Ecology

Genome’s collection and phylogenetic analysisThe study examined the genomes of 139 isolates, 61 of environmental samples (ENV) and 78 clinical (CLI) (Supplementary Table 1, Supplementary Fig. 1), with origin in 21 countries: USA (23/139, 17%), UK, Portugal and Spain (each 15/139, 33%), China (14/139, 10%), Germany (13/139, 9%), Thailand (11/139, 8%) and other countries (each  More

Backman, C. R. The worlds of medieval Europe. (Oxford University Press, 2003).Brown, P. The World of Late Antiquity. From Marcus Aurelius to Muhammad. (Thames & Hudson, 1971).Brown, P. The Making of Late Antiquity. (Harvard University Press, 1978).Holmes, G. The Oxford History of Medieval Europe. (Oxford University Press, 2002).Hoffmann, R. C. An environmental history of medieval Europe. (Cambridge University Press, 2014).Ward-Perkins, B. The Fall of Rome: And the End of Civilization. (Oxford University Press, 2006).Wickham, C. Framing the Early Middle Ages: Europe and the Mediterranean, 400–800. (Oxford University Press, 2006).Wickham, C. The inheritance of Rome: a history of Europe from 400 to 1000. (Penguin Books, 2010).Wickham, C. Medieval Europe. (Yale University Press, 2016).Halsall, G. The sources and their interpretations. In The New Cambridge Medieval History, Volume 1 c.500–c.700 (ed. Fouracre, P.) 56–92 (Cambridge University Press, 2005).Alexander, M. M., Gerrard, C. M., Gutiérrez, A. & Millard, A. R. Diet, society, and economy in late medieval Spain: Stable isotope evidence from Muslims and Christians from Gandía, Valencia. Am. J. Phys. Anthropol. 156, 263–273 (2015).PubMed 
Article 

Google Scholar 
Alexander, M. M., Gutiérrez, A., Millard, A. R., Richards, M. P. & Gerrard, C. M. Economic and socio-cultural consequences of changing political rule on human and faunal diets in medieval Valencia (c. fifth–fifteenth century AD) as evidenced by stable isotopes. Archaeol. Anthropol. Sci. 11, 3875–3893 (2019).Article 

Google Scholar 
Dotsika, E., Michael, D. E., Iliadis, E., Karalis, P. & Diamantopoulos, G. Isotopic reconstruction of diet in Medieval Thebes (Greece). J. Archaeol. Sci. Rep. 22, 482–491 (2018).
Google Scholar 
Francisci, G. et al. Strontium and oxygen isotopes as indicators of Longobards mobility in Italy: an investigation at Povegliano Veronese. Sci. Rep. 10, 11678 (2020).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Guede, I. et al. Isotope analyses to explore diet and mobility in a medieval Muslim population at Tauste (NE Spain). PLOS ONE 12, e0176572 (2017).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Hakenbeck, S., McManus, E., Geisler, H., Grupe, G. & O’Connell, T. Diet and mobility in Early Medieval Bavaria: A study of carbon and nitrogen stable isotopes. Am. J. Phys. Anthropol. 143, 235–249 (2010).PubMed 
Article 

Google Scholar 
Hughes, S. S., Millard, A. R., Chenery, C. A., Nowell, G. & Pearson, D. G. Isotopic analysis of burials from the early Anglo-Saxon cemetery at Eastbourne, Sussex, U.K. J. Archaeol. Sci. Rep. 19, 513–525 (2018).
Google Scholar 
Kaupová, S. D. et al. Diet in transitory society: isotopic analysis of medieval population of Central Europe (ninth–eleventh century AD, Czech Republic). Archaeol. Anthropol. Sci. 10, 923–942 (2018).Article 

Google Scholar 
Lamb, A. L., Evans, J., Buckley, R. & Appleby, J. Multi-isotope analysis demonstrates significant lifestyle changes in King Richard III. J. Archaeol. Sci. 50, 559–565 (2014).CAS 
Article 

Google Scholar 
López-Costas, O. & Müldner, G. Fringes of the empire: Diet and cultural change at the Roman to post-Roman transition in NW Iberia. Am. J. Phys. Anthropol. 161, 141–154 (2016).Article 

Google Scholar 
Lubritto, C. et al. New Dietary Evidence on Medieval Rural Communities of the Basque Country (Spain) and Its Surroundings from Carbon and Nitrogen Stable Isotope Analyses: Social Insights, Diachronic Changes and Geographic Comparison: Palaeodietary Evidence on Medieval Basque Rural Communities. Int. J. Osteoarchaeol. 27, 984–1002 (2017).Article 

Google Scholar 
MacRoberts, R. A. et al. Diet and mobility during the Christian conquest of Iberia: The multi-isotopic investigation of a 12th–13th century military order in Évora. Portugal. J. Archaeol. Sci. Rep. 30, 102210 (2020).
Google Scholar 
Miclon, V. et al. Social characterization of the medieval and modern population from Joué-lès-Tours (France): Contribution of oral health and diet. BMSAP 31, 77–92 (2017).Article 

Google Scholar 
Mion, L. et al. The influence of religious identity and socio-economic status on diet over time, an example from medieval France. Archaeol. Anthropol. Sci. 11, 3309–3327 (2019).Article 

Google Scholar 
Müldner, G. & Richards, M. P. Stable isotope evidence for 1500 years of human diet at the city of York, UK. Am. J. Phys. Anthropol. 133, 682–697 (2007).PubMed 
Article 

Google Scholar 
Price, T. D., Peets, J., Allmäe, R., Maldre, L. & Oras, E. Isotopic provenancing of the Salme ship burials in Pre-Viking Age Estonia. Antiquity 90, 1022–1037 (2016).Article 

Google Scholar 
Tafuri, M. A., Goude, G. & Manzi, G. Isotopic evidence of diet variation at the transition between classical and post-classical times in Central Italy. J. Archaeol. Sci. Rep. 21, 496–503 (2018).
Google Scholar 
Torino, M. et al. Convento di San Francesco a Folloni: the function of a Medieval Franciscan Friary seen through the burials. Herit. Sci. 3, 27 (2015).Article 
CAS 

Google Scholar 
Toso, A., Gaspar, S. Banha da Silva, R., Garcia, S. J. & Alexander, M. High status diet and health in Medieval Lisbon: a combined isotopic and osteological analysis of the Islamic population from São Jorge Castle, Portugal. Archaeol. Anthropol. Sci. 11, 3699–3716 (2019).Article 

Google Scholar 
Barrett, J. H. et al. Interpreting the expansion of sea fishing in medieval Europe using stable isotope analysis of archaeological cod bones. J. Archaeol. Sci. 38, 1516–1524 (2011).Article 

Google Scholar 
Dreslerová, D. et al. Maintaining soil productivity as the key factor in European prehistoric and Medieval farming. J. Archaeol. Sci. Rep. 35, 102633 (2021).
Google Scholar 
Evans, J., Tatham, S., Chenery, S. R. & Chenery, C. A. Anglo-Saxon animal husbandry techniques revealed through isotope and chemical variations in cattle teeth. Appl. Geochem. 22, 1994–2005 (2007).ADS 
CAS 
Article 

Google Scholar 
Fisher, A. & Thomas, R. Isotopic and zooarchaeological investigation of later medieval and post-medieval cattle husbandry at Dudley Castle, West Midlands. Environ. Archaeol. 17, 151–167 (2012).Article 

Google Scholar 
Halley, D. J. & Rosvold, J. Stable isotope analysis and variation in medieval domestic pig husbandry practices in northwest Europe: absence of evidence for a purely herbivorous diet. J. Archaeol. Sci. 49, 1–5 (2014).CAS 
Article 

Google Scholar 
Hamerow, H. et al. An Integrated Bioarchaeological Approach to the Medieval ‘Agricultural Revolution’: A Case Study from Stafford, England, c. AD 800–1200. Eur. J. Archaeol. 23, 585–609 (2020).Article 

Google Scholar 
Hamilton, J. & Thomas, R. Pannage, Pulses and Pigs: Isotopic and Zooarchaeological Evidence for Changing Pig Management Practices in Later Medieval England. Mediev. Archaeol. 56, 234–259 (2012).Article 

Google Scholar 
Hammond, C. & O’Connor, T. Pig diet in medieval York: carbon and nitrogen stable isotopes. Archaeol. Anthropol. Sci. 5, 123–127 (2013).Article 

Google Scholar 
Kovačiková, L. et al. Pig-Breeding Management in the Early Medieval Stronghold at Mikulčice (Eighth–Ninth Centuries, Czech Republic). Environ. Archaeol. 1–15, https://doi.org/10.1080/14614103.2020.1782583 (2020).Lahtinen, M. Isotopic Evidence for Environmental Adaptation in Medieval Iin Hamina, Northern Finland. Radiocarbon 59, 1117–1131 (2017).CAS 
Article 

Google Scholar 
Müldner, G., Britton, K. & Ervynck, A. Inferring animal husbandry strategies in coastal zones through stable isotope analysis: new evidence from the Flemish coastal plain (Belgium, 1st–15th century AD). J. Archaeol. Sci. 41, 322–332 (2014).Article 

Google Scholar 
Orton, D. C. et al. Stable Isotope Evidence for Late Medieval (14th–15th C) Origins of the Eastern Baltic Cod (Gadus morhua) Fishery. PLoS ONE 6, e27568 (2011).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Reitsema, L. J., Kozłowski, T. & Makowiecki, D. Human–environment interactions in medieval Poland: a perspective from the analysis of faunal stable isotope ratios. J. Archaeol. Sci. 40, 3636–3646 (2013).CAS 
Article 

Google Scholar 
Sirignano, C. et al. Animal husbandry during Early and High Middle Ages in the Basque Country (Spain). Quat. Int. 346, 138–148 (2014).Article 

Google Scholar 
Vogel, J. C. & Van Der Merwe, N. J. Isotopic Evidence for Early Maize Cultivation in New York State. Am. Antiq. 42, 238–242 (1977).CAS 
Article 

Google Scholar 
Van Der Merwe, N. J. & Vogel, J. C. 13C Content of human collagen as a measure of prehistoric diet in woodland North America. Nature 276, 815–816 (1978).ADS 
PubMed 
Article 

Google Scholar 
Leng, M. J. Isotopes in Palaeoenvironmental Research. Isotopes in Palaeoenvironmental Research (Springer, 2006).Meier-Augenstein, W. Stable Isotope Forensics: An Introduction to the Forensic Application of Stable Isotope Analysis. (Wiley, 2011).Archaeological Science: An Introduction. (Cambridge University Press, 2020).Fiorentino, G., Ferrio, J. P., Bogaard, A., Araus, J. L. & Riehl, S. Stable isotopes in archaeobotanical research. Veg. Hist. Archaeobotany 24, 215–227 (2015).Article 

Google Scholar 
Hedges, R. E. M., Stevens, R. E. & Richards Michael. P. Bone as a stable isotope archive for local climatic information. Quat. Sci. Rev. 23, 959–965 (2004).ADS 
Article 

Google Scholar 
Lahtinen, M., Arppe, L. & Nowell, G. Source of strontium in archaeological mobility studies—marine diet contribution to the isotopic composition. Archaeol. Anthropol. Sci. 13, 1 (2021).Article 

Google Scholar 
Lee-Thorp, J. A. On Isotopes and Old Bones. Archaeometry 50, 925–950 (2008).CAS 
Article 

Google Scholar 
Lightfoot, E. & O’Connell, T. C. On the Use of Biomineral Oxygen Isotope Data to Identify Human Migrants in the Archaeological Record: Intra-Sample Variation, Statistical Methods and Geographical Considerations. PLOS ONE 11, e0153850 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Makarewicz, C. A. Stable isotopes in pastoralist archaeology as indicators of diet, mobility, and animal husbandry practices. in Isotopic Investigations of Pastoralism in Prehistory (eds. Ventresca Miller, A. & Makarewicz, C. A.) (Routledge, 2017).Pederzani, S. & Britton, K. Oxygen isotopes in bioarchaeology: Principles and applications, challenges and opportunities. Earth-Sci. Rev. 188, 77–107 (2019).ADS 
CAS 
Article 

