Philippa Kaur

Deforestation, in places such as the Amazon, contributes to biodiversity loss.Credit: Ivan Valencia/Bloomberg/Getty

Researchers are relieved that a pivotal summit to finalize a new global agreement to save nature will go ahead this year, after two-years of delays because of the pandemic. But they say the hard work of negotiating an ambitious deal lays ahead.The United Nations Convention on Biological Diversity (CBD) announced yesterday that the meeting will move from Kunming in China to Montreal in Canada. The meeting of representatives from almost 200 member states of the CBD — known as COP15 — will now run from 5 to 17 December. China will continue as president of the COP15 and Huang Runqiu, China’s minister of ecology and environment, will continue as chairman.Conservation and biodiversity scientists were growing increasingly concerned that China’s strict ‘zero COVID’ strategy, which uses measures such as lockdowns to quash all infections, would force the host nation to delay the meeting again. Researchers warned that another setback to the agreement, which aims to halt the alarming rate of species extinctions and protect vulnerable ecosystems, would be disastrous for countries’ abilities to meet ambitious targets to protect biodiversity over the next decade.“We are relieved and thankful that we have a firm date for these critically important biodiversity negotiations within this calendar year,” says Andrew Deutz, an expert in biodiversity law and finance at the Nature Conservancy, a conservation group in Virginia, US. “The global community is already behind in agreeing, let alone implementing, a plan to halt and reverse biodiversity loss by 2030,” he says.With the date now set, Anne Larigauderie, executive secretary of the Intergovernmental Platform on Biodiversity and Ecosystem Services, says the key to success in Montreal will be for the new global biodiversity agreement to focus on the direct and indirect drivers of nature loss, and the behaviors that underpin them. “Policy should be led by science, action adequately resourced and change should be transformative,” she adds.New locationThe decision to move the meeting came about after representatives of the global regions who make up the decision-making body of the COP reached a consensus to shift it to Montreal. China and Canada then thrashed out the details of how the move would work. The CBD has provisions that if a host country is unable to hold a COP, the meeting shifts to the home of the convention’s secretariat, Montreal.Announcing the decision, Elizabeth Mrema, executive secretary of the CBD, said in a statement, “I want to thank the government of China for their flexibility and continued commitment to advancing our path towards an ambitious post 2020 Global Biodiversity Framework.”In a statement, Runqiu said, “China would like to emphasize its continued strong commitment, as COP president, to ensure the success of the second part of COP 15, including the adoption of an effective post 2020 Global Biodiversity Framework, and to promote its delivery throughout its presidency.”China also agreed to pay for ministers from the least developed countries and small Island developing states to travel to Montreal to participate in the meeting.Work aheadPaul Matiku, an environmental scientist and head of Nature Kenya, a conservation organization in Nairobi, Kenya, says the move “is a welcome decision” after “the world lost patience after a series of postponements”.But he says that rich nations need to reach deeper into their pockets to help low- and middle-income countries — which are home to much of the world’s biodiversity — to implement the deal, including meeting targets such as protecting at least 30% of the world’s land and seas and reducing the rate of extinction. Disputes over funding already threaten to stall the agreement. At a meeting in Geneva in March, nations failed to make progress on the new deal because countries including Gabon and Kenya argued that the US$10 billion of funding per year proposed in the draft text of the agreement was insufficient. They called for $100 billion per year in aid.“The extent to which the CBD is implemented will depend on the availability of predictable, adequate financial flows from developed nations to developing country parties,” says Matiku.Talks on the agreement are resuming in Nairobi from 21-26 June, where Deutz hopes countries can find common ground on key issues such as financing before heading to Montreal. Having a firm date set for the COP15 will help push negotiations forward, he says.“Negotiators only start to compromise when they are up against a deadline. Now they have one,” he says. More

Breed, M. F. et al. The potential of genomics for restoring ecosystems and biodiversity. Nat. Rev. Genet. 20, 615–628 (2019).CAS 
PubMed 
Article 

Google Scholar 
Carpenter, S. R., Stanley, E. H. & Vander Zanden, M. J. State of the world’s freshwater ecosystems: Physical, chemical, and biological changes. Annu. Rev. Environ. Resour. 36, 75–99 (2011).Article 

Google Scholar 
Geist, J. Integrative freshwater ecology and biodiversity conservation. Ecol. Indic. 11, 1507–1516 (2011).Article 

Google Scholar 
Jeppesen, E., Søndergaard, M., Meerhoff, M., Lauridsen, T. L. & Jensen, J. P. Shallow lake restoration by nutrient loading reduction–some recent findings and challenges ahead. Hydrobiologia 584, 239–252 (2007).CAS 
Article 

Google Scholar 
Søndergaard, M. & Jeppesen, E. Anthropogenic impacts on lake and stream ecosystems, and approaches to restoration. J. Appl. Ecol. 44, 1089–1094 (2007).Article 

Google Scholar 
Marburg, A. E., Turner, M. G. & Kratz, T. K. Natural and anthropogenic variation in coarse wood among and within lakes. J. Ecol. 94, 558–568 (2006).Article 

Google Scholar 
Schindler, D. W. Recent advances in the understanding and management of eutrophication. Limnol. Oceanogr. 51, 356–363 (2006).ADS 
Article 

Google Scholar 
Lau, S. S. S. & Lane, S. N. Continuity and change in environmental systems: The case of shallow lake ecosystems. Prog. Phys. Geogr. Earth Environ. 25, 178–202 (2001).Article 

Google Scholar 
Brinkhurst, R. O. Distribution and abundance of Tubificid (Oligochaeta) species in Toronto harbour, Lake Ontario. J. Fish. Res. Board Can. 27, 1961–1969 (1970).Article 

Google Scholar 
Wood, L. W. & Chua, K. E. Glucose flux at the sediment-water interface of Toronto Harbour, Lake Ontario, with reference to pollution stress. Can. J. Microbiol. 19, 413–420 (1973).CAS 
PubMed 
Article 

Google Scholar 
Nriagu, J. O., Wong, H. K. T. & Snodgrass, W. J. Historical records of metal pollution in sediments of Toronto and Hamilton harbours. J. Gt. Lakes Res. 9(3), 365–373 (1983).CAS 
Article 

Google Scholar 
Toronto & Region Remedial Action Plan. Metro Toronto and Region Remedial Action Plan (1989).Dahmer, S. C., Matos, L. & Morley, A. Restoring Toronto’s waters: Progress toward delisting the Toronto and Region area of concern. Aquat. Ecosyst. Health Manag. 21, 229–233 (2018).Article 

Google Scholar 
Munawar, M., Norwood, W., McCarthy, L. & Mayfield, C. In situ bioassessment of dredging and disposal activities in a contaminated ecosystem: Toronto Harbour. Hydrobiologia https://doi.org/10.1007/978-94-009-1896-2_62 (1989).Article 

Google Scholar 
Dahmer, S. C., Matos, L. & Jarvie, S. Assessment of the degradation of aesthetics beneficial use impairment in the Toronto and region area of concern. Aquat. Ecosyst. Health Manag. 21, 276–284 (2018).Article 

Google Scholar 
Metro Toronto and Region Remedial Action Plan. Within Reach: 2015 Toronto an Region Remedial Action Plan Progress Report (2016).Burniston, D. & Waltho, J. Report on Sediment Quality in the Toronto Inner Harbour 2007 (2011).Elbrecht, V., Vamos, E. E., Meissner, K., Aroviita, J. & Leese, F. Assessing strengths and weaknesses of DNA metabarcoding-based macroinvertebrate identification for routine stream monitoring. Methods Ecol. Evol. 8, 1265–1275 (2017).Article 

Google Scholar 
Emilson, C. E. et al. DNA metabarcoding and morphological macroinvertebrate metrics reveal the same changes in boreal watersheds across an environmental gradient. Sci. Rep. 7, 12777 (2017).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Aylagas, E., Borja, Á., Muxika, I. & Rodríguez-Ezpeleta, N. Adapting metabarcoding-based benthic biomonitoring into routine marine ecological status assessment networks. Ecol. Indic. 95, 194–202 (2018).Article 

Google Scholar 
Bush, A. et al. Studying ecosystems with DNA metabarcoding: Lessons from biomonitoring of aquatic macroinvertebrates. Front. Ecol. Evol. 7, 434 (2019).Article 

Google Scholar 
Serrana, J. M., Miyake, Y., Gamboa, M. & Watanabe, K. Comparison of DNA metabarcoding and morphological identification for stream macroinvertebrate biodiversity assessment and monitoring. Ecol. Indic. 101, 963–972 (2019).Article 

Google Scholar 
Fernández, S., Rodríguez-Martínez, S., Martínez, J. L., Garcia-Vazquez, E. & Ardura, A. How can eDNA contribute in riverine macroinvertebrate assessment? A metabarcoding approach in the Nalón River (Asturias, Northern Spain). Environ. DNA 1, 385–401 (2019).Article 

Google Scholar 
Hajibabaei, M. et al. Watered-down biodiversity? A comparison of metabarcoding results from DNA extracted from matched water and bulk tissue biomonitoring samples. PLoS ONE 14, e0225409 (2019).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Baird, D. J. & Hajibabaei, M. Biomonitoring 2.0: A new paradigm in ecosystem assessment made possible by next-generation DNA sequencing. Mol. Ecol. 21, 2039–2044 (2012).PubMed 
Article 

Google Scholar 
Hajibabaei, M., Baird, D. J., Fahner, N. A., Beiko, R. & Golding, G. B. A new way to contemplate Darwin’s tangled bank: How DNA barcodes are reconnecting biodiversity science and biomonitoring. Philos. Trans. R. Soc. B. Biol. Sci. 371, 20150330 (2016).Article 
CAS 

