Philippa Kaur

Patterson, J. et al. Nat. Sustain. 4, 841–850 (2021).Article 

Google Scholar 
Reid, A. J. et al. Biol. Rev. 94, 849–873 (2019).Article 

Google Scholar 
Vollmer, D. & Harrison, I. J. Environ. Res. Lett. 16, 011005 (2021).Article 

Google Scholar 
Zeitoun, M. et al. Glob. Environ. Change 39, 143–154 (2016).Article 

Google Scholar 
Bezerra, M. O. et al. Environ. Manage. 69, 815–834 (2022).Article 

Google Scholar 
Souter, N. J. et al. Water 12, 788 (2020).Article 
CAS 

Google Scholar 
Akhmouch, A., Clavreul, D. & Glas, P. Water Int. 43, 5–12 (2018).Article 

Google Scholar 
Andersson, E. Ambio 51, 1–8 (2022).Article 

Google Scholar 
Huntington, H. P. et al. Nat. Sustain. 4, 672–679 (2021).Article 

Google Scholar 
Soames Job, R. F. Am. J. Public Health 78, 163–167 (1988).Article 
CAS 

Google Scholar 
Poff, N. L. et al. Nat. Clim. Change 6, 25–34 (2016).Article 

Google Scholar 
Diaz-Kope, L. & Miller-Stevens, K. Public Works Management and Policy 20, 29–48 (2015).Article 

Google Scholar 
OECD Financing a Water Secure Future (OECD Publishing, 2022).Cardascia, S. Financing Water Infrastructure and Landscape Approaches in Asia and the Pacific. Background Paper for 5th Roundtable on Financing Water (OECD Publishing, 2019).Schlager, E. & Blomquist, W. Embracing Watershed Politics (University Press of Colorado, 2008).Wehn, U., Collins, K., Anema, K., Basco-Carrera, L. & Lerebours, A. Water Int. 43, 34–59 (2018).Article 

Google Scholar 
Shaad, K., Souter, N. J., Vollmer, D., Regan, H. M. & Bezerra, M. O. Environ. Manage. 69, 752–767 (2022).Article 

Google Scholar  More

Qin, Y. et al. Improved estimates of forest cover and loss in the Brazilian Amazon in 2000–2017. Nat. Sustain. 2, 764–772 (2019).Article 

Google Scholar 
Qin, Y. et al. Carbon loss from forest degradation exceeds that from deforestation in the Brazilian Amazon. Nat. Clim. Change 11, 442–448 (2021).Article 

Google Scholar 
Jenkins, C., Pimm, S. & Joppa, L. Global patterns of terrestrial vertebrate diversity and conservation. Proc. Natl Acad. Sci. USA 110, E2602–E2610 (2013).Article 
CAS 

Google Scholar 
Nogueira, E., Yanai, A., de Vasconcelos, S., de Alencastro, G. & Fearnside, P. Brazil’s Amazonian protected areas as a bulwark against regional climate change. Reg. Environ. Change 18, 573–579 (2018).Article 

Google Scholar 
Ochoa-Quintero, J., Gardner, T., Rosa, I., Ferraz, S. & Sutherland, W. Thresholds of species loss in Amazonian deforestation frontier landscapes. Conserv. Biol. 29, 440–451 (2015).Article 

Google Scholar 
Cabral, A., Saito, C., Pereira, H. & Laques, A. Deforestation pattern dynamics in protected areas of the Brazilian Legal Amazon using remote sensing data. Appl. Geogr. 100, 101–115 (2018).Article 

Google Scholar 
Nepstad, D. et al. Inhibition of Amazon deforestation and fire by parks and Indigenous lands. Conserv. Biol. 20, 65–73 (2006).Article 
CAS 

Google Scholar 
Ricketts, T. et al. Indigenous lands, protected areas, and slowing climate change. PLoS Biol. 8, e1000331 (2010).Article 

Google Scholar 
Herrera, D., Pfaff, A. & Robalino, J. Impacts of protected areas vary with the level of government: comparing avoided deforestation across agencies in the Brazilian Amazon. Proc. Natl Acad. Sci. USA 116, 14916–14925 (2019).Article 
CAS 

Google Scholar 
Jusys, T. Changing patterns in deforestation avoidance by different protection types in the Brazilian Amazon. PLoS ONE 13, e0195900 (2018).Article 

Google Scholar 
Matricardi, E. et al. Long-term forest degradation surpasses deforestation in the Brazilian Amazon. Science 369, 1378–1382 (2020).Article 
CAS 

Google Scholar 
Silva, C. et al. Benchmark maps of 33 years of secondary forest age for Brazil. Sci. Data 7, 269 (2020).Article 

Google Scholar 
Laurance, W. et al. The future of the Brazilian Amazon. Science 291, 438–439 (2001).Article 
CAS 

Google Scholar 
Laurance, W. et al. Development of the Brazilian Amazon. Response. Science 292, 1652–1654 (2001).
Google Scholar 
Silveira, J. Development of the Brazilian Amazon. Science 292, 1651–1654 (2001).Article 
CAS 

Google Scholar 
Kauano, É., Silva, J., Diniz, J. & Michalski, F. Do protected areas hamper economic development of the Amazon region? An analysis of the relationship between protected areas and the economic growth of Brazilian Amazon municipalities. Land Use Policy 92, 104473 (2020).Article 

Google Scholar 
Silveira, F., Ferreira, M., Perillo, L., Carmo, F. & Neves, F. Brazil’s protected areas under threat. Science 361, 459–459 (2018).Article 
CAS 

Google Scholar 
Begotti, R. & Peres, C. Brazil’s indigenous lands under threat. Science 363, 592–592 (2019).Article 

Google Scholar 
Fearnside, P. Deforestation of the Brazilian Amazon. Oxford Research Encyclopedias: Environmental Science (Oxford Univ. Press, 2017); https://doi.org/10.1093/acrefore/9780199389414.013.102Ferreira, J. et al. Brazil’s environmental leadership at risk. Science 346, 706–707 (2014).Article 
CAS 

Google Scholar 
Villén-Pérez, S., Anaya-Valenzuela, L., Conrado da Cruz, D. & Fearnside, P. Mining threatens isolated indigenous peoples in the Brazilian Amazon. Glob. Environ. Change 72, 102398 (2022).Article 

Google Scholar 
Tollefson, J. Illegal mining in the Amazon hits record high amid Indigenous protests. Nature 598, 15–16 (2021).Article 
CAS 

Google Scholar 
Silva, C. et al. The Brazilian Amazon deforestation rate in 2020 is the greatest of the decade. Nat. Ecol. Evol. 5, 144–145 (2021).Article 

Google Scholar 
Vale, M. et al. The COVID-19 pandemic as an opportunity to weaken environmental protection in Brazil. Biol. Conserv. 255, 108994 (2021).Article 

Google Scholar 
Charlier, P. & Varison, L. Is COVID-19 being used as a weapon against Indigenous Peoples in Brazil? Lancet 396, 1069–1070 (2020).Article 
CAS 

Google Scholar 
Davidson, E. et al. The Amazon basin in transition. Nature 481, 321–328 (2012).Article 
CAS 

Google Scholar 
Ferrante, L. & Fearnside, P. Brazil’s new president and ‘ruralists’ threaten Amazonia’s environment, traditional peoples and the global climate. Environ. Conserv. 46, 261–263 (2019).Article 

Google Scholar 
PRODES Legal Amazon Deforestation Monitoring System (INPE, 2020); http://www.obt.inpe.br/OBT/assuntos/programas/amazonia/prodesHansen, M. et al. High-resolution global maps of 21st-century forest cover change. Science 342, 850–853 (2013).Article 
CAS 

Google Scholar 
Qin, Y. et al. Annual dynamics of forest areas in South America during 2007–2010 at 50 m spatial resolution. Remote Sens. Environ. 201, 73–87 (2017).Article 

Google Scholar 
Collection 6 of the Annual Land Use Land Cover Maps of Brazil (MapBiomas Project, accessed 10 July 2022); https://mapbiomas.org/enTree Cover Loss (Global Forest Watch, 2021); https://www.globalforestwatch.org/map/?modalMeta=tree_cover_lossFuller, C., Ondei, S., Brook, B. & Buettel, J. Protected-area planning in the Brazilian Amazon should prioritize additionality and permanence, not leakage mitigation. Biol. Conserv. 248, 108673 (2020).Article 

Google Scholar 
Nolte, C., Agrawal, A., Silvius, K. & Soares, B. Governance regime and location influence avoided deforestation success of protected areas in the Brazilian Amazon. Proc. Natl Acad. Sci. USA 110, 4956–4961 (2013).Article 
CAS 

Google Scholar 
Tesfaw, A. et al. Land-use and land-cover change shape the sustainability and impacts of protected areas. Proc. Natl Acad. Sci. USA 115, 2084–2089 (2018).Article 
CAS 

Google Scholar 
OECD Environmental Performance Reviews: Brazil (OECD, 2015).Campos-Silva, J. et al. Sustainable-use protected areas catalyze enhanced livelihoods in rural Amazonia. Proc. Natl Acad. Sci. USA 118, e2105480118 (2021).Article 
CAS 

Google Scholar 
Fearnside, P., Nogueira, E. & Yanai, A. Maintaining carbon stocks in extractive reserves in Brazilian Amazonia. Desenvolv. Meio. Ambie. 48, 446–476 (2018).
Google Scholar 
Nelson, A. & Chomitz, K. Effectiveness of strict vs. multiple use protected areas in reducing tropical forest fires: a global analysis using matching methods. PLoS ONE 6, e22722 (2011).Article 
CAS 

Google Scholar 
BenYishay, A., Heuser, S., Runfola, D. & Trichler, R. Indigenous land rights and deforestation: evidence from the Brazilian Amazon. J. Environ. Econ. Manag. 86, 29–47 (2017).Article 

Google Scholar 
Bonilla-Mejía, L. & Higuera-Mendieta, I. Protected areas under weak institutions: evidence from Colombia. World Dev. 122, 585–596 (2019).Article 

Google Scholar 
Baragwanath, K. & Bayi, E. Collective property rights reduce deforestation in the Brazilian Amazon. Proc. Natl Acad. Sci. USA 117, 20495–20502 (2020).Article 
CAS 

Google Scholar 
Mangonnet, J., Kopas, J. & Urpelainen, J. Playing politics with environmental protection: the political economy of designating protected areas. J. Politics 84, 1453–1468 (2022).Article 

Google Scholar 
Nepstad, D. et al. Slowing Amazon deforestation through public policy and interventions in beef and soy supply chains. Science 344, 1118–1123 (2014).Article 
CAS 

Google Scholar 
Brando, P. M. et al. Abrupt increases in Amazonian tree mortality due to drought–fire interactions. Proc. Natl Acad. Sci. USA 111, 6347–6352 (2014).Article 
CAS 

Google Scholar 
West, T. & Fearnside, P. Brazil’s conservation reform and the reduction of deforestation in Amazonia. Land Use Policy 100, 105072 (2021).Article 

Google Scholar 
Soares-Filho, B. et al. Cracking Brazil’s forest code. Science 344, 363–364 (2014).Article 
CAS 

Google Scholar 
Ferrante, L. & Fearnside, P. Military forces and COVID-19 as smokescreens for Amazon destruction and violation of indigenous rights. J. Geogr. Soc. 151, 258–263 (2020).
Google Scholar 
Jiménez-Muñoz, J. et al. Record-breaking warming and extreme drought in the Amazon rainforest during the course of El Niño 2015–2016. Sci. Rep. 6, 33130 (2016).Article 