Google Scholar 
Styring, A. K. et al. Disentangling the effect of farming practice from aridity on crop stable isotope values: A present-day model from Morocco and its application to early farming sites in the eastern Mediterranean. Anthr. Rev. 3, 2–22 (2016).
Google Scholar 
Szpak, P. Complexities of nitrogen isotope biogeochemistry in plant-soil systems: implications for the study of ancient agricultural and animal management practices. Front. Plant Sci. 5 (2014).Roberts, P. et al. Calling all archaeologists: guidelines for terminology, methodology, data handling, and reporting when undertaking and reviewing stable isotope applications in archaeology. Rapid Commun. Mass Spectrom. 32, 361–372 (2018).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Cubas, M. et al. Latitudinal gradient in dairy production with the introduction of farming in Atlantic Europe. Nat. Commun. 11, 2036 (2020).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wilkin, S. et al. Economic Diversification Supported the Growth of Mongolia’s Nomadic Empires. Sci. Rep. 10, 3916 (2020).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wang, X. et al. The Circulation of Ancient Animal Resources Across the Yellow River Basin: A Preliminary Bayesian Re-evaluation of Sr Isotope Data From the Early Neolithic to the Western Zhou Dynasty. Front. Ecol. Evol. 9, 16 (2021).ADS 
CAS 

Google Scholar 
Leggett, S., Rose, A. & Praet, E. & Le Roux, P. Multi-tissue and multi-isotope (δ13C, δ15N, δ18O and 87/86Sr) data for early medieval human and animal palaeoecology. Ecology 102, e03349 (2021).PubMed 
Article 

Google Scholar 
Mallet, S. & Stansbie, D. Substance and Subsistence. in English Landscapes and Identities. Investigating Landscape Change from 1500 BC to AD 1086 (eds. Gosden, C. & Green, C.) (Oxford University Press, 2021).Buikstra, J. E. & Ubelaker, D. H. Standards for Data Collection from Human Skeletal Remains: Proceedings of a Seminar at the Field Museum of Natural History. (Arkansas Archeological Survey, 1994).Cocozza, C., Cirelli, E., Groß, M., Teegen, W.-R. & Fernandes, R. Compendium Isotoporum Medii Aevi (CIMA). Pandora https://doi.org/10.48493/s9nf-1q80 (2021).Cocozza, C. & Fernandes, R. Amalthea: A Database of Isotopic Measurements on Archaeological and Forensic Tooth Dentine Increments. J. Open Archaeol. Data 9, 4 (2021).Article 

Google Scholar 
Etu-Sihvola, H. et al. The dIANA database – Resource for isotopic paleodietary research in the Baltic Sea area. J. Archaeol. Sci. Rep. 24, 1003–1013 (2019).
Google Scholar 
Fernandes, R. et al. The ARCHIPELAGO Archaeological Isotope Database for the Japanese Islands. J. Open Archaeol. Data 9, 3 (2021).Article 

Google Scholar 
Scheibner, A. Prähistorische Ernährung in Vorderasien und Europa. Eine kulturgeschichtliche Synthese auf der Basis ausgewählter Quellen. Berl. Archäol. Forschungen 16 (2016).Williams, A. N., Ulm, S., Smith, M. & Reid, J. AustArch: a database of 14C and non-14C ages from archaeological sites in Australia: composition, compilation and review. Internet Archaeol. 36, 1–12 (2014).
Google Scholar 
Ambrose, S. H. Preparation and characterization of bone and tooth collagen for isotopic analysis. J. Archaeol. Sci. 17, 431–451 (1990).Article 

Google Scholar 
DeNiro, M. J. Postmortem preservation and alteration of in vivo bone collagen isotope ratios in relation to palaeodietary reconstruction. Nature 317, 806–809 (1985).ADS 
CAS 
Article 

Google Scholar 
Nehlich, O. & Richards, M. P. Establishing collagen quality criteria for sulphur isotope analysis of archaeological bone collagen. Archaeol. Anthropol. Sci. 1, 59–75 (2009).Article 

Google Scholar 
van Klinken, G. J. Bone Collagen Quality Indicators for Palaeodietary and Radiocarbon Measurements. J. Archaeol. Sci. 26, 687–695 (1999).Article 

Google Scholar 
van der Plicht, J., Wijma, S., Aerts, A. T., Pertuisot, M. H. & Meijer, H. A. J. Status report: The Groningen AMS facility. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At. 172, 58–65 (2000).ADS 
Article 

Google Scholar 
Prasad, G. V. R., Culp, R. & Cherkinsky, A. δ13C correction to AMS data: Values derived from AMS vs IRMS values. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At. 455, 244–249 (2019).ADS 
CAS 
Article 

Google Scholar 
Pollard, A. M., Pellegrini, M. & Lee-Thorp, J. A. Technical note: Some observations on the conversion of dental enamel δ18Op values to δ18Ow to determine human mobility. Am. J. Phys. Anthropol. 145, 499–504 (2011).CAS 
Article 

Google Scholar 
Chenery, C. A., Pashley, V., Lamb, A. L., Sloane, H. J. & Evans, J. A. The oxygen isotope relationship between the phosphate and structural carbonate fractions of human bioapatite. Rapid Commun. Mass Spectrom. 26, 309–319 (2012).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Lehn, C., Rossmann, A. & Mayr, C. Stable isotope relationships between apatite phosphate (δ18O), structural carbonate (δ18O, δ13C), and collagen (δ2H, δ13C, δ15N, δ34S) in modern human dentine. Rapid Commun. Mass Spectrom. 34, e8674 (2020).CAS 
PubMed 
Article 

Google Scholar 
R Core Team. R: A Language and Environment for Statistical Computing. (R Foundation for Statistical Computing, 2021).Chang, W., Cheng, J., Allaire, J., Xie, Y. & McPherson, J. Shiny: web application framework for R. R Package Version 1, 2017 (2017).
Google Scholar 
Cocozza, C., Fernandes, R., Ughi, A., Groß, M. & Alexander, M. M. Investigating infant feeding strategies at Roman Bainesse through Bayesian modelling of incremental dentine isotopic data. Int. J. Osteoarchaeol. 31, 429–439 (2021).Article 

Google Scholar 
Sołtysiak, A. & Fernandes, R. Much ado about nothing: assessing the impact of the 4.2 kya event on human subsistence patterns in northern Mesopotamia using stable isotope analysis. Antiquity 95, 1145–1160 (2021).Article 

Google Scholar 
Bonafini, M., Pellegrini, M., Ditchfield, P. & Pollard, A. M. Investigation of the ‘canopy effect’ in the isotope ecology of temperate woodlands. J. Archaeol. Sci. 40, 3926–3935 (2013).Article 

Google Scholar 
Montanari, M. Alimentazione e cultura nel Medioevo. (Laterza, 1988).Castiglioni, E. & Rottoli, M. Broomcorn millet, foxtail millet and sorghum in north Italian Early Medieval sites. Post-Class. Archaeol. 3, 131–144 (2013).
Google Scholar 
Rippon, S., Wainwright, A. & Smart, C. Farming Regions in Medieval England: The Archaeobotanical and Zooarchaeological Evidence. Mediev. Archaeol. 58, 195–255 (2014).Article 

Google Scholar 
Lewit, T. Pigs, presses and pastoralism: farming in the fifth to sixth centuries AD: Farming in the fifth to sixth centuries. Early Mediev. Eur. 17, 77–91 (2009).Article 

Google Scholar 
MacKinnon, M. Consistency and change: zooarchaeological investigation of Late Antique diets and husbandry techniques in the Mediterranean region. Antiq. Tardive 27, 135–148 (2019).Article 

Google Scholar 
Salvadori, F. The transition from late antiquity to early Middle Ages in Italy. A zooarchaeological perspective. Quat. Int. 499, 35–48 (2019).Article 

Google Scholar 
Witcher, R. Agricultural Production in Roman Italy. in A Companion to Roman Italy (ed. Cooley, A. E.) 459–482 (Wiley, 2016).Pearson, K. L. Nutrition and the Early-Medieval Diet. Speculum 72, 1–32 (1997).Article 

Google Scholar 
Salesse, K. et al. IsoArcH.eu: An open-access and collaborative isotope database for bioarchaeological samples from the Graeco-Roman world and its margins. J. Archaeol. Sci. Rep. 19, 1050–1055 (2018).
Google Scholar 
Winklerová, D. Zooarchaeological and archaeobotanical indicators for aspects of diet in medieval Kingdom of Bohemia. In Food in the Medieval Rural Environment: Processing, Storage, Distribution of Food (eds. Klápšte, J. & Sommer, P.) 421–429 (Brepols Publishers, 2011).Gyulai, F. The history of broomcorn millet (Panicum miliaceum L.) In the Carpathian-basin in the mirror of archaeobotanical remains II. From the roman age until the late medieval age. Columella J. Agric. Environ. Sci. 1 (2014).Iacumin, P., Galli, E., Cavalli, F. & Cecere, L. C4-consumers in southern europe: The case of friuli V.G. (NE-Italy) during early and central middle ages. Am. J. Phys. Anthropol. 154, 561–574 (2014).CAS 
PubMed 
Article 

Google Scholar 
Bynum, C. W. Holy feast and holy fast: the religious significance of food to medieval women. (Univiversity of California Press, 2000).Garnsey, P. Food & Society Classical Antiquity. (Cambridge University Press, 2008).James, P. Food Provisions for Ancient Rome: A Supply Chain Approach. (Routledge).Minniti, C. L’approvvigionamento alimentare a Roma nel Medioevo: analisi dei resti faunistici provenienti dalle aree di scavo della Crypta Balbi e di Santa Cecilia. In Atti del III Convegno Nazionale di Archeozoologia (eds. Fiore, I., Malerba, G. & Chilardi, S.) 469–492 (Istituto poligrafico e Zecca dello Stato, 2005).Fernandes, R., Millard, A. R., Brabec, M., Nadeau, M.-J. & Grootes, P. Food Reconstruction Using Isotopic Transferred Signals (FRUITS): A Bayesian Model for Diet Reconstruction. PLoS ONE 9, e87436 (2014).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Fernandes, R., Grootes, P., Nadeau, M.-J. & Nehlich, O. Quantitative diet reconstruction of a Neolithic population using a Bayesian mixing model (FRUITS): The case study of Ostorf (Germany). Am. J. Phys. Anthropol. 158, 325–340 (2015).PubMed 
Article 

Google Scholar 
Nehlich, O. The application of sulphur isotope analyses in archaeological research: A review. Earth-Sci. Rev. 142, 1–17 (2015).ADS 
CAS 
Article 

Google Scholar 
Sayle, K. L. et al. Application of 34S analysis for elucidating terrestrial, marine and freshwater ecosystems: Evidence of animal movement/husbandry practices in an early Viking community around Lake Mývatn, Iceland. Geochim. Cosmochim. Acta 120, 531–544 (2013).ADS 
CAS 
Article 

Google Scholar 
Alt, K. W. et al. Lombards on the Move – An Integrative Study of the Migration Period Cemetery at Szólád, Hungary. PLoS ONE 9, e110793 (2014).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Brettell, R., Evans, J., Marzinzik, S., Lamb, A. & Montgomery, J. ‘Impious Easterners’: Can Oxygen and Strontium Isotopes Serve as Indicators of Provenance in Early Medieval European Cemetery Populations? Eur. J. Archaeol. 15, 117–145 (2012).Article 