Google Scholar 
Beermann, A. J., Zizka, V. M. A., Elbrecht, V., Baranov, V. & Leese, F. DNA metabarcoding reveals the complex and hidden responses of chironomids to multiple stressors. Environ. Sci. Eur. 30, 26 (2018).Article 

Google Scholar 
Bush, A. et al. DNA metabarcoding reveals metacommunity dynamics in a threatened boreal wetland wilderness. Proc. Natl. Acad. Sci. 117, 8539–8545 (2020).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Compson, Z. G. et al. Chapter Two—Linking DNA Metabarcoding and Text Mining to Create Network-Based Biomonitoring Tools: A Case Study on Boreal Wetland Macroinvertebrate Communities. In Advances in Ecological Research Vol. 59 (eds Bohan, D. A. et al.) 33–74 (Academic Press, 2018).
Google Scholar 
Fernandes, K. et al. DNA metabarcoding—A new approach to fauna monitoring in mine site restoration. Restor. Ecol. 26, 1098–1107 (2018).Article 

Google Scholar 
Fernandes, K. et al. Invertebrate DNA metabarcoding reveals changes in communities across mine site restoration chronosequences. Restor. Ecol. 27, 1177–1186 (2019).Article 

Google Scholar 
Poikane, S. et al. Benthic macroinvertebrates in lake ecological assessment: A review of methods, intercalibration and practical recommendations. Sci. Total Environ. 543, 123–134 (2016).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Macher, J.-N. et al. Comparison of environmental DNA and bulk-sample metabarcoding using highly degenerate cytochrome c oxidase I primers. Mol. Ecol. Resour. 18, 1456–1468 (2018).CAS 
PubMed 
Article 

Google Scholar 
Marshall, N. T. & Stepien, C. A. Macroinvertebrate community diversity and habitat quality relationships along a large river from targeted eDNA metabarcode assays. Environ. DNA 2, 572–586 (2020).Article 

Google Scholar 
Metro Toronto and Region Remedial Action Plan. Updates on Actions 2013–2014. (2013).López-López, E. & Sedeño-Díaz, J. E. Biological indicators of water quality: The role of fish and macroinvertebrates as indicators of water quality. In Environmental Indicators (eds Armon, R. H. & Hänninen, O.) 643–661 (Springer Netherlands, 2015). https://doi.org/10.1007/978-94-017-9499-2_37.Chapter 

Google Scholar 
Berry, O. et al. A Comparison of Morphological and DNA Metabarcoding Analysis of Diets in Exploited Marine Fishes (2015).Sweeney, B. W., Battle, J. M., Jackson, J. K. & Dapkey, T. Can DNA barcodes of stream macroinvertebrates improve descriptions of community structure and water quality?. J. N. Am. Benthol. Soc. 30, 195–216 (2011).Article 

Google Scholar 
Banerji, A. et al. Spatial and temporal dynamics of a freshwater eukaryotic plankton community revealed via 18S rRNA gene metabarcoding. Hydrobiologia 818, 71–86 (2018).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Porter, T. M. et al. Widespread occurrence and phylogenetic placement of a soil clone group adds a prominent new branch to the fungal tree of life. Mol. Phylogenet. Evol. 46, 635–644 (2008).CAS 
PubMed 
Article 

Google Scholar 
Rosling, A. et al. Archaeorhizomycetes: Unearthing an ancient class of ubiquitous soil fungi. Science 333, 876–879 (2011).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Mandaville, S. M. Benthic Macroinvertebrates in Freshwaters—Taxa Tolerance Values, Metrics, and Protocols, vol. 128. http://lakes.chebucto.org/H-1/tolerance.pdf (2002).Trzcinski, M. K. et al. The effects of food web structure on ecosystem function exceeds those of precipitation. J. Anim. Ecol. 85, 1147–1160 (2016).PubMed 
Article 

Google Scholar 
Liu, X. & Wang, H. Contrasting patterns and drivers in taxonomic versus functional diversity, and community assembly of aquatic plants in subtropical lakes. Biodivers. Conserv. 27(12), 3103–3118 (2018).Article 

Google Scholar 
Kovalenko, K. E., Brady, V. J., Ciborowski, J. J. H., Ilyushkin, S. & Johnson, L. B. Functional changes in littoral macroinvertebrate communities in response to watershed-level anthropogenic stress. PLoS ONE 9, e101499 (2014).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Luiza-Andrade, A., Montag, L. F. A. & Juen, L. Functional diversity in studies of aquatic macroinvertebrates community. Scientometrics 111, 1643–1656 (2017).Article 

Google Scholar 
MacMillan, G. A., Chételat, J., Heath, J. P., Mickpegak, R. & Amyot, M. Rare earth elements in freshwater, marine, and terrestrial ecosystems in the eastern Canadian Arctic. Environ. Sci. Process. Impacts 19, 1336–1345 (2017).CAS 
PubMed 
Article 

Google Scholar 
Pastorino, P. et al. Macrobenthic invertebrates as tracers of rare earth elements in freshwater watercourses. Sci. Total Environ. 698, 134282 (2020).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Kulaš, A. et al. Ciliates (Alveolata, Ciliophora) as bioindicators of environmental pressure: A karstic river case. Ecol. Indic. 124, 107430 (2021).Article 

Google Scholar 
Persaud, D., Lomas, T., Boyd, D. & Mathai, S. Historical Development and Quality of the Toronto Waterfront Sediments (1985).Milani, D. & Grapentine, L. Assessment of Sediment Quality in the Bay of Quinte Area Of Concern (2000).Reynoldson, T. B., Bailey, R. C., Day, K. E. & Norris, R. H. Biological guidelines for freshwater sediment based on BEnthic Assessment of SedimenT (the BEAST) using a multivariate approach for predicting biological state. Aust. J. Ecol. 20(1), 198–219 (1995).Article 

Google Scholar 
Geller, J., Meyer, C., Parker, M. & Hawk, H. Redesign of PCR primers for mitochondrial cytochrome c oxidase subunit I for marine invertebrates and application in all-taxa biotic surveys. Mol. Ecol. Resour. 13, 851–861 (2013).CAS 
PubMed 
Article 

Google Scholar 
Leray, M. et al. A new versatile primer set targeting a short fragment of the mitochondrial COI region for metabarcoding metazoan diversity: Application for characterizing coral reef fish gut contents. Front. Zool. 10, 34 (2013).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Zhan, A. et al. High sensitivity of 454 pyrosequencing for detection of rare species in aquatic communities. Methods Ecol. Evol. 4, 558–565 (2013).Article 

Google Scholar 
Gibson, J. et al. Simultaneous assessment of the macrobiome and microbiome in a bulk sample of tropical arthropods through DNA metasystematics. Proc. Natl. Acad. Sci. 111, 8007–8012 (2014).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Gibson, J. F. et al. Large-scale biomonitoring of remote and threatened ecosystems via high-throughput sequencing. PLoS ONE 10, e0138432 (2015).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Porter, T. M. & Hajibabaei, M. METAWORKS: A flexible, scalable bioinformatic pipeline for multi-marker biodiversity assessments. bioRxiv https://doi.org/10.1101/2020.07.14.202960 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
Köster, J. & Rahmann, S. Snakemake—a scalable bioinformatics workflow engine. Bioinformatics 28, 2520–2522 (2012).PubMed 
Article 
CAS 

Google Scholar 
Anon. Conda. (2016).Porter, T. M. & Hajibabaei, M. Automated high throughput animal CO1 metabarcode classification. Sci. Rep. 8, 4226 (2018).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
Porter, T. M. Eukaryote CO1 Reference set for the RDP Classifier (Zenodo, 2017) https://doi.org/10.5281/zenodo.4741447.Book 

Google Scholar 
Porter, T. M. SILVA 18S Reference Set for the RDP Classifier(Zenodo, 2018) https://doi.org/10.5281/zenodo.4741433.Book 

Google Scholar 
R Core Team. R: A Language and Environment for Statistical Computing (R Core Team, 2020).
Google Scholar 
Wickham, H. ggplot2: Elegant Graphics for Data Analysis (Springer-Verlag, 2009). https://doi.org/10.1007/978-0-387-98141-3.Book 
MATH 

Google Scholar 
Oksanen, J. et al. vegan: Community Ecology Package (2020).Komsta, L. & Novomestky, F. moments: Moments, cumulants, skewness, kurtosis and related tests (2015).U.S. Environmental Protection Agency. Freshwater Biological Traits Database (Final Report) EPA/600/R-11/038F. (2012)U.S. Environmental Protection Agency. Freshwater Biological Traits Database (2012).Schmidt-Kloiber, A. & Hering, D. An online tool that unifies, standardises and codifies more than 20,000 European freshwater organisms and their ecological preferences. Ecol. Indic. 53, 271–282 (2015).Article 

Google Scholar 
Moog, O. Fauna Aquatica Austriaca – Catalogue for autecological Classification of Austrian Aquatic Organisms (1995).Tachet, H., Bournaud, M., Richoux, P., Usseglio-Polatera, P. Invertébrés d’eau douce – systématique, biologie, écologie (2010).Nally, R. M. & Walsh, C. J. Hierarchical partitioning public-domain software. Biodivers. Conserv. https://doi.org/10.1023/B:BIOC.0000009515.11717.0b (2004).Article 

