod communities at late summer in the Amerasian Basin. Arctic Ocean. Plos One. 14, e0219319 (2019).Article 
CAS 

Google Scholar 
Gislason, A. & Silva, T. Abundance, composition, and development of zooplankton in the Subarctic Iceland Sea in 2006, 2007, and 2008. ICES J. Mar. Sci. 69, 1263–1276 (2012).Article 

Google Scholar 
Zhukova, N. G., Nesterova, V. N., Prokopchuk, I. P. & Rudneva, G. B. Winter distribution of euphausiids (Euphausiacea) in the Barents Sea (2000–2005). Deep-Sea Res. Part II(56), 1959–1967 (2009).Article 
ADS 

Google Scholar 
Dalpadado, P. & Skjoldal, H. R. Abundance, maturity and growth of the krill species Thysanoessa inermis and T. longicaudata in the Barents Sea. Mar. Ecol. Prog. Ser. 144, 175–183 (1996).Article 
ADS 

Google Scholar 
Koszteyn, J., Timofeev, S., Węsławski, J. M. & Malinga, B. Size structure of Themisto abyssorum Boeck and Themisto libellula (Mandt) populations in European Arctic seas. Polar Biol. 15, 85–92 (1995).Article 

Google Scholar 
Dalpadado, P., Borkner, N., Bogstad, B. & Mehl, S. Distribution of Themisto (Amphipoda) spp. in the Barents Sea and predator-prey interactions. ICES J. Mar. Sci. 58, 876–895 (2001).Article 

Google Scholar 
Macnaughton, M. O., Thormar, J. & Berge, J. Sympagic amphipods in the Arctic pack ice: Redescriptions of Eusirus holmii Hansen, 1887 and Pleusymtes karstensi (Barnard, 1959). Polar Biol. 30, 1013–1025 (2007).Article 

Google Scholar 
Kraft, A., Graeve, M., Janssen, D., Greenacre, M. & Falk-Petersen, S. Arctic pelagic amphipods: Lipid dynamics and life strategy. J. Plankton Res. 37, 790–807 (2015).Article 
CAS 

Google Scholar 
Kreibich, T., Hagen, W. & Saborowski, R. Food utilization of two pelagic crustaceans in the Greenland Sea: Meganyctiphanes norvegica (Euphausiacea) and Hymenodora glacialis (Decapoda, Caridea). Mar. Ecol. Prog. Ser. 413, 105–115 (2010).Article 
ADS 
CAS 

Google Scholar 
Geoffroy, M. et al. Increased occurrence of the jellyfish Periphylla periphylla in the European high Arctic. Polar Biol. 41, 2615–2619 (2018).Article 

Google Scholar 
Grigor, J. J., Søreide, J. E. & Varpe, Ø. Seasonal ecology and life-history strategy of the high-latitude predatory zooplankter Parasagitta elegans. Mar. Ecol. Prog. Ser. 499, 77–88 (2014).Article 
ADS 

Google Scholar 
Maclennan, D. N., Fernandes, P. G. & Dalen, J. A consistent approach to definitions and symbols in fisheries acoustics. ICES J. Mar. Sci. 59, 365–369 (2002).Article 

Google Scholar 
Gjøsæter, H. & Ushakov, N. G. Acoustic estimates of the Barents Sea Arctic cod Stock (Boreogadus saida). Forage Fishes in Marine Ecosystems. Alaska Sea Grant Collage Program, University of Alaska Fairbanks 97:01, 485–504 (1997).Raskoff, K. A., Hopcroft, R. R., Kosobokova, K. N., Purcell, J. E. & Youngbluth, M. Jellies under ice: ROV observations from the Arctic 2005 hidden ocean expedition. Deep-Sea Res. Part II(57), 111–126 (2010).Article 
ADS 

Google Scholar 
Bluhm, B. A. et al. The Pan-Arctic continental slope: Sharp gradients of physical processes affect pelagic and benthic ecosystems. Front. Mar. Sci. 2020, 7 (2020).
Google Scholar 
Hop, H. et al. Pelagic ecosystem characteristics across the atlantic water boundary current from Rijpfjorden, Svalbard, to the Arctic Ocean During Summer (2010–2014). Front. Mar. Sci. 2019, 6 (2019).
Google Scholar 
Mumm, N. Composition and distribution of mesozooplankton in the Nansen Basin, Arctic Ocean, during summer. Polar Biol. 13, 451–461 (1993).Article 

Google Scholar 
Ona, E. & Nielsen, J. Acoustic detection of the Greenland shark (Somniosus microcephalus) using multifrequency split beam echosounder in Svalbard waters. Prog. Oceanogr. 206, 102842 (2022).Article 

Google Scholar 
Gjøsæter, H., Ingvaldsen, R. & Christiansen, J. S. Acoustic scattering layers reveal a faunal connection across the Fram Strait. Prog. Oceanogr. 185, 102348 (2020).Article 

Google Scholar 
Ingvaldsen, R. B., Gjosaeter, H., Ona, E. & Michalsen, K. Atlantic cod (Gadus morhua) feeding over deep water in the high Arctic. Polar Biol. 40, 2105–2111 (2017).Article 

Google Scholar 
Chawarski, J., Klevjer, T. A., Coté, D. & Geoffroy, M. Evidence of temperature control on mesopelagic fish and zooplankton communities at high latitudes. Front. Mar. Sci. 2022, 9 (2022).
Google Scholar 
Chernova, N. V. Catching of Greenland halibut Reinhardtius hippoglossoides (Pleuronectidae) on the shelf edge of the Laptev and East Siberian Seas. J. Ichthyol. 57, 219–227 (2017).Article 

Google Scholar 
Benzik, A. N., Budanova, L. K. & Orlov, A. M. Hard life in cold waters: Size distribution and gonads show that Greenland halibut temporarily inhabit the Siberian Arctic. Water Biol. Secur. 1, 100037 (2022).Article 

Google Scholar 
Olsen, L. M. et al. A red tide in the pack ice of the Arctic Ocean. Sci. Rep. 9, 9536 (2019).Article 
ADS 

Google Scholar 
Assmy, P. et al. Leads in Arctic pack ice enable early phytoplankton blooms below snow-covered sea ice. Sci. Rep. 7, 40850 (2017).Article 
ADS 
CAS 

Google Scholar 
Leu, E., Søreide, J. E., Hessen, D. O., Falk-Petersen, S. & Berge, J. Consequences of changing sea-ice cover for primary and secondary producers in the European Arctic shelf seas: Timing, quantity, and quality. Prog. Oceanogr. 90, 18–32 (2011).Article 
ADS 

Google Scholar 
Drivdal, M. et al. Connections to the deep: Deep vertical migrations, an important part of the life cycle of Apherusa glacialis, an arctic ice-associated amphipod. Front. Mar. Sci. 2021, 8 (2021).
Google Scholar 
Scoulding, B., Chu, D., Ona, E. & Fernandes, P. G. Target strengths of two abundant mesopelagic fish species. J. Acoust. Soc. Am. 137, 989–1000 (2015).Article 
ADS 

Google Scholar 
Popova, E. E., Yool, A., Aksenov, Y. & Coward, A. C. Role of advection in Arctic Ocean lower trophic dynamics: A modeling perspective. J. Geophys. Res. 118, 1571–1586 (2013).Article 
ADS 

Google Scholar 
Saunders, R. A., Ingvarsdóttir, A., Rasmussen, J., Hay, S. J. & Brierley, A. S. Regional variation in distribution pattern, population structure and growth rates of Meganyctiphanes norvegica and Thysanoessa longicaudata in the Irminger Sea, North Atlantic. Prog. Oceanogr. 72, 313–342 (2007).Article 
ADS 

Google Scholar 
Tarling, G. A. et al. Can a key boreal Calanus copepod species now complete its life-cycle in the Arctic? Evidence and implications for Arctic food-webs. Ambio 51, 333–344 (2022).Article 

Google Scholar 
Purcell, J. E., Juhl, A. R., Manko, M. K. & Aumack, C. F. Overwintering of gelatinous zooplankton in the coastal Arctic Ocean. Mar. Ecol. Prog. Ser. 591, 281–286 (2018).Article 
ADS 

Google Scholar 
Purcell, J. E., Hopcroft, R. R., Kosobokova, K. N. & Whitledge, T. E. Distribution, abundance, and predation effects of epipelagic ctenophores and jellyfish in the western Arctic Ocean. Deep-Sea Res. Part II(57), 127–135 (2010).Article 
ADS 

Google Scholar 
Solvang, H. K. et al. Distribution of rorquals and Atlantic cod in relation to their prey in the Norwegian high Arctic. Polar Biol. 44, 761–782 (2021).Article 

Google Scholar 
Ingvaldsen, R. B. et al. Physical manifestations and ecological implications of Arctic Atlantification. Nat. Rev. Earth Environ. 2, 874–889 (2021).Article 
ADS 

Google Scholar 
Flores, H. et al. Macrofauna under sea ice and in the open surface layer of the Lazarev Sea, Southern Ocean. Deep-Sea Res. Part II(58), 1948–1961 (2011).Article 
ADS 

Google Scholar 
Godø, O. R., Valdemarsen, J. W. & Engås, A. Comparison of efficiency of standard and experimental juvenile gadoid sampling trawls. ICES Mar. Sci. Symp. 196, 196–201 (1993).
Google Scholar 
Klevjer, T. et al. Micronekton biomass distribution, improved estimates across four north Atlantic basins. Deep-Sea Res. Part II. 180, 104691 (2020).Article 

Google Scholar 
Krafft, B. A. et al. Distribution and demography of Antarctic krill in the Southeast Atlantic sector of the Southern Ocean during the austral summer 2008. Polar Biol. 33, 957–968 (2010).Article 

Google Scholar 
Foote, K. G. Maintaining precision calibrations with optimal copper spheres. J. Acoust. Soc. Am. 73, 1054–1063 (1983).Article 
ADS 

Google Scholar 
Korneliussen, R. J. et al. Acoustic identification of marine species using a feature library. Methods Oceanogr. 17, 187–205 (2016).Article 

Google Scholar 
Lavergne, T. et al. Version 2 of the EUMETSAT OSI SAF and ESA CCI sea-ice concentration climate data records. Cryosphere. 13, 49–78 (2019).Article 
ADS 

Google Scholar 
Firing, E., Ramada, J. & Caldwell, P. Processing ADCP Data with the CODAS Software System Version 3.1. Joint Institute for Marine and Atmospheric Research University of Hawaii. http://currents.soest.hawaii.edu/docs/adcp_doc/index.html (1995).Padman, L. & Erofeeva, S. A barotropic inverse tidal model for the Arctic Ocean. Geophys. Res. Lett. 31, 256 (2004).Article 

Google Scholar  More

Guillou, L. et al. Widespread occurrence and genetic diversity of marine parasitoids belonging to Syndiniales (Alveolata). Environ. Microbiol. 10, 3349–3365 (2008).Article 
CAS 

Google Scholar 
Massana, R. Eukaryotic picoplankton in surface oceans. Annu. Rev. Microbiol. 65, 91–110 (2011).Article 
CAS 