Google Scholar 
Ferrante, L. & Fearnside, P. The Amazon’s road to deforestation. Science 369, 634–634 (2020).Article 

Google Scholar 
Feng, X. et al. How deregulation, drought and increasing fire impact Amazonian biodiversity. Nature 597, 516–521 (2021).Article 
CAS 

Google Scholar 
Aragão, L. et al. 21st century drought-related fires counteract the decline of Amazon deforestation carbon emissions. Nat. Commun. 9, 536 (2018).Article 

Google Scholar 
Silva, J., Barbosa, L., Topf, J., Vieira, I. & Scarano, F. Minimum costs to conserve 80% of the Brazilian Amazon. Perspect. Ecol. Conserv. 20, 216–222 (2022).
Google Scholar 
Lovejoy, T. & Nobre, C. Amazon tipping point. Sci. Adv. 4, eaat2340 (2018).Article 

Google Scholar 
Xiao, X., Biradar, C., Czarnecki, C., Alabi, T. & Keller, M. A simple algorithm for large-scale mapping of evergreen forests in tropical America, Africa and Asia. Remote Sens. 1, 355–374 (2009).Article 

Google Scholar 
Natural Protected Areas and Indigenous Territories Maps in Brazil (RAISG, 2018); https://www.amazoniasocioambiental.org/en/ More

Plant species and pollinatorsMedicago sativa L. (Fabaceae), also called alfalfa or lucerne, is a perennial legume with flowers arranged in a cluster or raceme. It is a self-compatible plant with fairly high outcrossing rate (5.3–30%)46, and it requires insect visits for seed production47. No plant material was collected for this study. Honey bees, Apis mellifera, and alfalfa leafcutting bees, Megachile rotundata, are used as managed pollinators in alfalfa seed-production fields in the USA while bumble bees are commonly used in alfalfa breeding47.Experimental design and pollinator observationsFive 11 m × 11 m patches of M. sativa plants were set up in an east–west linear arrangement at the West Madison Agricultural Research Station in Madison, Wisconsin, USA. Within each patch, we transplanted 169 young plants grown from seeds in the greenhouse, each placed 90 cm apart. These plants grew and, at flowering, a plant had an average of 30.65 ± 16.4 stems per plant, with 4.93 ± 3.41 racemes per stem, and 7.53 ± 2.44 open flowers per raceme.A honey bee hive was placed approximately 100 m from the patches and a bumble bee hive was set up at the center of the southern edge of the patches. For leafcutting bees, a 60 × 30 × 7.6 cm bee board was set up in each of two boxes placed 1/3 and 2/3 along the southern edge of the patches and a half gallon of bees was released at periodic intervals throughout the alfalfa flowering season.Over two consecutive summers, observers followed bees foraging in the alfalfa patches, marked each raceme visited in succession within a foraging bout with a numbered clip, and recorded the number of flowers visited per raceme. After a bee had left a patch, observers went back to the marked racemes and measured the distance and direction traveled between consecutive racemes. Directions were recorded as one of the cardinal directions: North (N), South (S), East (E) or West (W), or inter-cardinal directions: Northeast (NE), Southeast (SE), Northwest (NW) and Southwest (SW). The frequency distributions of distances and directions traveled between two successive racemes are presented for each bee species each year in Figs. 1 (distances) and 2 (directions). The low pollinator abundance permitted observers to follow individual bees foraging in a patch. Little interference among bee species was observed in the patches.Figure 1Frequency distributions for distances traveled between consecutive racemes (cm) for each bee species each year.Full size imageFigure 2Frequency distributions of directions traveled between consecutive racemes for each bee species each year.Full size imageModel for the distance traveled between consecutive racemesWe first determined whether a statistical model best described the distance traveled between consecutive racemes (Modeled Distance), and examined whether the model differed among bee species. We used mixed effect linear models (proc Mixed in SAS 9.3)48 to identify the model that best described the distance traveled by pollinators between consecutive racemes. The model included loge distance as a linear function of loge flower number and bee species as fixed effects. The distance traveled between consecutive racemes and the number of flowers visited per raceme were log transformed prior to analyses in order to improve the models’ residuals. In addition, we included patch and foraging bout as random effects in the model. A foraging bout includes the racemes visited in succession from the time a bee is spotted in a patch to the time it leaves that patch. We used foraging bout instead of individual bee as the random effect because bees were not individually marked in this study. Moreover, to take into consideration the potential correlation between successive observations within a foraging bout, we added clip to the model. Clip 1 represents the first and second racemes visited in the foraging bout; clip 2, the second and third, and so on. Clip was added to the model either as a random effect or as a repeated measure with an AR(1) structure. The combination of random clip and random foraging bout creates a model that is sometimes called the “compound symmetry” model. The AR(1) structure represents correlations that decline exponentially as the gap between measurements increases such that measurements closer together in time are more strongly correlated than measurements further apart. Because we expected bees to visit flowers at close proximity when resources are abundant, we chose this correlation structure as a good potential descriptor of the way distances might be correlated within foraging bouts. We started with a full model which included loge flower number, bee species, patch, foraging bout, and clip either as a random effect or as a repeated measure with an AR(1) structure. We then removed variables and compared models by inspecting AIC values and the p values for each term in the model. We considered both low AIC and statistically significant (p  More

Agostini, S. et al. Ocean acidification drives community shifts towards simplified non-calcified habitats in a subtropical–temperate transition zone. Sci. Rep. 8, 11354 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Walther, G.-R. et al. Ecological responses to recent climate change. Nature 416, 389–395 (2002).Article 
CAS 
PubMed 

Google Scholar 
Gilbert, B. & Levine, J. M. Ecological drift and the distribution of species diversity. Proc. Biol. Sci. 284, 20170507 (2017).PubMed 
PubMed Central 

Google Scholar 
White, E. P. et al. A comparison of the species–time relationship across ecosystems and taxonomic groups. Oikos 112, 185–195 (2006).Article 

Google Scholar 
Sax, D. F. & Gaines, S. D. Species invasions and extinction: the future of native biodiversity on islands. Proc. Natl Acad. Sci. USA 105, 11490–11497 (2008).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Thompson, J. N. Rapid evolution as an ecological process. Trends Ecol. Evol. 13, 329–332 (1998).Article 
CAS 
PubMed 

Google Scholar 
Post, D. M. & Palkovacs, E. P. Eco-evolutionary feedbacks in community and ecosystem ecology: interactions between the ecological theatre and the evolutionary play. Philos. Trans. R. Soc. Lond. B 364, 1629–1640 (2009).Article 

Google Scholar 
Reznick, D. N. & Travis, J. Experimental studies of evolution and eco-evo dynamics in guppies (Poecilia reticulata). Annu. Rev. Ecol. Evol. Syst. https://doi.org/10.1146/annurev-ecolsys-110218-024926 (2019).Hendry, A. P. Eco-evolutionary Dynamics (Princeton Univ. Press, 2020).Schoener, T. W. The newest synthesis: understanding the interplay of evolutionary and ecological dynamics. Science 331, 426–429 (2011).Article 
CAS 
PubMed 

Google Scholar 
Yoshida, T., Jones, L. E., Ellner, S. P., Fussmann, G. F. & Hairston, N. G. Rapid evolution drives ecological dynamics in a predator–prey system. Nature 424, 303–306 (2003).Article 
CAS 
PubMed 

Google Scholar 
Hansen, S. K., Rainey, P. B., Haagensen, J. A. J. & Molin, S. Evolution of species interactions in a biofilm community. Nature 445, 533–536 (2007).Article 
CAS 
PubMed 

Google Scholar 
Hillesland, K. L. & Stahl, D. A. Rapid evolution of stability and productivity at the origin of a microbial mutualism. Proc. Natl Acad. Sci. USA 107, 2124–2129 (2010).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Turcotte, M. M., Reznick, D. N. & Hare, J. D. The impact of rapid evolution on population dynamics in the wild: experimental test of eco-evolutionary dynamics. Ecol. Lett. 14, 1084–1092 (2011).Article 
PubMed 

Google Scholar 
Lawrence, D. et al. Species interactions alter evolutionary responses to a novel environment. PLoS Biol. 10, e1001330 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Celiker, H. & Gore, J. Clustering in community structure across replicate ecosystems following a long-term bacterial evolution experiment. Nat. Commun. 5, 4643 (2014).Article 
CAS 
PubMed 

Google Scholar 
Andrade-Domínguez, A. et al. Eco-evolutionary feedbacks drive species interactions. ISME J. 8, 1041–1054 (2014).Article 
PubMed 

Google Scholar 
Reznick, D. Hard and soft selection revisited: how evolution by natural selection works in the real world. J. Hered. 107, 3–14 (2016).Article 
PubMed 

Google Scholar 
Matthews, B., Aebischer, T., Sullam, K. E., Lundsgaard-Hansen, B. & Seehausen, O. Experimental evidence of an eco-evolutionary feedback during adaptive divergence. Curr. Biol. 26, 483–489 (2016).Article 
CAS 
PubMed 

Google Scholar 
Harcombe, W. R., Chacón, J. M., Adamowicz, E. M., Chubiz, L. M. & Marx, C. J. Evolution of bidirectional costly mutualism from byproduct consumption. Proc. Natl Acad. Sci. USA 115, 12000–12004 (2018).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Preussger, D., Giri, S., Muhsal, L. K., Oña, L. & Kost, C. Reciprocal fitness feedbacks promote the evolution of mutualistic cooperation. Curr. Biol. https://doi.org/10.1016/j.cub.2020.06.100 (2020).Adamowicz, E. M., Muza, M., Chacón, J. M. & Harcombe, W. R. Cross-feeding modulates the rate and mechanism of antibiotic resistance evolution in a model microbial community of Escherichia coli and Salmonella enterica. PLoS Pathog. 16, e1008700 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Rodríguez-Verdugo, A. & Ackermann, M. Rapid evolution destabilizes species interactions in a fluctuating environment. ISME J. 15, 450–460 (2021).Article 
PubMed 

Google Scholar 
Barber, J. N. et al. The evolution of coexistence from competition in experimental co-cultures of Escherichia coli and Saccharomyces cerevisiae. ISME J. 15, 746–761 (2021).Article 
CAS 
PubMed 

Google Scholar 
Hart, S. F. M., Chen, C.-C. & Shou, W. Pleiotropic mutations can rapidly evolve to directly benefit self and cooperative partner despite unfavorable conditions. eLife 10, e57838 (2021).Article 
PubMed 
PubMed Central 

Google Scholar 
Kokko, H. et al. Can evolution supply what ecology demands? Trends Ecol. Evol. 32, 187–197 (2017).Article 
PubMed 

Google Scholar 
Nuismer, S. Introduction to Coevolutionary Theory (Macmillan Learning, 2017).Stoltzfus, A. & McCandlish, D. M. Mutational biases influence parallel adaptation. Mol. Biol. Evol. 34, 2163–2172 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Payne, J. L. et al. Transition bias influences the evolution of antibiotic resistance in Mycobacterium tuberculosis. PLoS Biol. 17, e3000265 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Storz, J. F. et al. The role of mutation bias in adaptive molecular evolution: insights from convergent changes in protein function. Philos. Trans. R. Soc. Lond. B 374, 20180238 (2019).Article 
CAS 

Google Scholar 
Gomez, K., Bertram, J. & Masel, J. Mutation bias can shape adaptation in large asexual populations experiencing clonal interference. Proc. Biol. Sci. 287, 20201503 (2020).CAS 
PubMed 
PubMed Central 