Google Scholar  More

Parra-Lopez, C., Groot, J. C. J., Carmona-Torres, C. & Rossing, W. A. H. Integrating public demands into model-based design for multifunctional agriculture: an application to intensive Dutch dairy landscapes. Ecol. Econ. 67(4), 538–551 (2008).Article 

Google Scholar 
Pinto-Correia, T., Guiomar, N., Guerra, C.A. et al. Assessing the ability of rural (2016)UPA. Desarrollo rural. Oportunidades Desaprovechadas La Tierra 254, 31–33 (2016).
Google Scholar 
Abreu, I., Nunes, J. M. & Mesias, F. J. Can rural development Be measured? Design and application of a synthetic index to Portuguese municipalities. Soc. Indic. Res. 145, 1107–1123 (2019).Article 

Google Scholar 
Doxiadis, C. A. Ekistics: an introduction to the science of human settlements (Oxford University Press, 1968).
Google Scholar 
Algeciras, J. A. R., Coch, H. & Perez, G. D. L. P. Human thermal comfort conditions and urban planning in hot-humid climates-The case of Cuba. Int. J. Biometeorol. 60, 1151–1164 (2016).Article 

Google Scholar 
Zhang, H., Zhang, S. & Liu, Z. Evolution and influencing factors of China’s rural population distribution patterns since 1990. PLoS ONE 15, e0233637 (2020).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
Eurostat. Eurostat Regional Yearbook. 2019 Edition. Publications Office of the European Union, Luxembourg (2019)Overview of CAP Reform 2014–2020. Agricultural Policy Perspectives. Brief, no. 5, December 2013. European Commission.Marsden, T. & Sonnino, R. Rural development and the regional state: denying multifunctional agriculture in the UK. J. Rural Stud. 24(4), 422–431 (2008).Article 

Google Scholar 
Adamowicz, M. Normative Aspects of Rural Development Strategy and Policy in The European Union Normative Aspects of Rural Development Strategy and Policy in The European Union, (2018)Léon, Y. Rural development in Europe: a research frontier for agricultural economists. Eur. Rev. Agric. Econ. 32, 301–317 (2005).Article 

Google Scholar 
Biegańska, J., Środa-Murawska, S., Kruzmetra, Z. & Swiaczny, F. Peri-Urban development as a significant rural development trend. Quaest. Geogr. 37, 125–140 (2018).Article 

Google Scholar 
Lee I.-H. Change of rural development policy in South Korea After Korean War. J. Reg City Plan, 2021.Oh, Y.-Y. et al. The selection of proper resource and change of salinity in Helianthus tuberosus L. cultivated in Saemangeum reclaimed tidal land. Korean J. Environ. Agric. 37, 73–78 (2018).Article 

Google Scholar 
Yoon, J.-Y., Jeong, J.-H. & Choi, S.-K. Validation of reference genes for quantifying changes in physiological gene expression in apple tree under cold stress and virus infection. Radiat. Prot. Dosim. 26, 144–158 (2020).
Google Scholar 
Faradiba, F. & Zet, L. The impact of climate factors, disaster, and social community in rural development. J. Asian Finance Econ. Bus. 7, 707–717 (2020).Article 

Google Scholar 
Kaneko, M., Ohta, R., Vingilis, E. & Mathews, M. Thomas Robert freeman; systematic scoping review of factors and measures of rurality: toward the development of a rurality index for health care research in Japan. BMC Health Services Res. 21, 1–11 (2021).Article 

Google Scholar 
Yokoyama, S. Sustainable activities for rural development, New Frontiers in Regional Science: Asian Perspectives, (2019).Georgios, C., & Barraí, H. Social innovation in rural governance: a comparative case study across the marginalised rural EU. J. Rural Stud. (2021)Michalek, J. & Zarnekow, N. Application of the rural development index to analysis of rural regions in Poland and Slovakia. Soc. Indic. Res. 105, 1–37 (2012).Article 

Google Scholar 
Liu, Y., Wang, G. & Zhang, F. Spatio-temporal dynamic patterns of rural area development in eastern coastal China. Chin. Geogr. Sci. 23, 173–181 (2013).Article 

Google Scholar 
Kim, T.-H. & Yang, S.-R. Construction of the rural development index: the case of Vietnam. J. Rural Dev. 39, 113–142 (2016).
Google Scholar 
Houkai, W. Current top ten frontier issues [J]in the study of agriculture. Rural Areas Rural Econ. China 4, 2–6 (2019).
Google Scholar 
Hu, Y., Fu, R. & Jin, S. Ecological environment concern in the organic link between poverty alleviation and rural revitalization. Reform 10, 141–148 (2019).
Google Scholar 
Zhang H., Gao L., & Yan K. On the theoretical origin, main innovation and realization path of rural revitalization thought rural economy in China, (11), 2–16 (2018).Feiwei, S. & Zegan, X. Construction and empirical analysis of the index system of beautiful villages in Zhejiang Province. J. Huazhong Agric. Univ. (Social Sciences Edition) 02, 45-51+132 (2017).
Google Scholar 
Research Group of Shanghai Rural Revitalization Index. Construction and evaluation of the index system of rural revitalization in Shanghai. Sci. Dev. 9, 56–63 (2020).World Bank, Expanding the Measure of Wealth. Indicators of Environmentally Sustainable Development. World Bank, Washington, D.C. (1997)Hicks, D. A. The inequality-adjusted human development index: a constructive proposal. World Dev. 25, 1283–1298 (1997).ADS 
Article 

Google Scholar 
Zhao, R., Shao, C. & He, R. Spatiotemporal evolution of ecosystem health of China’s Provinces based on SDGs. Int. J Environ. Res. Public Health 18, 10569 (2021).PubMed 
PubMed Central 
Article 

Google Scholar 
Kageyama, A., Desenvolvimento rural : conceitos e aplicaçao ao caso brasileiro. UFRGS Editora, Porto Alegre (Brasil) (2008).Abreu, I. Construçao de um índice de desenvolvimento rural e sua aplicaçao ao Alto Alentejo. Instituto Polit´ecnico de Portalegre (2014)Castellani, V. & Sala, S. Sustainable performance index for tourism policy development. Tour. Manag. 31, 871–880 (2009).Article 

Google Scholar 
Hashemi, N. The role of ecotourism in sustainable rural development. J. Rural Dev. Stud. 13(3), 173–188 (2010).
Google Scholar 
Alkire, S., Conconi, A., & Seth, S. Multidimensional Poverty Index 2013: Brief methodological note and results. Oxford Poverty and Human Development Initiative (OPHI) (2014b)Alkire, S., Foster, J. & Santos, M. E. Where did identification go?. J. Econ. Inequal. 9, 501–505 (2011).Article 

Google Scholar 
Alkire, S. et al. Multidimensional poverty measurement and analysis (Oxford University Press, Oxford, 2015).MATH 
Book 

Google Scholar 
Alkire, S., & Seth, S. Identifying destitution through linked subsetsof multidimensionally poor: an ordinal approach, OPHI Working Paper 99. University of Oxford (2016)Li, X., Yang, H., Jia, J., Shen, Y. & Liu, J. Index system of sustainable rural development based on the concept of ecological livability. Environ. Impact Assess. Rev. 86, 1–12 (2021).
Google Scholar 
Guo, X. & Hu, Y. Construction of evaluation index system of rural revitalization level. Agric. Econ. Manag. 05, 5–15 (2020).
Google Scholar 
Kong, X. & Xia, J. The value logic relation and synergy path choice between rural revitalization strategy and rural integration development. J. Northwest Univ. (Philosophy and Social Sciences Edition) 49(02), 10–18 (2019).
Google Scholar 
Wen, T. Three hundred years: the context and development of Chinese rural construction. Open Age. (04) (2016)Ren, C. A Study on the basis, constraints and institutional supply of industrial prosperity. Acad. Acad. 07, 15–27 (2018).
Google Scholar 
Ye, X., Cheng, Y., Zhao, J. & Ning, X. Rural revitalization during the 14th Five-year plan: trend judgment, general thinking and safeguard mechanism. Rural Econ. 09, 1–9 (2020).
Google Scholar 
Zhu, Q. The sociological explanation of the prosperity of rural industry-industry in the context of rural revitalization. J. China Agric. Univ. (Social Sciences Edition) 35(03), 89–95 (2018).
Google Scholar 
Bithas, K. A bioeconomic approach to sustainability with ecological thresholds as an operational indicator. Environ. Sustain. Indic. 6, 100027 (2020).Article 

Google Scholar 
Zheng, X. The East Asian experience of Rural Revitalization and its Enlightenment to China—Take Japan and South Korea as an example. Lanzhou J. 11, 200–208 (2019).ADS 

Google Scholar 
Srivastava, P. K., Kulshreshtha, K., Monhanty, C. S., Pushpangadan, P. & Singh, A. Stakeholder-based SWOT analysis for successful municipal solid waste managementin Lucknow, India. Waste Manag 25(5), 531–537 (2005).CAS 
PubMed 
Article 

Google Scholar 
Alcon, F., Tapsuwan, S., Martínez-Paz, J. M., Brouwer, R. & Miguel, M. Forecasting deficit irrigation adoption using a mixed stakeholder assessment methodology. Technol. Forecast. Soc. Change 83, 183–193. https://doi.org/10.1016/j.techfore.2013.07.003 (2014).Article 

Google Scholar 
Chen, Y., Yang, G., Sweeney, S. & Feng, Y. Household biogas use in rural China: a study of opportunities and constraints. Renew. Sust. Energ. Rev. 14(1), 545–549 (2010).Article 

Google Scholar 
Yeh, C. H. A problem-based selection of multi-attribute decision-making methods. Int. Trans. Oper. Res. 9(2), 169–181 (2002).MATH 
Article 