Google Scholar 
Rocke, E., Pachiadaki, M. G., Cobban, A., Kujawinski, E. B. & Edgcomb, V. P. Protist community grazing on prokaryotic prey in deep ocean water masses. PLoS ONE 10, e0124505 (2015).Article 

Google Scholar 
de Vargas, C. et al. Eukaryotic plankton diversity in the sunlit ocean. Science 348, 1261605 (2015).Article 

Google Scholar 
Ibarbalz, F. M. et al. Global trends in marine plankton diversity across kingdoms of life. Cell 179, 1084–1097 (2019).Article 
CAS 

Google Scholar 
Cordier, T. et al. Patterns of eukaryotic diversity from the surface to the deep-ocean sediment. Sci. Adv. 8, https://doi.org/10.1126/sciadv.abj9309 (2022).Giner, C. R. et al. Marked changes in diversity and relative activity of picoeukaryotes with depth in the world ocean. ISME J. 14, 437–449 (2020).Article 

Google Scholar 
Obiol, A. et al. A metagenomic assessment of microbial eukaryotic diversity in the global ocean. Mol. Ecol. Resour. 20, 718–731 (2020).Article 
CAS 

Google Scholar 
Pernice, M. C. et al. Large variability of bathypelagic microbial eukaryotic communities across the world’s oceans. ISME J. 10, 945–958 (2016).Article 

Google Scholar 
Santoferrara, L. et al. Perspectives from ten years of protist studies by high‐throughput metabarcoding. J. Eukaryot. Microbiol. 67, 612–622 (2020).Article 

Google Scholar 
Schoenle, A. et al. High and specific diversity of protists in the deep-sea basins dominated by diplonemids, kinetoplastids, ciliates and foraminiferans. Commun. Biol. 4, 1–10 (2021).Article 

Google Scholar 
Sommeria-Klein, G. et al. Global drivers of eukaryotic plankton biogeography in the sunlit ocean. Science 374, 594–599 (2021).Article 
CAS 

Google Scholar 
Tremblay, J. É. et al. Global and regional drivers of nutrient supply, primary production and CO2 drawdown in the changing Arctic Ocean. Prog. Oceanogr. 139, 171–196 (2015).Article 

Google Scholar 
Zoccarato, L., Pallavicini, A., Cerino, F., Umani, S. F. & Celussi, M. Water mass dynamics shape Ross Sea protist communities in mesopelagic and bathypelagic layers. Prog. Oceanogr. 149, 16–26 (2016).Article 

Google Scholar 
Biggs, T. E. G., Huisman, J. & Brussaard, C. P. D. Viral lysis modifies seasonal phytoplankton dynamics and carbon flow in the Southern Ocean. ISME J. 15, 3615–3622 (2021).Article 
CAS 

Google Scholar 
Clarke, L. J., Bestley, S., Bissett, A. & Deagle, B. E. A globally distributed Syndiniales parasite dominates the Southern Ocean micro-eukaryote community near the sea-ice edge. ISME J. 13, 734–737 (2019).Article 
CAS 

Google Scholar 
Gast, R. J., Fay, S. A. & Sanders, R. W. Mixotrophic activity and diversity of Antarctic marine protists in austral summer. Front. Mar. Sci. 5, 13 (2018).Article 

Google Scholar 
Grattepanche, J. D., Jeffrey, W. H., Gast, R. J. & Sanders, R. W. Diversity of microbial eukaryotes along the West Antarctic Peninsula in austral spring. Front. Microbiol. 13, 844856 (2022).Article 

Google Scholar 
Hamilton, M. et al. Spatiotemporal variations in Antarctic protistan communities highlight phytoplankton diversity and seasonal dominance by a novel cryptophyte lineage. mBio 12, e0297321 (2021).Article 

Google Scholar 
Lin, Y. et al. Decline in plankton diversity and carbon flux with reduced sea ice extent along the Western Antarctic Peninsula. Nat. Commun. 12, 4948 (2021).Article 
CAS 

Google Scholar 
Martin, K. et al. The biogeographic differentiation of algal microbiomes in the upper ocean from pole to pole. Nat. Commun. 12, 5483 (2021).Article 
CAS 

Google Scholar 
Vernet, M. et al. The Weddell Gyre, Southern Ocean: present knowledge and future challenges. Rev. Geophysics 57, 623–708 (2019).Article 

Google Scholar 
Callahan, J. E. The structure and circulation of deep water in the Antarctic. Deep‐Sea Res. 19, 563–575 (1972).
Google Scholar 
Janout, M. A. et al. FRIS revisited in 2018: on the circulation and water masses at the Filchner and Ronne ice shelves in the southern Weddell Sea. J. Geophys. Res.: Oceans 126, e2021JC017269 (2021).Article 

Google Scholar 
Orsi, A. H., Smethie, W. M. & Bullister, J. L. On the total input of Antarctic waters to the deep ocean: a preliminary estimate from chlorofluorocarbon measurements. J. Geophys. Res. 107, 3122 (2002).Article 

Google Scholar 
Hoppema, M., Fahrbach, E. & Schröder, M. On the total carbon dioxide and oxygen signature of the circumpolar deep water in the Weddell Gyre. Oceanol. Acta 20, 783–798 (1997).CAS 

Google Scholar 
Karstensen, J. & Tomczak, M. Age determination of mixed water masses using CFC and oxygen data. J. Geophys. Res. 103, 18599–18609 (1998).Article 
CAS 

Google Scholar 
De Cáceres, M. & Legendre, P. Associations between species and groups of sites: indices and statistical inference. Ecology 90, 3566–3574 (2009).Article 

Google Scholar 
De Cáceres, M., Legendre, P. & Moretti, M. Improving indicator species analysis by combining groups of sites. Oikos 119, 1674–1684 (2010).Article 

Google Scholar 
Dufrene, M. & Legendre, P. Species assemblages and indicator species: the need for a flexible asymetrical approach. Ecol. Monogr. 67, 345–366 (1997).
Google Scholar 
Agogué, H., Lamy, D., Neal, P. R., Sogin, M. L. & Herndl, G. J. Water mass-specificity of bacterial communities in the North Atlantic revealed by massively parallel sequencing. Mol. Ecol. 20, 258–274 (2011).Article 

Google Scholar 
Celussi, M., Bergamasco, A., Cataletto, B., Umani, S. F. & Del Negro, P. Water masses bacterial community structure and microbial activities in the Ross Sea, Antarctica. Antarct. Sci. 22, 361–370 (2010).Article 

Google Scholar 
Galand, P. E., Potvin, M., Casamayor, E. O. & Lovejoy, C. Hydrography shapes bacterial biogeography of the deep Arctic Ocean. ISME J. 4, 564–576 (2010).Article 

Google Scholar 
Hamdan, L. J. Ocean currents shape the microbiome of Arctic marine sediments. ISME J. 7, 685–696 (2013).Article 
CAS 

Google Scholar 
Wilkins, D., van Sebille, E., Rintoul, S. R., Lauro, F. M. & Cavicchioli, R. Advection shapes Southern Ocean microbial assemblages independent of distance and environment effects. Nat. Commun. 4, 2457 (2013).Article 

Google Scholar 
Flegontova, O. et al. Extreme diversity of diplonemid eukaryotes in the ocean. Curr. Biol. 26, 3060–3065 (2016).Article 
CAS 

Google Scholar 
Barnes, M. A. et al. Environmental conditions influence eDNA persistence in aquatic systems. Environ. Sci. Technol. 48, 1819–1827 (2014).Article 
CAS 

Google Scholar 
Jeong, H. J. et al. Growth, feeding and ecological roles of the mixotrophic and heterotrophic dinoflagellates in marine planktonic food webs. Ocean Sci. 45, 65–91 (2010).Article 
CAS 

Google Scholar 
Stoecker, D. K., Hansen, P. J., Caron, D. A. & Mitra, A. Mixotrophy in the marine Plankton. Ann. Rev. Mar. Sci. 9, 311–335 (2016).Article 

Google Scholar 
Boeuf, D. et al. Biological composition and microbial dynamics of sinking particulate organic matter at abyssal depths in the oligotrophic open ocean. Proc. Natl Acad. Sci. USA 116, 11824–11832 (2019).Article 
CAS 

Google Scholar 
Gutierrez-Rodriguez, A. et al. High contribution of Rhizaria (Radiolaria) to vertical export in the California Current Ecosystem revealed by DNA metabarcoding. ISME J. 13, 964–976 (2019).Article 
CAS 

Google Scholar 
Lampitt, R. S., Salter, I. & Johns, D. Radiolaria: major exporters of organic carbon to the deep ocean. Glob. Biogeochem. Cycles 23, GB1010 (2009).Article 

Google Scholar 
Suzuki, N. & Not, F. In Marine Protists: Diversity and Dynamics 179–222 (Springer Japan, 2015).Decelle, J. et al. Diversity, ecology and biogeochemistry of cyst-forming Acantharia (Radiolaria) in the oceans. PLoS ONE 8, e53598 (2013).Article 
CAS 

Google Scholar 
Tashyreva, D. et al. Diplonemids—a review on “new“ flagellates on the oceanic block. Protist 173, 125868 (2022).Article 
CAS 

Google Scholar 
Flegontova, O. et al. Environmental determinants of the distribution of planktonic diplonemids and kinetoplastids in the oceans. Environ. Microbiol 22, 4014–4031 (2020).Article 
CAS 

Google Scholar 
Xu, D. et al. Microbial eukaryote diversity and activity in the water column of the South China sea based on DNA and RNA high throughput sequencing. Front. Microbiol. 8, 1121 (2017).Article 

Google Scholar 
Bråte, J. et al. Radiolaria associated with large diversity of marine alveolates. Protist 163, 767–777 (2012).Article 

Google Scholar 
Strassert, J. F. H. et al. Single cell genomics of uncultured marine alveolates shows paraphyly of basal dinoflagellates. ISME J. 12, 304–308 (2017).Article 

Google Scholar 
Yabuki, A. & Tame, A. Phylogeny and reclassification of Hemistasia phaeocysticola (Scherffel) Elbrächter & Schnepf, 1996. J. Eukaryot. Microbiol. 62, 426–429 (2015).Article 

Google Scholar 
Larsen, J. & Patterson, J. Some flagellates (Protista) from tropical marine sediments. J. Nat. Hist. 24, 801–937 (1990).Article 

Google Scholar 
Prokopchuk, G. et al. Trophic flexibility of marine diplonemids – switching from osmotrophy to bacterivory. ISME J. 16, 1409–1419 (2022).Article 
CAS 

Google Scholar 
Arístegui, J. & Gasol, J. Microbial oceanography of the dark ocean’s pelagic realm. Limnol. Oceanogr. 54, 1501–1529 (2009).Article 

Google Scholar 
Amaral-Zettler, L. A., McCliment, E. A., Ducklow, H. W. & Huse, S. M. A method for studying protistan diversity using massively parallel sequencing of V9 hypervariable regions of small-subunit ribosomal RNA genes. PLoS ONE 4, e6372 (2009).Article 

Google Scholar 
Mahé, F., Rognes, T., Quince, C., de Vargas, C. & Dunthorn, M. Swarm v2: highly-scalable and high-resolution amplicon clustering. PeerJ 3, e1420 (2015).Article 