Google Scholar 
Venkataram, S., Monasky, R., Sikaroodi, S. H., Kryazhimskiy, S. & Kacar, B. Evolutionary stalling and a limit on the power of natural selection to improve a cellular module. Proc. Natl Acad. Sci. USA 117, 18582–18590 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Hom, E. F. Y. & Murray, A. W. Niche engineering demonstrates a latent capacity for fungal–algal mutualism. Science 345, 94–98 (2014).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Wolfe, B. E. & Dutton, R. J. Fermented foods as experimentally tractable microbial ecosystems. Cell 161, 49–55 (2015).Article 
CAS 
PubMed 

Google Scholar 
Chacón, J. M., Hammarlund, S. P., Martinson, J. N. V., Smith, L. B. & Harcombe, W. R. The ecology and evolution of model microbial mutualisms. Annu. Rev. Ecol. Evol. Syst. 52, 363–384 (2021).Article 

Google Scholar 
Blasche, S., Kim, Y., Oliveira, A. P. & Patil, K. R. Model microbial communities for ecosystems biology. Curr. Opin. Syst. Biol. 6, 51–57 (2017).Article 

Google Scholar 
Levy, S. F. et al. Quantitative evolutionary dynamics using high-resolution lineage tracking. Nature 519, 181–186 (2015).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Venkataram, S. et al. Development of a comprehensive genotype-to-fitness map of adaptation-driving mutations in yeast. Cell 166, 1585–1596.e22 (2016).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Jones, E. I., Bronstein, J. L. & Ferrière, R. The fundamental role of competition in the ecology and evolution of mutualisms. Ann. N. Y. Acad. Sci. 1256, 66–88 (2012).Article 
PubMed 

Google Scholar 
Boyer, S., Hérissant, L. & Sherlock, G. Adaptation is influenced by the complexity of environmental change during evolution in a dynamic environment. PLoS Genet. 17, e1009314 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Blundell, J. R. et al. The dynamics of adaptive genetic diversity during the early stages of clonal evolution. Nat. Ecol. Evol. 3, 293–301 (2019).Article 
PubMed 

Google Scholar 
Good, B. H., Rouzine, I. M., Balick, D. J., Hallatschek, O. & Desai, M. M. Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations. Proc. Natl Acad. Sci. USA 109, 4950–4955 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Good, B. H., Martis, S. & Hallatschek, O. Adaptation limits ecological diversification and promotes ecological tinkering during the competition for substitutable resources. Proc. Natl Acad. Sci. USA 115, E10407–E10416 (2018).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Zhu, Y. O., Siegal, M. L., Hall, D. W. & Petrov, D. A. Precise estimates of mutation rate and spectrum in yeast. Proc. Natl Acad. Sci. USA 111, E2310–E2318 (2014).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Dunham, M. J. et al. Characteristic genome rearrangements in experimental evolution of Saccharomyces cerevisiae. Proc. Natl Acad. Sci. USA 99, 16144–16149 (2002).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Yona, A. H. et al. Chromosomal duplication is a transient evolutionary solution to stress. Proc. Natl Acad. Sci. USA 109, 21010–21015 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Sunshine, A. B. et al. The fitness consequences of aneuploidy are driven by condition-dependent gene effects. PLoS Biol. 13, e1002155 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Gerrish, P. J. & Lenski, R. E. The fate of competing beneficial mutations in an asexual population. Genetica 102-103, 127–144 (1998).Article 
CAS 
PubMed 

Google Scholar 
Desai, M. M. & Fisher, D. S. Beneficial mutation–selection balance and the effect of linkage on positive selection. Genetics 176, 1759–1798 (2007).Article 
PubMed 
PubMed Central 

Google Scholar 
Schiffels, S., Szöllosi, G. J., Mustonen, V. & Lässig, M. Emergent neutrality in adaptive asexual evolution. Genetics 189, 1361–1375 (2011).Article 
PubMed 
PubMed Central 

Google Scholar 
Nguyen, Ba,A. N. et al. High-resolution lineage tracking reveals travelling wave of adaptation in laboratory yeast. Nature 575, 494–499 (2019).Article 

Google Scholar 
Foster, K. R., Shaulsky, G., Strassmann, J. E., Queller, D. C. & Thompson, C. R. L. Pleiotropy as a mechanism to stabilize cooperation. Nature 431, 693–696 (2004).Article 
CAS 
PubMed 

Google Scholar 
Sachs, J. L., Mueller, U. G., Wilcox, T. P. & Bull, J. J. The evolution of cooperation. Q. Rev. Biol. 79, 135–160 (2004).Article 
PubMed 

Google Scholar 
Harcombe, W. Novel cooperation experimentally evolved between species. Evolution 64, 2166–2172 (2010).PubMed 

Google Scholar 
Vasi, F., Travisano, M. & Lenski, R. E. Long-term experimental evolution in Escherichia coli. II. Changes in life-history traits during adaptation to a seasonal environment. Am. Nat. 144, 432–456 (1994).Article 

Google Scholar 
MacArthur, R. H. & Wilson, E. O. The Theory of Island Biogeography (Princeton Univ. Press, 2001).Reznick, D., Bryant, M. J. & Bashey, F. r- and K-selection revisited: the role of population regulation in life-history evolution. Ecology 83, 1509–1520 (2002).Article 

Google Scholar 
Mueller, L. D. & Ayala, F. J. Trade-off between r-selection and K-selection in Drosophila populations. Proc. Natl Acad. Sci. USA 78, 1303–1305 (1981).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Novak, M., Pfeiffer, T., Lenski, R. E., Sauer, U. & Bonhoeffer, S. Experimental tests for an evolutionary trade-off between growth rate and yield in E. coli. Am. Nat. 168, 242–251 (2006).Article 
PubMed 

Google Scholar 
Bachmann, H. et al. Availability of public goods shapes the evolution of competing metabolic strategies. Proc. Natl Acad. Sci. USA 110, 14302–14307 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Lipson, D. A. The complex relationship between microbial growth rate and yield and its implications for ecosystem processes. Front. Microbiol. 6, 615 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Orivel, J. et al. Trade-offs in an ant–plant–fungus mutualism. Proc. Biol. Sci. 284, 20161679 (2017).PubMed 
PubMed Central 

Google Scholar 
Fritts, R. K. et al. Enhanced nutrient uptake is sufficient to drive emergent cross-feeding between bacteria in a synthetic community. ISME J. 14, 2816–2828 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Wortel, M. T., Noor, E., Ferris, M., Bruggeman, F. J. & Liebermeister, W. Metabolic enzyme cost explains variable trade-offs between microbial growth rate and yield. PLoS Comput. Biol. 14, e1006010 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Cheng, C. et al. Laboratory evolution reveals a two-dimensional rate-yield tradeoff in microbial metabolism. PLoS Comput. Biol. 15, e1007066 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Luckinbill, L. S. r and K selection in experimental populations of Escherichia coli. Science 202, 1201–1203 (1978).Article 
CAS 
PubMed 

Google Scholar 
Oxman, E., Alon, U. & Dekel, E. Defined order of evolutionary adaptations: experimental evidence. Evolution 62, 1547–1554 (2008).Article 
PubMed 

Google Scholar 
Jasmin, J.-N., Dillon, M. M. & Zeyl, C. The yield of experimental yeast populations declines during selection. Proc. Biol. Sci. 279, 4382–4388 (2012).PubMed 
PubMed Central 

Google Scholar 
Laan, L., Koschwanez, J. H. & Murray, A. W. Evolutionary adaptation after crippling cell polarization follows reproducible trajectories. eLife 4, e09638 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Blount, Z. D., Lenski, R. E. & Losos, J. B. Contingency and determinism in evolution: replaying life’s tape. Science 362, eaam5979 (2018).Article 
PubMed 

Google Scholar 
Fukami, T. Historical contingency in community assembly: integrating niches, species pools, and priority effects. Annu. Rev. Ecol. Evol. Syst. 46, 1–23 (2015).Article 

Google Scholar 
Rainey, P. B. & Travisano, M. Adaptive radiation in a heterogeneous environment. Nature 394, 69–72 (1998).Article 
CAS 
PubMed 

Google Scholar 
Meyer, J. R. et al. Repeatability and contingency in the evolution of a key innovation in phage lambda. Science 335, 428–432 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Herron, M. D. & Doebeli, M. Parallel evolutionary dynamics of adaptive diversification in Escherichia coli. PLoS Biol. 11, e1001490 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Hillesland, K. L. et al. Erosion of functional independence early in the evolution of a microbial mutualism. Proc. Natl Acad. Sci. USA 111, 14822–14827 (2014).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Meroz, N., Tovi, N., Sorokin, Y. & Friedman, J. Community composition of microbial microcosms follows simple assembly rules at evolutionary timescales. Nat. Commun. 12, 2891 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
MacLean, R. C. The tragedy of the commons in microbial populations: insights from theoretical, comparative and experimental studies. Heredity 100, 471–477 (2008).Article 
CAS 
PubMed 

Google Scholar 
Dunn, B. et al. Recurrent rearrangement during adaptive evolution in an interspecific yeast hybrid suggests a model for rapid introgression. PLoS Genet. 9, e1003366 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Barillot, E., Lacroix, B. & Cohen, D. Theoretical analysis of library screening using a N-dimensional pooling strategy. Nucleic Acids Res. 19, 6241–6247 (1991).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Baym, M., Shaket, L., Anzai, I. A., Adesina, O. & Barstow, B. Rapid construction of a whole-genome transposon insertion collection for Shewanella oneidensis by Knockout Sudoku. Nat. Commun. 7, 13270 (2016).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Baym, M. et al. Inexpensive multiplexed library preparation for megabase-sized genomes. PLoS ONE 10, e0128036 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Venkataram, S., Kuo, H., Hom, E., Kryazhimskiy, S. Early adaptation in a microbial community is dominated by mutualism-enhancing mutations. Dryad https://doi.org/10.6076/D14K5X (2022). More

Potts, S. G. et al. Global pollinator declines: trends, impacts and drivers. Trends Ecol. Evol. 25, 345–353 (2010).Article 
PubMed 

Google Scholar 
Lautenbach, S., Seppelt, R., Liebscher, J. & Dormann, C. F. Spatial and temporal trends of global pollination benefit. PLoS ONE 7, e35954 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Ollerton, J., Winfree, R. & Tarrant, S. How many flowering plants are pollinated by animals? Oikos 120, 321–326 (2011).Article 

Google Scholar 
Rodger, J. G. et al. Widespread vulnerability of flowering plant seed production to pollinator declines. Sci. Adv. 7, eabd3524 (2021).Article 
PubMed 
PubMed Central 

Google Scholar 
Biesmeijer, J. C. et al. Parallel declines in pollinators and insect-pollinated plants in Britain and the Netherlands. Science 313, 351–354 (2006).Article 
CAS 
PubMed 

Google Scholar 
Bennett, J. M. et al. Land use and pollinator dependency drives global patterns of pollen limitation in the Anthropocene. Nat. Commun. 11, 3999 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Tylianakis, J. M., Didham, R. K., Bascompte, J. & Wardle, D. A. Global change and species interactions in terrestrial ecosystems. Ecol. Lett. 11, 1351–1363 (2008).Article 
PubMed 

Google Scholar 
Hegland, S. J., Nielsen, A., Lázaro, A., Bjerknes, A.-L. & Totland, Ø. How does climate warming affect plant–pollinator interactions? Ecol. Lett. 12, 184–195 (2009).Article 
PubMed 

Google Scholar 
Thébault, E. & Fontaine, C. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329, 853–856 (2010).Article 
PubMed 