Google Scholar 
Chakraborty, S., & Yeh, C. -H. A simulation comparison of normalization procedures for TOPSIS, In 2009 International Conference on Computers & Industrial Engineering, IEEE, 2009.Yoon, K. & Hwang, C. L. Multiple attribute decision making. Eur. J. Oper. Res. 4(4), 287–288 (1995).
Google Scholar 
Sharma, N., Khan, Z.A., Siddiquee, A.N., Wahid, M.A. Proc. Inst. Mech. Eng. Part C:J. Mech. Eng. Sci. 233 (2019) 1–10.Maniraj, S. & Thanigaivelan, R. Optimization of electrochemical micromachining process parameters for machining of AMCs with different % compositions of GGBS using Taguchi and TOPSIS methods. Trans. Indian Inst. Met. 72, 3057–3066 (2019).CAS 
Article 

Google Scholar 
Martinez-Fernandez, C. et al. Shrinking cities in Australia, Japan, Europe and the USA: From a global process to local policy responses. Prog. Plan. 105, 1–48 (2016).Article 

Google Scholar 
Mo, G. Green poverty reduction: the value orientation and realization path of ecological poverty alleviation in the battle against poverty—a series of studies on the mechanism of improving the performance of precision poverty alleviation. Modern Econ. Discuss. 11, 10–14 (2016).
Google Scholar 
Wu, L. Echanism and path selection of poverty alleviation in deep-poverty areas. Chin. Soft Sci. 7, 63–70 (2018).
Google Scholar 
Shengzu, Gu. et al. Countermeasure reflections on advancing the poverty relief in the 13th five-year plan. China Financial Res 2, 7–16 (2016).
Google Scholar 
Xie, Z. & Xunwu, J. Giving full play to the advantages of financial financing to help lift out of poverty. China Finance 3, 83–84 (2018).
Google Scholar 
Chen, W. A Way to realize the effective linkage between poverty relief and rural revitalization. Guizhou Soc. Sci. 1, 11–14 (2020).
Google Scholar 
Bijker, R. & Haartsen, T. More than counterurbanisation: migration to popular andless-popular rural areas in the Netherlands. Popul. Space Place 18, 643–657 (2012).Article 

Google Scholar  More

Sherr, E. B. & Sherr, B. F. Role of microbes in pelagic food webs: A revised concept. Limnol. Oceanogr. 33, 1225–1227 (1988).ADS 
Article 

Google Scholar 
Weisse, T. Pelagic microbes—Protozoa and the microbial food web. In The Lakes Handbook, Vol. 1—Limnology and Limnetic Ecology (eds O’Sullivan, P. & Reynolds, C. S.) 417–460 (Blackwell Science Ltd, 2004).
Google Scholar 
Foissner, W. Protist diversity: Estimates of the near-imponderable. Protist 150, 363–368 (1999).CAS 
PubMed 
Article 

Google Scholar 
Sommer, U. & Sommer, F. Cladocerans versus copepods: The cause of contrasting top–down controls on freshwater and marine phytoplankton. Oecologia 147, 183–194 (2006).ADS 
PubMed 
Article 

Google Scholar 
Wiackowski, K., Brett, M. T. & Goldman, C. R. Differential effects of zooplankton species on ciliate community structure. Limnol. Oceanogr. 39, 486–492 (1994).ADS 
Article 

Google Scholar 
Armengol, L., Calbet, A., Franchy, G., Rodríguez-Santos, A. & Hernández-León, S. Planktonic food web structure and trophic transfer efficiency along a productivity gradient in the tropical and subtropical Atlantic Ocean. Sci. Rep. 9, 2044. https://doi.org/10.1038/s41598-019-38507-9 (2019).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Carrick, H. J., Fahnenstiel, G. L., Stoermer, E. F. & Wetzel, R. G. The importance of zooplankton-protozoan trophic couplings in Lake Michigan. Limnol. Oceanogr. 36, 1335–1345. https://doi.org/10.4319/lo.1991.36.7.1335 (1991).ADS 
Article 

Google Scholar 
Jack, J. D. & Gilbert, J. J. Effects of metazoan predators on ciliates in freshwater plankton communities. J. Eukaryot. Microbiol. 44, 194–199. https://doi.org/10.1111/j.1550-7408.1997.tb05699.x (1997).Article 

Google Scholar 
Sanders, R. W. & Wickham, S. A. Planktonic protozoa and metazoa: Predation, food quality and population control. Mar. Microb. Food Webs 7, 197–223 (1993).
Google Scholar 
Kiørboe, T. How zooplankton feed: Mechanisms, traits and trade-offs. Biol. Rev. 86, 311–339. https://doi.org/10.1111/j.1469-185X.2010.00148.x (2011).Article 
PubMed 

Google Scholar 
Gliwicz, Z. M. Zooplankton. The Lakes Handbook: Limnology and Limnetic Ecology Vol. 1 (eds P. O’Sullivan & C. S. Reynolds) 461–516 (Blackwell Science Ltd, 2004).Wickham, S. A. The direct and indirect impact of Daphnia and cyclops on a freshwater microbial food web. J. Plankton Res. 20, 739–755 (1998).Article 

Google Scholar 
Gilbert, J. J. Suppression of rotifer populations by Daphnia: A review of the evidence, the mechanisms, and the effects on zooplankton community structure. Limnol. Oceanogr. 33, 1286–1303 (1988).ADS 
Article 

Google Scholar 
Lampert, W. & Muck, P. Multiple aspects of food limitation in zooplankton communities: The Daphnia-Eudiaptomus example. Ergebnisse der Limnologie/Adv. Limnol. 21, 311–322 (1985).
Google Scholar 
Kiørboe, T. What makes pelagic copepods so successful?. J. Plankton Res. 33, 677–685. https://doi.org/10.1093/plankt/fbq159 (2011).Article 

Google Scholar 
Paffenhöfer, G.-A. Heterotrophic protozoa and small metazoa: Feeding rates and prey-consumer interactions. J. Plankton Res. 20, 121–133 (1998).Article 

Google Scholar 
Forró, L., Korovchinsky, N. M., Kotov, A. A. & Petrusek, A. Global diversity of cladocerans (Cladocera; Crustacea) in freshwater. In Freshwater Animal Diversity Assessment 177–184 (Springer, 2007).Jack, J. D. & Gilbert, J. J. Susceptibilities of different-sized ciliates to direct suppression by small and large cladocerans. Freshw. Biol. 29, 19–29 (1993).Article 

Google Scholar 
Jürgens, K. Impact of Daphnia on planktonic microbial food webs—A review. Mar. Microb. Food Webs 8, 295–324 (1994).
Google Scholar 
Calbet, A. & Saiz, E. The ciliate-copepod link in marine ecosystems. Aquat. Microb. Ecol. 38, 157–167. https://doi.org/10.3354/ame038157 (2005).Article 

Google Scholar 
Saiz, E. & Calbet, A. Scaling of feeding in marine calanoid copepods. Limnol. Oceanogr. 52, 668–675 (2007).ADS 
Article 

Google Scholar 
Steinberg, D. K. & Landry, M. R. Zooplankton and the ocean carbon cycle. Ann. Rev. Mar. Sci. 9, 413–444 (2017).PubMed 
Article 

Google Scholar 
Pierce, R. W. & Turner, J. T. Ecology of planktonic ciliates in marine food webs. Rev. Aquat. Sci. 6, 139–181 (1992).
Google Scholar 
Oghenekaro, E. U. & Chigbu, P. Population dynamics and life history of marine cladocera in the maryland coastal bays, USA. J. Coast. Res. 35, 1225–1236 (2019).Article 

Google Scholar 
Pestorić, B., Lučić, D & Joksimović, D. Cladocerans spatial and temporal distribution in the coastal south Adriatic waters (Montenegro). Stud. Mar. 25, 101–120 (2011).Adrian, R. & Schneider-Olt, B. Top-down effects of crustacean zooplankton on pelagic microorganisms in a mesotrophic lake. J. Plankton Res. 21, 2175–2190. https://doi.org/10.1093/plankt/21.11.2175 (1999).Article 

Google Scholar 
Burns, C. W. & Schallenberg, M. Relative impacts of copepods, cladocerans and nutrients on the microbial food web of a mesotrophic lake. J. Plankton Res. 18, 683–714. https://doi.org/10.1093/plankt/18.5.683 (1996).Article 

Google Scholar 
Field, C. B., Behrenfeld, M. J., Randerson, J. T. & Falkowski, P. Primary production of the biosphere: Integrating terrestrial and oceanic components. Science 281, 237–240 (1998).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Lewis, W. M. Jr. Global primary production of lakes: 19th Baldi Memorial Lecture. Inland Waters 1, 1–28 (2011).Article 

Google Scholar 
Moore, C. et al. Processes and patterns of oceanic nutrient limitation. Nat. Geosci. 6, 701–710. https://doi.org/10.1038/NGEO1765 (2013).ADS 
CAS 
Article 

Google Scholar 
Gilbert, J. J. Jumping behavior in the oligotrich ciliates Strobilidium velox and Halteria grandinella and its significance as a defense against rotifers. Microb. Ecol. 27, 189–200 (1994).CAS 
PubMed 
Article 

Google Scholar 
Weisse, T. & Sonntag, B. Ciliates in planktonic food webs: communication and adaptive response. In Biocommunication of Ciliates (eds Witzany, G. & Nowacki, M.) 351–372 (Springer International Publishing, 2016).
Google Scholar 
Burns, C. W. & Gilbert, J. J. Predation on ciliates by freshwater calanoid copepods: Rates of predation and relative vulnerabilities of prey. Freshw. Biol. 30, 377–393. https://doi.org/10.1111/j.1365-2427.1993.tb00822.x (1993).Article 