Google Scholar 
Kolisko, M. et al. EukRef-excavates: seven curated SSU ribosomal RNA gene databases. Database 2020, baaa080 (2020).
Google Scholar 
Adl, S. M. et al. Revisions to the classification, nomenclature, and diversity of eukaryotes. J. Eukaryot. Microbiol. 66, 4–119 (2019).Article 

Google Scholar 
Salazar, G. et al. Gene expression changes and community turnover differentially shape the global ocean metatranscriptome. Cell 179, 1068–1083 (2019).Article 
CAS 

Google Scholar  More

Dulvy, N. K., Sadovy, Y. & Reynolds, J. D. Extinction vulnerability in marine populations. Fish Fish. 4, 25–64 (2003).Article 

Google Scholar 
Fowler S. L. et al. Sharks, Rays and Chimaeras: The Status of the Chondrichthyan Fishes. IUCN/SSC Shark Specialist Group, Gland, Switzerland and Cambridge, UK (2005).Dulvy, N. K. et al. Extinction risk and conservation of the world’s sharks and rays. Elife 3, e00590 (2014).Article 

Google Scholar 
Lack M. & Sant G. Illegal, Unreported and Unregulated Shark Catch: A review of current knowledge and action. Department of the Environment, Water, Heritage and the Arts and TRAFFIC, Canberra http://www.traffic.org/fish/ (2008).Rose D.A. An Overview of World Trade in Sharks and Other Cartilaginous Fishes. TRAFFIC International, Cambridge, UK (1996).Lam, V. Y. & Sadovy, M. Y. The sharks of South East Asia–unknown, unmonitored and unmanaged. Fish Fish 12, 51–74 (2011).Article 

Google Scholar 
Kessel S.T. Investigation into the behaviour and population dynamics of the lemon shark (Negaprion brevirostris). Cardiff University (United Kingdom) (2010).Morrissey, J. F. & Gruber, S. H. Habitat selection by juvenile lemon sharks Negaprion brevirostris. Environ. Biol. Fishes 38, 311–319 (1993).Article 

Google Scholar 
Filmalter, J. D., Dagorn, L. & Cowley, P. D. Spatial behaviour and site fidelity of the sicklefin lemon shark Negaprion acutidens in a remote Indian Ocean atoll. Mari. Biol. 160, 2425–2436 (2013).Article 

Google Scholar 
DiBattista, J. D. et al. A genetic assessment of polyandry and breeding site fidelity in lemon sharks. Mol. Ecol. 17, 3337–3351 (2008).Article 

Google Scholar 
Wetherbee, B. M., Gruber, S. H. & Rosa, R. S. Movement patterns of juvenile lemon sharks Negaprion brevirostris within Atol das Rocas, Brazil: A nursery characterized by tidal extremes. Mar. Ecol. Prog. Seri. 343, 283–293 (2007).Article 
ADS 

Google Scholar 
Feldheim, K. A. et al. Two decades of genetic profiling yields first evidence of natal philopatry and long-term fidelity to parturition sites in sharks. Mol. Ecol. 23, 110–117 (2014).Article 

Google Scholar 
Stevens J. D. et al. Diversity, abundance and habitat utilisation of sharks and rays: Final report to West Australian Marine Science Institute. CSIRO, editor. Hobart (2009).Schultz, J. K. et al. Global phylogeography and seascape genetics of the lemon sharks (genus Negaprion). Mol. Ecol. 17, 5336–5348 (2008).Article 
CAS 

Google Scholar 
Mourier, J., Buray, N., Schultz, J. K., Clua, E. & Planes, S. Genetic network and breeding patterns of a sicklefin lemon shark (Negaprion acutidens) population in the Society Islands, French Polynesia. PLoS ONE 8, e73899 (2013).Article 
ADS 
CAS 

Google Scholar 
Speed, C. W. et al. Reef shark movements relative to a coastal marine protected area. Reg. Stud. Mar. Sci. 3, 58–66 (2016).
Google Scholar 
Huang, Z. Marine Species and Their Distribution in China’s Seas (Krieger Publishing Company, 2001).
Google Scholar 
Chang, C. W., Huang, C. S. & Wang, S. I. Species composition and sizes of fish in the lagoon of dongsha island (Pratas Island), Dongsha Atoll of the South China sea. Platax 2012, 25–32 (2012).
Google Scholar 
Pillans, R. D. et al. Long-term acoustic monitoring reveals site fidelity, reproductive migrations, and sex specific differences in habitat use and migratory timing in a large coastal shark (Negaprion acutidens). Front. Mar. Sci. 8, 616633 (2021).Article 

Google Scholar 
Daly-Engel, T. S. et al. Global phylogeography with mixed-marker analysis reveals male-mediated dispersal in the endangered scalloped hammerhead shark (Sphyrna lewini). PLoS ONE 7, e29986 (2012).Article 
ADS 
CAS 

Google Scholar 
Félix-López, D. G. et al. Possible female philopatry of the smooth hammerhead shark Sphyrna zygaena revealed by genetic structure patterns. J. Fish Biol. 94, 671–679 (2019).Article 

Google Scholar 
Nosal, A. P., Caillat, A., Kisfaludy, E. K., Royer, M. A. & Wegner, N. C. Aggregation behavior and seasonal philopatry in male and female leopard sharks Triakis semifasciata along the open coast of southern California, USA. Mar. Ecol. Prog. Ser. 499, 157–175 (2014).Article 
ADS 

Google Scholar 
Jirik, K. E. & Lowe, C. G. An elasmobranch maternity ward: Female round stingrays Urobatis halleri use warm, restored estuarine habitat during gestation. J. Fish. Biol. 80(5), 1227–1245 (2012).Article 
CAS 

Google Scholar 
Jacoby, D. M., Croft, D. P. & Sims, D. W. Social behaviour in sharks and rays: Analysis, patterns and implications for conservation. Fish Fish 13(4), 399–417 (2012).Article 

Google Scholar 
Su, S. H., Liu, S. Y. V., Liu, K. M. & Tsai, W. P. Development and characterization of novel microsatellite loci for an endangered hammerhead shark Sphyrna lewini by using shotgun sequencing. Taiwania 65(2), 261–263 (2020).
Google Scholar 
Dieringer, D. & Schlötterer, C. Microsatellite analyser (MSA): A platform independent analysis tool for large microsatellite data sets. Mol. Ecol. Notes 3, 167–169 (2003).Article 
CAS 

Google Scholar 
Van Oosterhout, C., Hutchinson, W. F., Wills, D. P. & Shipley, P. Micro-checker: Software for identifying and correcting genotyping errors in microsatellite data. Mol. Ecol. Notes 4, 535–538 (2004).Article 

Google Scholar 
Pritchard, J. K., Stephens, M. & Donnelly, P. Inference of population structure using multilocus genotype data. Genetics 155, 945–959 (2000).Article 
CAS 

Google Scholar 
Falush, D., Stephens, M. & Pritchard, J. K. Inference of population structure using multilocus genotype data: Dominant markers and null alleles. Mol. Ecol. Notes 7, 574–578 (2007).Article 
CAS 

Google Scholar 
Earl, D. A. & VonHoldt, B. M. Structure harvester: A website and program for visualizing structure output and implementing the Evanno method. Conserv. Genet. Resour. 4, 359–361 (2012).Article 

Google Scholar 
Jakobsson, M. & Rosenberg, N. A. CLUMPP: A cluster matching and permutation program for dealing with label switching and multimodality in analysis of population structure. Bioinformatics 23(14), 1801–1806 (2007).Article 
CAS 

Google Scholar 
Peakall, R. & Smouse, P. E. GenAlEx 6.5: Genetic analysis in excel population genetic software for teaching and research–an update. Bioinformatics 28, 2537–2539 (2012).Article 
CAS 

Google Scholar 
Kamvar, Z. N., Tabima, J. F. & Grünwald, N. J. POPPR: An R package for genetic analysis of populations with clonal, partially clonal, and/or sexual reproduction. PeerJ 2, e281 (2014).Article 

Google Scholar 
Kalinowski, S. T., Wagner, A. P. & Taper, M. L. ML-Relate: A computer program for maximum likelihood estimation of relatedness and relationship. Mol. Ecol. Resour. 6, 576–579 (2006).Article 
CAS 

Google Scholar 
Do, C. et al. NeEstimator v2: Re-implementation of software for the estimation of contemporary effective population size (Ne) from genetic data. Mol. Ecol. Resour. 14, 209–214 (2014).Article 
CAS 

Google Scholar 
Oh, B. Z. et al. Contrasting patterns of residency and space use of coastal sharks within a communal shark nursery. Mar. Freshw. Res. 68, 1501–1517 (2017).Article 

Google Scholar 
McClelland J. Genetic Assessment of Breeding Patterns and Population Size of the Sicklefin Lemon Shark Negaprion acutidens in a Tropical Marine Protected Area: Implications for Conservation and Management (Doctoral dissertation, University of York) (2020).Compagno L. J .V. FAO species catalogue Sharks of the world: An annotated and illustrated catalogue of shark species known to date. FAO Fish. Synop. No. 125 Rome 4, 1–655 (1984).Stevens, J. D. Life-history and ecology of sharks at aldabra Atoll. Indian Ocean. Proc R Soc. B 222, 79–106 (1984).ADS 

Google Scholar 
Kool, J. T., Moilanen, A. & Treml, E. A. Population connectivity: Recent advances and new perspectives. Landsc. Ecol. 28, 165–185 (2013).Article 

Google Scholar 
Ruzzante, D. E. et al. Effective number of breeders, effective population size and their relationship with census size in an iteroparous species Salvelinus fontinalis. Proc. R Soc. B 283, 20152601 (2016).Article 

Google Scholar 
Van Wyngaarden, M. et al. Identifying patterns of dispersal, connectivity and selection in the sea scallop, Placopecten magellanicus, using RADseq-derived SNPs. Evol. Appl. 10, 102–117 (2017).Article 

Google Scholar 
Frankham, R., Bradshaw, C. J. A. & Brook, B. W. Genetics in conservation management: Revised recommendations for the 50/500 rules, Red list criteria and population viability analyses. Biol. Conserv. 170, 56–63 (2014).Article 

Google Scholar 
Pazmiño, D. A., Maes, G. E., Simpfendorfer, C. A., Salinas-de-León, P. & van Herwerden, L. Genome-wide SNPs reveal low effective population size within confined management units of the highly vagile Galapagos shark (Carcharhinus galapagensis). Conserv. Genet. 18, 1151–1163 (2017).Article 

Google Scholar 
Waples, R. S. & Do, C. Linkage disequilibrium estimates of contemporary Ne using highly variable genetic markers: A largely untapped resource for applied conservation and evolution. Evol. Appl. 3, 244–262 (2010).Article 

Google Scholar 
Dudgeon, C. L. & Ovenden, J. R. The relationship between abundance and genetic effective population size in elasmobranchs: An example from the globally threatened zebra shark Stegostoma fasciatum within its protected range. Conserv. Genet. 16, 1443–1454 (2015).Article 