Google Scholar 
Lever, J. J., van Nes, E. H., Scheffer, M. & Bascompte, J. The sudden collapse of pollinator communities. Ecol. Lett. 17, 350–359 (2014).Article 
PubMed 

Google Scholar 
Valdovinos, F. S. et al. Species traits and network structure predict the success and impacts of pollinator invasions. Nat. Commun. 9, 2153 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Waser, N. M., Chittka, L., Price, M. V., Williams, N. M. & Ollerton, J. Generalization in pollination systems, and why it matters. Ecology 77, 1043–1060 (1996).Article 

Google Scholar 
Brosi, B. J. Pollinator specialization: from the individual to the community. New Phytol. 210, 1190–1194 (2016).Article 
PubMed 

Google Scholar 
Elmqvist, T. et al. Response diversity, ecosystem change, and resilience. Front. Ecol. Environ. 1, 488–494 (2003).Article 

Google Scholar 
Waser, N. M. & Ollerton, J. Plant–Pollinator Interactions: From Specialization to Generalization (Univ. of Chicago Press, 2006).Ashman, T.-L., Arceo-Gómez, G., Bennett, J. M. & Knight, T. M. Is heterospecific pollen receipt the missing link in understanding pollen limitation of plant reproduction? Am. J. Bot. 107, 845–847 (2020).Article 
PubMed 

Google Scholar 
Garibaldi, L. A. et al. Trait matching of flower visitors and crops predicts fruit set better than trait diversity. J. Appl. Ecol. 52, 1436–1444 (2015).Article 

Google Scholar 
CaraDonna, P. J. et al. Seeing through the static: the temporal dimension of plant–animal mutualistic interactions. Ecol. Lett. 24, 149–161 (2021).Article 
PubMed 

Google Scholar 
Burkle, L. A., Marlin, J. C. & Knight, T. M. Plant–pollinator interactions over 120 years: loss of species, co-occurrence, and function. Science 339, 1611–1615 (2013).Article 
CAS 
PubMed 

Google Scholar 
Jacquemin, F. et al. Loss of pollinator specialization revealed by historical opportunistic data: insights from network-based analysis. PLoS ONE 15, e0235890 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Mathiasson, M. E. & Rehan, S. M. Wild bee declines linked to plant–pollinator network changes and plant species introductions. Insect Conserv. Divers. 13, 595–605 (2020).Article 

Google Scholar 
Bennett, J. M. et al. A review of European studies on pollination networks and pollen limitation, and a case study designed to fill in a gap. AoB Plants 10, ply068 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Doré, M., Fontaine, C. & Thébault, E. Relative effects of anthropogenic pressures, climate, and sampling design on the structure of pollination networks at the global scale. Glob. Change Biol. 27, 1266–1280 (2021).Article 

Google Scholar 
Rader, R. et al. Non-bee insects are important contributors to global crop pollination. Proc. Natl Acad. Sci. USA 113, 146–151 (2016).Article 
CAS 
PubMed 

Google Scholar 
Post, E. et al. Ecological dynamics across the arctic associated with recent climate change. Science 325, 1355–1358 (2009).Article 
CAS 
PubMed 

Google Scholar 
Hung, K.-L. J., Kingston, J. M., Albrecht, M., Holway, D. A. & Kohn, J. R. The worldwide importance of honey bees as pollinators in natural habitats. Proc. R. Soc. B 285, 20172140 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Kearns, C. A. Anthophilous fly distribution across an elevation gradient. Am. Midl. Nat. 127, 172–182 (1992).Article 

Google Scholar 
Kevan, P. G. Insect pollination of high arctic flowers. J. Ecol. 60, 831–847 (1972).Article 

Google Scholar 
Tiusanen, M., Hebert, P. D. N., Schmidt, N. M. & Roslin, T. One fly to rule them all—muscid flies are the key pollinators in the arctic. Proc. Roy. Soc. B 283, 20161271 (2016).Article 

Google Scholar 
Weiner, C., Werner, M., Linsenmair, K. E. & Blüthgen, N. Land use intensity in grasslands: changes in biodiversity, species composition and specialisation in flower visitor networks. Basic Appl. Ecol. 12, 292–299 (2011).Article 

Google Scholar 
Rader, R., Edwards, W., Westcott, D. A., Cunningham, S. A. & Howlett, B. G. Pollen transport differs among bees and flies in a human-modified landscape. Divers. Distrib. 17, 519–529 (2011).Article 

Google Scholar 
Bartley, T. J. et al. Food web rewiring in a changing world. Nat. Ecol. Evol. 3, 345–354 (2019).Article 
PubMed 

Google Scholar 
Ghisbain, G., Gérard, M., Wood, T. J., Hines, H. M. & Michez, D. Expanding insect pollinators in the Anthropocene. Biol. Rev. 96, 2755–2770 (2021).Article 
PubMed 

Google Scholar 
Silén, F. Blombiologiska iakttagelser i Kittilä Lappmark. Medd. Soc. Fauna Flora Fennica 31, 80–99 (1906).
Google Scholar 
Clavel, J., Julliard, R. & Devictor, V. Worldwide decline of specialist species: toward a global functional homogenization? Front. Ecol. Environ. 9, 222–228 (2011).Article 

Google Scholar 
Erhardt, A. Pollination of Dianthus superbus L. Flora 185, 99–106 (1991).Article 

Google Scholar 
Witt, T., Jürgens, A., Geyer, R. & Gottsberger, G. Nectar dynamics and sugar composition in flowers of Silene and Saponaria species (Caryophyllaceae). Plant Biol. 1, 334–345 (1999).Article 
CAS 

Google Scholar 
Morales, C. L. & Traveset, A. Interspecific pollen transfer: magnitude, prevalence and consequences for plant fitness. Crit. Rev. Plant Sci. 27, 221–238 (2008).Article 
CAS 

Google Scholar 
Ashman, T.-L. & Arceo-Gómez, G. Toward a predictive understanding of the fitness costs of heterospecific pollen receipt and its importance in co-flowering communities. Am. J. Bot. 100, 1061–1070 (2013).Article 
PubMed 

Google Scholar 
Orford, K. A., Vaughan, I. P. & Memmott, J. The forgotten flies: the importance of non-syrphid Diptera as pollinators. Proc. R. Soc. B 282, 20142934 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Stavert, J. R. et al. Hairiness: the missing link between pollinators and pollination. PeerJ 4, e2779 (2016).Article 
PubMed 
PubMed Central 

Google Scholar 
Doyle, T. et al. Pollination by hoverflies in the Anthropocene. Proc. R. Soc. B 287, 20200508 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
Albrecht, M., Schmid, B., Hautier, Y. & Müller, C. B. Diverse pollinator communities enhance plant reproductive success. Proc. R. Soc. B. 279, 4845–4852 (2012).Article 
PubMed 
PubMed Central 

Google Scholar 
Fründ, J., Dormann, C. F., Holzschuh, A. & Tscharntke, T. Bee diversity effects on pollination depend on functional complementarity and niche shifts. Ecology 94, 2042–2054 (2013).Article 
PubMed 

Google Scholar 
Magrach, A., Molina, F. P. & Bartomeus, I. Niche complementarity among pollinators increases community-level plant reproductive success. Peer Commun. J. 1, e1 (2021).Article 

Google Scholar 
Giménez-Benavides, L., Dötterl, S., Jürgens, A., Escudero, A. & Iriondo, J. M. Generalist diurnal pollination provides greater fitness in a plant with nocturnal pollination syndrome: assessing the effects of a Silene–Hadena interaction. Oikos 116, 1461–1472 (2007).
Google Scholar 
Vázquez, D. P., Blüthgen, N., Cagnolo, L. & Chacoff, N. P. Uniting pattern and process in plant–animal mutualistic networks: a review. Ann. Bot. 103, 1445–1457 (2009).Article 
PubMed 
PubMed Central 

Google Scholar 
Vizentin-Bugoni, J., Debastiani, V. J., Bastazini, V. A. G., Maruyama, P. K. & Sperry, J. H. Including rewiring in the estimation of the robustness of mutualistic networks. Methods Ecol. Evol. 11, 106–116 (2020).Article 

Google Scholar 
Brosi, B. J. & Briggs, H. M. Single pollinator species losses reduce floral fidelity and plant reproductive function. Proc. Natl Acad. Sci. USA 110, 13044–13048 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Pekkarinen, A. & Teräs, I. Zoogeography of Bombus and Psithyrus in northwestern Europe (Hymenoptera, Apidae). Ann. Zool. Fennici 30, 187–208 (1993).
Google Scholar 
Arbetman, M. P., Gleiser, G., Morales, C. L., Williams, P. & Aizen, M. A. Global decline of bumblebees is phylogenetically structured and inversely related to species range size and pathogen incidence. Proc. R. Soc. B 284, 20170204 (2017).Article 
PubMed 
PubMed Central 

Google Scholar 
Kerr, J. T. et al. Climate change impacts on bumblebees converge across continents. Science 349, 177–180 (2015).Article 
CAS 
PubMed 

Google Scholar 
Arceo-Gómez, G., Barker, D., Stanley, A., Watson, T. & Daniels, J. Plant–pollinator network structural properties differentially affect pollen transfer dynamics and pollination success. Oecologia 192, 1037–1045 (2020).Article 
PubMed 

Google Scholar 
de Santiago-Hernández, M. H. et al. The role of pollination effectiveness on the attributes of interaction networks: from floral visitation to plant fitness. Ecology 100, e02803 (2019).Article 
PubMed 

Google Scholar 
Koch, V., Zoller, L., Bennett, J. M. & Knight, T. M. Pollinator dependence but no pollen limitation for eight plants occurring north of the Arctic Circle. Ecol. Evol. 10, 13664–13672 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
Loboda, S., Savage, J., Buddle, C. M., Schmidt, N. M. & Høye, T. T. Declining diversity and abundance of High Arctic fly assemblages over two decades of rapid climate warming. Ecography 41, 265–277 (2018).Article 

Google Scholar 
Høye, T. T., Post, E., Schmidt, N. M., Trøjelsgaard, K. & Forchhammer, M. C. Shorter flowering seasons and declining abundance of flower visitors in a warmer Arctic. Nat. Clim. Change 3, 759–763 (2013).Article 

Google Scholar 
Soroye, P., Newbold, T. & Kerr, J. Climate change contributes to widespread declines among bumble bees across continents. Science 367, 685–688 (2020).Article 
CAS 
PubMed 

Google Scholar 
Zattara, E. E. & Aizen, M. A. Worldwide occurrence records suggest a global decline in bee species richness. One Earth 4, 114–123 (2021).Article 

Google Scholar 
Bartomeus, I., Stavert, J. R., Ward, D. & Aguado, O. Historical collections as a tool for assessing the global pollination crisis. Philos. Trans. R. Soc. B 374, 20170389 (2019).Article 

Google Scholar 
Rakosy, D., Ashman, T.-L., Zoller, L., Stanley, A. & Knight, T. M. Integration of historic collections can shed light on patterns of change in plant–pollinator interactions and pollination service. Func. Ecol. https://doi.org/10.1111/1365-2435.14211 (2022).Hyne, C. J. C. W. Through Arctic Lapland (A. and C. Black, 1898).Knuth, P. Handbuch der Blütenbiologie, unter Zugrundelegung von Herman Müllers Werk: ‘Die Befruchtung der Blumen durch Insekten’ (W. Engelmann, 1898).Zoller, L. & Knight, T. M. Historical records of plant-insect interactions in subarctic Finland.BMC Res. Notes 15, 317 (2022).Article 
PubMed 
PubMed Central 