Google Scholar 
Lampert, W. & Sommer, U. Limnoecolgy 2nd edn. (Oxford University Press, 2007).
Google Scholar 
Almeda, R., Someren Gréve, H. & Kiørboe, T. Prey perception mechanism determines maximum clearance rates of planktonic copepods. Limnol. Oceanogr. 63, 2695–2707. https://doi.org/10.1002/lno.10969 (2018).ADS 
Article 

Google Scholar 
Holling, C. S. The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Entomol. 91, 293–320 (1959).Article 

Google Scholar 
Fenchel, T. Ecology of protozoa. The Biology of Free-living Phagotrophic Protists (Science Tech./Springer, 1987).
Google Scholar 
Weisse, T. et al. Functional ecology of aquatic phagotrophic protists—Concepts, limitations, and perspectives. Eur. J. Protistol. 55, 50–74. https://doi.org/10.1016/j.ejop.2016.03.003 (2016).Article 
PubMed 

Google Scholar 
Wickham, S. A. Cyclops predation on ciliates: Species-specific differences and functional responses. J. Plankton Res. 17, 1633–1646 (1995).Article 

Google Scholar 
Coats, D. W. & Bachvaroff, T. R. Parasites of tintinnids. In The Biology and Ecology of Tintinnid Ciliates: Models for Marine Plankton (eds Dolan, R. et al.) 145–170 (Wiley, 2012).Chapter 

Google Scholar 
Guillou, L. et al. Widespread occurrence and genetic diversity of marine parasitoids belonging to Syndiniales (Alveolata). Environ. Microbiol. 10, 3349–3365. https://doi.org/10.1111/j.1462-2920.2008.01731.x (2008).CAS 
Article 
PubMed 

Google Scholar 
Brun, P. G., Payne, M. R. & Kiørboe, T. A trait database for marine copepods. Earth Syst. Sci. Data 9, 99–113. https://doi.org/10.5194/essd-9-99-2017 (2017).ADS 
Article 

Google Scholar 
Armengol, L., Franchy, G., Ojeda, A., Santana-del Pino, Á. & Hernández-León, S. Effects of copepods on natural microplankton communities: Do they exert top-down control?. Mar. Biol. 164, 136. https://doi.org/10.1007/s00227-017-3165-2 (2017).Article 

Google Scholar 
Moriarty, R. & O’Brien, T. Distribution of mesozooplankton biomass in the global ocean. Earth Syst. Sci. Data 5, 45–55 (2013).ADS 
Article 

Google Scholar 
Landry, M. R., Al-Mutairi, H., Selph, K. E., Christensen, S. & Nunnery, S. Seasonal patterns of mesozooplankton abundance and biomass at Station ALOHA. Deep Sea Res. Part II Top. Stud. Oceanogr. 48, 2037–2061 (2001).ADS 
Article 

Google Scholar 
Turner, J. T. The importance of small planktonic copepods and their roles in pelagic marine food webs. Zool. Stud. 43, 255–266 (2004).
Google Scholar 
Heneghan, R. F. et al. A functional size-spectrum model of the global marine ecosystem that resolves zooplankton composition. Ecol. Model. 435, 109265. https://doi.org/10.1016/j.ecolmodel.2020.109265 (2020).CAS 
Article 

Google Scholar 
Wang, Q. et al. Predicting temperature impacts on aquatic productivity: Questioning the metabolic theory of ecology’s “canonical” activation energies. Limnol. Oceanogr. 64, 1172–1185. https://doi.org/10.1002/lno.11105 (2019).ADS 
Article 

Google Scholar 
Montagnes, D. J. Ecophysiology and behavior of tintinnids. In The Biology and Ecology of Tintinnid Ciliates: Models for Marine Plankton (eds Dolan, R. et al.) 85–121 (Wiley, 2012).Chapter 

Google Scholar 
McManus, G. B. & Santoferrara, L. F. Tintinnids in microzooplankton communities. In The Biology and Ecology of Tintinnid Ciliates: Models for Marine Plankton (eds Dolan, R. et al.) 198–213 (Wiley, 2012).Chapter 

Google Scholar 
Fileman, E., Petropavlovsky, A. & Harris, R. Grazing by the copepods Calanus helgolandicus and Acartia clausi on the protozooplankton community at station L4 in the Western English Channel. J. Plankton Res. 32, 709–724. https://doi.org/10.1093/plankt/fbp142 (2010).CAS 
Article 

Google Scholar 
Zeldis, J. R. & Décima, M. Mesozooplankton connect the microbial food web to higher trophic levels and vertical export in the New Zealand Subtropical Convergence Zone. Deep Sea Res. Part I Oceanogr. Res. Pap. 155, 103146. https://doi.org/10.1016/j.dsr.2019.103146 (2020).CAS 
Article 

Google Scholar 
Stoecker, D. K. Predators of tintinnids. In The Biology and Ecology of Tintinnid Ciliates: Models for Marine Plankton (eds Dolan, J. R. et al.) 122–144 (Wiley, 2012).Chapter 

Google Scholar 
Levinsen, H. & Nielsen, T. G. The trophic role of marine pelagic ciliates and heterotrophic dinoflagellates in arctic and temperate coastal ecosystems: A cross-latitude comparison. Limnol. Oceanogr. 47, 427–439. https://doi.org/10.4319/lo.2002.47.2.0427 (2002).ADS 
Article 

Google Scholar 
Gallienne, C. & Robins, D. Is Oithona the most important copepod in the world’s oceans?. J. Plankton Res. 23, 1421–1432. https://doi.org/10.1093/plankt/23.12.1421 (2001).Article 

Google Scholar 
Stoecker, D. K. & Egloff, D. A. Predation by Acartia tonsa Dana on planktonic ciliates and rotifers. J. Exp. Mar. Biol. Ecol. 110, 53–68 (1987).Article 

Google Scholar 
Stoecker, D. & Pierson, J. Predation on protozoa: Its importance to zooplankton revisited. J. Plankton Res. 41, 367–373. https://doi.org/10.1093/plankt/fbz027 (2019).Article 

Google Scholar 
Diehl, S. & Feissel, M. Intraguild prey suffer from enrichment of their resources: A microcosm experiment with ciliates. Ecology 82, 2977–2983 (2001).Article 

Google Scholar 
Broglio, E., Saiz, E., Calbet, A., Trepat, I. & Alcaraz, M. Trophic impact and prey selection by crustacean zooplankton on the microbial communities of an oligotrophic coastal area (NW Mediterranean Sea). Aquat. Microb. Ecol. 35, 65–78 (2004).Article 

Google Scholar 
Sommer, U. et al. Beyond the Plankton Ecology Group (PEG) Model: Mechanisms driving plankton succession. Annu. Rev. Ecol. Evol. Syst. 43, 429–448. https://doi.org/10.1146/annurev-ecolsys-110411-160251 (2012).Article 

Google Scholar 
IGKB. Jahresbericht der Internationalen Gewässerschutzkommission für den Bodensee: Limnologischer Zustand des Bodensees Nr. 43 (2018–2019), 128 https://www.igkb.org/oeffentlichkeitsarbeit/limnologischer-zustand-des-sees-gruene-berichte/. (2020).Wetzel, R. G. Limnology—Lake and River Ecosystems 3rd edn. (Academic Press, 2001).
Google Scholar 
Kumar, R. Effects of Mesocyclops thermocyclopoides (Copepoda: Cyclopoida) predation on the population growth patterns of different prey species. J. Freshw. Ecol. 18, 383–393. https://doi.org/10.1080/02705060.2003.9663974 (2003).Article 

Google Scholar 
Porter, K. G., Pace, M. L. & Battey, F. J. Ciliate protozoans as links in freshwater planktonic food chains. Nature 277, 563–565 (1979).ADS 
Article 

Google Scholar 
Landry, M. & Fagerness, V. Behavioral and morphological influences on predatory interactions among marine copepods. Bull. Mar. Sci. 43, 509–529 (1988).
Google Scholar 
Krainer, K.-H. & Müller, H. Morphology, infraciliature and ecology of a nerw planktonic ciliate, Histiobalantium bodamicum n. sp. (Scuticociliatida: Histiobalantiidae). Eur. J. Protistol. 31, 389–395 (1995).Article 

Google Scholar 
Lu, X., Gao, Y. & Weisse, T. Functional ecology of two contrasting freshwater ciliated protists in relation to temperature. J. Eukaryot. Microb. 68, e12823. https://doi.org/10.1111/jeu.12823 (2021).CAS 
Article 

Google Scholar 
Menden-Deuer, S. & Lessard, E. J. Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton. Limnol. Oceanogr. 45, 569–579. https://doi.org/10.4319/lo.2000.45.3.0569 (2000).ADS 
CAS 
Article 

Google Scholar 
Bergkemper, V. & Weisse, T. Phytoplankton response to the summer heat wave 2015—A case study from Lake Mondsee, Austria. Inland Waters 7, 88–99. https://doi.org/10.1080/20442041.2017.1294352 (2017).CAS 
Article 

Google Scholar 
Crosbie, N. D., Teubner, K. & Weisse, T. Flow-cytometric mapping provides novel insights into the seasonal and vertical distributions of freshwater autotrophic picoplankton. Aquat. Microb. Ecol. 33, 53–66. https://doi.org/10.3354/ame033053 (2003).Article 