Google Scholar 
Feldheim, K. A., Gruber, S. H. & Ashley, M. V. Population genetic structure of the lemon shark (Negaprion brevirostris) in the western Atlantic: DNA microsatellite variation. Mol. Ecol. 10, 295–303 (2001).Article 
CAS 

Google Scholar 
Feldheim, K. A., Gruber, S. H. & Ashley, M. V. The breeding biology of lemon sharks at a tropical nursery lagoon. Proc. R. Soc. Lond. B 269, 1471–2954 (2002).Article 

Google Scholar 
Portnoy, D., McDowell, J. R., Thompson, K., Musick, J. A. & Graves, J. E. Isolation and characterization of five dinucleotide microsatellite loci in the sandbar shark, Carcharhinus plumbeus. Mol. Ecol. Notes 6, 431–433 (2006).Article 
CAS 

Google Scholar  More

A visionary and interdisciplinary scientist who brought a fearless passion to everything she did, inspiring all those around her.
Alma Dal Co tragically passed away on 14 November 2022 at the age of 33, doing what she loved most — spearfishing near the Italian island of Pantelleria. Alma was a visionary scientist at the beginning of what was promising to become a stellar career. As a physicist turned biologist, Alma wanted to unravel how complexity emerges from simplicity. Despite her young age, she had already made an important impact on the field by showing how the activities of microbial communities emerge from interactions between individual cells. Alma was a warm and caring friend, and a committed and inspiring mentor. She pursued science with fearless passion, creativity, vision and dedication.Alma Dal Co in 2016 in Joshua Tree National Park, California. Photograph by Simon van Vliet.Alma had an exceptionally sharp and creative mind, and an insatiable curiosity. She kept exploring new directions, working on everything from gene-regulatory circuits to microbial communities, to developmental processes. She was the embodiment of a true interdisciplinary scientist, combining state-of-the-art experiments with advanced computational approaches. The unifying theme of her work was to understand how interactions between individuals (be it fish, microorganisms or pancreatic cells) give rise to complex behaviour at higher levels of organization. She strived to derive simple, quantitative rules to explain the complexity that we see around us. Alma believed that science is a team effort: she was generous with her time, and always happy to discuss ideas and share resources. No matter where she went, she quickly connected with people, built formal and informal networks, and fostered collaborations and friendships.Alma was born in Turin and grew up in Venice, in Italy. Her true home, however, was Pantelleria, an Italian island in the Mediterranean Sea off the coast of Sicily. Alma spent her summers in the sea from an early age, developing a deep and lasting bond with it. The sea was not only a place to recharge, but also a source of inspiration: Alma became fascinated by the intricate behaviours of octopuses and schools of fish, creating a lasting sense of wonder about the natural world. Alma’s primary education focused on the humanities, but most of all music. In 2002, she was accepted to the conservatorium in Venice to study the piano. However, her love for the natural world remained and in 2007 she started studying physics in Padua. In 2011, she finished her BSc in physics and a year later her education at the conservatorium. Both a career in music and in science were an option, but Alma chose science and moved to Turin to study the physics of complex systems. Music always remained important in her life, and she played the piano whenever she could.Alma’s transition to biology started in Turin in the laboratory of Michelle Caselle, where she used mathematical models to study gene regulatory networks. She discovered how the regulation of gene expression can reduce stochastic fluctuations and provide robustness to the expression of an organism’s phenotype (A. Dal Co et al. Nucleic Acids Res. 45, 1069–1078; 2017). In 2014, she exchanged the blackboard for the wet lab, and moved to Zurich, Switzerland, to start her PhD with Martin Ackermann at ETH and the aquatic research institute Eawag. Despite the struggles of having to learn hands-on biology without formal training, she was not deterred from pursuing a highly challenging project.Alma developed an innovative approach to gain a mechanistic understanding of how metabolic interactions between individual microbial cells determine the dynamics of spatially structured communities. She quantified the growth of single cells in a synthetic microbial community and developed computational tools to infer their interaction network. She showed that cells in these communities live in a small world: they only interact with few neighbours (A. Dal Co et al. Nat. Ecol. Evol. 4, 366–375; 2020). This short interaction range limits the growth of mutually dependent microorganisms, thereby counteracting the evolution of metabolic specialization. Moreover, Alma developed a mathematical framework to quantitatively predict the dynamics of microbial communities from the molecular properties of the underlying intercellular interactions (S. van Vliet et al. PLoS Comput. Biol. 18, e1009877; 2022). Together, these works have made an important contribution to our understanding of how microbial communities function, and they have inspired numerous follow-up projects, both by Alma herself (for example, A. Dal Co et al. Phil. Trans. R. Soc. B 374, 20190080; 2019) and by others in the field (for example, J. van Gestel et al. Nat. Commun. 12, 2324; 2021).Alma finished her PhD in 2019, winning the ETH medal for an outstanding thesis. She then moved to Harvard to study developmental processes, together with Michael Brenner. She quickly developed a large network of collaborators and designed an innovative project to study pancreatic islet formation. However, COVID-19-related laboratory restrictions brought an early end to these plans, and Alma instead developed a novel computational framework that can be applied to both animal tissues and microbial communities to study how local cell–cell interactions can create spatial structure at the scale of multicellular systems.In September 2021, Alma started an assistant professorship at the University of Lausanne. At the age of 32, she was one of youngest professors ever appointed there. Thanks to her leadership, she quickly assembled a highly interdisciplinary, collaborative and cohesive team of talented young scientists. The group’s research was as varied as Alma’s interests. A major theme was to gain a quantitative understanding of how cell–cell interactions affect the function and structure of microbial communities and other multicellular systems. Her group combines state-of-the art experimental tools such as optogenetics, microfluidics and single-cell imaging, with computational approaches and mathematical modelling to study the dynamics of a wide range of model systems.During her very short career as an assistant professor, Alma was a core member of the Swiss National Research Program on microbiome research (https://nccr-microbiomes.ch); was awarded two major grants; established a large network of collaborators; and was invited to present her work at numerous international meetings. Most importantly, Alma fostered a strong sense of community, both in her group and beyond — creating an open, inclusive and interactive space to discuss science and life.Interacting with Alma was never dull: her passion and energy were infectious and her curiosity and openness a source of inspiration. She always kept you on your toes with her constant stream of pointed questions. But most of all, her easy laugh and positive energy made working with her an extraordinarily joyous experience.With Alma the world has lost a visionary scientist. We are deeply saddened that we will never see what other discoveries she would have made. However, it offers some conciliation to see how profoundly Alma has impacted the people around her, leaving a lasting impression even on those she only briefly met. Her vision, spirit and leadership have profoundly changed many around her and will continue to be a source of inspiration for many years to come. More