Google Scholar 
Knipper, C. et al. Mobility in Thuringia or mobile Thuringians: A strontium isotope study from early medieval Central Germany. In Population Dynamics in Prehistory and Early History (eds. Kaiser, E., Burger, J. & Schier, W.) 287–310, https://doi.org/10.1515/9783110266306.287 (De Gruyter, 2012).Winter-Schuh, C. & Makarewicz, C. A. Isotopic evidence for changing human mobility patterns after the disintegration of the Western Roman Empire at the Upper Rhine. Archaeol. Anthropol. Sci. 11, 2937–2955 (2019).Article 

Google Scholar 
Biddle, M. & Kjølbye-Biddle, B. Repton and the Vikings. Antiquity 66, 36–51 (1992).Article 

Google Scholar 
Biddle, M. & Kjølbye-Biddle, B. Repton and the ‘great heathen army’, 873–4. In Vikings and the Danelaw (eds. Graham-Campbell, J., Hall, R., Jesch, J. & Parsons, D. N.) 45–96 (Oxbow, 2001).Budd, P., Millard, A., Chenery, C., Lucy, S. & Roberts, C. Investigating population movement by stable isotope analysis: a report from Britain. Antiquity 78, 127–141 (2004).Article 

Google Scholar 
Jarman, C. L., Biddle, M. & Higham, T. & Bronk Ramsey, C. The Viking Great Army in England: new dates from the Repton charnel. Antiquity 92, 183–199 (2018).Article 

Google Scholar 
Roffey, S. et al. Investigation of a Medieval Pilgrim Burial Excavated from the Leprosarium of St Mary Magdalen Winchester, UK. PLoS Negl. Trop. Dis. 11, e0005186 (2017).PubMed 
PubMed Central 
Article 

Google Scholar  More

Mathematical theoryWe consider a biological response (e.g. body size, survival, biodiversity) to two environmental drivers (i.e. any abiotic or biotic factor) but the same idea may be applied to a larger number of drivers. The response depends of a set of predictors consisting in the magnitudes (m1 and m2) and time scales of fluctuation of two drivers (i = 1, 2); in addition, the response is quantified at least once after the fluctuations have been experienced (Fig. 1a).Time is defined using two different frames; chronological (= clock) time (measured by clocks) and biological time. For the “clock” time scales of the fluctuations (t1, t2) there are associated biological times (τ1, τ2). Likewise, for the clock time at which the response is quantified (({t}^{^*})) there is an associated biological time (τ({^*})).Biological time is the proportion of (clock) time needed to reach a life history event (e.g. moulting, maturity). Hence, for t1, t2 and t({^*}) we obtain τi = ti/D and τ({^*}) = t({^*})/D, (D = clock time needed to reach such life history event). We express the τi and τ({^*}) in terms of a function L = 1/D. For instance, for t({^*}) we obtain:$${tau }^{^*}={t}^{^*}cdot{L}$$
(1)
where L = L(ω) = D−1(ω) characterises the timing of a life history event (with units as the inverse of clock time units). L depends on the set of predictors ω associated to the fluctuations; an important set of predictors will be defined by thermal fluctuations (the amplitude and time scales), which in ectotherm species have a strong influence on developmental time32,33. We find by differentiation that L provides the transform function between clock and biological time frames; for instance, if L does not depend on any ti we have L = dτ/dti.The response is expressed as a function of the predictors defined above, as R(m1, m2, t1, t2, t({^*})) = r[m1, m2, τ1 (t1), τ2(t2), τ({^*})]. The contribution of each predictor to the response is better understood by the partial derivatives with respect to each predictor; this defines a system of partial differential equations (PDE; Supplementary note 1) which expressed in matrix form give the following matrix equation.$$left[begin{array}{c}frac{dR}{d{m}_{1}}\ frac{dR}{d{m}_{2}}\ frac{dR}{d{t}_{1}}\ frac{dR}{d{t}_{2}}\ frac{dR}{d{t}^{^*}}end{array}right]=left[begin{array}{ccccc}1& frac{d{m}_{2}}{d{m}_{1}}& frac{d{tau }_{1}}{d{m}_{1}}& frac{d{tau }_{2}}{d{m}_{1}}& frac{d{tau }^{^*}}{d{m}_{1}}\ frac{d{m}_{1}}{d{m}_{2}}& 1& frac{d{tau }_{1}}{d{m}_{2}}& frac{d{tau }_{2}}{d{m}_{2}}& frac{d{tau }^{^*}}{d{m}_{2}}\ frac{d{m}_{1}}{d{t}_{1}}& frac{d{m}_{2}}{d{t}_{1}}& frac{d{tau }_{1}}{d{t}_{1}}& frac{d{tau }_{2}}{d{t}_{1}}& 0\ frac{d{m}_{1}}{d{t}_{2}}& frac{d{m}_{2}}{d{t}_{2}}& frac{d{tau }_{1}}{d{t}_{2}}& frac{d{tau }_{2}}{d{t}_{2}}& 0\ 0& 0& 0& 0& frac{d{tau }^{^*}}{d{t}^{^*}}end{array}right]cdot left[begin{array}{c}frac{dr}{d{m}_{1}}\ frac{dr}{d{m}_{2}}\ frac{dr}{d{tau }_{1}}\ frac{dr}{d{tau }_{2}}\ frac{dr}{d{tau }^{^*}}end{array}right]$$
(2)
In the PDE (Eq. 2), the left-hand side is a vector column of the derivatives of the response in clock time (R), with respect to each predictor; the right-hand side is the standard (= inner) product of a matrix (M) by a vector of the derivatives of the response in biological time (r), i.e. R = Mr. The matrix contains the derivatives of the predictors with respect to each other, with time both expressed in clock or biological scales; one can think of M as an object containing coefficients that transform r into R in the same way as a constant (= 1000) would transform kilometres into meters of distance. The large number of terms in M highlights the considerable diversity and the challenges in quantifying responses to multivariate environmental fluctuations. We show below how to use Eq. (2) to quantify the effect of fluctuating environmental drivers on biological responses, as mediated by biological time.First, we note that M contains three groups of terms: (1) Terms accounting for situations where the magnitude of a driver affects the magnitude of the second driver (e.g. temperature drives oxygen concentration in aquatic habitats): these are dmi/dmj for any i, j = 1, 2. (2) Terms accounting for cases where the magnitudes and time scales of stressors are related: dmi/dtj and dmi/dti. (3) Terms where biological time depends on the magnitude or time scale of the environmental fluctuation dτi/dtj and dτi/dmj. The terms of groups (1) and (2) are zero when they are mutually independent, such as in a factorial experiment with orthogonal manipulation. We will set those to zero in the rest of this analysis.Second, we note that for group (3) there are three scenarios: (3a) biological time does not depend on any environmental driver. This is the trivial case where biological time is proportional to clock time, not considered here; M is simplified to a diagonal matrix, i.e. with constants in the diagonal, and zero’s otherwise leading to a single constant term per equation (3b). Biological time depends on the magnitudes of any or both drivers. In such case, τ1 τ2, and τ({^*}) will be driven by the same equation: if τi = ti · L (m1, m2) we obtain dτi/dtj = dτi/dti = L (m1, m2). (3c) Biological time depends on the time scale of the fluctuations: in such case, differentiating Eq. (1) with respect to time, we obtain dτi/dti = L + ti dL/dti.Here, we explore four special cases where the equations are simplified to highlight the importance of biological time in modifying the responses as compared to clock time. We start with the simplest case where there is a single environmental variable and then we consider cases with two variables. We focus on cases representing the most frequent experiments carried out on multiple driver research, i.e. factorial manipulations where terms of the groups 1 and 2 are zero.Case 1: responses to the magnitude of a single variableWe start with the simplest case i.e. where the response is driven by the magnitude of a single driver, e.g. temperature (= m). Examples of this case are laboratory experiments quantifying the effect of temperature on body mass or survival of a given species, or mesocosm experiments quantifying effects of temperature on species richness where thermal treatments are kept constant over time. Here, the response is quantified at different times, both in the clock and biological frames. In such case we have R(m, t({^*})) = r[m, τ({^*})(m, t({^*}))] and the PDEs simplify to.$$frac{dR}{dm}=frac{partial r}{partial m}+frac{partial r}{partial {tau }^{^*}}cdot frac{d{tau }^{^*}}{dm}$$
(3)
From Eq. (3), and because dR/dm ≠ dr/dm, we see that the response to the magnitude of the driver depends on a component quantifying the effect biological time: as long as dτ({^*})/dm ≠ 0 the time reference frame affects the observed effect of m on the response. The simulation illustrated in Fig. 2 shows a case where there are differences between the observed responses at clock vs biological times. In the simulated experiment, there is a strong effect of the magnitude of the driver on the response at clock time, but such effect is much less pronounced at biological time. By contrast, there is no effect when the response is measured in the biological time frame.Figure 2Case 1: Response to the magnitude of a single variable (m). Horizontal line: measurement taken at clock time t({^*}) = t({^*})c; note that, along the line, the response increase with m (it crosses the colour gradient). Curve with yellow circles: measurements taken at a constant biological time (τ({^*})c = 100); along the curve, the response does not vary with m. The equations used were: R = m(0.5t({^*})), τ({^*}) = t. m giving r = 0.5. τ({^*}) not depending on m.Full size imageEquation (3) (details in Supplementary code 1) captures an obvious but important feature of experiments manipulating temperature over the development of ectotherms, for instance, from birth to metamorphosis; namely that there is no consistent definition of a simultaneous event across the different time frames. Experiments are usually stopped at different clock times because organisms must be sampled at the same biological time. All points located in the horizonal line in Fig. 3 represent simultaneous events, as defined in clock time occurring at different temperatures (e.g. whether an animal is dead or alive); however, simultaneous events occurring in biological time are represented by the points on the curve. Hence, Fig. 2 gives a geometric representation of such fact. Temperature as a driver of developmental rates32 is a central candidate to produce responses that differ at clock vs biological time.
We explore further this case with an example where the response is expressed as a function of time and an instantaneous rate μ(m) quantifying for instance mortality, growth or biomass loss. For this example, we obtain R(m, t({^*})) = r[μ(m), τ({^*})(m, t({^*}))]. By differentiating in both sides, we get:$$frac{dR}{dm}=frac{partial r}{partial mu }cdot frac{dmu }{dm}+frac{partial r}{partial {tau }^{^*}}cdot frac{d{tau }^{^*}}{dm}$$
(4)
Equation (4) shows that m affects the response through two components: the instantaneous rate (dμ/dm) and the biological time (dτ({^*})/dm). We call the first component “eco-physiological” and the second component “phenological” (m drives the timing of a biological event, e.g. time to maturation). Those components are not evident if the response is expressed in clock time; otherwise we would obtain dR/dm = ∂R/∂μ · dμ/dm.In order to better understand Eq. (4), consider an example where the response is biomass loss experienced by an organism during the process of migration (e.g. towards a feeding or reproductive ground); when the access to food during migration is very limited the result should be a decrease in body mass reserves through time. Let biomass (B) be modelled as an exponential decaying function of time and an instantaneous rate of biomass loss μ; let μ depend on temperature (= m) such that, μ = μ(m). In such case we obtain:$$B(m,t)={e}^{-mu left(mright)cdot {t}^{^*}}={e}^{-mu left(mright)cdot {tau }^{^*}left(m,{t}^{^*}right)}$$
(5)
By differentiation in both sides of Eq. (5) we get:$$frac{dB}{dm}={-e}^{-mu left(mright)cdot {tau }^{^*}left(m,{t}^{^*}right)}left{{tau }^{^*}cdot frac{dmu }{dm}+mu cdot frac{d{tau }^{^*}}{dm}right}$$
(6)
Equation (6) shows the eco-physiological (dμ/dm) and phenological components (dτ({^*})/dm) within the brackets. If μ responds linearly to temperature, then dμ/dm would be represented by a constant quantifying the thermal sensitivity of biomass loss; the value of such constant would depend on physiological processes associated to use of reserves to sustain movement and the basal metabolic rate. Likewise, if τ({^*}) responds linearly to temperature, the dτ({^*})/dm would be driven by a constant controlling the sensitivity of developmental time to temperature.Because biomass is a trait that is central to fitness, Eq. (6) gives the indirect contribution of phenological and physiological responses to fitness. Assuming that fitness should be maximised, adaptive responses should involve the mitigation of negative effect of m on both components of Eq. (5), represented by the partial derivative of the right-hand term. For instance, organisms with the ability to minimise the eco-physiological effect (through e.g. a compensatory physiological mechanisms) or the phenological effect (e.g. shortening the exposure time) would complete the migration minimal loss of reserves.By generalization, Eqs. (4–6) help us to provide biological meaning to the terms of the matrix M: any term of the form dτ({^*})/dmj, dτi/dmj or dτi/dtj represents the effect of an environmental driver on the timing of a phenological event; hence, they are phenological components. Terms that contain the effect of an environmental variable on an instantaneous rate are eco-physiological components. By substitution we find that the terms of the matrix in Eq. (2) can be classified in two categories according to whether the component is eco-physiological (E) or phenological (P):$$left[begin{array}{ccccc}E& 0& P& P& P\ 0& E& P& P& P\ 0& 0& P& P& 0\ 0& 0& P& P& 0\ 0& 0& 0& 0& Pend{array}right]$$
(7)
Case 2: multiple driver responsesHere we expand the previous case by looking at a response to the magnitude of two different drivers; i.e. keeping the levels of each driver constant over the duration of the experiment. Examples of this case are experiments quantifying the effect of temperature and nutrient load on body mass (e.g. in a rearing containers) or species richness (e.g. in mesocosms). This case is represented by the terms of first two rows of the matrix and the vectors of Eq. (2), with the terms of the remaining rows set to zero. Here, there are different scenarios, but we focus on the one highlighting the importance of biological time.Consider a case where biological time depends on the magnitude of the first driver while the response is explicitly driven by the magnitude of the second driver (Fig. 4). For instance, the response may be the survival rate of a host organism exposed to different temperature and parasitic load. The response in clock time is described as R(mP, t({^*})). The driver controlling the biological time is temperature (mT) while the parasitic load (mP) controls survival. In such case, dτ({^*})/∂mP = 0, dR/dmP ≠ 0 and dR/dmT = 0. Although by definition the response in clock time does not depend on mT , it will do so in biological time. This is because, applying the matrix multiplication in Eq. (2), we obtain:
$$frac{partial R}{partial {m}_{T}}=frac{partial r}{partial {m}_{T}}+frac{partial r}{partial tau *}cdot frac{dtau *}{d{m}_{T}}$$
(8a)
$$0=frac{partial r}{partial {m}_{T}}+frac{partial r}{partial tau *}cdot frac{dtau *}{d{m}_{T}}$$
(8b)
$$frac{partial r}{partial {m}_{T}}=-frac{partial r}{partial tau *}cdot frac{dtau *}{d{m}_{T}}$$
(8c)
The second right-hand term in Eq. (8a) quantifies the effect of temperature on the response mediated by biological time. In order to better understand the responses, consider a simple linear response: R = R0 − mP·t({^*}) and notice that, for a fixed clock time (t({^*})c) the effect of the magnitude of parasitism is constant (dR/dmP = −t({^*})c); hence, the response can be understood, geometrically, as a flat surface with slope not depending on temperature. Now, note that under the specific conditions of our example, r = R0 − mP·τ({^*})/L(mT). Hence, for a fixed biological time (τ({^*})c) we obtain ∂r/∂mP = −τ({^*})c/L(mT); i.e. the importance of the parasitic effect depends now on temperature. In addition, this example is valid for the case of additive effects of any two environmental drivers: assuming R = R0 − (a1·mP + a2· mT)·t({^*}) (a1, a2 are constants), we obtain dR/dmP = −a1t({^*}); however, ∂r/∂mP = −a1τ({^*})c/L(mT). In words, additive effects observed in clock time become interactive in biological time. This is illustrated in the simulation (Supplementary code 2) depicted in Fig. 4: the response in clock time depends on a single driver (parasite load); however, the response in biological time is interactive, i.e. the effect of parasite load depends on temperature.Figure 3Case 2: Multiple driver responses. (A) Modelled responses (colour scale) at a specific clock (t({^*}) = 40) and biological times (τ({^*}) = 1), showing an interactive effect only in the biological time frame. (B) Interaction plots of the responses for specific levels of temperature and a second driver showing that the effect high temperature mitigates the negative effect of the second driver on the response. The response was modelled with as a sigmoidal function R = exp(−t({^*})φ) with φ = 0.1[1 + exp(m2/2)]−1 to produce a strong gradient in the range of m2 = 25–30 units. The biological time was modelled based on the effect of temperature on the development of marine organisms33 as so that t({^*}) = τ({^*}) exp[−22.47 + 0.64/(k(m1 + 273)], i.e., using the Arrhenius equation with k: Boltzmann constant (≈ 8.617 10–5 eV K−1).Full size imageCase 3: role of clock and biological time scale of fluctuationPrevious examples did not consider, the time scale of the fluctuations as drivers of the response. Here we explore how a biological variable (= survival rate) responds to different levels of magnitude of a driver (= temperature) and to simultaneously changing the time scale of a fluctuation (from clock to biological time) of a second driver (= food limitation). As model, we use larval stages of a crab because there is sufficient information on the effect of temperature and food levels on survival and the timing of moulting33,34.We performed the so-called point-of-reserve-saturation experiment (PRS35), i.e. exposing groups of recently hatched larvae of the crab Hemigrapsus sanguineus to different initial feeding periods (= our time scale of fluctuation), after which they were starved until they either died or moulted to the second larval stage (Supplementary Fig. 1). H. sanguineus is originated from East Asia but has invaded the Atlantic shores of North America and North Europe36,37. This experiment was carried out at 4 temperature levels (15–21 °C), within the range of thermal tolerance of larvae of this species, i.e. where the magnitude of temperature does not affect survival38,39. In addition, because there is a single level of food limitation (= starvation), the magnitude of food limitation (mF) is not considered as a variable in the example.The response variable was the proportion of first stage larvae surviving the moulting event to the second stage, set to biological time τ({^*}) = 1. In response to different starvation periods (preceded by feeding), the survival shows a sigmoidal pattern35, characterised by a parameter, PRS50. This is the point of development where larval reserves are “saturated”; i.e. enough reserves have been accumulated during the previous feeding period to ensure survival and moulting to the next stage.Under the conditions of the experiment, the survival proportion (= R) is driven only by the time scale of a fluctuation (here t1 = t, τ1 = τ for simplicity), characterised by the starvation period; hence, R = R(t) = r[τ(t)] given that there is a single time of observation fixed to τ({^*}) = 1. Because biological time does not depend t, we get L = dτ/dt and:$$frac{dR}{dt}=frac{partial r}{partial tau }cdot mathcal{L}({m}_{2})$$
(9)
Equation (9) is represented in the PDE by the terms of row 3 and column 4 of M multiplied by the term of row 3 of the column vector r; dτ/dt = L(m), m represents the magnitude of temperature.The relationship between biological time and temperature was best explained by a power function D(T) = aTb (Fig. 4A, Supplementary Table 1, Supplementary Fig. 2), in consistence with previous studies36,40. The interaction between starvation time and temperature was weak (Supplementary Fig. 3); best models retained starvation time only at 21 °C where the percentage of explained variance was still low (R2  More