Google Scholar 
Dokulil, M. T. & Teubner, K. Deep living Planktothrix rubescens modulated by environmental constraints and climate forcing. Hydrobiologia 698, 29–46 (2012).CAS 
Article 

Google Scholar 
Weisse, T., Lukić, D. & Lu, X. Container volume may affect growth rates of ciliates and clearance rates of their microcrustacean predators in microcosm experiments. J. Plankton Res. 43, 288–299. https://doi.org/10.1093/plankt/fbab017 (2021).Article 
PubMed 
PubMed Central 

Google Scholar 
Bergkemper, V. & Weisse, T. Do current European lake monitoring programmes reliably estimate phytoplankton community changes? Hydrobiologia 824, 143–162. https://doi.org/10.1007/s10750-017-3426-6 (2018).CAS 
Article 

Google Scholar 
Rosen, R. A. Length-dry weight relationships of some freshwater zooplanktona. J. Freshw. Ecol. 1, 225–229 (1981).Article 

Google Scholar 
Frost, B. W. Effects of size and concentration of food particles on the feeding behavior of the marine planktonic copepod Calanus pacificus. Limnol. Oceanogr. 17, 805–815 (1972).ADS 
Article 

Google Scholar 
RStudio Team. RStudio: Integrated Development Environment for R.RStudio, http://www.rstudio.com/ (PBC, 2021).Burnham, K. P. & Anderson, D. R. Multimodel inference: Understanding AIC and BIC in model selection. Sociol. Methods Res. 33, 261–304. https://doi.org/10.1177/0049124104268644 (2004).MathSciNet 
Article 

Google Scholar 
Hansen, P. J., Bjørnsen, P. K. & Hansen, B. W. Zooplankton grazing and growth: Scaling within the 2–2,000-μm body size range. Limnol. Oceanogr. 42, 687–704. https://doi.org/10.4319/lo.1997.42.4.0687 (1997).ADS 
Article 

Google Scholar  More

Foote, M. The evolution of morphological diversity. Annu. Rev. Ecol. Syst. 28, 129–152 (1997).Article 

Google Scholar 
Félix, M. A. Phenotypic evolution with and beyond genome evolution. Curr. Top. Dev. Biol. 119, 291–347 (2016).PubMed 
Article 
CAS 

Google Scholar 
Carroll, S. B. Evo-devo and an expanding evolutionary synthesis: A genetic theory of morphological evolution. Cell 134, 25–36 (2008).CAS 
PubMed 
Article 

Google Scholar 
Harvey, P. & Pagel, M. The Comparative Method in Evolutionary Biology. (Oxford University Press, 1991).Huxley, J. S. & Teissier, G. Terminology of relative growth. Nature 137, 780–781 (1936).ADS 
Article 

Google Scholar 
Klingenberg, C. P. Size, shape, and form: Concepts of allometry in geometric morphometrics. Dev. Genes Evol. 226, 113–137 (2016).PubMed 
PubMed Central 
Article 

Google Scholar 
Russell, E. S. Form and Function: A Contribution to the History of Animal Morphology. (John Murray, 1916).Goswami, A. & Polly, P. D. Methods for studying morphological integration and modularity. Paleontol. Soc. Pap. 16, 213–243 (2010).Article 

Google Scholar 
Vidal-García, M., Byrne, P. G., Roberts, J. D. & Keogh, J. S. The role of phylogeny and ecology in shaping morphology in 21 genera and 127 species of Australo-Papuan myobatrachid frogs. J. Evol. Biol. 27, 181–192 (2014).PubMed 
Article 

Google Scholar 
Erwin, D. H. Disparity: Morphological pattern and developmental context. Palaeontology 50, 57–73 (2007).Article 

Google Scholar 
Fišer, C., Robinson, C. T. & Malard, F. Cryptic species as a window into the paradigm shift of the species concept. Mol. Ecol. 27, 613–635 (2018).PubMed 
Article 

Google Scholar 
Wilson, D. E. & Mittermeier, R. A. Handbook of the Mammals of the World: Volume 8: Insectivores. vol. 8 (Lynx Edicions, 2018).Jacquet, F. et al. Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): From a forest origin to broad ecological expansion across Africa. BMC Evol. Biol. 15, 71. https://doi.org/10.1186/s12862-015-0344-y (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Ceríaco, L. M. P. et al. Description of a new endemic species of shrew (Mammalia, Soricomorpha) from PrÍncipe Island (Gulf of Guinea). Mammalia 79, 325–341 (2015).Article 

Google Scholar 
Nicolas, V. et al. Multilocus phylogeny of the Crocidura poensis species complex (Mammalia, Eulipotyphla): Influences of the palaeoclimate on its diversification and evolution. J. Biogeogr. 46, 871–883 (2019).Article 

Google Scholar 
Konečný, A., Hutterer, R., Meheretu, Y. & Bryja, J. Two new species of Crocidura (Mammalia: Soricidae) from Ethiopia and updates on the Ethiopian shrew fauna. J. Vertebr. Biol. 69, 20064.1. https://doi.org/10.25225/jvb.20064 (2020).Article 

Google Scholar 
Couvreur, T. L. P. et al. Tectonics, climate and the diversification of the tropical African terrestrial flora and fauna. Biol. Rev. 96, 16–51 (2021).PubMed 
Article 

Google Scholar 
Mayr, E. & O’Hara, R. J. The biogeographic evidence supporting the Pleistocene forest refuge hypothesis. Evolution 40, 55–67 (1986).PubMed 
Article 

Google Scholar 
Wiens, J. J. & Graham, C. H. Niche conservatism: Integrating evolution, ecology, and conservation biology. Annu. Rev. Ecol. Evol. Syst. 36, 519–539 (2005).Article 

Google Scholar 
Smith, T. B., Wayne, R. K., Girman, D. J. & Bruford, M. W. A role for ecotones in generating rainforest biodiversity. Science 276, 1855–1857 (1997).CAS 
Article 

Google Scholar 
Needham, A. E. & Hardy, A. C. The form-transformation of the abdomen of the female pea-crab, Pinnotheres pisum Leach. Proc. R Soc. Lond. Ser. B Biol. Sci. 137, 115–136 (1950).ADS 
CAS 

Google Scholar 
Hanken, J. & Hall, B. K. The Skull, Volume 3: Functional and Evolutionary Mechanisms. (University of Chicago Press, 1993).Hautier, L., Lebrun, R. & Cox, P. G. Patterns of covariation in the masticatory apparatus of hystricognathous rodents: Implications for evolution and diversification. J. Morphol. 273, 1319–1337 (2012).PubMed 
Article 

Google Scholar 
Aristide, L. et al. Multiple factors behind early diversification of skull morphology in the continental radiation of New World monkeys. Evolution 72, 2697–2711 (2018).PubMed 
Article 

Google Scholar 
Hardin, G. The competitive exclusion principle. Science 131, 1292–1297 (1960).ADS 
CAS 
PubMed 
Article 

Google Scholar 
Denys, C. et al. Shrews (Mammalia, Eulipotyphla) from a biodiversity hotspot, Mount Nimba (West Africa), with a field identification key to species. Zoosystema 43, 729–757 (2021).Article 

Google Scholar 
Estevo, C. A., Nagy-Reis, M. B. & Nichols, J. D. When habitat matters: Habitat preferences can modulate co-occurrence patterns of similar sympatric species. PLoS One 12, e0179489. https://doi.org/10.1371/journal.pone.0179489 (2017).CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Spaeth, P. A. Morphological convergence and coexistence in three sympatric North American species of Microtus (Rodentia: Arvicolinae). J. Biogeogr. 36, 350–361 (2009).Article 

Google Scholar 
Adams, D. C., Berns, C. M., Kozak, K. H. & Wiens, J. J. Are rates of species diversification correlated with rates of morphological evolution?. Proc. R. Soc. B Biol. Sci. 276, 2729–2738 (2009).Article 

Google Scholar 
Caumul, R. & Polly, P. D. Phylogenetic and environmental components of morphological variation: Skull, mandible, and molar shape in marmots (marmota, Rodentia). Evolution 59, 2460–2472 (2005).PubMed 
Article 

Google Scholar 
Da Silva, F. O. et al. The ecological origins of snakes as revealed by skull evolution. Nat. Commun. 9, 376. https://doi.org/10.1038/s41467-017-02788-3 (2018).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Hirano, T., Kameda, Y., Kimura, K. & Chiba, S. Substantial incongruence among the morphology, taxonomy, and molecular phylogeny of the land snails Aegista, Landouria, Trishoplita, and Pseudobuliminus (Pulmonata: Bradybaenidae) occurring in East Asia. Mol. Phylogenet. Evol. 70, 171–181 (2014).PubMed 
Article 

Google Scholar 
Ge, D., Yao, L., Xia, L., Zhang, Z. & Yang, Q. Geometric morphometric analysis of skull morphology reveals loss of phylogenetic signal at the generic level in extant lagomorphs (Mammalia: Lagomorpha). Contrib. Zool. 84, 267–284 (2015).Article 

Google Scholar 
Zou, Z. & Zhang, J. Morphological and molecular convergences in mammalian phylogenetics. Nat. Commun. 7, 12758. https://doi.org/10.1038/ncomms12758 (2016).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Ananjeva, N. B. Current state of the problems in the phylogeny of squamate reptiles (Squamata, Reptilia). Biol. Bull. Rev. 9, 119–128 (2019).Article 

Google Scholar 
Revell, L. J., Harmon, L. J. & Collar, D. C. Phylogenetic signal, evolutionary process, and rate. Syst. Biol. 57, 591–601 (2008).PubMed 
Article 