Research areaThe YREB covers Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Guizhou, and Yunnan. It includes the Yangtze River Delta urban agglomerations (YRDUA), Yangtze River midstream urban agglomeration (YRMUA), and Chengdu-Chongqing urban agglomeration (CCUA). With a regional area of 2.05 million km2, the YREB runs through the eastern, central and western regions in China32. In 2019, the total GDP of YREB is 45.8 trillion yuan, accounting for 46.2% of the national GDP. The YREB plays a pivotal strategic support and leading role in the overall situation of stable economic growth in China33. At the same time, the contradiction between the shortage of land resources and economic growth in the YREB is very prominent. Therefore, this paper selects 107 cities in YREB as the research sample. The specific geographic locations are shown in Fig. 2. This article uses ARCGIS 10.2 version to draw the map. The URL link is http://demo.domain.com:6080/arcgis/services.Figure 2The geographic location of the YREB in China.Full size imageResearch methodsGlobal Malmquist–Luenberger indexUGLUE refers to the effective utilization degree of land elements under certain input of other elements. The green utilization of urban land mainly comes from three aspects: first, improve the utilization intensity of the existing actual input land, that is, increase the input intensity of other elements of the unit land area. Second, reduce the input of land in the production process to avoid excessive waste of land. Third, promote the optimal allocation of land elements among production units. Technical efficiency refers to the maximum degree that all factor inputs need to expand or shrink in equal proportion when all production units reach the production frontier. However, for production units with high technical efficiency, the factor allocation structure may not be reasonable. The land factors may still have the problem of under-input or over-input, resulting in the reduction of UGLUE.Pastor and Lovell34 proposed a global index, which uses all the inspection periods of each decision-making unit as a benchmark to construct the production frontier. According to the current benchmark construction period t, the production possibility set reference set is defined as follows:$$P_{C}^{t} (x^{t} ) = left{ {left. {(y^{t} ,b^{t} )} right|x^{t} {kern 1pt} can{kern 1pt} , produce{kern 1pt} , b^{t} ,y^{t} } right}$$
(1)
The global benchmark is defined as: (P_{G} = P_{C}^{1} , cup ,P_{C}^{2} , cup , cdots ,P_{C}^{t}), The subscripts C and G represent the current benchmark and the global benchmark respectively. The ML index of decision-making unit i is calculated based on the current reference benchmark:$$ML^{S} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{C}^{S} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{C}^{S} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}}$$
(2)
Among them, the superscript S indicates two adjacent periods, t period and t + 1 period. The subscript C indicates the current benchmark, which is a simplified directional distance function. (ML^{s} > 1), indicates that the productivity increases. (ML^{s} < 1), indicates that the productivity decreases.According to Hofmann et al.35, the GMLI is defined as follows:$$GMLI^{t,t + 1} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}}$$ (3) Among them, (D_{G}^{T} (x,y,b) = max left{ {alpha |(y - alpha y,b - alpha b) in P_{G} (x)} right}). (GMLI^{t,t + 1} > 1) indicates that the productivity has increased. (GMLI^{t,t + 1} < 1) indicates that the productivity decreases. The GMLI is further broken down as follows:$$begin{aligned} & GMLI^{t,t + 1} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}} \ & quad = frac{{1 + D_{G}^{t} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{t + 1} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}} times left[ {frac{{(1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} ))/(1 + D_{C}^{T} (x^{t} ,y^{t} ,b^{t} ))}}{{(1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} ))/(1 + D_{C}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} ))}}} right] \ & quad = frac{{TE^{t + 1} }}{{TE^{t} }} times left( {frac{{BPG_{t + 1}^{t + 1} }}{{BPG_{t}^{t + 1} }}} right) = EC_{t}^{t + 1} times BPC_{t}^{t + 1} \ end{aligned}$$ (4) Among them, TE is the change of technological progress. EC is the change of technological efficiency. The change of technological progress reflects the change of the highest technical level. The improvement of the highest technical level often requires the introduction and innovation of advanced technology, which often requires a large amount of investment. The change of technical efficiency reflects the gap with the highest technical level. Narrowing the gap with the highest technical level often requires improvements in internal management and governance structures. (BPG_{t}^{t + 1}) is the “best practitioner gap” between the current period and overall technological frontier. (BPC_{t}^{t + 1}) measures the changes in the “best practitioner gap” between two periods (technological changes). (BPC_{t}^{t + 1} , > , 1 ,) indicates technological progress. (BPC_{t}^{t + 1} < 1) indicates technology regress.Econometric techniques of industrial agglomeration on UGLUEIn recent years, many scholars used the traditional SPM for empirical analysis, which is a basic measurement model suitable for panel data. Therefore, this article firstly uses the traditional SPM to analyze the impact of industrial agglomeration on UGLUE. The formula is:$$begin{aligned} ln UGLUE_{it} & = alpha_{0} + alpha_{1} ln RZI_{it} + alpha_{2} ln RZI_{it} *ln RZI_{it} + alpha_{3} ln RDI_{it} + alpha_{4} ln EC_{it} \ & quad + alpha_{5} ln GDP_{it} + alpha_{6} ln TEC_{it} + alpha_{7} ln ROAD_{it} + alpha_{8} ln GOV_{it} + varepsilon_{it} \ end{aligned}$$ (5) Among them, ε is the disturbance term. i represents the city, i in this paper involves 107 cities in YREB. t represents the time, and the range of t in this paper is from 2007 to 2016. UGLUE is the explained variable, which represents the UGLUE. RZI and RDI are explanatory variables, representing industrial specialization agglomeration and industrial diversification agglomeration. EC is the industrial structure. GDP is the level of economic development. TEC is the level of technology. ROAD is the level of infrastructure. GOV is the degree of government intervention. (alpha_{1}) to (alpha_{8}) is the coefficient of each variable.Formula (5) assumes that the UGLUE changes with the changes of various influencing factors in the current period. That is, there is no time lag effect. But in reality, land use often has a time lag effect. The previous level has a non-negligible impact on the current results. Therefore, this paper selects the dynamic panel model for empirical analysis. However, there is often a two-way causal relationship between industrial agglomeration and UGLUE, which may cause endogenous bias. For example, cities with higher UGLUE levels tend to have higher levels of economic development, which promotes industrial agglomeration in this city. Therefore, this paper adopts the method of system GMM for regression analysis of dynamic panel model. Compared with mixed OLS, system GMM can make full use of sample information, select appropriate lag terms as instrumental variables36. It can effectively solve the endogeneity problem between industrial agglomeration and UGLUE. Based on the above analysis, this paper introduces the first-order lag term of UGLUE on the basis of formula (5). The DPM is as follows:$$begin{aligned} ln UGLUE_{it} & = beta_{0} + tau ln UGLUE_{i(t - 1)} + beta_{1} ln RZI_{it} + beta_{2} ln RZI_{it} times ln RZI_{it} + beta_{3} ln RDI_{it} \ & quad + beta_{4} ln EC_{it} + beta_{5} ln GDP_{it} + beta_{6} ln TEC_{it} + beta_{7} ln ROAD_{it} + beta_{8} ln GOV_{it} + varepsilon_{{{text{it}}}} \ end{aligned}$$ (6) Among them, (tau) is the first-order lag coefficient of UGLUE, reflecting the time lag effect of UGLUE.Variable descriptionExplained variableThe GMLI is used to measure the UGLUE of 107 cities in YREB. According to existing research37, the following core evaluation index of UGLUE are selected (see Table 1). Regarding input indicators, we mainly choose land element input M, labor element input L, and capital element input K as input indicators. Regarding output indicators, we choose the added value of the secondary and tertiary industries in the municipal area as the expected output, and use the GDP deflator to convert it into a comparable value. At the same time, pollution indicators such as industrial wastewater emissions, industrial sulfur dioxide emissions, and industrial smoke (dust) emissions are selected as undesired output. Since the GMLI reflects the growth rate of UGLUE, this paper assumes that the GMLI in 2006 is 1, and then multiplies the calculated GMLI year by year to obtain the development level of UGLUE in each city from 2007 to 2016.Table 1 Input and output index.Full size tableExplanatory variablesIndustrial specialization index ZI is usually used to measure the specialization level of urban industries. The specialization index is represented by the share of the employment of the industry in the total employment of the city:$$ZI_{i} = Max_{j} (S_{ij} )$$ (7) Nextly, we use the relative specialization index to make a horizontal comparison of the specialization level between different cities:$$RZI_{i} = Max(S_{ij} /S_{j} )$$ (8) The most common measure of the level of industrial diversification is the Herfindahl–Hirschman Index (HHI). For city i, the HHI is the sum of the square sum of employment shares of all industries in the city. The diversification index is the reciprocal of the HHI:$$DZ_{i} = frac{1}{{sumlimits_{j} {S_{ij}^{2} } }}$$ (9) The expression of relative diversification index is as follows:$$RDI_{i} = {1 mathord{left/ {vphantom {1 {sumlimits_{j} {left| {S_{ij} - S_{j} } right|} }}} right. kern-0pt} {sumlimits_{j} {left| {S_{ij} - S_{j} } right|} }}$$ (10) Among them, Sij is the employment proportion of j industry in city i, and Sj is the proportion of the total employment of the national j industry. The greater value of RZI and RDI, the higher level of industrial specialization and diversification.Control variablesRegarding control variables, we choose the following variables as control variables.Industrial structure (EC): The continuous optimization of industrial structure promotes the improvement of UGLUE through three aspects: saving land, increasing land income and promoting the optimal allocation of land resources. This paper selects the added value of the tertiary industry as a percentage of GDP (take the logarithm) to express.Technological level (TEC): The higher the technological innovation level of a city is, the more it promotes the use of input elements and the transformation of innovation results, thereby improving the UGLUE. This paper selects the proportion of science and technology expenditure to fiscal expenditure (take the logarithm) to represent.Economic development level (GDP): The continuous economic development promote the rational allocation of various production factors and increase the level of urban land output, thereby improving the UGLUE. This paper selects GDP per capita (take the logarithm) to express.Road infrastructure level (ROAD): The continuous improvement of infrastructure reduces transportation costs and transaction costs, and promotes communication externalities between producers, consumers, and between producers and consumers. This paper selects the average road area per capita (take the logarithm) to express.Government behavior (GOV): Fiscal expenditure is an important means for the government to carry out macro-control. Appropriate fiscal expenditure makes up for market shortages, improves factor flow and resource allocation efficiency, and realizes positive economic externalities. This paper selects the proportion of fiscal expenditure to GDP (take the logarithm) to express. We can see the meaning of specific variables from Table 2.Table 2 The descriptive statistics of variables.Full size tableData sourceThe object of this thesis is the 107 cities in YREB from 2007 to 2016. The urban construction land area data comes from the "China Urban Construction Statistical Yearbook", and the rest of the index data all come from the "China City Statistical Yearbook". The URL link is https://www.cnki.net/. In order to maintain the integrity of the data, this article uses the average method to fill in the missing values. In addition, because Chaohu City began to be under the jurisdiction of Hefei City in 2011, Bijie City and Tongren City in Guizhou Province only became prefecture-level cities in 2011. The three cities and Pu'er City are taken from the sample to maintain the continuity of data. More

The Campbell et al. model provides an excellent framework to identify species whose extinction leads to community collapse and species whose reintroduction can restore the community (see Fig. 2 for an illustration of these processes). Our first objective, finding the effect of species extinction on the rest of the species in an established community, is achievable using the concept of Logical Domain of Influence (LDOI)41; the LDOI represents the influence of a (set of) fixed node state(s) on the rest of the components in a system. In this section we first present our proposed method to calculate the LDOI for the Boolean threshold functions governing the Campbell et al. model of plant–pollinator community assembly. Then we verify that the simplified logical functions preserve the LDOI and hence can be implemented to further analyze the effect of extinction in plant–pollinator networks. Next, we address one of the main questions that motivated this study: Can stable motif driver set analysis facilitate the identification of keystone species? We discuss the identification of the driver sets of inactive stable motifs and motif groups and present the results of stabilizing these sets to measure the magnitude of the effect of species extinction on the communities. Lastly we discuss possible prevention and mitigation measures based on the knowledge acquired from driver sets of stable motifs and motif groups.Figure 2Illustration of species extinction and restoration in a hypothetical 6-species community. (a) The interaction network (on the left), and the maximal richness community possible for this network (the community with the most established species). Nodes highlighted with green represent established species. (b) The initial extinction of two species, po_1 and po_2 (left) and the community that results after cascading extinctions (right). Nodes highlighted with grey represent extinct species. (c) An intervention to restore pl_2 (left), which induces the restoration of further species, finally leading to a restored community with all the species present (right). The nodes highlighted with teal represent the restored species.Full size imageLDOI in the Boolean threshold modelThe LDOI concept was originally defined on Boolean functions expressed in a disjunctive prime form. Here we extend it to Boolean threshold functions. We implemented it as a breadth first search on the interaction network, as exemplified in Fig. 3. Assume that we want to find the LDOI of a (set of) node(s) (S_0={n_1,dots ,n_N}) and their specific fixed state (Q(S_0)={sigma _{n_1},dots ,sigma _{n_N}}). Starting from the set (S_0), the next set of nodes (S_1) that can acquire a fixed state due to the influence of (Q(S_0)) consists of the nodes that have an incoming edge from the nodes in the set (S_0) in the interaction network. The nodes in set (S_1) are the subject of the first search level. For each node (n_i in S_0) and (n^prime _i in S_1) we assume a “worst case scenario” (i.e., maximal opposition of the effect of (n_i) on (n^prime _i) from other regulators) to find the possible sufficiency relationships between the two. There are five cases:

1.

If (n_i) is a positive regulator of (n^prime _i), then (sigma _{n_i}=1) is a candidate for being sufficient for (sigma _{n^prime _i}=1). We assume that all other positive regulators of (n^prime _i) that have an unknown state (i.e., are not in (Q(S_0))) are inactive and all negative regulators of (n^prime _i) that have an unknown state are active. If (sum _j W_{ij} > 0) under this assumption, then the active state of (n_i) is sufficient to activate (n^prime _i). The virtual node (n^prime _i) that corresponds to (sigma _{n^prime _i}=1) is added to LDOI((Q(S_0))).

2.

If (n_i) is a positive regulator of (n^prime _i), then (sigma _{n_i}=0) is a candidate for being sufficient for (sigma _{n^prime _i}=0). We assume all other positive regulators of (n^prime _i) that have an unknown state are active and all negative regulators of (n^prime _i) that have an unknown state are inactive. If (sum _j W_{ij}le 0) under this assumption, then the inactive state of (n_i) is sufficient to deactivate (n^prime _i). The virtual node (sim n^prime _i) that corresponds to (sigma _{n^prime _i}=0) is added to LDOI((Q(S_0))).

3.

If (n_i) is a negative regulator of (n^prime _i), then (sigma _{n_i}=1) is a candidate for being sufficient for (sigma _{n^prime _i}=0). We assume all positive regulators of (n^prime _i) that have an unknown state are active and all other negative regulators of (n^prime _i) that that have an unknown state are inactive. If (sum _j W_{ij}le 0) under this assumption, then the active state of (n_i) is sufficient to deactivate (n^prime _i). The virtual node (sim n^prime _i) that corresponds to (sigma _{n^prime _i}=0) is added to LDOI((Q(S_0))).

4.

If (n_i) is a negative regulator of (n^prime _i), then (sigma _{n_i}=0) is a candidate for being sufficient for (sigma _{n^prime _i}=1). We assume all positive regulators of (n^prime _i) that have an unknown state are inactive and all other negative regulators of (n^prime _i) that that have an unknown state are active. If (sum _j W_{ij} > 0) under this assumption, then the inactive state of (n_i) is sufficient to activate (n^prime _i). The virtual node (n^prime _i) that corresponds to (sigma _{n^prime _i}=1) is added to the LDOI((Q(S_0))).