Google Scholar 
Zoller, L. & Knight, T. M. Historical records of plant–insect interactions in subarctic Finland. figshare https://doi.org/10.6084/m9.figshare.c.5828663.v4 (2022).Zoller, L., Bennett, J. M. & Knight, T. M. Diel-scale temporal dynamics in the abundance and composition of pollinators in the arctic summer. Sci. Rep. 10, 21187 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2020).Hsieh, T. C., Ma, K. H. & Chao, A. iNEXT: an R package for rarefaction and extrapolation of species diversity (Hill numbers). Methods Ecol. Evol. 7, 1451–1456 (2016).Article 

Google Scholar 
Klotz, S., Kühn, I. & Durka, W. Biolflor Database (UFZ—Centre for Environmental Research Leipzig-Halle, 2002); https://www.ufz.de/biolflor/index.jspOksanen, J. et al. vegan: Community ecology package. R version 2.5.7 (2020).Chao, A., Chazdon, R. L., Colwell, R. K. & Shen, T.-J. Abundance-based similarity indices and their estimation when there are unseen species in samples. Biometrics 62, 361–371 (2006).Article 
PubMed 

Google Scholar 
Dormann, C. F. et al. bipartite: Visualising bipartite networks and calculating some (ecological) indices. R version 2.16 (2021).Blüthgen, N., Menzel, F. & Blüthgen, N. Measuring specialization in species interaction networks. BMC Ecol. 6, 9 (2006).Article 
PubMed 
PubMed Central 

Google Scholar 
Stefan, V. & Knight, T. M. bootstrapnet: Bootstrap network metrics. R version 1.0.0 https://valentinitnelav.github.io/bootstrapnet/ (2021).Poisot, T., Canard, E., Mouillot, D., Mouquet, N. & Gravel, D. The dissimilarity of species interaction networks. Ecol. Lett. 15, 1353–1361 (2012).Article 
PubMed 

Google Scholar 
Poisot, T. Dissimilarity of species interaction networks: quantifying the effect of turnover and rewiring. Peer Community Journal 2, e35 (2022).Article 

Google Scholar 
Dormann, C. F. How to be a specialist? Quantifying specialisation in pollination networks. Netw. Biol. 1, 1 (2011).
Google Scholar  More

Wahl, M., Hay, M. E. & Enderlein, P. Effects of epibiosis on consumer–prey interactions. Hydrobiologia 355, 49–59 (1997).Article 

Google Scholar 
Fernandez-Leborans, G., Zitzler, K. & Gabilondo, R. Protozoan ciliate epibionts on the freshwater shrimp Caridina (Crustacea, Decapoda, Atyidae) from the Malili lake system on Sulawesi (Indonesia). J. Nat. Hist. 40, 1983–2000 (2006).Article 

Google Scholar 
Puckett, G. L. & Carman, K. R. Ciliate epibiont effects on feeding, energy reserves, and sensitivity to hydrocarbon contaminants in an estuarine harpactacoid copepod. Estuaries 25, 372–381 (2002).Article 

Google Scholar 
Fernandez-Leborans, G. Epibiosis in Crustacea: an overview. Crustaceana 83, 549–640 (2010).Article 

Google Scholar 
Regali-Seleghim, M. H. & Godinho, M. J. Peritrich epibiont protozoans in the zooplankton of a subtropical shallow aquatic ecosystem (Monjolinho Reservoir, São Carlos, Brazil). J Plankton Res. 26, 501–508 (2004).Article 

Google Scholar 
Bickel, S. L., Tang, K. W. & Grossart, H. P. Ciliate epibionts associated with crustacean zooplankton in German lakes: distribution, motility, and bacterivory. Front. Microbiol. 3, 1–11 (2012).Article 

Google Scholar 
Souissi, A., Souissi, S. & Hwang, J. S. The effect of epibiont ciliates on the behavior and mating success of the copepod Eurytemora affinis. J. Exp. Mar. Biol. Ecol. 445, 38–43. https://doi.org/10.1016/j.jembe.2013.04.002 (2013).Article 

Google Scholar 
Willey, R. L., Cantrell, P. A. & Threlkeld, S. T. Epibiotic euglenoid flagellates increase the susceptibility of some zooplankton to fish predation. Limnol. Oceanogr. 35, 952–959 (1990).Article 
ADS 

Google Scholar 
Ólafsdóttir, S. H. & Svavarsson, J. Ciliate (Protozoa) epibionts of deep-water asellote isopods (Crustacea): pattern and diversity. J. Crust. Biol. 22, 607–618 (2002).Article 

Google Scholar 
Kumari, S., Kumar, R., Sarkar, U. K. & Das, B. S. Record of epibiont ciliates (Ciliophora: Peritrichia) living on freshwater invertebrates in a floodplain wetland. J. Inland Fish. Soc. India. 53, 210–214. https://doi.org/10.47780/jifsi.52.3.2021 (2021).Article 

Google Scholar 
Utz, L. R. P. & Coats, D. W. Spatial and temporal patterns in the occurrence of peritrich ciliates as epibionts on calanoid copepods in the Chesapeake Bay, USA. J. Eukaryot. Microbiol. 52, 236–244 (2005).Article 

Google Scholar 
Utz, L. R. P. & Coats, D. W. Telotroch formation, survival and attachment in the epibiotic peritrich Zoothamnium intermedium (Ciliophora, Oligohymenophorea). Invert. Biol. 127, 237–248 (2008).Article 

Google Scholar 
Ohtsuka, S., et al. Symbiosis of planktonic copepods and mysids with epibionts and parasites in the Northpacific: diversity and interactions. In New Frontiers in Crustacean Biology, 1–14, Brill (2011).Sługocki, Ł et al. Passenger for millenniums: association between stenothermic microcrustacean and suctorian epibiont – the case of Eurytemora lacustris and Tokophyra sp. Sci. Rep. 10, 1–10. https://doi.org/10.1038/s41598-020-66730-2 (2020).Article 

Google Scholar 
Fernandez-Leborans, G. A review of the species of protozoan epibionts on crustaceans. III. Chonotrich ciliates. Crustaceana 74, 581–607. https://doi.org/10.1163/156854001300228852 (2001).Article 

Google Scholar 
Fernandez-Leborans, G. & Tato- Porto, M. L. A review of the species of the protozoan epibionts on crustaceans. I. Peritrich ciliates. Crustaceana 73, 643–683. https://doi.org/10.1163/156854000504705 (2000).Article 

Google Scholar 
Utz, L. R. P. & Coats, D. W. The role of motion in the formation of free living stages and attachment of the peritrich epibiont Zoothamnium intermedium (Ciliophora, Peritrichia). Biosciências 13, 69–74 (2005).
Google Scholar 
Pan, Y. et al. Effects of epibiotic diatoms on the productivity of the Calanoid Copepod Acartia tonsa (Dana) in intensive aquaculture systems. Front. Mar. Sci. 8, 2296–7745. https://doi.org/10.3389/fmars.2021.728779 (2021).Article 

Google Scholar 
Bickel, S. L., Tang, K. W. & Grossart, H. P. Ciliate epibionts associated with crustacean zooplankton in German lakes: distribution, motility, and bacterivory. Front. Microbiol. 3, 243. https://doi.org/10.3389/fmicb.2012.00243 (2012).Article 

Google Scholar 
De Domitrovic, Y. Z. et al. Epibiont algae on planktic micro-crustaceans from a subtropical shallow lake (Argentina). Algol. Stud. 127, 29–38 (2008).Article 

Google Scholar 
Ohman, M. D. Behavioral responses of zooplankton to predation. Bull. Mar. Sci. 43(3), 530–550 (1988).
Google Scholar 
Acevedo-Trejos, E., Marañón, E. & Merico, A. Phytoplankton size diversity and ecosystem function relationships across oceanic regions. Proc. Roy. Soc. B Biol. Sci. 285, 2180621. https://doi.org/10.1098/rspb.2018.0621 (2018).Article 

Google Scholar 
Francesco, P. et al. Interacting temperature, nutrients and Zooplankton Grazing Control Phytoplankton size-abundance relationships in eight Swiss Lakes. Front. Microbiol. 10, 1664–2302. https://doi.org/10.3389/fmicb.2019.03155 (2020).Article 

Google Scholar 
Carman, K. & Dobbs, F. C. Epibiotic microorganisms on copepods and other marine crustaceans. Microsci. Res. Tech. 37, 116–135 (1997).Article 

Google Scholar 
Cabral, A. F. et al. Spatial and temporal occurrence of Rhabdostyla cf. chronomi Kahl, 1933 (Ciliophora, Peritrichia) as an epibiont on chironomid larvae in a lotic system in the neotropics. Hydrobiologia 644, 351–359 (2010).Article 

Google Scholar 
Burris, Z. & Dam, H. G. Deleterious effects of the ciliate epibiont Zoothamnium sp. On fitness of the copepod Acartia tonsa. J. Plankton Res. 36, 788–799. https://doi.org/10.1093/plankt/fbt137 (2014).Article 

Google Scholar 
Yin, Y. et al. Hidden defensive morphology in rotifers: benefits, costs, and fitness consequences. Sci. Rep. 7, 4488. https://doi.org/10.1038/s41598-017-04809-z (2017).Article 
ADS 

Google Scholar 
Gilbert, J. J. & Shröder, T. The ciliate epibiont Epistylis Pygmaeum: selection for zooplankton hosts, reproduction and effect on two rotifers. Freshw. Biol. 48, 878–893 (2003).Article 

Google Scholar 
Gilbert, J. J. Morphological and behavioural responses of a rotifer to the predator Asplanchna. J. Plankton Res. 36, 1576–1584. https://doi.org/10.1093/plankt/fbu075 (2014).Article 

Google Scholar 
Fernandez-Leborans, G. Epibiosis in crustacea: an overview. Crustaceana 83(5), 549–640. https://doi.org/10.1163/001121610X491059 (2010).Article 

Google Scholar 
Iyer, N. & Rao, T. R. Epizoic mode of life in Brachionus rubens Ehrenberg as a deterrent against predation by Asplanchna intermedia Hudson. Hydrobiologia 313, 377–380 (1995).Article 

Google Scholar 
Boyan, B. D., Lotz, E. M. & Schwartz, Z. Roughness and hydrophilicity as osteogenic biomimetic surface properties. Tissue Eng. 23, 1479–1489. https://doi.org/10.1089/ten.TEA.2017.0048 (2017).Article 

Google Scholar 
Ubuo, E. E. et al. the direct cause of amplified wettability: roughness or surface chemistry?. J. Compos. Sci. 5, 213. https://doi.org/10.3390/jcs5080213 (2021).Article 

Google Scholar 
Gilbert, J. J. Attachment behavior in the rotifer Brachionus rubens: induction by Asplanchna and effect on sexual reproduction. Hydrobiologia 844, 9–20. https://doi.org/10.1007/s10750-018-3805-7 (2019).Article 

Google Scholar 
Kumar, R. Effect of Mesocyclops thermocyclopoides (Copepoda, Cyclopoida) predation on population dynamics of different prey: a laboratory study. J. Freshwater Ecol. 18, 383–393. https://doi.org/10.1080/02705060.2003.966397 (2003).Article 

Google Scholar 
Bulut, H. & Saler, S. Presence of an epibiont Epistylis sp. (Protozoa, Ciliophora) on some zooplankton. Fresenius Environ. Bull. 26(11), 6334–6339 (2017).
Google Scholar 
Threlkeld, S. T., Chiavelli, D. A. & Willey, R. L. The organization of zooplankton epibiont communities. Trends Ecol Evol. 8, 317–321 (1993).Article 