Chai et al. Stable water isotope and surface heat flux simulation using ISOLSM: Evaluation against in-situ measurements. J. Hydrol. 523, 67–78 (2015).Article 

Google Scholar 
Brooks et al. Stable isotope estimates of evaporation: Inflow and water residence time for lakes across the United States as a tool for national lake water quality assessments. Limnol. Oceanogr. 59, 2150–2165 (2014).Article 

Google Scholar 
Good, S. P., Noone, D. & Bowen, G. Hydrologic connectivity constrains partitioning of global terrestrial water fluxes. Science 349, 175–177 (2015).CAS 
Article 

Google Scholar 
Gupta, A., Gerber, E. P. & Lauritzen, P. H. Numerical impacts on tracer transport: A proposed intercomparison test of atmospheric general circulation models. Quart. J. Roy. Meteor. Soc. 146, 3937–3964 (2020).Article 

Google Scholar 
Kanner, L. C., Buenning, N. H., Stott, L. D., Timmermann, A. & Noone, D. The role of soil processes in d18O. Global Biogeochem. Cycles 28, 239–252 (2014).CAS 
Article 

Google Scholar 
Remondi, F., Kircher, J. W., Burlando, P. & Fatichi, S. Water flux tracking with a distributed hydrologic model to quantify controls on the spatio-temporal variability of transit time distributions. Water Resour. Res. 54, 3081–3099 (2018).Article 

Google Scholar 
Abbott, B. W. et al. Using multi-tracer inference to move beyond single catchment ecohydrology. Earth-Sci. Rev. 160, 19–42 (2016).Article 

Google Scholar 
Krause, P., Boyle, D. P. & Bäse, F. Comparison of different efficiency criteria for hydrological model assessment. Adv. in Geosci. 5, 89–97 (2005).Article 

Google Scholar 
Bowen, G. J. & Good, S. P. Incorporating water isotopes in hydrological and water resource investigations. Wiley Interdiscip. Rev.: Water 2, 107–119 (2015).Article 

Google Scholar 
McGuire, K. J. & McDonnell, J. J. A review and evaluation of catchment transit time modeling. J. Hydrol. 330, 543–563 (2006).Article 

Google Scholar 
Sprenger, M. et al. The demographics of water: A review of water ages in the critical zone. Rev. Geophys. 57, 800–834 (2019).Article 

Google Scholar 
Turnadge, C. & Smerdon, B. D. A review of methods for modelling environmental tracers in groundwater: Advantages of tracer concentration simulation. J. Hydrol. 519, 3674–3689 (2014).CAS 
Article 

Google Scholar 
Fiorella, R. et al. Calibration Strategies for Detecting Macroscale Patterns in NEON Atmospheric Carbon Isotope Observations. J. Geophys. Res. Biogeosci. 126 (2021).Xiao, W., Wei, Z. & Wen, X. Evapotranspiration partitioning at the ecosystem scale using the stable isotope method—A review. Agric For Meteorol. 263, 346–361 (2018).Article 

Google Scholar 
Wu, Y. et al. Stable isotope measurements show increases in corn water use efficiency under deficit irrigation. Sci Rep 8, 14113 (2018).Article 

Google Scholar 
Al-Oqaili, F., Good, S. P., Frost, K. & Higgins, C. W. Differences in soil evaporation between row and interrow positions in furrowed agricultural fields. Vadose Zone J. 19, e20086 (2020).CAS 
Article 

Google Scholar 
Bowen, G. J., Cai, Z., Fiorella, R. P. & Putman, A. L. Isotopes in the water cycle: Regional- to global-scale patterns and applications. Annu. Rev. Earth Planet. Sci. 47, 453–479 (2019).CAS 
Article 

Google Scholar 
Lu, X. et al. Partitioning of evapotranspiration using a stable isotope technique in an arid and high temperature agricultural production system. Agric. Water Manag. 179, 103–109 (2017).Article 

Google Scholar 
Wieser, G. et al. Stable water use efficiency under climate change of three sympatric conifer species at the alpine treeline. Front. Plant Sci. 7, 799 (2016).Article 