Google Scholar 
Klingenberg, C. P. & Marugán-Lobón, J. Evolutionary covariation in geometric morphometric data: Analyzing integration, modularity, and allometry in a phylogenetic context. Syst. Biol. 62, 591–610 (2013).PubMed 
Article 

Google Scholar 
Cardini, A. & Polly, P. D. Larger mammals have longer faces because of size-related constraints on skull form. Nat. Commun. 4, 2458. https://doi.org/10.1038/ncomms3458 (2013).ADS 
CAS 
Article 
PubMed 

Google Scholar 
Esquerré, D., Sherratt, E. & Keogh, J. S. Evolution of extreme ontogenetic allometric diversity and heterochrony in pythons, a clade of giant and dwarf snakes. Evolution 71, 2829–2844 (2017).PubMed 
Article 

Google Scholar 
Marroig, G. & Cheverud, J. M. Size as a line of least evolutionary resistance: Diet and adaptive morphological radiation in New World monkeys. Evolution 59, 1128–1142 (2005).PubMed 
Article 

Google Scholar 
Cornette, R., Tresset, A., Houssin, C., Pascal, M. & Herrel, A. Does bite force provide a competitive advantage in shrews? The case of the greater white-toothed shrew. Biol. J. Linn. Soc. 114, 795–807 (2015).Article 

Google Scholar 
Rodgers, G. M., Downing, B. & Morrell, L. J. Prey body size mediates the predation risk associated with being “odd”. Behav. Ecol. 26, 242–246 (2015).Article 

Google Scholar 
Damuth, J. Population density and body size in mammals. Nature 290, 699–700 (1981).ADS 
Article 

Google Scholar 
Verschuren, D. Decadal and century-scale climate variability in tropical Africa during the past 2000 years. In Past Climate Variability Through Europe and Africa (eds. Battarbee, R. W., Gasse, F. & Stickley, C. E.) 139–158 (Springer Netherlands, 2004). https://doi.org/10.1007/978-1-4020-2121-3_8.Smith, T. B., Schneider, C. J. & Holder, K. Refugial isolation versus ecological gradients. Genetica 112, 383–398 (2001).PubMed 
Article 

Google Scholar 
Brown, W. L. Jr. & Wilson, E. O. Character displacement. Syst. Biol. 5, 49–64 (1956).
Google Scholar 
Vogel, P. et al. Genetic identity of the critically endangered Wimmer’s shrew Crocidura wimmeri. Biol. J. Linn. Soc. 111, 224–229 (2014).Article 

Google Scholar 
Esselstyn, J. A. et al. Fourteen new, endemic species of shrew (genus Crocidura) from Sulawesi reveal a spectacular island radiation. Bull. Am. Mus. Nat. Hist. 454, 1–108 (2021).Article 

Google Scholar 
Evin, A., Bonhomme, V. & Claude, J. Optimizing digitalization effort in morphometrics. Biol. Methods Protoc. 5, bpaa023. https://doi.org/10.1093/biomethods/bpaa023 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
Blomberg, S. P., Garland, T. & Ives, A. R. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution 57, 717–745 (2003).PubMed 
Article 

Google Scholar 
Adams, D. C. A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data. Syst. Biol. 63, 685–697 (2014).PubMed 
Article 

Google Scholar 
Kembel, S. W. et al. Picante: R tools for integrating phylogenies and ecology. Bioinformatics 26, 1463–1464 (2010).CAS 
PubMed 
Article 

Google Scholar 
Revell, L. J. phytools: Phylogenetic Tools for Comparative Biology (and Other Things). (2021).Fick, S. E. & Hijmans, R. J. WorldClim 2: New 1-km spatial resolution climate surfaces for global land areas. Int. J. Climatol. 37, 4302–4315 (2017).Article 

Google Scholar 
Pebesma, E. Simple features for R: Standardized support for spatial vector data. R J. 10, 439 (2018).Article 

Google Scholar 
Oksanen, J. et al. vegan: Community Ecology Package. (2020).Dray, S., Legendre, P. & Peres-Neto, P. R. Spatial modelling: A comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecol. Model. 196, 483–493 (2006).Article 

Google Scholar 
Borcard, D., Gillet, F. & Legendre, P. Numerical Ecology with R. (Springer, 2018).Dray, S. et al. adespatial: Multivariate Multiscale Spatial Analysis. (2021).Collyer, M. & Adams, D. RRPP: Linear Model Evaluation with Randomized Residuals in a Permutation Procedure. (2021).Kassambara, A. rstatix: Pipe-Friendly Framework for Basic Statistical Tests. (2021).Borcard, D., Legendre, P. & Drapeau, P. Partialling out the spatial component of ecological variation. Ecology 73, 1045–1055 (1992).Article 

Google Scholar 
Rohlf, F. J. & Corti, M. Use of two-block partial least-squares to study covariation in shape. Syst. Biol. 49, 740–753 (2000).CAS 
PubMed 
Article 

Google Scholar 
Schlager, S., Jefferis, G. & Ian, D. Morpho: Calculations and Visualisations Related to Geometric Morphometrics. (2020). More