Google Scholar 
Iyer, N. & Rao, T. R. Effect of epizoic rotifer Brachionus rubens on the population growth of three cladoceran species. Hydrobiologia 255(256), 325–332 (1993).Article 

Google Scholar 
Ramírez-Ballesteros, M., Fernandez-Leborans, G., Mayén-Estrada, R. New record of Epistylis hentscheli (Ciliophora, Peritrichia) as an epibiont of Procambarus (Austrocambarus) sp. (Crustacea, Decapoda) in Chiapas, Mexico. ZooKeys. 782, 1–9. https://doi.org/10.3897/zookeys.782.26417 (2018).Wu, H.X., Feng, M.G. Mass mortality of larval Eriocheir sinensis (Decapoda: Grapsidae) population bred under facility conditions: possible role of Zoothamnium sp. (Peritrichida: Vorticellidae) epiphyte. J. Invertebr. Pathol. 86, 59–60 (2004).Kumar, R. et al. Potential of three aquatic predators to control mosquitoes in the presence of alternative prey: a comparative experimental assessment. Mar. Freshw. Res. 59, 817–835 (2008).Article 

Google Scholar 
Kumar, R., Sami Souissi, S. & Hwang, J. S. Vulnerability of carp larvae to copepod predation as a function of larval age and body length. Aquaculture. 338, 274–283 (2012).Rao, T. R. & Kumar, R. Patterns of prey selectivity in the cyclopoid copepod Mesocyclops thermocyclopoides. Aquat. Ecol. 36, 411–424 (2002).Article 

Google Scholar 
Kumar, R. & Rao, T. R. Predation on Mosquito Larvae by Mesocyclops thermocyclopoides (Copepoda: Cyclopoida) in the Presence of Alternate Prey. Int Rev Hydrobiol. 88, 570–581 (2003).Article 

Google Scholar 
Baldrighi, E. et al. The cost for biodiversity: records of ciliate-nematode epibiosis with the description of three new Suctorian species. Diversity 12, 224. https://doi.org/10.3390/d12060224 (2020).Article 

Google Scholar 
Morado, J. F. & Small, E. B. Ciliate parasites and related diseases of Crustacea: a review. Rev. Fish. Sci. 3, 275–354 (1995).Article 

Google Scholar 
Lúcia, S. L., Safi Kam, W., Tang, Ryan, B. Carnegie. Investigating the epibiotic peritrich Zoothamnium intermedium Precht, 1935: Seasonality and distribution of its relationships with copepods in Chesapeake Bay (USA), Eur. J. Protistol. 84, 125880, https://doi.org/10.1016/j.ejop.2022.125880 (2022).Coats, D. W. & Heinbokel, J. F. A study of reproduction and other life cycle phenomena in planktonic protists using an acridine orange fluorescence technique. Mar. Biol. 67, 71–79. https://doi.org/10.1007/BF00397096 (1982).Article 

Google Scholar 
Montagnes, D. J. S. A Quantitative Protargol Stain (QPS) for Ciliates: method description and test of its quantitative nature. Mar. Microb. Food Webs. 2, 83–93 (1987).
Google Scholar 
Montagnes, D. J. S. & Lynn, D. H. A Quantitative Protargol stain (QPS) for ciliates and other protists. In Handbook of methods in aquatic microbial ecology (eds Kemp, P. et al.) 229–240 (Lewis Publishers, 1993).
Google Scholar 
Warren, A. Revision of the genus Vorticella (Ciliophora: Peritrichida). Bull. Br. Museum Nat. History 50, 48–52 (1986).
Google Scholar 
Foissner, W. et al. Intraclass evolution and classification of the Colpodea (Ciliophora). J. Eukaryot. Microbiol. 58, 397–415 (2011).Article 

Google Scholar 
Foissner, W., Berger, H. & Kohmann, F. Taxonomische und oekologische Revision der Ciliaten des Saprobiensystems—Band II: Peritrichia, Heterotrichida, Odontostomatida – Informationsberichte des Bayr. Landesamtes fuer Wasserwirtschaft. Heft 5(92), 1–502 (1992).
Google Scholar 
Santoferrara, L. F., Alder, V. V. & McManus, G. B. Phylogeny, classification and diversity of Choreotrichia and Oligotrichia (Ciliophora, Spirotrichea). Mol. Phylogenet. Evol. 112, 12–22 (2017).Article 

Google Scholar 
Hudson, P. L. et al. Cyclopoid and Harpacticoid Copepods of the Laurentian Great Lakes. Ohio Biol. Survey Bull. New Series. 12, 50 (1998).
Google Scholar 
Hudson, P. L et al. Cyclopoid copepods of the Laurentian Great Lakes US Geological Survey, Great Lakes Science Center, Ann Arbor, Michigan. Available: www.glsc.usgs.gov/greatlakescopepods/Key.asp (2003).Kumar, R., Muhid, P., Dahms, H. U., Sharma, J. & Hwang, J.-S. Biological mosquito control is affected by alternative prey. Zool. Stud. 54, 55. https://doi.org/10.1186/s40555-015-0132-9 (2015).Article 

Google Scholar 
Chesson, J. The estimation and analysis of preference and its relationship to foraging models. Ecology 64, 1297–1304 (1983).Article 