Google Scholar 
Pataki, D. E. et al. The application and interpretation of Keeling plots in terrestrial carbon cycle research. Global Biogeochem. Cycles, 17 (2003).Miller, J. B., & Tans, P. P., Calculating isotopic fractionation from atmospheric measurements at various scales. Tellus, 55 (2003).Finkenbiner, C. E., Good, S. P., Allen, S. T., Fiorella, R. P. & Bowen, G. J. A statistical method for generating temporally downscaled geochemical tracers in precipitation. J. Hydrometeorol. 22 (2021).NEON (National Ecological Observatory Network). Precipitation (DP1.00006.001), RELEASE-2022. https://doi.org/10.48443/6wkc-1p05. Dataset accessed from https://data.neonscience.org on May 12, 2022.Lunch, C. K. & Laney, C. M. NEON (National Ecological Observatory Network). neonUtilities: Utilities for working with NEON data. R package version 1.3.4. https://github.com/NEONScience/NEON-utilities (2020).Lee, R. and S. Weintraub. NEON User Guide to Stable Isotopes in Precipitation (NEON.DPI.00038) Version B. NEON (National Ecological Observatory Network). (2021).IAEA: Global network of isotopes in precipitation. https://www.iaea.org/services/networks/gnip 2020.Allen, S. T., Kirchner, J. W. & Goldsmith, G. R. Predicting spatial patterns in precipitation isotope (δ2H and δ18O) seasonality using sinusoidal isoscapes. Geophys. Res. 45, 4859–4868 (2018).
Google Scholar 
Craig, H. Isotopic variations in meteoric waters. Science 133, 1702–1703 (1961).CAS 
Article 

Google Scholar 
Dansgaard, W. Stable isotopes in precipitation. Tellus 16, 436–468 (1964).Article 

Google Scholar 
Sklar, A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris. 8, 229–231 (1959).MATH 

Google Scholar 
NEON (National Ecological Observatory Network). Bundled data products – eddy covariance (DP4.00200.001). https://data.neonscience.org (2021).Good, S. P., Soderberg, K., Wang, L., & Caylor, K. K. Uncertainties in the assessment of the isotopic composition of surface fluxes: A direct comparison of techniques using laser‐based water vapor isotope analyzers. J. Geophys. Res. Atmos. 177 (2012).Wutzler, T. et al. Basic and extensible post-processing of eddy covariance flux data with REddyProc. Biogeosci. 15, 5015–5030 (2018).CAS 
Article 

Google Scholar 
Zobitz, J. M., Keener, J. P., Schnyder, H. & Bowling, D. R. Sensitivity analysis and quantification of uncertainty for isotopic mixing relationships in carbon cycle research. Agric For Meteorol. 136, 56–75 (2006).Article 

Google Scholar 
Wehr, R. & Saleska, S. R. An improved isotopic method for partitioning net ecosystem-atmosphere CO2 exchange. Agric For Meteorol. 214, 515–531 (2015).Article 

Google Scholar 
Bailey, A., Noone, D., Berkelhammer, M., Steen-Larsen, H. C. & Sato, P. The stability and calibration of water vapor isotope ratio measurements during long-term deployments. Atmos. Meas. Tech. 8, 4521–4538 (2015).CAS 
Article 

Google Scholar 
Rambo, J., Lai, C., Farlin, J., Schroeder, M. & Bible, K. Vapor isotope ratios using off-axis cavity-enhanced absorption spectroscopy. J Atmos. Ocean Technol. 28, 1448–1457 (2011).Article 

Google Scholar 
Finkenbiner, C. The National Ecological Observation Network Daily Isotopic Composition of Environmental Exchanges (NEON-DICEE) Dataset, HydroShare, https://doi.org/10.4211/hs.e74edc35d45441579d51286ea01b519f (2022). More

InvasionWe used freshwater fish biodiversity data collated by and described in Milardi, et al.47. In summary, the dataset included 3777 sites sampled 1999–2014, recorded a total of 99 different fish species (35 of which were exotic and already established, even if some are restricted to areas with thermal springs), spanned  > 11 degrees of longitude (~ 1200 km) and 10 degrees of latitude (~ 1100 km), covering streams at altitudes -2.7–2500 m above sea level. Community turnover was not a relevant factor in our study, because fish communities are typically stable over these timescales and the data was collected in a restricted timeframe within each area29,39. Furthermore, time elapsed since last introductions was sufficient to analyze distribution patterns after major invasions had already occurred see e.g.23,48.Abundance of each species sampled during the monitoring was recorded with Moyle classes (Moyle and Nichols, 1973), which were weighted according to body-size classes in order to obtain a body-mass-corrected abundance, hereafter referred to simply as abundance. We then calculated an invasion degree, i.e. the share of introduced species in freshwater fish communities, based on the abundance of introduced and native species see e.g.9,49. A high invasion degree equals to a high share of introduced species and a low share of native species.We also selected the top 10 invasive species as further response variables, under the assumption that these would be the main components of the invasion degree, but would respond to different invasion drivers based on each species’ ecology. Invasiveness rank was defined through an index obtained by multiplying colonization (share of sites colonized) and prevalence (average relative abundance in the fish community) of each introduced species. The relative abundance of each of these species in the fish community was used as a response variable, being a measure comparable to invasion degree for single species.Invasion driversWe tested a combination of geographical, climate and anthropogenic impact factors as potential drivers of invasion. To avoid temporal mismatches, we chose time periods that overlapped as much as possible with our biological data.We used basin area, altitude and slope (derived from a seamless digital elevation model of the whole Italian territory at 10 m resolution, Tarquini, et al.50) as geographical variables.We derived climate data from available series of long-term national monitoring (http://www.scia.isprambiente.it/). We used daily air temperature (2000–2009), measured at a total of 2266 sites throughout the country, as a proxy for temperature regimes. We also used cumulated annual precipitations, number of annual dry days (precipitation  More