Study areaThe NCA encompasses an area of 8292 km2 and in 2020 had approximately 87,000 inhabitants23, who are primarily dependent on livestock for their livelihoods. It is a multiple-use area where people coexist with wildlife and livestock, and practise pastoralism with transhumance, characterised by seasonal movements of livestock for accessing resources such as grazing areas and water. The NCA comprises eleven administrative wards: Alailelai, Endulen, Eyasi, Laitole, Kakesio, Misigiyo, Ngorongoro, Naiyobi, Nainokanoka, Ngoile and Olbalbal (Fig. 1). The NCA was chosen for our study as it is known to be hyperendemic for anthrax4,17,20. In addition, informal consultations we held prior to the study, as well as tailored data collection at the community and household level, indicated that local communities have a good understanding of the disease in humans and animals, and of practices around carcass and livestock management that increase risks, particularly in certain locations and periods of the year24.Figure 1Locations of participatory mapping. Map showing the 11 administrative wards of the Ngorongoro Conservation Area in northern Tanzania and the locations where participatory mapping sessions took place (red dots). The maps were produced in QGIS 2.18.2 using data from the National Bureau of Statistics, Tanzania (http://www.nbs.go.tz/).Full size imageEthics approval and consent to participateThe study received approval from the National Institute for Medical Research, Tanzania, with reference number NIMRJHQ/R.8a/Vol. IX/2660; the Tanzania Commission for Science and Technology (numbers 2016-94-NA-2016-88 (O. R. Aminu), 2016-95-NA-2016-45 (T. L. Forde) and 2018-377-NA-2016-45 (T. Lembo)); Kilimanjaro Christian Medical University College Ethics Review Committee (certificate No. 2050); and the University of Glasgow College of Medical Veterinary & Life Sciences Ethics Committee (application number 200150152). Approval and permission to access communities and participants were also obtained from relevant local authorities. Written informed consent was obtained from all participants involved in the study. All data collected were analysed anonymously, ensuring the confidentiality of participants. All research activities were performed in accordance with relevant guidelines and regulations.Participatory mappingA participatory mapping approach based on methodology previously tested in East Africa25 was employed to define areas of anthrax risk for animals in the NCA based on community knowledge. Georeferenced maps of the NCA were produced using data from Google and DigitalGlobe (2016). The maps used datum Arc 1960/UTM zone 36S and grid intervals of 1000 km and were produced at 1:10,000 and 1:50,000 scales, in order to provide participants with a choice. Ten participatory mapping focus groups were held at ward administrative level (Fig. 1) in order to identify areas in the NCA that communities perceive as posing a high risk of anthrax. One mapping exercise was held in each ward. Ngoile and Olbalbal wards were covered at the same time and treated as one, as they had only recently (in 2015) been split from one ward (Olbalbal). Each session had between ten and thirteen participants, who consisted of village and ward administrators, animal health professionals (including community animal health workers and livestock field officers), community leaders, and selected community members. These participants represented members of the community concerned with animal health and owning livestock and, as such, were likely to hold in-depth knowledge relating to community experience of animal health and disease, including anthrax. Participants were recruited by consulting with animal health professionals as well as village and ward administrators, who gave permission to conduct the mapping sessions.The mapping sessions were conducted in Swahili and translated into English by an interpreter. Participants’ general knowledge of the area was first verified by testing whether they could correctly identify popular locations such as health centres, places of worship, markets and schools. Subsequently, participants discussed among themselves and came to a consensus about areas they considered to be at high risk of anthrax. Specifically, we asked them to identify locations they perceived as areas where they considered their animals to be at risk of being exposed to anthrax. These areas were drawn on the maps provided (Fig. 2). While they did not locate areas where the animals had succumbed to disease, we also asked for generic information on locations where anthrax outbreaks had occurred in the past to define areas that could be targeted for active surveillance of cases. In order to improve the fidelity of the data, participants defined risk areas in relation to their own locality (ward) and locations where their animals access resources. Therefore, the areas were not defined by administrative boundaries, as communities may access locations outside their wards, for instance for grazing or watering. The resulting maps were scanned, digitised and analysed as detailed in the following sections. Further detail on the participatory mapping process is provided in the Supplementary Methods (Additional File 1).Figure 2Participatory mapping of anthrax risk areas in the Ngorongoro Conservation Area. Images show (A) the set-up of a mapping session, (B) participants engaged during a session and (C) an example of a 1:50,000 scale map annotated by participants. The map was created with QGIS opensource mapping software. The basemap used was a scanned and geo-referenced full colour 1:50,000 scale topographic map produced by the Surveys & Mapping Division, Ministry of Lands, Housing & Human Settlements, Dar es Salaam, Tanzania. The grid is based on the Arc1960 UTM 36S projection and datum. The map was exported from QGIS in Acrobat Pdf format to enable it to be printed at suitable sizes for using in the fieldwork and to be manually annotated during the participatory mapping.Full size imageDigitisation of maps and generation of random pointsScanned maps were saved as PDF files and converted to high resolution TIFF files for digitisation in QGIS 2.18.2-Las Palmas free OpenSource software26. All maps were georeferenced with geographical coordinates during production and reference points were available to enable the precise mapping of all locations. The digitization was carried out using the QGIS digitizing tools and by creating polygon layers of the defined risk areas.Sourcing data on the environmental predictors of anthraxAvailable soil and environmental data (250 m grid) for Tanzania were obtained from various sources (Table 1). From the available data, we selected the following seven variables which have previously been shown to contribute to or explain the risk of anthrax based on the biology of B. anthracis (Table 1).Table 1 Environmental factors with potential to influence anthrax occurrence.Full size tableCation exchange capacity (CEC)Measured in cmol/kg, CEC is the total capacity of the soil to retain exchangeable cations such as Ca2+, Mg2+ etc. It is an inherent soil characteristic and is difficult to alter significantly. It influences the soil’s ability to hold on to essential nutrients and provides a buffer against soil acidification27. CEC has been reported to be positively correlated with anthrax risk. In addition, CEC is a proxy for calcium content, which may contribute to anthrax risk in a pH-dependent manner as explained below19,22.Predicted topsoil pH (pH)Soil pH below 6.0 (acidic soil) is thought to inhibit the viability of spores19 thus a positive effect of higher pH on the risk of anthrax is expected. It has been suggested that the exosporium of B. anthracis is negatively charged in soils with neutral to slightly alkaline pH. This negative charge attracts positively charged cations in soil, mainly calcium, enabling the spores to be firmly attached to soil particles and calcium to be maintained within the spore core, thereby promoting the viability of B. anthracis19,28.Distance to inland water bodies (DOWS)Both the distance from water and proximity to water may increase anthrax risk. Distance to inland water may indicate the degree to which an area is dry/arid. Anthrax outbreaks have been shown to occur in areas with very dry conditions19. Although anthrax occurrence has also been associated with high soil moisture, this relates more to the spore germination in the environment (a mechanism that is disputed) and the concentration of spores in moist humus that amount to an infectious dose18,29. Spores will survive much longer in soils with low moisture content19. Low moisture may also be associated with low vegetation which results in animals grazing close to the soil, increasing the risk of ingesting soil with spores. Hampson et al. reported that anthrax outbreaks occurred close to water sources in the Serengeti ecosystem of Tanzania in periods of heavy rainfall20, and Steenkamp et al. found that close proximity to water bodies was key to the transmission of B. anthracis spores in Kruger National Park, South Africa22. Water is an important resource for livestock and a large number of animals may congregate at water sources during dry seasons. The close proximity of a water source to a risk area may increase the chance of infection, particularly during periods of high precipitation which might unearth buried spores.Average enhanced vegetation index (EVI)Vegetation density may influence the likelihood of an animal ingesting soil or inhaling dust that may be contaminated with spores. Grazing animals are more likely to encounter bacteria in soil with low vegetation density20, although there is a possibility that spores can be washed onto higher vegetation by the action of water19. Vegetation index may also reflect the moisture content of soil. Arid/dry conditions favour the formation and resistance of spores in the environment, thus lower vegetation may be associated with the occurrence of anthrax.Average daytime land surface temperature (LSTD)Anthrax has been more commonly reported to occur in regions with warmer climates worldwide. Minett observed that under generally favourable conditions and at 32 °C to 37 °C, sporulation of B. anthracis occurs readily but vegetative cells are more likely to disintegrate at temperatures below 21 °C30. Another hypothesis for the association of high temperature with anthrax occurrence is altered host immune response to disease due to stress caused by elevated temperatures19. In addition, elevated temperatures are usually associated with arid areas where vegetation is low, limiting access to adequate nutrition, which in turn affects immunity. Similarly, in hotter climates where infectious diseases occur more often, host interactions with other pathogens may modulate immune response to anthrax31. In this case, a lower infectious and lethal dose of spores would be sufficient to cause infection and death, respectively19. Contact with and ingestion of soil, spores and abrasive pasture is also higher with low vegetation in hot and arid areas19,32. In boreal regions such as in northern Canada, where anthrax occurs in wood bison, and Siberia, the disease is more commonly reported in the summer19. We therefore hypothesised a positive effect of LSTD on the risk of anthrax.SlopeSpores of B. anthracis are hypothesized to persist more easily in flat landscapes that are characterised by shallow slopes19, as it is thought that wind and water may disperse spores more easily along areas with a higher slope gradient, thereby decreasing the density of spores to levels that may be insufficient to cause infection in a susceptible host. Therefore, we expected a negative relationship between slope and the risk of anthrax.Predicted topsoil organic carbon content (SOC)Organic matter (g/kg) may aid spore persistence by providing mechanical support. The negatively charged exosporium of spores is attracted to the positive charges on hummus-rich soil, thus anthrax is thought to persist in soil rich in organic matter18. Based on available evidence, we expected a positive effect of SOC on the risk of anthrax.Creating the datasetThe annotated and digitised maps yielded polygons of high-risk areas within the NCA (Fig. 3). After digitization, 5000 random points were generated33 to cover the 8292 km2 area of the NCA. This enabled us to obtain distinct points allowed by the 250 m grid resolution of the environmental variables. Points falling within the defined risk areas were selected to represent risk areas while those falling outside represented low-risk areas. Measures of the environmental characteristics associated with individual points were obtained with the ‘add Raster data to points’ feature in QGIS.Figure 3Ngorongoro Conservation Area map showing (A) defined risk areas (in red) and (B) distance to settlements. For analysis, 5000 random points were generated throughout the area; points falling within 4.26 km of human settlements (the average distance herds are moved from settlements in a day as determined through interviews of resident livestock owners) were retained for analysis (n = 2173, shown in blue in 3a). The maps were created in QGIS 2.18.2 using data from the National Bureau of Statistics, Tanzania (http://www.nbs.go.tz/).Full size imageIn order to focus on areas of greatest risk to humans and livestock and to exclude locations that are not accessible, only points within a certain range of distance from settlements were included (Fig. 3). On average, herders in the NCA move their livestock 4.26 km away from settlements for grazing and watering during the day (unpublished data obtained through a cross-sectional survey of 209 households). Thus, only points falling within this distance from settlements were selected, providing us with data on areas where infection is most likely to occur. Data on locations of settlements were obtained from satellite imagery and included permanent residences as well as temporary settlements (e.g. seasonal camps set up after long distance movement away from permanent settlements, typically in the dry season, in search of pasture and water). These data were collated from the Center for International Earth Science Information Network (CIESIN).After adjusting for accessibility of resource locations using the average distance moved by livestock, 2173 points were retained for analysis, of which 239 (11%) fell within high-risk areas.Data analysisAll statistical analyses were carried out in R (v 4.1.0) within the RStudio environment34. The aims of the statistical analysis were to infer the relationship between anthrax risk areas as determined through participatory mapping and the environmental factors identified in Table 1, and to use this relationship to make spatial predictions of anthrax risk across the study area. We achieved both aims by modelling the binary risk status (high or low) of the randomly generated points as a function of their environmental characteristics in a Bayesian spatial logit-binomial generalised linear mixed-effects model (GLMM), implemented in the package glmmfields35. Spatial autocorrelation (residual non-independence between nearby points) was accounted for by including spatial random effects in the GLMM. We chose relatively non-informative priors for the intercept and the covariates, using Student’s t-distributions centred at 0 and wide variances (intercept: df = 3, location = 0, scale = 10; betas: df = 3, location = 0, scale = 3). For the spatial Gaussian Process and the observation process scale parameters, we adopted the default glmmfields settings and used half-t priors (both gp_theta and gp_sigma: df = 3, location = 0, scale = 5), and 12 knots. To achieve convergence, the models were run for 5000 iterations35.First, univariable models were fitted to estimate unadjusted associations between each environmental factor (CEC, pH, DOWS, EVI, LSTD, slope, and SOC; Table 1; Supplementary Table S1) and high- and low-risk areas. Second, we constructed multivariable models by fitting multiple environmental variables (Supplementary Table S2). Three variables, SOC, slope and EVI showed a strongly right-skewed distribution and were therefore log-transformed prior to GLMM analysis to prevent excessive influence of outliers. All predictor variables were centred to zero mean and scaled to unit standard deviation for analysis, and odds ratios were rescaled back to the original units for ease of interpretation. Prior to fitting the multivariable GLMM, the presence of collinearity among the predictor variables—which were all continuous—was assessed using variance inflation factors (VIFs)36, calculated with the car package and illustrated using scatter plots (Supplementary Fig. S1)36. Three predictor variables showed a VIF greater than 3 (LSTD, ln EVI and pH with VIFs of 6.8, 4.2 and 3.5, respectively). Removal of LSTD and ln EVI reduced all VIFs to below 3, therefore these two variables were excluded from the multivariable regression analysis37.The model performance was assessed by calculating the area under the receiver operating characteristic curve. The predicted probability of being an anthrax high-risk area was determined and depicted on a map of the NCA using a regular grid of points generated throughout the NCA with one point sampled every 500 m.Consent for publicationPermission to publish was granted by the National Institute for Medical Research, Tanzania. 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

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