Google Scholar  More

Sets of interaction-associated mutants change across interactive conditionsTo investigate how microbial interactions are reorganized in a microbial community with increasing complexity, we reconstructed in vitro a modified bloomy rind cheese-associated microbiome on Cheese Curd Agar plates (CCA plates) as described in our previous work14 Growth as a biofilm on agar plates models the surface-associated growth of these communities, and allows inclusion of the filamentous fungus, P. camemberti, which grows poorly in shaken liquid culture. The original community is composed of the gamma-proteobacterium H. alvei, the yeast G. candidum and the mold P. camemberti. Using a barcoded transposon library of the model bacterium E. coli as a probe to identify interactions, we investigated microbial interactions in 2-species cultures (E. coli + 1 community member), in 3-species cultures (E. coli + 2 community members) and in 4-species cultures (or whole community: E. coli + 3 community members) (Fig. 1a).Figure 1Changes of E. coli’s genes associated with interaction-associated mutants in 2-species, 3-species and 4-species cultures. (a) Experimental design for the identification of interaction-associated mutants in 7 interactive conditions from the Brie community. The E. coli RB-TnSeq Keio_ML9 (Wetmore et al. 2015) is either grown alone or in 2, 3 or 4 species cultures to calculate E. coli gene fitness in each condition (in triplicate). Interaction fitness effect (IFE) is calculated for each gene in each interactive culture as the difference of the gene fitness in the interactive condition and in growth alone. IFE that are significantly different from 0 (two-sided t-test, Benjamini–Hochberg correction for multiple comparisons) highlight interaction-associated mutants in an interactive condition. (b) Volcanoplots of IFEs calculated for each interactive condition. Adjusted p-values lower than 0.1 highlight significant IFEs. Negative IFEs (blue) identify negative interactions and positive IFE (red) identify positive interactions. Numbers on each plot indicate the number of negative (blue) or positive (red) IFEs. (c) Functional analysis of the interaction-associated genes (significant IFEs). Genes of interaction-associated mutants have been separated into two groups: negative IFE and positive IFE. For each group, we represent the STRING network of the genes associated with interaction-associated mutants (Nodes). Edges connecting the genes represent both functional and physical protein association and the thickness of the edges indicates the strength of data support (minimum required interaction score: 0.4—medium confidence). Nodes are colored based on their COG annotation and the size of each node is proportional to the number of interactive conditions in which that given gene has been found associated with a significant IFE. Higher resolution of the networks with apparent gene names are found in Supplementary Figs. 2, 3.Full size imageQuantification of species’ final CFUs after 3 days of growth highlighted consistent growth for H. alvei and G. candidum independent of the culture condition and slightly reduced growth for E. coli in interactive conditions compared to growth alone (Dunnett’s test against growth alone; adjusted-p value ≤ 5%) except for the 2-species growth with P. camemberti (Supplementary Fig. 1). Although we were unable to quantify spores of P. camemberti after three days, growth of P. camemberti was visually evident in all of the expected samples. Quantitative analysis of E. coli’s library final growth using an epistatic model highlighted that the growth of E. coli in the 3-species and 4-species condition can be predicted from the corresponding 2-species growths (Supplementary Fig. 1).Previously, we developed an assay and a pipeline to identify microbial genes associated with interactions by adapting the original RB-TnSeq approach19 to allow for consistent implementation of biological replicates as well as for direct quantitative comparison of fitness values between different culture conditions15. More specifically, the original RB-TnSeq assay relies on the use of a dense pooled library of randomly barcoded transposon mutants of a given microorganism (RB-TnSeq library)19 containing multiple insertion mutants for each gene as well as intergenic insertion mutants. Measuring the variation of the abundance of each transposon mutant before and after growth, the pipeline allows the calculation of a fitness value for each insertion-mutant as well as a fitness value for each gene corresponding to the average of the insertion-mutants’ fitness of the associated genes across biological replicates. A negative fitness indicates that disruption of this gene decreases growth of the mutant relative to a wild type strain, whereas a positive fitness value indicates increased growth in the studied condition. Then, we infer the interactions based on the effects of insertion-mutants between interactive growth and growth alone. In other words, we measure and compare gene fitness across the different studied conditions. Any significant change in fitness values identifies an interaction-associated mutant. The subsequent analysis of interactions, including the inference of the interaction mechanisms and the comparison of interactions across the different interactive conditions, is mainly based on the nature of the disrupted genes by the transposon and their characterized function. Also, by measuring interactions as the difference of fitness value of a given gene between growth with other species and growth alone, we consider that interactions between insertion-mutants of the RB-TnSeq library are controlled and included in our calculation. Then, any interaction-associated mutant predominantly identifies inter-species interactions.In this work, we used the E. coli RB-TnSeq Keio_ML9 library19 and grew it for 3 days alone or in the seven different interactive conditions studied here (Fig. 1a). This library contains 152,018 pooled insertion mutants with an average of 16 individual insertion mutants per gene and many intergenic insertion mutants. For each interactive condition, we calculated the Interaction Fitness Effect (IFE) associated with 3699 E. coli genes as the difference between the gene fitness in the studied interactive condition and the gene fitness in growth alone (Supplementary Data 1). Negative IFE occurs when gene fitness decreases in the interactive condition, and positive IFE occurs when gene fitness improves in the interactive condition. We then tested for all the IFEs that are significantly different from 0 (adjusted p-value ≤ 0.1; two-sided t-test and Benjamini–Hochberg correction for multiple comparison20) to screen for interactions and to identify, in each condition, the insertion-mutants that are associated with inter-species interactions. Here, we identified between 6 (with P. camemberti) and 71 (with H. alvei + P. camemberti) significant IFEs per condition (Fig. 1b). Both negative IFEs and positive IFEs were found in each interactive condition except for the 2-species culture with P. camemberti, where only negative interactions were identified. A total of 330 significant IFEs associated with 218 unique genes were identified (as the same gene can be associated with a significant IFE in multiple conditions) including 125 genes associated with negative IFE and 120 genes associated with positive IFE (Supplementary Figs. 2, 3). Altogether, we didn’t notice any strong correlation between the number and type of IFE identified by condition and the overall growth impact measured on E. coli.
To gain insight into the interaction mechanisms among microbes, we next analyzed the functions of the genes of the interaction-associated mutants (i.e., genes associated with a significant IFE). Here, the vast majority of the genes associated with interaction-associated mutants are part of an interaction network (Fig. 1c). These STRING networks connect genes that code for proteins that have been shown or are predicted to contribute to a shared function, with or without having to form a complex21. A significant fraction of the interaction-associated mutants associated with a negative IFE are part of amino acid biosynthesis and transport (17%—Fig. 1c and Supplementary Figs. 2, 4), and more specifically with histidine, tryptophan and arginine biosynthesis. This points to competition for these nutrients between E. coli and the other species. Another large set of interaction-associated mutants is related to nucleotide metabolism and transport (14%—Fig. 1c and Supplementary Figs. 2, 5), highlighting competitive interactions for nucleotides and/or their precursors. The majority of the associated genes relate to purine nucleotides and more specifically to the initial steps of their de novo biosynthesis associated with the biosynthesis of 5-aminoimidazole monophosphate (IMP) ribonucleotide. Of the genes associated with interaction-mutants with a positive IFE, 15% are related to amino acid biosynthesis and transport (Fig. 1c and Supplementary Figs. 3, 4), suggesting cross feeding of amino acids between E. coli and the other species. More specifically, this includes phosphoserine, serine, homoserine, threonine, proline and arginine. The presence of amino acid biosynthetic genes among both negative and positive IFEs indicate that trophic interactions (competition versus cross-feeding) depend on the type of amino-acid and/or the species interacting with E. coli. For both negative and positive IFEs, numerous genes of the associated interaction-mutants were annotated as transcriptional regulators (Fig. 1c and Supplementary Figs. 2, 3) emphasizing the importance of transcriptional reprogramming in response to interactions. These transcriptional regulators include metabolism regulators as well as regulators of growth, cell cycle and response to stress. Finally, these interaction-associated mutants and the infered interaction mechanisms are consistent with previous findings in this microbiome14 as well as in a study of bacterial-fungal interactions involving E. coli and cheese rind isolated fungal species15. While this approach allows us to infer the interaction mechanisms that are happening between the transposon library and the other species, further experimental validation would be needed to confirm that these interactions more generally happen between a WT strain and the other species.Introduction of a third interacting species deeply reshapes microbial interactionsThe differences in the number and sign of significant IFEs observed among the different interactive conditions, with different numbers of interaction species, suggest that the number and type of interacting partners influence interaction mechanisms. To characterize how the interactions are reorganized with community complexity, we then investigated if and how the genetic basis of interactions changes when the number of interacting partners increases by comparing the genes associated with interaction-associated mutants with significant IFE in 2-species cultures, in 3-species cultures and then in 4-species cultures.First, we have identified 104 IFEs associated with 98 genes in 2-species cultures as well as 168 IFEs associated with 136 unique genes in 3-species conditions (Supplementary Fig. 6 and Supplementary Data 2). Comparing these gene sets, we can identify how the interaction-associated mutants change when a third-species is added to a 2-species culture. We identified 45 genes associated with 2-species interaction-associated mutants maintained in at least one 3-species condition (maintained interaction-mutants), 55 genes associated with 2-species interaction-associated mutants no longer associated with interaction in any 3-species condition (dropped interaction-mutants) and 100 genes associated with 3-species interaction-associated mutants that aren’t related to any 2-species interaction-associated mutants (emergent interaction-mutants) (Fig. 2a, Supplementary Fig. 6 and Supplementary Data 3). Both dropped and emerging interaction-associated mutants represent 3-species HOIs; the third species either removes an existing interaction or brings about a new one.Figure 2Comparison of the genetic basis of interaction for 2-species and 3-species conditions. (a) Venn Diagram of 2-species and 3-species sets of genes related to interaction-associated mutants. This Venn Diagram identifies 2-species interaction-mutants that are dropped when a third species is introduced (Left side; Dropped interaction-mutants = any 2-species gene that is not found in any 3-species condition), 2-species interaction-mutants that are maintained in at least one associated 3-species condition (Intersection; Maintained interaction-mutants) and interaction-mutants that are specific to 3-species condition (Right side; Emerging interaction-mutants). (b) Functional analysis of the genes associated with dropped, maintained and emerging interaction-mutants from 2-species to 3-species. Each dot represents the fraction of genes of the studied gene set associated with a given COG category (Number of genes found in the category / Total number of genes in the gene set). The color of the dots indicates the general COG group of the COG category: Teal: Metabolism; Blue: Information storage and processing; Orange: Cellular Processes and Signaling; Grey: Unknown or no COG category. (c) Species-level analysis of 3-species HOIs: for each 2-species condition, we measure the fraction of interaction-mutants that are dropped in associated 3-species cultures (Dropped in 3-species) or maintained in at least one of the 3-species cultures (Maintained in 3-species); for each 3-species condition, we measure the fraction of interaction-mutants that have been conserved from at least one associated 2-species condition (Maintained from 2-species) or that are emerging with 3-species (Emerging in 3-species).Full size imageWe further carried out functional analysis of the genes related to maintained, dropped and emerging interaction-mutants to elucidate whether maintained and HOIs interaction-mutants would be associated with specific functions and thus interaction mechanisms (Fig. 2b). For each set of genes, we calculated the fraction of genes of that set associated with a given COG ontology category. Metabolism and transport is the most observed COG group (Fig. 2b—teal dots). For genes related to maintained interaction-mutants, this indicates that some trophic interactions can be maintained from 2-species to 3-species conditions. For instance, serine biosynthetic genes serA, serB and serC as well as threonine biosynthetic genes thrA, thrB and thrC are associated with positive IFEs in the 2-species condition with G. candidum as well as in the 3-species conditions involving G. candidum (Supplementary Fig. 4). This suggests that, (i) G. candidum facilitates serine and threonine cross feeding and (ii) this cross-feeding is still observed when another species is introduced. However, metabolism-related genes identified among the dropped and emerging interaction-mutants indicate that many trophic interactions are also rearranged through HOIs. Genes associated with lactate catabolism (lldP and lldD) and lactate metabolism regulation (lldR) have a negative IFE in the 2-species culture with H. alvei, suggesting competition for lactate between E. coli and H. alvei. Yet, mutants of these genes are no longer associated with a significant IFE when at least another partner is introduced (Supplementary Fig. 7). Histidine biosynthesis genes hisA, hisB, hisD, hisH and hisI are associated with interaction-mutants with negative IFE in the 2-species culture with H. alvei and sometimes in the 3 species culture with H. alvei + P. camemberti. However, the negative IFE is alleviated whenever G. candidum is present, suggesting that potential competition for histidine between E. coli and H. alvei is alleviated by this fungal species (Supplementary Fig. 4). Also, genes related to the COG section “Information storage and processing” are mostly found among genes of HOIs-mutants suggesting a fine-tuning of specific cellular activity depending on the interacting condition. For instance, we identified many transcriptional regulators of central metabolism among the dropped interaction-mutants genes (rbsR and lldR) and the emerging interaction-mutants genes (purR, puuR, gcvR and mngR), highlighting again the reorganization of trophic interactions associated with HOIs. Also, many transcriptional regulators broadly associated with growth control, cell cycle and response to stress were found among the emerging interaction-mutants genes with 3-species (hyfR, chpS, sdiA, slyA and rssB), underlining a noticeable modification of E. coli’s growth environment with 3-species compare to with 2-species.Finally, we further aimed to understand whether HOIs are associated with the introduction of any specific species (Fig. 2c and Supplementary Fig. 8). We observe that interaction-associated mutants with H. alvei are more likely to be dropped, as 65% of them are alleviated by the introduction of a fungal species (Fig. 2c). This can be seen, for instance, with the reorganization of E. coli and H. alvei trophic interactions following the introduction of G. candidum (alleviation of lactate and histidine competition for instance). Also, we observe that 76% of the interactions in the 3-species cultures with H. alvei + P. camemberti and 65% in the 3-species culture with H. alvei + G. candidum are emerging interaction-mutants (compared to 38% of emerging interaction-associated mutants in the 3-species condition with G. candidum + P. camemberti) (Fig. 2c). For the interaction-associated mutans found in the 3-species with H. alvei + P. camemberti, they include for instance the genes associated with purine de novo biosynthesis (purR, purF, purN, purE, purC) and the genes associated with pyrimidine de novo biosynthesis (pyrD, pyrF, pyrC, carA and ulaD), suggesting important trophic HOIs. For the 3-species condition with H. alvei + G. candidum, emerging interaction-mutants include for example the transcriptional regulator genes chpS, sdiA and slyA, indicating the presence of a stress inducing environment. Together, these observations suggest that the introduction of a fungal partner may introduce multiple 3-species HOIs by both canceling existing interactions and introducing new ones.HOIs are prevalent