In this section, we provide quantitative evaluation for both spatial coverage and temporal dynamics of ReaLSAT dataset.Spatial coverageSince the dataset was created using satellite imagery analysis, it can provide more comprehensive coverage than existing datasets. However, using an automated process also has its challenges. It can invariably lead to the detection of spurious waterbodies because of issues in data (e.g., due to errors in GSW maps used as inputs in ReaLSAT).To provide more insights into the types of lakes and potential issues in the spatial coverage of ReaLSAT, we randomly sampled 5,000 lakes out of 435,717 that are only present in ReaLSAT (i.e., not available in the HydroLAKES dataset). A human annotator used Google’s satellite imagery base layer to categorize these lakes. Figure 5a shows the geographical distribution of these lakes, and Fig. 5b shows the distribution of different lake types in the sample set. Out of the 5,000 lakes, the human annotator identified 2,019 traditional lakes and reservoirs where sufficient water was visible in the satellite imagery. Another 551 lakes in the sample set showed signs of a bowl-like depression but with no (or very little) water visible in the satellite imagery and were labeled as ephemeral. There were 861 other lakes that were tagged as farm ponds because they showed geometric patterns of farming in the imagery. This diversity of waterbody types discovered by ReaLSAT that were previously unreported by HydroLakes highlights one of the strengths of our approach. In limnology, the origin/type of lake is a very important regulator of ecosystem dynamics. For instance, reservoirs will have faster water flow/lower residence time than natural lakes, and therefore nutrient and carbon processing rates will differ; floodplain lakes may dry periodically, leading to the denudation of sediments; and farm ponds will likely have much higher rates of nutrient loading and methane production than non-agriculturally influenced lakes. Hence, capturing a more comprehensive range of waterbody categories can enable various scientific studies where knowing the origin/lake type could provide a critical understanding of the process.Fig. 5(a) Geographic location of 5000 randomly selected lakes used for manual evaluation of lake type. (b) Allocation of the 5000 manually referenced lakes to specific lake types. Regular implies a traditional lake or reservoir. Unverifiable implies that the lake type could not be identified based on the available Google Earth imagery.Full size imageAlong with the lentic water types discovered in the sampled set, we also found that ReaLSAT identified 603 river segments missed by our morphological score filter. As stated earlier, this is an inherent challenge with automated approaches that use a fixed score threshold for eliminating river segments. Another 239 lakes were tagged as wetlands because of significant vegetation inside and around the lake polygon. There were also 97 lakes that were adjacent to rivers, which were labeled as riverine or floodplain lakes that were formed as a result of river channels meandering over time. Furthermore, there were 59 lakes where the polygons represented only a small portion of a larger lake and were labeled as partial. Finally, for 571 polygons, there was not enough evidence to tag them in any of the above categories. Since Google imagery represents only a single snapshot in time, these 571 waterbodies could not be definitively labeled as spurious (hence, they were labeled as unverifiable), highlighting a limitation of this evaluation pipeline. In particular, a vast majority of these waterbodies appear to be ephemeral based on their surface area timeseries (completely dry for extended periods of time). Hence, if the satellite imagery layer is from one of these timesteps, the annotator would not be able to confirm the presence of the lake.To assess whether we would obtain a similar distribution of different waterbody categories in existing datasets, we performed a similar evaluation on another 5,000 lakes sampled from ReaLSAT where each polygon has some overlap (greater than 1 pixel) with a polygon from HydroLAKES. In this sampled set, the annotator identified 4,030 lakes as traditional lakes or reservoirs, 370 as ephemeral, 138 as farm ponds, 6 as river segments, 66 as wetlands, 95 as riverine or floodplain lakes, 20 as partial, and 275 as unverifiable.Compared to previous distribution, this set of 5,000 waterbodies contains relatively fewer river segments and wetlands polygons in HydroLAKES, because these categories were manually identified and removed during HydroLAKES database creation6. Similary, this set contains relatively few farm ponds because HydroLAKES was created by manual curation of existing static databases and hence does not contain new farm ponds that got created over the years.Temporal dynamicsTo assess the quality of surface extent maps, we performed a quantitative evaluation on a random selection of extent maps. These extent maps were compared against reference maps created by a human annotator using a semi-automated pixel classification procedure. This strategy of creating reference maps is used extensively in the remote sensing literature (e.g. see36,37,38,39). Next, we describe our evaluation process in detail.Sample selectionThere are 462,574 lakes out of 681,137 total lakes where the label updates (corrections and imputations) by the ORBIT approach have trust scores within our chosen thresholds (as described in the methods section). To evaluate these candidate lakes effectively, we focus on lake extent maps where the ORBIT approach resulted in a different map than the underlying GSW extent based map. Hence, we remove maps where no updates were made by the ORBIT approach (neither corrections nor imputations) from the candidate pool of extent maps used for evaluation. We also remove maps where the percentage of missing labels was more than 90% because these maps tend to suffer from significant cloud coverage. Hence, it would be challenging to generate reference maps. Since the GSW dataset has a significant amount of missing data for most places in the world before 2000, we evaluated maps only from 2000 onwards. These three filters left us with a total of 51,077,278 water extent maps considered for selection. Figure 6a shows the distribution of percentage pixels updated made by the ORBIT approach in these water extent maps. To evaluate the robustness of our approach in comparison to GSW maps, we randomly selected 10,000 water extent maps such that extents with significant updates are given higher weight to reduce the skew in distribution towards extents with relative less updates (Fig. 6b).Fig. 6Distribution of updates made by the ORBIT approach. (a) distribution using candidate water extents (b) distribution using randomly selected 10000 water extent maps for evaluation.Full size imageSample pruningFrom these randomly selected water extent maps, we removed maps for which a reference map could not be generated due to clouds or the inability of the annotator to distinguish between land and water. A final set of 2,095 water extent maps were considered for evaluation. Figure 7a shows the distribution of percentage updates in the final set of evaluation extents and Fig. 7b shows the geographical distribution of these extent maps.Fig. 7Summary of the dataset used for evaluating water extent maps. (a) Distribution of updates made by the ORBIT approach in the water extent maps selected for evaluation. (b) Geographical location of the lakes in the evaluation set.Full size imageReference map generationFor these water extent maps, we created ground truth reference maps using a semi-automatic labeling process37,38,39. Specifically, the annotator selects land and water samples to train an SVM (Support Vector Machine) classification model for each image. The annotator keeps adding samples until a stable map is generated. As a final step, the annotator masks out pixels affected by clouds, cloud shadows, and any other region where the annotator is not confident about the accuracy of the reference labels. This process enables a quick and robust generation of reference maps. Supplementary Fig. S7 shows one of the reference maps in the evaluation set. While this strategy of comparing maps is different from the traditional approach of comparing pixels (often selected using stratified sampling), it provides a much more exhaustive evaluation of surface extent maps. The reference maps used for evaluation in this study are also available as part of the dataset.ComparisonTo compare the extent maps generated by ReaLSAT with the reference maps, we used accuracy as the evaluation metric, a widely used metric to measure the quality of classification maps. Accuracy is simply defined as the ratio of pixels with correct labels over a total number of pixels. Specifically, we assign 1 to water pixels and 0 to land pixels. Since GSW based extent maps contain missing labels, they are assigned a value of 0.5 to reflect the uncertainty between land and water. Accuracy is then calculated as follows:$$Accuracy=1-frac{1}{Rast C}mathop{sum }limits_{i=1}^{R}mathop{sum }limits_{j=1}^{C}left|ReferenceMap[i,j]-PredictedMap[i,j]right|$$
(2)
where, R is the number of rows and C is the number of columns of the map.When the accuracy of RealSAT and GSW labels are compared, a vast majority of points lie above the diagonal 1:1 line, which implies that ReaLSAT labels were more accurate overall (Fig. 8a). In Fig. 8 the points are colored based on % of pixels where GSW labels were missing. To better show the improvement in RealSAT labeling, we plot the distribution of the difference in accuracy values between the two datasets as shown in Fig. 8b. A positive value indicates that the surface extent map from the ReaLSAT dataset had better accuracy than the map from the GSW dataset and vice versa. For ease of visualization, we plot this distribution after excluding cases where the accuracy from both datasets was equal. The positively skewed distribution demonstrates the efficacy of the ORBIT approach.Fig. 8Comparison of accuracy values using GSW labels vs ReaLSAT labels. (a) Scatter plot of accuracy values using GSW labels vs ReaLSAT labels. (b) Histogram of difference in accuracy between ReaLSAT labels vs GSW labels. Positive value represents cases where ReaLSAT labels were more accurate than GSW labels. (c) Histogram of difference in accuracy values for the scenario where pixels labelled as land by both products as well as ground truth were removed to reduce the skew of surrounding land pixel on the accuracy values.Full size imageNote that the shape of a lake will influence the number of land pixels surrounding it, which might bias the accuracy values. For example, the reference map shown in Supplementary Fig. S7 contains more than 70% of land pixels. To address this bias, we also calculated accuracy values after removing pixels that were labeled as land by both datasets as well as the ground truth. This variation allows a more strict evaluation of water extent maps. Figure 8c shows the distribution of the difference in accuracy values under this scenario (after excluding cases with equal accuracy). As shown, a vast majority of the distribution is still towards positive values. Furthermore, the distribution has a larger spread towards high positive values, suggesting significant improvement made by the ORBIT approach.From Fig. 8, we can see that for some cases ReaLSAT based extent maps are less accurate relative to GSW. As described earlier, violation of assumptions made by the ORBIT approach could lead to the observed poor performance. Out of 2,095 extent maps, GSW labels show better accuracy than ReaLSAT for 323 of them. On visual analysis of errors in these maps, we found that 165 maps are slightly different only at the lake’s boundary. We categorized the remaining extent maps based on the reason behind the observed poor performance. In particular, 45 maps have poor performance due to occlusion of water surface by algae, 18 maps contain farm ponds, 8 contain mining lakes, 27 maps have unreliable bathymetry, 30 maps have issues due to the weighting factor used by ORBIT approach, and 30 maps have class conditional missing data. All the reference maps and corresponding maps from GSW and ReaLSAT are provided with the dataset.Next, we describe some of these cases in detail.Impact of algae: It can be difficult to visually differentiate surface algae or floating aquatic plants from terrestrial vegetation40, as they have similar reflectance spectra. Therefore, surface algal blooms often get incorrectly labeled as land in the reference maps. However, in most cases, the appearance and disappearance of algae on a lake are independent of the bathymetry. Thus, algae pixels get detected as physically inconsistent by the ORBIT approach, and consequently, these pixels are updated based on the labels of other pixels without algae. In many cases, while the accuracy with respect to the reference map is poor (because algae get labeled as land), ReaLSAT based extent maps are closer to the true extent of the lake. For example, Supplementary Fig. S8 illustrates the impact of algae on the extent mapping of Center Lake, Texas. In this example, the bimodal distribution of fraction values (either low or high) reveals high confidence in lake persistence (Supplementary Fig. S8b). On Oct 22, 2008, false-color composite processing of LANDSAT-5 imagery reveals a strong vegetative signal on the west side of the lake (Supplementary Fig. S8c). Since we know that this is a lake, we can assume that the west side of the lake is experiencing a large surface algal bloom with a similar reflectance to the surrounding terrestrial landscape. Because of the strong vegetative reflectance signal, the semi-automated reference mapping labels the west side of the lake as land (Supplementary Fig. S8d), as does most GSW labels (Supplementary Fig. S8e). Conversely, the ReaLSAT extent map labels the west side of the lake as water (Supplementary Fig. S8f). However, we calculate accuracy based on the semi-automated reference map (Supplementary Fig. S8d). Due to this, the GSW extent map is considered more accurate than the ReaLSAT map, even though this is not true because the reference map is incorrectly labeled. Therefore, some negative accuracy values may be a misrepresentation of reality due to surface algal blooms.Impact of variable bathymetry: Even though we tried to remove lakes with unreliable bathymetry by using score-based filters defined in an earlier section, not all cases were removed. For example, agricultural ponds often have small sections that are connected and change shape based on agricultural needs. Supplementary Fig. S9 highlights an example of labeling issues on agricultural ponds in Mexico. In this area, satellite imagery and the GSW fraction map confirm the presence of agricultural ponds (Supplementary Fig. S9a,b). These individual ponds are filled and drained based on operational decisions and do not follow a consistent pattern of growing or shrinking. Thus, the ORBIT approach can introduce spurious updates in water extent maps for these farms. In the Landsat-5 imagery from 2009–10–08, some of the ponds are dry, while others are filled (Supplementary Fig. S9c). This distribution of water is evident from a visual inspection and is confirmed in the semi-automated reference map (Supplementary Fig. S9d). Due to the similar elevations between the individual pond sections, the ORBIT approach spuriously fills the remaining sections with water based on the incorrectly learned bathymetry (Supplementary Fig. S9f). While quantification of such uncertainties is outside the scope of this paper, we hope that the wider research community can use RealSAT to address such questions. In particular, changes in bathymetry of a lake can be identified using spatial-temporal patterns in the label corrections. Specifically, if the elevation of some pixels in a lake increases after a certain time (e.g., sediment deposits leading to increase the elevation of a pixel), they will appear as physically inconsistent to the ORBIT framework, and hence the labels for these locations will be changed from land to water much more frequently after this increase in elevation.Impact of bias in errors and missing data: As mentioned earlier in the methods section, based on our observation, the confidence of water labels is higher than land labels in the GSW dataset. To account for this bias, we used a weighting factor of 3 for the water class. While this weighting factor improves the ORBIT approach’s performance in most cases, this assumption leads to an overestimation of water for some lakes. For example, Supplementary Fig. S10 compares the water extent maps with and without the weighting factor for a small reservoir in eastern Brazil. As we can see, the GSW labels contain false positives, and due to the weighting factor of 3, ORBIT prefers to update the land labels to water which further increases the number of false positives, as shown in Supplementary Fig. S10e. However, if we use a weighting factor of 1 for this example, the ORBIT approach can effectively remove many of the false positives in the GSW map, as shown in Supplementary Fig. S10f.Similarly, apart from missing data due to clouds in the GSW dataset, there can also be missing values on pixels where the GSW classification model is not confident. Hence, for some water extent maps, class-dependent missing data (compared to missing data which is class independent) adversely impact the ORBIT approach. For example, Supplementary Fig. S11 shows a water extent map for Zhongleng Reservoir in China, where missing data along the eastern edges is not independent but has resulted from ambiguous pixels around the lake where the GSW’s approach was not confident. In such a scenario, the ORBIT approach heavily relies on information from nearby timesteps to infer labels for missing pixels, leading to errors in ReaLSAT maps if there is a significant variation in lake extent in nearby timesteps, as shown in Supplementary Fig. S11e. More

Harbach, C. J. et al. Delayed senescence in soybean: Terminology, research update, and survey results from growers. Plant Health Progress 17, 76–83 (2016).Article 

Google Scholar 
Hobbs, H. A. et al. Green stem disorder of soybean. Plant Dis. 90, 513–518 (2006).CAS 
PubMed 
Article 

Google Scholar 
Hill, C. B., Hartman, G. L., Esgar, R. & Hobbs, H. A. Field evaluation of green stem disorder in soybean cultivars. Crop Sci. 46, 879–885 (2006).Article 

Google Scholar 
Morita, K. et al. (2006) Effect of green stem on soiled bean index at harvest of soybean by combine harvester. Hokuriku Crop Sci. 41, 107–109 (2006) (in Japanese).
Google Scholar 
Ogiwara, H. Delayed leaf senescence. In: Agriculture, Forestry and Fisheries Research Council of Japan, ed. Soybean-technical development for improving national food self-sufficiency ratio. Annotated bibliography of Agriculture, Forestry, and Fisheries Research, vol. 27, 291–294 (2002). (in Japanese).Crafts-Brandner, S. J. & Egli, D. B. Sink removal and leaf senescence in soybean. Plant Physiol. 85, 662–666 (1987).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Crafts-Brandner, S. J., Below, F. E., Harper, J. E. & Hageman, R. H. Effects of pod removal on metabolism and senescence of nodulating and nonnodulating soybean isolines. Plant Physiol. 75, 311–317 (1984).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Egli, D. B. & Bruening, W. P. Depodding causes green-stem syndrome in soybean. Crop Manag. 5(1), 1–9. https://doi.org/10.1094/CM-2006-0104-01-RS (2006).Article 

Google Scholar 
Htwe, N. M. P. S. et al. Leaf senescence of soybean at reproductive stage is associated with induction of autophagy-related genes, GmATG8c, GmATG8i and GmATG4. Plant Prod. Sci. 14, 141–147 (2011).CAS 
Article 

Google Scholar 
Leopold, A. C., Niedergang-Kamien, E. & Janick, J. Experimental modification of plant senescence. Plant Physiol. 34, 570–573 (1959).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Mondal, M. H., Brun, W. A. & Brenner, M. L. Effects of sink removal on photosynthesis and senescence in leaves of soybean (Glycine max L.) plants. Plant Physiol. 61, 394–397 (1978).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wittenbach, V. A. Effect of pod removal on leaf senescence in soybean. Plant Physiol. 70, 1544–1548 (1982).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wittenbach, V. A. Effect of pod removal on leaf photosynthesis and soluble protein composition of field-grown soybeans. Plant Physiol. 73, 121–124 (1983).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Wittenbach, V. A. Purification and characterization of a soybean leaf storage glycoprotein. Plant Physiol. 73, 125–129 (1983).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Staswick, P. E. Developmental regulation and the influence of plant sinks on vegetative storage protein gene expression in soybean leaves. Plant Physiol. 89, 309–315 (1989).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Sato, J., Shiraiwa, T., Sakashita, M., Tsujimoto, Y. & Yoshida, R. The occurrence of delayed stem senescence in relation to trans-zeatin riboside level in the xylem exudate in soybeans grown under excess-wet and drought soil conditions. Plant Prod. Sci. 10, 460–467 (2007).Article 

Google Scholar 
Takehara, T. et al. Occurrence of delayed leaf senescence of soybean caused by Rhizoctonia aerial blight in Japan. Jpn. Agric. Res. Q. 50, 201–208 (2016).Article 

Google Scholar 
Boethel, D. J. et al. Delayed maturity associated with southern green stink bug (Heteroptera: Pentatomidae) injury at various soybean phenological stages. J. Econ. Entomol. 93, 707–712 (2000).CAS 
PubMed 
Article 