5.

If none of the past four sufficiency checks are satisfied, the node (n^prime _i) will be visited again in the next search levels.

The second set of nodes that can be influenced, (S_2), are the nodes that have an incoming edge from the nodes in the set (S_1). The algorithm goes over these nodes in the second search level as described above. This search continues to all the levels of the search algorithm until all nodes are visited (possibly multiple times) and either acquire a fixed state and are added to the LDOI or their state will be left undetermined at the end of the algorithm. In Fig. 3, we illustrate this search to find the LDOI((sim )pl_1). The first search level is (S_1={)po_1, po_3(}); (sim )pl_1 is sufficient to deactivate po_3, but not po_1. As a result, (sim )po_3(in ) LDOI((sim )pl_1). This process continues until all levels are visited and at the end of the algorithm LDOI((sim )pl_1()={sim )po_3, (sim )pl_2, (sim )pl_3, (sim )pl_4, (sim )pl_5, (sim )po_1, (sim )po_2 (}).Figure 3Breadth first search of the interaction network to find the LDOI of a (set of) fixed note state(s) in Boolean threshold functions governing the dynamics of plant–pollinator networks. (a) An interaction network with five plants and 3 pollinators. (b) The breadth first search in the case of starting from the node state (sim )pl_1. The nodes with incoming edges from pl_1 make up (S_1={)po_1, po_3(}). The second sufficiency check is satisfied for node state (sim )po_3, as a result (sim )po_3(in ) LDOI((sim )pl_1). The same process is applied for node po_1, but none of the sufficiency checks are satisfied, so this node will be visited again later. The next level of the search consists of the nodes that have incident edges from (S_1), i.e., (S_2={)pl_2, pl_3, pl_4, pl_5(}). The second sufficiency check is satisfied for all of these nodes and they are all fixed to their inactive state in the LDOI((sim )pl_1). Lastly, we reach (S_3={)po_1, po_2(}). Node po_1 is reached again, and with both its positive regulators fixed to their inactive states the second sufficiency check is satisfied and node po_1 is fixed to its inactive state as well. The same holds for po_2 and hence LDOI((sim )pl_1()={sim )po_3, (sim )pl_2, (sim )pl_3, (sim )pl_4, (sim )pl_5, (sim )po_1, (sim )po_2 (}).Full size imageTo measure the accuracy of the simplification method originally introduced in28, we analyzed logical domains of influence in 6000 networks with 50–70 nodes. These networks are among the largest in our ensembles and have the most complex structures. We randomly selected (sets of) inactive node states, found their LDOIs using the Boolean threshold functions and the simplified Boolean functions, and compared the two resulting LDOIs. We used 8 single node states and 8 combinations of size 2 to 4 for each network. We found that in all cases the LDOI calculated using the simplified Boolean functions matches the LDOI calculated using the Boolean threshold functions.Next, we analyzed (sets of) active node states and their LDOIs in the same ensembles of networks. Similar to the previous analysis, we used 8 single node states and 8 combinations of size 2 to 4 for each network. Our analysis shows that in 77.1% of the cases the LDOI calculated using the simplified Boolean functions matches the LDOI calculated using the Boolean threshold functions. In 22% of the cases the LDOI calculated from the simplified Boolean functions contains the LDOI calculated from the threshold functions, and it also contains extra active node states, overestimating the LDOI by 57.5% on average. These additional members of the LDOI result from the fact that the simplified Boolean functions contain fewer negative regulators than the threshold functions. The guiding principle of the simplification method is that the probability of (H(x)=1) conserves the probability of each node having an active state across all the states it can have. In contrast, the probability of the propagation of the active state is not necessarily preserved and tends to be higher in the simplified Boolean model; thus the LDOI of the active node states is overestimated in some cases.In the rest of the cases (about 1%), the LDOI calculated from the simplified Boolean functions does not fully capture the LDOI calculated from the threshold functions. This again is caused by the sparsification of the negative edges in the simplified Boolean functions. In the threshold functions, the activation of 4 or more negative regulators of a target node combined with one active positive regulator is sufficient to deactivate the target node, i.e., there might be inactive node states in the LDOI of a set of active node states. However, some of these negative regulators drop in the simplified Boolean model and the inactive state of the target node is not necessarily in the LDOI of the set of active node states in the simplified case. This is the rare mechanism by which the simplified model might underestimate the influence of active node states on the rest of the network.In the following section we are interested in analyzing the effect of species extinction on the established community, i.e., we look at the LDOI of (sets of) inactive node states. Observing that the influence of extinction of species is measured correctly in the simplified Boolean models, we conclude that these models can be utilized to further analyze the process of extinction and its ecological implications.Stable motif based identification of species whose loss leads to cascading extinctionsEach stable motif or motif group can have multiple driver sets; stabilization of each driver set leads to the stabilization of the whole motif or motif group. In plant–pollinator interaction networks, the stable motifs either represent a sub-community (when the constituent nodes stabilize in their active states) or the simultaneous extinction of all species in the group (when the constituent nodes stabilize to their inactive states). Stabilization of the nodes in the driver set of an inactive stable motif results in stabilization of all the nodes in the stable motif to their inactive state, i.e., cascading extinction of the constituent species.The knowledge gained from stable motif analysis and the network of functional relationships offers insight into the cascading effect of an extinction that constitutes a driver set of an inactive stable motif. The magnitude of this effect depends on (i) the number of nodes that the inactive stable motif contains and (ii) the number of virtual nodes (including motifs and motif groups) corresponding to inactive species that are logically determined by the stabilization of the inactive stable motif.To investigate the role of stable motifs in the study of species extinction in plant–pollinator networks, we simulated extinctions that drive inactive stable motifs in 6000 networks with the sizes of 50–70 nodes. We considered driver sets of size 1, 2, or 3, and implemented them by fixing the corresponding node(s) to its (their) inactive state. As a point of comparison, we also performed a “control” analysis using the same networks with the same size of initial extinction; however, the candidates of initial extinction are inactive node states that do not drive stable motifs or motif groups. Based on the properties of the drivers of stable motifs, one expects that following the extinction of driver species, cascading extinctions of other species follow, while the same does not necessarily hold for non-driver species. As a result, we expect to observe greater damage to the original community when driver species become extinct.We assume that the “maximal richness community”—the community (attractor) in which the largest number of species managed to establish—is the subject of species extinction. This maximal richness community results from the stabilization of all active stable motifs. All other attractors that have some established species contain a subset of all active stable motifs and thus will contain a subset of the species of the maximal richness community. While for a generic Boolean model with multiple attractors one expects that a perturbed version of the model also has multiple attractors, this specific perturbation of a plant–pollinator model (namely, extinction of species in the maximal richness community) has a single attractor. We prove this by contradiction. Assume there are two separate attractors in the perturbed model, which means that there is at least one node that has opposite states in these two attractors. Note that this bi-stability is the result of the perturbation and not a property of the original system as the maximal richness community (an attractor) is the starting point for the introduced extinction. Specifically, the inactive state of the extinct node has to lead to the stabilization of another node to its active versus inactive states in the two separate attractors. The only case in which the stabilization of an inactive node state can result in the stabilization of an active node state is if there is a negative edge from the former to the latter in the interaction network after simplification. Since the Boolean function in 2 is inhibitor dominant, the negative regulators that remain in the Boolean model must be in their inactive states in the maximal richness attractor. As they are already inactive (extinct), they are not candidates for extinction. The only nodes that are candidates for extinction are the ones that positively regulate other nodes; perturbing the system by fixing these candidates to their inactive states cannot lead to the active state of a target node. In conclusion, bi-stability is not possible.We found the new attractor of the system given the (combination of) inactive node state(s) using the the functions percolate_and_remove_constants() and trap_spaces() from the pyboolnet Python package. We quantify the effects of the initial extinction(s) on the maximal richness attractor by the percentage change in the number of active species, which we call damage percentage. Note that this choice of maximal richness community as the reference and starting point allows us to detect the cascading extinctions following the initial damage.In Fig. 4 the left column plots show the average damage percentage caused by the extinction of 1 (top panel), 2 (middle panel), or 3 (bottom panel) species that represent driver sets of stable motifs and motif groups, while the right column plots illustrate the average damage percentage as a result of the extinction of 1, 2 or 3 species that represent non-driver nodes. Comparing the two columns, one can notice that stabilization of the driver sets of stable motifs and motif groups leads to considerably larger damage to the communities. This is due to the fact that stabilization of driver sets ensures the stabilization of entire inactive stable motifs and motif groups and hence ensures cascading extinctions. Comparing the plots in the left column, we see that the larger the driver sets are, the larger the damage to the community becomes. This is because larger driver sets are more likely to stabilize larger stable motifs and motif groups. This figure illustrates the significance of stable motifs and their driver sets in the study of species extinction in plant–pollinator communities.Figure 4Histogram plots illustrating the average percentage of the damage caused in an established community after the extinction of species. This analysis is performed over 6000 networks with the size of 50–70 nodes. To study the extinction of species we started from the maximal richness community, then we fixed the nodes that correspond to the focal species to the their inactive states. The original extinctions are excluded from the damage percentages. The left column plots show the average damage percentage caused to the maximal richness community by the extinction of a driver set of size 1 (top), 2 (middle), or 3 (bottom) of an inactive stable motif or motif group. For each network, we determined all the relevant driver sets of one stable motif or motif group, we performed the extinction and calculated the resulting damage, then we calculated the average damage percentage over all data points collected for the same network. The right column plots show the average damage percentage caused to the maximal richness community by the extinction of 1 (top), 2 (middle), and 3 (bottom) non-driver, randomly chosen nodes. Each time a randomly selected combination of non-driver nodes were the subject of simultaneous extinction until all combinations are explored and then we calculated the average damage percentage over all data points collected for each network. The number of networks that qualify for each of these 6 categories differ (e.g., some networks have a stable motif with a driver set of size 2 but no stable motif with a driver set of size 3). In the left column 5529, 3212, and 1980 networks and in the right column 5779, 5626, and 5423 networks qualified respectively. The red lines represent the mean value of all the presented data points in each plot.Full size imageIn Fig. 4 left column, the full driver set of one inactive stable motif or motif group was stabilized. However, the species that become extinct might only contain a subset of a driver set of a stable motif or motif group, i.e., they only stabilize a subset of the inactive node states in the stable motif or motif group. We compare the extinction effect caused by the stabilization of a full driver set of four nodes with the effect of the extinction of four nodes that contain a partial driver set in Fig. 5 using the batch of the largest networks in this study, i.e, the batch that contains networks with 30 nodes representing plant species and 40 nodes representing pollinator species. This choice is due to the fact that the existence of stable motifs and motif groups having a driver set of four node states is highly probable in larger networks. As expected, the stabilization of the complete driver set leads to greater damage. Stabilization of the same number of nodes that contain a partial driver set leads to significantly less damage and species loss in the community; the median damage percentage in the case of stabilization of partial driver sets is 22.6% while it is 69.2% in the case of stabilization of the full driver sets. We also note that damage of more than 90% occurs rarely and is only possible when a full driver set is stabilized (see Fig. 5 right plot). This suggests that the motif groups that lead to total extinction tend to have a driver set with more than four nodes; in other words, only the simultaneous extinction of five or more species would lead to total community collapse.Figure 5Histogram plots illustrating the average percentage of the damage caused in an established community after the extinction of species. This analysis is performed over 1000 networks with the size of 70 nodes (30 nodes representing plant species and 40 nodes representing pollinator species). The original extinctions are excluded from the damage percentages. The left plot shows the average damage percentage caused to the maximal richness community by the extinction of 2 species that are a subset of the 4-node driver set of an inactive stable motif or motif group plus 2 randomly selected non-driver species. The right plot shows the damage percentage caused to the maximal richness community by the extinction of 4-node driver sets of the same inactive stable motifs and motif groups. Each time the driver set of one stable motif or motif group was the subject of extinction and we calculated the average damage percentage over all data points collected for each network. 295 networks qualified for this analysis.Full size imageMotif driver set analysis outperforms structural measures in identifying keystone speciesThe literature on ecological networks offers multiple measures that reflect the importance of each species for community stability. One family of such measures is centrality (quantified by the network measures degree centrality and betweenness centrality). Previous studies45,46 have shown that species (nodes) with higher centrality scores are keystone species in ecological communities (i.e., species whose loss would dramatically change or even destroy the community). The nodes with highest in-degree centrality (such as pl_2 in Fig. 6a) represent generalist species that can receive beneficial interactions from multiple sources and survive. The nodes with highest betweenness centrality (such as pl_2 and po_2 in Fig. 6a) represent species that act as connectors and help the community survive. We find that high centrality corresponds to specific patterns in the expanded network: the inactive state of generalist or connector species is often the driver of a cascading extinction. Indeed, stable motif analysis of the expanded network in Fig. 6b confirms that there is an inactive stable motif (highlighted with grey) driven by the minimal set {(sim )pl_2}. The fact that node pl_2 is a stable motif driver means that in the case of the extinction of pl_2 the whole community collapses.To compare the effectiveness of stable motif analysis to the effectiveness of the more studied structural measures to identify keystone species, we performed an analysis similar to the previous section. We compared the magnitude of cascading extinctions in the case of extinction of stable motif driver nodes and of nodes with high values of previously introduced structural importance measures. Specifically, we used node betweenness centrality, node contribution to nestedness47, and mutualistic species rank (MusRank)22 to find crucial species based on their structural properties. For more details on definition and adaptation of these two measures see “Methods”. In this analysis, we used each measure to target species in the simplified Boolean models as follows:

1.

Betweenness centrality: The 10% of species with the highest betweenness centrality are chosen to be candidates for extinction.

2.

Node contribution to nestedness: The species with the most interactions tend to contribute the least to the community nestedness. Targeting them most likely leads to a faster community collapse48. As a result, 10% of species with the lowest contribution to network nestedness are chosen to be candidates for extinction. For more details on this measure, please see “Methods”.

3.

Pollinator MusRank: The pollinator species with the highest MusRank importance are more likely to interact with multiple plants, so the 10% of pollinator species with the highest importance are chosen to be candidates for extinction. For more details on this measure, please see “Methods”.

4.

Plant MusRank: The plant species with the highest MusRank importance are more likely to interact with multiple pollinators, so the 10% of plant species with the highest importance are chosen to be candidates for extinction.

Figure 7 illustrates the results of this analysis in 6000 networks with 50–70 nodes. In each network the 1-node, 2-node, and 3-node driver sets of inactive stable motifs are identified and made extinct. In the same networks 10% of nodes based on betweenness centrality, node contribution to nestedness, and node MusRank score were chosen to be candidates for extinction. To match the “driver set” data, all choices of 1, 2, or 3 nodes in these sets were explored and the damage was averaged over each extinction size for each network. We observe the cascading extinction and calculate the damage percentage relative to the maximal richness attractor. The plot represents the collective data over all initial simultaneous extinction sizes of 1, 2, and 3 species.Comparing the four methods, one notices that the histograms acquired using stable motif driver sets, node betweenness centrality, and node contribution to nestedness are very similar, showing a peak for the 10–20% bin of the damage, and a long tail that reaches a damage percentage of 80–100%. The MusRank score performs less well in identifying the crucial species. Also, the frequency of the higher damage percentages shows that node contribution to nestedness is the closest to the “driver set” method in identifying nodes whose extinction causes the collapse of the whole community, making it the best structural measure out of the three. Nevertheless, the driver set method finds keystone species that cannot be identified via structural measures, as the corresponding damage percentage histogram has the most prominent tail at the right edge of the panel. Indeed, stable motif driver sets identified 82%, 80%, and 546% more species whose extinction leads to 60% or higher damage to the community when compared to betweenness centrality, node nestedness, and node MusRank score based methods respectively.The reason for the higher effectiveness of driver set analysis is illustrated in Fig. 8 in which the MusRank score and node contribution to nestedness are calculated for two example networks. One can see how these two measures might incorrectly identify less vital species. In the left column of Fig. 8, MusRank identifies the node po_2, highlighted with green, as the most important species. However, this node does not have any outgoing edges; its extinction does not lead to any cascading extinction. The inability of the MusRank score to consider the direction of edges causes such misidentification. In the right column, the three nodes highlighted with yellow have the lowest contributions to network nestedness. The expanded network shows that these three nodes together are not able to cause full community collapse, while the three-node driver set of the inactive stable motif can. Since the nestedness definition depends on the number of mutual interactions, it might fail to identify some of the keystone nodes that are necessary to the stability of the community (for more details on node nestedness see “Methods”).Previously it was shown that identifying the stable motifs and their driver sets can successfully steer the system toward a desired attractor or away from unwanted ones37,38,43. Stable motif analysis of the Boolean model offers insight into the dynamical trajectories of the system; hence control strategies can be developed accordingly. In the next section we use stable motif driver sets to suggest control methods and analyze their efficiency.Figure 6Generalist species in the interaction network and the expanded network. (a) A simplified network consisting of 3 plant and 3 pollinator species. pl_2 is a generalist species, i.e., it has two incoming edges indicating that it can survive on either of its sources of pollination, po_1 or po_2. The expanded network in (b) illustrates that the stabilization of the grey stable motif stabilizes all the nodes to their inactive states, and hence causes full community collapse. (sim )pl_2 is the minimal driver set of the grey stable motif, consistent with the strong damage induced by the loss of a generalist species.Full size imageFigure 7Histogram plots illustrating the performance of driver set analysis versus structural measures in identifying keystone species. The analysis was done on 6000 networks with sizes of 50–70 nodes. The starting point is the maximal richness community, i.e., the attractor in which the most species establish. For each network 1, 2, and 3 node(s) were selected and simultaneously fixed to their inactive states. After the cascading damage the new attractor is compared to the maximal richness attractor to calculate the damage percentage. The structural measures—betweenness centrality, node nestedness contribution, and node MusRank score—were calculated for all nodes in each network; the top 10% according to the relevant ordering were candidates to being fixed to their inactive states. The network IDs were matched, i.e., only the networks that had candidate nodes according to all four measures for each extinction size are included in this plot. The total number of data points is 6360. The red solid lines represent the mean and the black dashed lines represent the median over all data points in each plot.Full size imageFigure 8Networks illustrating examples of when structural measures fail to identify keystone species. In both columns simplified networks consisting of 3 plant and 3 pollinator species are presented. The MusRank is calculated for all the nodes in the network in the left column and denoted in the node labels. The expanded network corresponding to this network is shown below. Node contribution to network nestedness is calculated for all the nodes in the network in the right column and denoted in the node labels. Similarly the expanded network that correspond to it is shown below. Note that these two networks have different edges. In the left column MusRank score identifies node po_2, highlighted with green, as the most important, while the expanded network shows that the extinction of po_2 does not cause any further damage to the community, as this node has no outgoing edges. This is due to the fact that MusRank calculation process fails to consider the directed network and replaces all the directed edges with undirected ones. The MusRank score does not identify po_3 as a crucial species; however, virtual node (sim )po_3, outlined with black in the expanded network is a driver of a stable motif that has all other nodes in its LDOI; the extinction of po_3 leads to full community collapse. In the right column, the nodes highlighted with yellow (pl_2, pl_3, and po_2) have the lowest node contribution to nestedness, which predicts that these nodes are likely crucial to the stability of the community. Analyzing the expanded network, one can see that these three nodes together are not able to drive the inactive stable motif highlighted with teal. The minimal driver set for this stable motif, outlined with black, consists of {(sim )po_1, (sim )po_2, (sim )po_3}; together these nodes drive the inactive stable motif and cause full community collapse. The nestedness-based measure was not able to capture the significance of nodes po2 and po_3.Full size imageDamage mitigation measures and strategies for endangered communitiesThere are two substantial questions related to managing the damage induced by species extinction: (1) How can one prevent the damage as much as possible? (2) Once the damage happens, the reintroduction of which species can restore the community and to what extent? In this section we aim to answer these questions in the context of the Campbell et al. model, implementing stable motif based network control. This analysis can inform agricultural and ecological strategies employed to prevent and mitigate damage.Damage preventionOne of the most important questions in ecology is what strategies to use so that we can prevent and avert extinction damage to the community. In this section we analyze how the knowledge from stable motif analysis and driver sets can be implemented to minimize the effect of extinction of keystone species in case of limited resources. Each attractor of the original system can have multiple control sets; stabilizing the node states in each control set ensures that the system reaches that specific attractor. The same information from the attractor control sets can be implemented to prevent the system from converging into unwanted attractors. Zañudo et al. illustrated that by blocking (not allowing to stabilize) the stable motifs that lead to the unwanted attractors, one can decrease the probability (sometimes to zero) that the system arrives in those attractors38. In order to block an attractor, the control sets of that attractor are identified and the negations of the node states in the control sets are externally imposed. This approach eliminates the undesired attractor; however, new attractors might form that are similar to the eliminated attractor. Campbell et al. showed that in order to avoid such new attractors one needs to block the parent motif, which in this case is the largest strongly connected subgraph of the expanded network that contains the inactive virtual nodes44. Here, we investigate how stable motif blocking based attractor control can identify the species whose preservation would offer the highest benefit in avoiding catastrophic damage to the community. This information would aid the development of management strategies in plant–pollinator communities.To avoid all attractors that lead to some degree of species extinction, one needs to block all the driver sets of all inactive stable motifs and motif groups in a given network. Implementing this in 100 randomly selected networks with 25 plant and 25 pollinator nodes, we found that 45.6% of the species in the maximal richness community need to be kept (prevented from extinction) to ensure the lack of cascading extinctions. Given that management resources are usually limited, active monitoring and conservation of almost half of the species in a community seems costly and impractical. Hence, we set a more feasible goal of identifying and blocking the driver set(s) of the largest inactive stable motif or motif group in each network. The same 100 networks containing 50 nodes are the subject of analysis in this section. The reason for performing the analysis in a relatively limited ensemble is that it involves the identification of all driver sets of the largest inactive stable motif or motif group, which is computationally expensive. For each network, the driver set of the largest inactive stable motif or motif group (which corresponds to the extinction of all the species in that group) is identified and blocked (that is, the corresponding species are not allowed to go extinct). Then the same number of species as in the driver set of that stable motif or motif group are selected and stabilized to their inactive state. We considered all combinations of node extinctions outside the blocked subset, calculated the damage percentage relative to the maximal richness community, and then averaged over all data points for each network. As a control, we repeated the analysis without blocking; the size of the initial extinction is the same as in the previous analysis for consistency.Figure 9 shows the result of the analysis described above for 100 networks. The left box and whiskers plot illustrates the damage percentage relative to the maximal richness community when the blocking feature is activated, while the right box and whiskers plot shows the damage percentage relative to the maximal richness community when the blocking is disabled. The average and median damage percentages are 14.96% and 13.04% respectively when the largest inactive stable motif or motif group was blocked and 24.73% and 20.38% when it was not. This (sim )10% difference in the average between the two sets of results, as well as the fewer cases of high-damage outliers in the left plot, demonstrates that by preventing the extinction of species identified by stable motif analysis, one can prevent catastrophic community damage considerably.To estimate the fraction of species that would need to be monitored to prevent their extinction, we compared the size of the maximal richness attractor and the size of the driver set of the largest stable motif. The maximal richness community represents an average of 32% of the original species pool, approximately 15 out of 50 species. The driver sets of the largest stable motifs had an average size of 2.5 node states over all 100 networks, i.e., about 16.6% of the maximal richness community. In