Google Scholar 
Islam, M. M. et al. Nitrogen manipulation affects leaf senescence during late seed filling in soybean. Acta Physiol. Plant. 39, 42 (2017).Article 
CAS 

Google Scholar 
Yamazaki, R., Katsube-Tanaka, T. & Shiraiwa, T. Effect of thinning and shade removal on green stem disorder in soybean. Plant Prod. Sci. 21, 83–92 (2018).CAS 
Article 

Google Scholar 
Yamazaki, R., Katsube-Tanaka, T., Kawasaki, Y., Katayama, K. & Shiraiwa, T. Effect of thinning on cultivar differences of green stem disorder in soybean. Plant Prod. Sci. 22, 311–318 (2019).CAS 
Article 

Google Scholar 
Board, J. E. & Tan, Q. Assimilatory capacity effects on soybean yield components and pod number. Crop Sci. 35, 846–851 (1995).Article 

Google Scholar 
Egli, D. B. Soybean reproductive sink size and short-term reductions in photosynthesis during flowering and pod set. Crop Sci. 50, 1971–1977 (2010).Article 

Google Scholar 
Wells, R., Schulze, L. L., Ashley, D. A., Boerma, H. R. & Brown, R. H. Cultivar differences in canopy apparent photosynthesis and their relationship to seed yield in soybean. Crop Sci. 22, 886–890 (1982).Article 

Google Scholar 
Islam, M. M. et al. Nitrogen redistribution and its relationship with the expression of GmATG8c during seed filling in soybean. J. Plant Physiol. 192, 71–74 (2016).CAS 
PubMed 
Article 

Google Scholar 
Zhao, X., Zheng, S. H. & Arima, S. Influence of nitrogen enrichment during reproductive growth stage on leaf nitrogen accumulation and seed yield in soybean. Plant Prod. Sci. 17, 209–217 (2014).CAS 
Article 

Google Scholar 
Brown, A. W. & Hudson, K. A. Transcriptional profiling of mechanically and genetically sink-limited soybeans. Plant Cell Environ. 40, 2307–2318 (2017).CAS 
PubMed 
Article 

Google Scholar 
Tranbarger, T. J., Franceschi, V. R., Hildebrand, D. F. & Grimes, H. D. The soybean 94-kilodalton vegetative storage protein is a lipoxygenase that is localized in paraveinal mesophyll cell vacuoles. Plant Cell 3, 973–987 (1991).CAS 
PubMed 
PubMed Central 

Google Scholar 
Melo, B. P. et al. Revisiting the soybean GmNAC superfamily. Front. Plant Sci. 9, 1864 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
Kim, H. J. et al. Gene regulatory cascade of senescence-associated NAC transcription factors activated by ETHYLENE-INSENSITIVE2-mediated leaf senescence signaling in Arabidopsis. J. Exp. Bot. 65, 4023–4036 (2014).PubMed 
PubMed Central 
Article 

Google Scholar 
Tucker, M. L., Burke, A., Murphy, C. A., Thai, V. K. & Ehrenfried, M. L. Gene expression profiles for cell wall-modifying proteins associated with soybean cyst nematode infection, petiole abscission, root tips, flowers, apical buds, and leaves. J. Exp. Bot. 58, 3395–3406 (2007).CAS 
PubMed 
Article 

Google Scholar 
Turner, G. W. et al. Experimental sink removal induces stress responses, including shifts in amino acid and phenylpropanoid metabolism, in soybean leaves. Planta 235, 939–954 (2012).CAS 
PubMed 
Article 

Google Scholar 
Roach, T. & Krieger-Liszkay, A. The role of the PsbS protein in the protection of photosystems I and II against high light in Arabidopsis thaliana. Biochim. Biophys. Acta Bioenerg. 1817, 2158–2165 (2012).CAS 
Article 

Google Scholar 
Horton, P., Ruban, A. V. & Walters, R. G. Regulation of light harvesting in green plants. Annu. Rev. Plant Physiol. Plant Mol. Biol. 47, 655–684 (1996).CAS 
PubMed 
Article 

Google Scholar 
Hutin, C. et al. Early light-induced proteins protect Arabidopsis from photooxidative stress. Proc. Natl. Acad. Sci. U.S.A. 100, 4921–4926 (2003).CAS 
PubMed 
PubMed Central 
Article 
ADS 

Google Scholar 
Wang, H. et al. Functional characterization of dihydroflavonol-4-reductase in anthocyanin biosynthesis of purple sweet potato underlies the direct evidence of anthocyanins function against abiotic stresses. PLoS ONE 8, e78484 (2013).CAS 
PubMed 
PubMed Central 
Article 
ADS 

Google Scholar 
Saravitz, D. M. & Siedow, J. N. The differential expression of wound-inducible lipoxygenase genes in soybean leaves. Plant Physiol. 110, 287–299 (1996).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Pimenta, M. R. et al. The stress-induced soybean NAC transcription factor GmNAC81 plays a positive role in developmentally programmed leaf senescence. Plant Cell Physiol. 57, 1098–1114 (2016).CAS 
PubMed 
Article 

Google Scholar 
Fujimoto, M. et al. Transcriptional switch for programmed cell death in pith parenchyma of sorghum stems. Proc. Natl. Acad. Sci. U.S.A. 115, 8783–8792 (2018).Article 
CAS 

Google Scholar 
Egli, D. B. Variation in leaf starch and sink limitations during seed filling in soybean. Crop Sci. 39, 1361–1368 (1999).CAS 
Article 

Google Scholar 
Board, J. E. & Harville, B. G. Late-planted soybean yield response to reproductive source/sink stress. Crop Sci. 38, 763–771 (1998).Article 

Google Scholar 
Fatichin, Zheng, S. H., Narasaki, K. & Arima, S. Genotypic adaptation of soybean to late sowing in southwestern Japan. Plant Prod. Sci. 16, 123–130 (2013).CAS 
Article 

Google Scholar 
Wakasugi, K. & Fujimori, S. Subsurface Water Level Control System “FOEAS” that promotes the full use of paddy fields. J. Jpn. Soc. Irrig. Drain. Rural Eng. 77, 705–708 (2009) (in Japanese).
Google Scholar 
Fehr, W. R. & Caviness, C. E. Stages of soybean development. Spec. Rep. 80. Iowa Agric. Home Econ. Exp. Stn. Iowa State Univ., Ames. (1977).Furuya, T. & Umezaki, T. Simplified distinction method of degree of delayed stem maturation of soybean plants. Jpn. J. Crop Sci. 62, 126–127 (1993) (in Japanese with English abstract).Article 

Google Scholar 
Kim, D. et al. TopHat2: Accurate alignment of transcriptomes in the presence of insertions, deletions and gene fusions. Genome Biol. 14, R36 (2013).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar  More

In our simulations for the autotrophs, we varied two of the three trade-off properties (level of defence, plasticity costs and defence costs; see Fig. 1b) at a time and kept the third one constant. This results in three constellations reflecting three different trade-offs between these properties (Table 1):

parallel: trade-off between defence and plasticity costs;

crossing: trade-off between defence costs and plasticity costs;

angle: trade-off between defence and defence costs.