ecological terms, given limited resources, the information gained from stable motif driver sets can help direct the conservation efforts toward the keystone species that play a key role in maintaining the rest of the community in a cost-effective manner.Figure 9Box plots comparing the damage communities face if the largest inactive stable motif or motif group is completely blocked, i.e., all the drivers of this inactive stable motif or motif group are prevented from stabilizing versus if the same stable motif or motif group is allowed to stabilize. This analysis was performed over 100 randomly selected networks that contain 25 plant and 25 pollinator nodes. All the driver sets of an inactive stable motif or motif group are identified. From left to right the box and whiskers plots show the average damage percentage relative to the maximal richness community if the largest inactive stable motif is blocked and the same quantity if the largest stable motif or motif group is not blocked respectively. For the left box and whiskers plot, all combinations of inactive node states except the driver sets are considered, and for the right box and whiskers plot all combinations are explored. Due to the computational complexity caused by combinatorial explosion, this analysis was performed over 100 randomly selected 50-node networks.Full size imageRestoration of a group of speciesAlthough human preservation efforts have been directed toward community conservation, there are many industrial activities that lead to ecosystem degradation. Ecologists are interested in developing restoration strategies to be deployed after a stable community is hit by catastrophic damage to recover biodiversity and the ecosystem functions it provides49. Here we propose that stable motif analysis and the driver sets identified from the expanded network can give insight into restoration measures. While we examined the inactive stable motifs in the study of species extinction, here we focus on the active stable motifs as our goal is to restore as much biodiversity as possible.Several network measures have been proposed to identify the species that if re-introduced would restore the community considerably. Two of the most studied algorithms include maximising functional complementarity (or diversity) and maximising functional redundancy50. The first strategy targets the restoration of the species that provide as many functions to the ecosystem as possible; this approach results in a community that has a maximal number of functions provided by different groups of species. Alternatively, maximising the functional redundancy yields a community in which several species perform the same function. While this resultant community might have a limited number of functions, it is robust. Both of these community restoration approaches have been studied extensively (e.g. see21).We hypothesize that restoring the species that constitute driver sets of active stable motifs can help maximise the number of species post-restoration. Since there is evidence that functional diversity correlates with the number of species in the community51, we compare the post-restoration communities identified by stable motif driving with the functional diversity maximisation approach. As discussed in section LDOI in the Boolean threshold model, the Boolean simplification of the threshold functions leads to an overestimation of the LDOI of active node states (compared to the original threshold functions) in some networks. We evaluate the negative effects of this overestimation by checking the effectiveness of the restored species in the original threshold model.The same 6000 networks we examined in the last section were the subject of this analysis. To create an unbiased initial community, we create the damaged communities by eliminating the same number of species from the maximal richness community as the number that will be restored. We identify the inactive stable motif or motif group with the driver set size of 1, 2, or 3 node states that causes the most damage to the maximal richness community. We then eliminate the species corresponding to this driver set to reach the most damaged community for the given size of the initial extinction. This community is the starting point for two analyses. In the stable motif driving approach we stabilized an active stable motif that has a driver set of the same size as the initial extinction to reach a post-restoration community and calculated the percentage of the extinct species that were restored. In the functional diversity maximization based approach we re-introduced the same number of species selected from the to 10% of species in terms of their contribution to functional diversity.To calculate the functional diversity of a community one needs to (1) define and construct a trait matrix, (2) determine the distance (trait dissimilarity) of pairs of species, (3) perform hierarchical clustering based on the distances to create a dendrogram, and (4) calculate the total branch length of the dendrogram, i.e., the sum of the length of all paths51,52. Petchey et al. argued that resource-use traits among plant and pollinator species can be used to classify the organisms into separate functional groups53 and Devoto et al. proposed the use of the adjacency matrix based on the interaction network as the trait matrix21. In this study we do the same and implement the bipartite adjacency matrix to construct the distance matrix.Since the networks of the Campbell et al. model are directed, we modify the algorithm in that we have two separate adjacency matrices, one denoting the edges incoming to plant species and the other denoting the edges incoming to pollinator species. The hierarchical clustering algorithm is then run on each of these matrices separately, resulting in a dendrogram for each adjacency matrix. If extinction occurs in a community, the functional diversity of the survived community can be determined by calculating the total branch length of the subset of the dendrogram that includes only the survived species. The restoration strategy using this method is to re-introduce the nodes whose branches add the most to the total branch length of this subset, i.e., maximise the functional diversity of the survived community54. For more details see “Methods”.In each network, the percentage of the extinct species that were restored was calculated and averaged over all data points for each restoration size and each network. Figure 10 illustrates the results of this investigation. Applied to the simplified Boolean model, the median restoration percentage in the case of active stable motif driver set method (blue plot) is 80%. The functional diversity maximization strategy to restoration (yellow plot) yields a lower median restoration percentage, 73%, as well as a large number of low-restoration outliers. Although one might argue that identifying beneficial species using the functional diversity maximization strategy works well, the higher percentage of the cases of 80–100% restoration in case of the active stable motif driver set analysis indicates that the latter identifies some of the most effective restorative species that are not identified via the former method. As in a minority of cases the simplified Boolean model overestimates the positive impact of the sustained presence of a species (see section LDOI in the Boolean threshold model), we sought to verify the effectiveness of the predicted restoration candidates in the original threshold model. The blue (respectively, yellow) box and whiskers plot on the right represents the restoration percentages of the same species as in the left blue (respectively, yellow) plot when these species are restored in the threshold model. The median of the right blue plot is 70%, while the median of the right yellow is 63%, preserving the advantage of the stable motif driver sets. We conclude that although the simplified Boolean model overestimates the restoration effectiveness of certain driver sets (visible in the fact that the lower whisker of the blue plot on the right goes well below the lower whisker of the blue plot on the left), stable motif driver sets are more effective in both comparisons.Figure 10Box and whiskers plots illustrating the average percentage of the extinct species that are restored following the stable motif driver set restoration strategy (blue) versus the functional diversity based approach (yellow). This analysis is performed over 6000 networks with sizes of 50–70 nodes. Starting from the maximal richness community, for each network one inactive stable motif with a driver set of 1, 2 or 3 nodes was stabilized to reach a new damaged community. This task was performed until the community with the most extinct species was identified. This is the community we set as the starting point for the restoration process using both methods. The pair on the left represents the two methods applied to the simplified Boolean model. For both methods we identified 1, 2, or 3 influential nodes for community restoration and we calculated the percentage of the extinct species that could be restored. The pair on the right represents restoring the same species identified by each method in the previous analysis in the original threshold model. In all analyses the community restoration percentage was averaged over all combinations of the same size, for each network and each method. The IDs of all networks are matched.Full size imageCommunity restoration via attractor controlAs illustrated in section “Restoration of a group of species”, stable motif analysis identifies promising and cost-effective group restoration strategies. In this section we aim to go further and identify interventions that can maximally restore a community. Previous stable motif based network control methods37,38,55 require a search for the smallest set of node states to control the system once the stable motif stabilization trajectories are identified. This smallest set may not contain a node from each stable motif in the sequence. In this work, however, we know that each stable motif or motif group needs to be controlled individually28 because the stabilization of none of the motifs results in the stabilization of another. As a result, the control set of each attractor is the same as the union of the driver sets of all members in the consistent combination corresponding to that attractor.In this section we examined this attractor control method by setting the communities with 70% or more of the species in the maximal richness community as the target, i.e., the attractors that have 70% of the species in the maximal richness community are assumed to be the desired attractors. We then recorded the size of the minimal control set needed to achieve each of these attractors. Note that stabilizing each of these control sets guarantees that the system reaches the corresponding attractor38.For this section, we analyzed 6000 networks that have 50–70 nodes. Figure 11 represents box-and-whiskers plots of the size of the minimal set of species that need to be restored, where the target community sizes are classified into three groups based on the percentage of the species relative to the maximal richness attractor. One can see that in half of the cases, the restoration of either 1 or 2 species manages to restore more than 70% of the maximal richness community. The largest set has 8 species that need to be restored; however, this data point is an outlier. As illustrated, driver set analysis and stable motif based attractor control can efficiently identify the species that play an influential restorative role and suggest management strategies that are effective at the scale of the whole community. To assess the impact of the LDOI inflation on this result, we used the restoration candidates identified by control sets of the attractors of the Boolean model in the threshold functions of a subset of networks. The results of comparing the restoration percentage is shown in Fig. 14. The first quartile, median and third quartile values are 78.26%, 86.6%, and 100% for the simplified Boolean models and 43.78%, 72.41%, and 85.71% for the threshold model.To further compare the results of restoration obtained from the two models we sorted the species in the order of their contribution to community restoration following a catastrophic damage. We randomly selected 100 of the largest (70-node) networks, which have the highest probability of a discrepancy between the threshold functions and the simplified Boolean model. In 72% of the cases the two rankings matched completely, and in the majority of the remaining cases only one species was misplaced in the simplified Boolean model-based ranking. To conclude, there is a significant advantage to the implementation of the simplified Boolean model and the drawback can be addressed by a follow-up checking on the original threshold functions.Figure 11The number of species that need to be restored to save 70% of more of the species in the maximal richness community. In this analysis 6000 networks with 50–70 nodes were the subject. For each networks all the attractors that have 70% or more of the species in the maximal richness attractor are identified and set to be the target attractors. The control set of these attractors are then classified into three groups based on the percentage as illustrated in the figure. From left to right, the box and whiskers represent the size of the control set of attractors that have 70–80%, 80–90%, and 90–100% of the species in the maximal richness attractor respectively.Full size image More