Table 1 Description of the three constellations parallel, crossing, and angle defining the position of the four phenotypes in the trait space of defence and growth rate.Full size tableIn all three constellations, the autotrophic species B spanned the entire defence range, i.e. it had a completely undefended phenotype Bu and a maximally defended phenotype Bd. A either had a more limited defence range (in constellations parallel and angle) or spanned the entire range as well (in constellation crossing), representing three distinct ways that the trade-off between defence, growth rate, and plasticity range may play out. For each constellation, we varied the maximum switching rate χmax over 5 orders of magnitude to investigate the effect of plasticity (Table 1, middle row). This parameter determines how rapidly a species can switch between phenotypes (see “Methods”, “Exchange rates”); higher values indicate faster adaptation. These results were also compared with a non-plastic baseline scenario where both phenotypes of each species are presented but χmax = 0 (Table 1, upper row), as well as a rigid scenario where the species have only a single phenotype (Table 1, bottom row). All parameters and their values can be found in Supplementary Table S1.In the following, we give a detailed description of the results for constellation parallel, where the autotroph species A and B have the same defence costs resulting in parallel trade-off lines between defence and growth rate, while varying the level of defence for A and varying the plasticity costs for B (Table 1, left column). We start with examining patterns for the phenotype biomasses, coexistence and community stability in the non-plastic baseline scenario “parallel 0”, and then compare the corresponding scenarios with a low exchange rate (“parallel 0.01”) and a high exchange rate (“parallel 1”). We next discuss the other two constellations (crossing and angle, Table 1) more briefly. Finally, we generalize across all scenarios and focus on the coexistence, the degree of maladaptive switching, and the consumer and total autotroph biomasses.Non-plastic baseline dynamics: scenario parallel 0
In this scenario, four single phenotypes unconnected by exchange compete with each other. Thus, species coexistence here depends entirely on phenotype coexistence: the trade-offs have to be such that for each species, at least one phenotype is a good enough competitor to survive. Which phenotypes survive depend on the two trade-off parameters, defence of the defended phenotype of species A (dAu) and plasticity costs for species B (pcB), which thus determine whether coexistence is possible.The defence costs were kept constant at an intermediate value of 0.3 for both species, resulting in parallel trade-off lines (Table 1, scenario “parallel 0”). The undefended phenotype of A, Au, is a growth-specialist with the highest growth rate of all phenotypes. The defended phenotype of the same species, Ad, has a defence between 0 and 0.9 and a relatively high growth rate, and can be viewed as a generalist. Species B has variable plasticity costs that lower the growth rate of both phenotypes. The defended phenotype of species B, Bd, has the lowest growth rate of all phenotypes but is very well-defended, and thus a defence-specialist. Its undefended phenotype, Bu, is as undefended as Au but has a lower growth rate; it is thus always an inferior competitor and inevitably goes extinct (Fig. 2c).Figure 2Biomasses, coexistence and trait space for scenario parallel 0. Biomasses of the four autotrophic phenotypes (a–d), their coexistence patterns (e), the consumer biomass (f) and the autotrophs’ trait values (g–j) (higher biomasses are shown by darker colours). Lines in (a–f) separate the regions I–III of different coexistence patterns. Note that in (a–f), the y-axis is reversed to show increasing fitness along all axes. An exemplary trait combination for every region is shown in (g–j); larger symbols indicate the surviving phenotypes. Shaded areas in (e) depict oscillating systems (quarter-lag predator–prey cycles in dense shading, antiphase cycles in loose shading).Full size imageAs Bu never survives, coexistence of the autotroph species requires the survival of defence-specialist Bd. Bd can only survive if Ad is not too defended, because Ad has a higher growth rate than Bd and will outcompete Bd in the “defended” niche otherwise (region Ib; Fig. 2d,h). A second criterion is that the plasticity costs for B must not be too high, because then the benefits of the defence of Bd no longer outweigh the costs, and it will go extinct even if there are no other highly defended phenotypes around (region Ia; Fig. 2d,g). In the regions where Bd goes extinct, species coexistence is not possible (Fig. 2e). The generalist Ad either survives by itself (region Ia in Fig. 2b,g) if its defence is low to intermediate, or together with the growth-specialist Au if its defence is high (region Ib in Fig. 2a,b,h). In the regions II and III where Bd survives, it never survives on its own, but always together with one of the phenotypes of A. It coexists with the growth-specialist Au if the plasticity costs are very low (region II in Fig. 2,i), and together with Ad if they are low to intermediate (region III in Fig. 2,j). These two regions do support species coexistence (Fig. 2e).In three of the four regions (Ib, II and III in Fig. 2f), consumer biomass is low, because the final community always contains a well-defended phenotype (Ad in region Ib, and Bd in regions II and III); the overall level of defence of the community is relatively high in these regions (Supplementary Figure S1). Conversely, consumer biomass is relatively high in region Ia, because the only surviving autotroph phenotype is relatively fast-growing and fairly undefended (Fig. 2f,g). The regions where a well-defended phenotype survives often show antiphase cycles (Ib, II and III in Fig. 2e). These cycles do not occur in the region where only Ad survives (Ia in Fig. 2e); but regular quarter-lag predator–prey cycles can be found here if Ad is almost entirely undefended.While the community defence (i.e. mean defence of the autotroph community) depends strongly on the coexisting phenotypes, the community growth rate is roughly constant because over the entire trait space, at least one phenotype with a high growth rate always survives (Supplementary Figure S1). The standing variance of the community defence was high when two phenotypes coexist as they occupy different niches along the defence axis (Fig. 2h–j). In contrast, the variance of the community growth rate was very low and almost constant across all regions.Effect of phenotypic plasticityEven a little bit of plasticity in the scenario parallel 0.01 (χmax = 0.01) can change the above patterns for coexistence, stability, and average consumer biomass (Fig. 3a–d). While the autotrophs are intuitively expected to benefit from being plastic, the effect of plasticity on consumer biomass always turned out to be positive (Fig. 3a). This may be explained by the fact that switching was always, on average, maladaptive (Fig. 3c,d), measured by the adaptation index Φ (see Eqs. (11–13) in “Methods”). This index combines information on the net “flow” of individuals due to switching (i.e. whether more undefended individuals switch to defended or vice versa) with the fitness difference between the two phenotypes, and thus measures whether overall, more individuals switch from a low-fitness to a high-fitness phenotype (adaptive) or the reverse (maladaptive). This index can approach zero, but is always negative at equilibrium (see Appendix B), indicating maladaptive switching.Figure 3Consumer biomass, autotroph coexistence and maladaptive switching for the scenarios parallel 0.01 (a–d) and parallel 1 (e–h). Consumer biomass (a,e), the autotroph coexistence patterns (b,f), and the autotrophs’ maladaptive switching Φ (c,d,g,h) (higher biomasses or more intensive maladaptive switching are shown by darker colours). Lines separate the regions I–III of different autotroph coexistence. The y-axis is reversed to follow the pattern of increasing fitness. Grey areas in (c,d,g,h) depict areas where the species was extinct. Shaded areas in b and f depict oscillating systems (quarter-lag predator–prey cycles in dense shading, antiphase cycles in loose shading).Full size imageThe most striking effect of plasticity was on coexistence, which was affected both positively and negatively by plasticity in different regions of the parameter space (Fig. 3b, Supplementary Figure S4a–d). A negative effect on coexistence is seen in region II, where the autotroph species previously coexisted (Fig. 2e), while with plasticity, B outcompeted A (Fig. 3b). Without plasticity, coexistence was possible in this region because Au and Bd survived; importantly, Au outcompeted Bu due to its higher growth rate, even though the difference between their growth rates is very small in this region (Fig. 2i). Plasticity reverses the competitive exclusion pattern between the two undefended phenotypes: Bu receives a constant flow of biomass from the well-defended Bd, which compensates for its slightly lower growth rate and allows it to outcompete Au. Thus, coexistence is reduced as a direct consequence of maladaptive switching.Plasticity can also promote coexistence, as the coexistence region now extends into former region Ib where the generalist Ad is highly defended (Fig. 2b, Supplementary Figure S1a). This is also an effect of maladaptive switching, though in this case the effect is indirect, mediated through the effect of plasticity on consumer biomass. Without plasticity, coexistence was impossible in region Ib because Bd was always outcompeted by Ad: even though the latter had a slightly lower level of defence, this was outweighed by its higher growth rate, making Ad the superior competitor over Bd. However, plasticity changes this because maladaptive switching increases the consumer biomass, which in turn alters the cost/ benefit balance of defence: Bd derives a stronger benefit from its high level of defence, which now outweighs the cost and allows it to survive. Coexistence through this mechanism is not possible when the plasticity costs for B are too high or when Ad is too well-defended, explaining the narrowing of the coexistence “tail” for high defence of Ad (Fig. 3b).While the patterns of coexistence changed when allowing for plasticity, the patterns in the trait values were nearly indistinguishable from the previous scenario (Supplementary Figure S1, S2). Finally, plasticity had a strong impact on the community dynamics, as most of the antiphase cycles were stabilized (Ib, II, III in Fig. 3b). Their area decreased sharply as these cycles were characterized by asynchronous dynamics between the two prey phenotypes, which were reduced by plasticity. In contrast, the area of the quarter-lag predator–prey cycles remained unaffected by plasticity.All the above patterns were found to a far stronger degree with a higher amount of plasticity (χmax = 1; Fig. 3e–h, Supplementary Figure S4e–h). Consumer biomass increased strongly everywhere (cf. Fig. 3a,e), reflecting the strong increase in the degree of maladaptive switching (cf. Fig. 3c,d,g,h). The higher exchange rates led to more synchronization between the phenotypes, extinguishing the antiphase cycles completely (Fig. 3f). It also decreased the biomass of both defended phenotypes (cf. Supplementary Figure S4b,d,f,h). This in turn led to a lower community defence and a higher community growth rate (Supplementary Figure S3) both contributing to a higher consumer biomass. Finally, there was a sharp decrease in the coexistence region for high plasticity (Fig. 3e). Region II, where B outcompetes A through maladaptive switching, doubled in size due to the much higher degree of maladaptive switching (Fig. 3g,h). Region I, where A outcompetes B, now also increased, when the level of defence of Ad is relatively low (Fig. 3e). This is again an indirect effect of maladaptive switching causing a strong increase in consumer biomass, affecting the cost/ benefit balance of defence: while Bd derives a strong benefit from its high level of defence, Bu is completely undefended, and is at an extra disadvantage because of its low growth rate. Thus, while Bd would have been able to survive by itself, the high exchange rate causes a strong source-sink dynamic that drives B extinct.Effect of plasticity in constellations crossing and angle
In constellation crossing the trade-off lines of both species cross in the trait space, as the level of defence is the same for both defended phenotypes; species B has a lower growth rate for its undefended phenotype than species A due to plasticity costs, while its defence costs are low and thus the growth rate of its defended phenotype is higher than for species A (Table 1, Supplementary Figure S5). Without plasticity the crossing trade-off lines lead to coexistence of both species in all simulations as Au and Bd were always the only survivors, mostly showing antiphase oscillations (Supplementary Figure S5).Allowing for phenotypic plasticity has the same results as were observed for constellation parallel: consumer biomass sharply increases (Fig. 4a,e); antiphase cycles are dampened or absent; and the area of coexistence decreases (Fig. 4b,f). All these changes are more pronounced for higher exchange rates (cf. Fig. 4a,b,e,f). Again, the biomass of the defended phenotypes decreased for high exchange rates (Supplementary Figure S6). Switching was always maladaptive for high exchange rates (Fig. 4g,h), and mostly maladaptive for low exchange rates (Fig. 4c,d). As was seen for constellation parallel, maladaptive switching was the reason for the decrease in coexistence. B can outcompete A when B has low plasticity costs. Bd has a much higher growth rate than Ad, while the undefended phenotypes have similar growth rates. The direction of competitive exclusion between Au and Bu is thus easily reversed by Bd donating biomass to the sink Bu, allowing B to occupy both niches and outcompete A (region II in Fig. 4b,f). The same mechanism happens in reverse for high plasticity and defence costs of B: the differences in growth rate for the undefended phenotypes are high, while the defended phenotypes have very similar growth rates. Au can support Ad, and A outcompetes B (region III in Fig. 4b,f).Figure 4Coexistence and maladaptive switching for scenario crossing 0.01 (a-d) and crossing 1 (e–h). Consumer biomass (a,e), the autotroph coexistence patterns (b,f), and the autotrophs’ maladaptive switching Φ (c,d,g,h) (higher biomasses or more intensive maladaptive switching are shown by darker colours). Lines separate the regions I–III of different autotroph coexistence. The x- and y-axis are reversed to follow the pattern of increasing fitness. Shaded areas in (b) depict antiphase cycles. Grey areas in (c,d,g,h) depict areas where the species was extinct. Shaded grey areas depict areas without simulations (cf. “Methods”). Note that (c,d,g,h) have each a different colour scale.Full size imageIn constellation angle there are no plasticity costs, and thus the undefended phenotypes Au and Bu have identical growth rates. The defended phenotypes take the same places in trait space as in the parallel constellation: Ad is a generalist, with a lower level of defence and a relatively high growth rate due to low defence costs, whereas Bd is a defence-specialist with a high level of defence but a low growth rate. This leads to the trade-off lines forming an angle (see Table 1). Without phenotypic plasticity, the coexistence patterns are the same as in constellation parallel, except that no competitive exclusion occurs between the undefended phenotypes; instead, they (neutrally) coexist in regions Ib, II and III (Supplementary Figure S7; cf. Fig. 2).With plasticity, neutral coexistence vanished: the defended phenotype that survived (Ad in region Ib, Bd in region III) could support the undefended phenotype of its own species, driving the other species extinct (Fig. 5b,f). As in the other constellations, the area of coexistence and the biomasses of the defended phenotypes decreased and antiphase cycles vanished with increasing χmax (Fig. 5b,f, Supplementary Figure S8), while maladaptive switching and the consumer biomass increased (Fig. 5).Figure 5Coexistence and maladaptive switching for scenario angle 0.01 (a–d) and angle 1 (e–h). Consumer biomass (a,e), the autotroph coexistence patterns (b,f), and the autotrophs’ maladaptive switching Φ (c,d,g,h) (higher biomasses or more intensive maladaptive switching are shown by darker colours). Lines separate the regions I–III of different autotroph coexistence. The y-axis is reversed to follow the pattern of increasing fitness. Shaded areas in (b) depict antiphase cycles. Grey areas in (c,d,g,h) depict areas where the species was extinct. Note that (c,d,g,h) have each a different colour scale.Full size imageGeneral resultsAs plasticity had very similar effects across all three constellations, we here generalize our results: we compare the three constellations for exchange rates over 5 orders of magnitude, as well as the non-plastic scenario and the rigid scenario (Table 1). That is, all simulations from one scenario (e.g. parallel 0) were summarized into one bar respective point in Fig. 6.Figure 6General patterns for coexistence, maladapative switching and biomasses. Share of surviving species in percent (A, B, coexistence or neutral coexistence) (a–c), median absolute value of maladaptive switching Φ (d–f) and median of total autotroph biomass (A + B), median consumer biomass C and share of defended phenotypes ((Ad + Bd)/(A + B)) (g–i) for the three constellations and increasing maximum exchange rates χmax. χmax = 0 denotes the non-plastic scenarios; *denotes the rigid scenarios. Maladaptive switching and the share of defended phenotypes do not apply for the rigid scenarios.Full size imageFor all constellations, the fraction of simulation runs leading to coexistence was highest in the non-plastic scenario and decreased with increasing χmax (Fig. 6a–c). In constellation parallel the share of coexistence for increasing χmax continuously decreased from 51 to 3% (Fig. 6a). In crossing, the share decreased from full to no coexistence (Fig. 6b). In angle, the share of coexistence was 88% in the non-plastic scenario when taking also neutral coexistence into account (Fig. 6c). Its share decreased to 9% for a χmax of 10 and increased again to 25% for the rigid scenario. Maladaptive switching increased for both species and all constellations for increasing χmax (Fig. 6d–f). The increased plasticity led to a lower total autotroph biomass and a lower share of defended phenotypes (Fig. 6g–i), which resulted in higher consumer biomass (Fig. 6g–i).Interestingly, and counterintuitively, the above patterns show that increasing the speed of plasticity (by increasing χmax) makes the system behave more like the rigid system. The coexistence patterns in scenarios with high χmax approach those of the rigid scenarios in two of the constellations (Fig. 6a,b). Similarly, the total autotroph and consumer biomasses approach the ones in the rigid scenarios (Fig. 6g–i). Thus, we found the higher χmax make the autotrophs not more adaptive, but behave more like non-adaptive species. More