in a 4-species communityTo further decipher whether microbial interactions continue to change with increasing community complexity, we investigated the changes in the genetic basis of interactions going from 3-species to 4-species experiments. We identified 58 interaction-associated mutants in the 4-species condition (E. coli with H. alvei + G. candidum + P. camemberti), compared with 145 interaction-associated mutants in any 3-species condition. Comparing the two sets of interaction-associated mutants and corresponding genes we identify: 26 3-species interaction-mutants that are maintained in the 4-species condition (including 16 directly from 2-species interactions), 115 3-species interaction-mutans that are no longer associated with interactions in the 4-species condition (dropped interaction-mutants) and 32 interaction-mutants that are observed solely in the 4-species condition (emerging interaction-mutants) (Fig. 3a, Supplementary Fig. 6 and Supplementary Data 3). Both dropped and emerging interaction-mutants represent 4-species HOIs. Here, HOIs are remarkably abundant when introducing a single new species and moving up from 3-species interactions to 4-species interactions. Functional analysis of the genes of maintained-mutants and HOI-mutants reveals the presence of many metabolism related genes in every gene set (Fig. 3), suggesting that some trophic interactions can be maintained from 3-species to 4-species interactions while some other trophic interactions are rearranged with HOIs. For instance, most of the genes of the initial steps of de novo purine biosynthesis have been found to be associated with a negative IFE in the 3 species condition with H. alvei + P. camemberti (purC, purE, purF, purL and purN) as well as in the pairwise condition with H. alvei for purH and purK (Supplementary Fig. 5), suggesting competition for purine initial precursor IMP in these conditions. Yet, the introduction of the yeast G. candidum as a fourth species cancels the negative IFE value, suggesting that the competition is no longer happening in its presence. Altogether, the observation of noticeable trophic HOIs moving up from 2 to 3 species and then from 3 to 4-species interaction highlights a consistent reorganization of trophic interactions along with community complexity. Also, genes related to Cell wall/membrane/envelope biogenesis are found abundantly among the 4-species emerging-mutants (Fig. 3b) and they represent the largest functional fraction of this gene set. These genes are associated with a negative IFE and are related to Enterobacterial Common Antigen (ECA) biosynthetic processes (wecG, wecB and wecA) (Supplementary Fig. 9). While the roles of ECA can be multiple but are not well defined22, they have been shown to be important for response to different toxic stress, suggesting the development of a specific stress in the presence of the four species.Figure 3Organization of the interactions in the 4-species community. (a) Venn Diagram of 3-species and 4-species sets of genes related to interaction-associated mutants. This Venn Diagram identifies 3-species interaction-mutants that are dropped when a fourth species is introduced (Left side; Dropped interaction-mutants = any 3-species interaction-associated mutant that is not found in the 4-species condition), 3-species interaction-mutants that are maintained in the 4-species condition (Intersection; Maintained interaction-mutants) and interaction-mutants that are specific to 4-species condition (Right side; Emerging interaction-mutants). (b) Functional analysis of the genes associated with dropped, maintained and emerging interaction-mutants from 3-species to 4-species. Each dot represents the fraction of genes of the studied gene set associated with a given COG category (Number of genes found in the category/Total number of genes in the gene set). The color of the dots indicates the general COG group of the COG category: Teal: Metabolism; Blue: Information storage and processing; Orange: Cellular Processes and Signaling; Grey: Unknown or no COG category. (c) Species-level analysis of 4-species HOIs: for each 3-species cultures we measure the fraction of interaction-genes that is conserved in the 4-species culture (Maintained in 4-species) and the fraction of interaction-genes that has been dropped (Dropped in 4-species). (d) Alluvial plots of the interaction genes across community complexity levels. (e) STRING network of the 4-species interaction genes (Nodes). Edges connecting the genes represent both functional and physical protein association and the thickness of the edges indicates the strength of data support (minimum required interaction score: 0.4—medium confidence). Nodes are colored based on the level of community complexity the genes are conserved from.Full size imageAs for the 2 to 3 species comparison, we investigated whether the introduction of a specific fourth species would be most likely associated with HOIs. The 3-species culture that appears to be the least affected by the introduction of a fourth member is with G. candidum + P. camemberti where 34% of the observed interactions are still conserved in the 4-species condition after the introduction of H. alvei (versus 22% for with H. alvei + G. candidum when P. camemberti is added and 21% for with H. alvei + P. camemberti when G. candidum is added) (Fig. 3c and Supplementary Fig. 10). Together, these observations suggest that, again, the introduction of a fungal partner may introduce multiple 4-species HOIs.Finally, by increasing the number of interacting species in our system and investigating interaction-mutants maintenance and modification with every increment of community complexity, we are able to build our understanding of the architecture of interactions in a microbial community. Altogether, we have observed a total of 218 individual interaction-associated mutants in any experiment. Only 16 of them (7%) were conserved across all levels of community complexity (Fig. 3d). Starting from 2-species interaction-mutants, 48% of them were maintained with 3-species and only 15% (16 out of 104) were still maintained with 4-species. Thus, we demonstrate here a progressive loss and replacement of 2-species interactions as community complexity increases and the prevalent apparition of HOIs. Tracking back the origins of the genetic basis of interactions in the 4-species experiment that represents the full community of our model, we identify that 28% of the full community interactions can be traced back to 2-species interactions, 18% are from 3-species interaction and 54% are specific to the 4-species interaction (Fig. 3d,e). Most of the maintained interaction-mutants from 2-species as well as from 3-species are associated with metabolism (Fig. 3d and Supplementary Fig. 11) while Signal transduction and cell membrane biosynthesis genes are most abundant among the 4-species interaction-mutants as previously mentioned. To conclude, this shows that the genetic basis of interactions and thus the sets of microbial interaction are deeply reprogrammed at every level of community complexity and illustrates the prevalence of higher order interactions (HOIs) even in simple communities.The majority of maintained 2-species interaction-mutants in the 4-species culture follows an additive conservation behaviorWhile HOIs are abundant in the 4-species condition, our data yet suggest that up to 28% of the interactions are maintained from 2-species interactions. However, we don’t know whether and how 2-species interactions are quantitatively affected by the introduction of other species and whether they would follow specific quantitative models of conservation. For instance, we can wonder how the strength of a given 2-species interaction is modified by the introduction of one or two other species, or how two 2-species interactions associated with the same gene will combine when all the species are present. In other words, can we treat species interactions as additive when we add multiple species? Such information would generate a deeper mechanistic understanding of the architecture of microbial interactions while allowing us to potentially predict some whole community interactions from 2-species interactions. Here, two main hypothetical scenarios can be anticipated. First, the conservation of 2-species interactions follows a linear or additive behavior, where the introduction of other species either doesn’t affect the strength of the conserved 2-species interaction or two similar 2-species interactions combine additively. The second scenario identifies non-linear or non-additive conservation of 2-species interactions, where the strength of the conserved 2-species interaction is modified by the introduction of other species or two similar 2-species interactions are not additive. The second scenario would encompass for instance synergistic effects or inhibitory effects following the introduction of more species. We next use an epistasis and quantitative genomics approach to understand whether interactions that are conserved follow a linear, or additive, pattern. For the 16 interaction-associated mutants that are associated with interaction in 2-species cultures, in associated 3-species cultures and in the 4-species condition, we use epistasis analysis to test the linear behavior of their IFE when the number of interacting species increases, as IFEs are quantitative traits related to the interaction strength. In multi-dimensional systems, an epistasis analysis quantifies the additive (or linear) behavior of conserved quantitative traits. In quantitative genetics, for instance, epistasis measures the quantitative difference in the effects of mutations introduced individually versus together18,23,24. Using a similar rationale, we can use IFEs as a quantitative proxy for interaction strength and test whether the IFEs of the maintained interaction genes in 3-species and in 4-species conditions result from the linear combination of associated 2-species IFEs (Fig. 4a). Nonlinear combination, or non-additivity of 2-species IFEs in higher community level also highlights higher-order interactions.Figure 4Quantitative analysis of IFE conservation for the interaction-associated mutants conserved from 2-species to 4-species conditions. (a) Schematized quantitative epistasis/non-linearity measured in 3-species conditions (with partner i and j). Epistasis (εij) is the difference between the individual IFE of partner i and partner j (red and orange bars) versus placing them together (green). Mathematically, we need three terms (IFEi, IFEj, and εij) to reproduce the observed IFE for the 3-species condition. (b) This analysis can be extended to higher levels of community complexity: 4-species (E. coli with 3-partners i, j, and k). The model first accounts for epistasis between i/j, i/k, and j/k. In this example, i and j exhibit epistasis; i/k and j/k are additive (dark blue and purple). The predicted IFE for the 4-species community is the sum of the individual 2-species effects (red, orange, light blue) and the 3-species epistatic terms (green). The 4-species epistatic coefficient is the difference between this low-order prediction and the observed IFE for the i,j,k community (pink). (c) Conservation profiles of the 16 2-species interaction-associated mutants conserved up to 4-species. 2-species conditions: a colored square indicates the 2-species condition(s) in which the interaction-associated mutant was identified; a grey square indicates non-significant 2-species IFEs. 3-species conditions: a teal square indicates that the associated IFE is associated with additive behavior from associated 2-species IFE (no εij epistatic coefficient), a red square indicates that the associated IFE displays non-additivity from 2-species IFE and thus epistasis, a grey square corresponds to a 3-species condition that is not associated with significant 2-species IFE (no epistasis analysis performed); 4-species condition: a teal square indicates that the associated IFE is associated with additive behavior (no εijk epistatic coefficient) , a red square indicates that the associated IFE is associated with non-additivity from lower-order IFE. (d) Comparison of the observed and predicted IFE for the genes and condition associated with 3-species and 4-species non-additive IFE.Full size imageWe adapted the pipeline Epistasis17, originally designed for quantitative genetics investigation. We implemented the linear model with the gene fitness values of the interaction-associated mutants for growth alone, for each of the 2-species conditions, for each of the 3-species cultures and for the 4-species condition. For each gene, the software finds the simplest mathematical model that reproduces the observed IFEs across all levels of community complexity. In the simplest case, the model will have a term describing the effects for adding each species individually to the E. coli alone culture; that term corresponds to the 2-species IFE. Then, if the IFE for two E. coli’s partners combined (3-species IFE) differs from the sum of their individual effects (corresponding 2-species IFE), the software adds a term capturing this epistasis (Fig. 4a). Here, we call that term 3-species epistatic coefficient or εi,j. Finally, if the IFE for the combined community (E. coli plus all three species; 4-species condition) differs from the prediction based on the 2-species and 3-species terms, the software will add a high-order interaction term to the model (Fig. 4b). Here, we name that term 4-species epistatic coefficient or εijk.We performed this analysis on the 16 interaction-associated mutants that are associated with interactions at every level of community complexity. To identify real additive behavior of IFE from non-additivity, we screen for 3-species epistatic coefficients and 4-species epistatic coefficients that are significantly different from 0 (adjusted p-value ≤ 0.01, Benjamini–Hochberg correction for multiple testing). We found that 13 interaction-associated mutants behaved additively from 2-species to 4-species culture, with no epistatic contributions in the 3-species conditions nor in the 4-species condition (Fig. 4c, (i)). One interaction-associated mutant (gene (gadW)) exhibited nonlinear conservation of IFE only in the 4-species condition, but additive IFE conservation from 2-species to 3-species (Fig. 4c, (ii)). Another interaction-associated mutant (gene (lsrG)) showed epistasis in one 3-species condition but no epistasis in the 4-species condition (Fig. 4c, (iii)) Finally, one interaction-associated mutant (gene (gltB)) displayed both non-additivity in 3-species and 4-species conditions (Fig. 4c, (iv)). If we look more closely at the genes related to interaction-associated mutant with an additive behavior, we find genes (betA, betT, purD and purH) that are associated with the conservation of negative IFEs (Supplementary Fig. 12). While betA and betT are associated with choline transport (betT) and glycine betaine biosynthesis from choline (betA)25, purD and purH are associated with de novo purine biosynthesis26. This suggests that requirements for glycine betaine biosynthesis from choline and for purine biosynthesis caused by microbial interactions, possibly due to competition for the nutrients used as precursors, are additively conserved from individual 2-species interactions requirements. Also, 5 genes associated with amino acid biosynthesis (serA, thrC, cysG, argG and proA) are associated with the additive conservation of positive IFE (Supplementary Fig. 12), suggesting that cross feeding can be additive when the community complexity increases. Altogether, this highlights the existence of 2-species interactions, including trophic ones, conserved in an additive fashion in the highest-level of complexity.This leaves 3 interaction-associated mutants (18%) of the maintained 2-species interaction-mutants, that are associated with non-additive behavior, and thus HOIs, at at least one higher level of community complexity (Fig. 4c—(ii), (iii) and (iv)). The interaction-associated mutant for the gene gadW is associated with non-additivity at the 4-species level, suggesting that while IFEs are additive in 3-species cultures, the introduction of a fourth species introduces HOI. Moreover, the observed 4-species IFE is greater than the IFE predicted by a linear model (Fig. 4d), highlighting a potential synergistic effect when the 4 species are together. The interaction-assoacited mutant for the gene lsrg is associated with non-additivity only at the 3-species culture w G.c + P.c. More specifically, this indicates that HOI arise when these 2 fungal species are interacting together with E. coli, but that no more HOI emerge when H. alvei is introduced (i.e., the 4-species IFE can be predicted by the linear combination of the lower levels IFEs). As the observed IFE for the 3-species condition w G.c + P.c is greater than the predicted IFE (Fig. 4c), this suggests a synergistic effect between the 2 fungal species. Finally, the interaction-associated mutants for the gene gltB is associated with non-additivity at both the 3-species and 4-species levels. For this interaction-associated mutant, the conservation of IFE is never associated with an additive model. Here, the observed 4-species IFE is not as negative as it would be as the result of the linear combination of the associated lower IFE (Fig. 4d), suggesting the existence of a possible IFE threshold, or plateau effect. Altogether, this indicates that maintained 2-species-interactions can follow nonlinear behaviors that could involve synergistic effects, inhibitory effects or constraints. More

In this section, we introduce flapping flight dynamics and describe the bird model used in our computational framework. Furthermore, we describe how such a dynamical model is used in order to identify steady and level flapping flight regimes, study their stability, and assess their energetic performance.Equations of motion modelling flapping flightFlight dynamics is restricted to the longitudinal plane and thus the bird main body is captured as a rigid-body with three degrees of freedom, i.e. two in translation and one in rotation. This model preserves symmetry with respect to this plane, without any lateral force and moment. The aerodynamic model of the wing relies on the theory of quasi-steady lifting line23. Additionally, the present work does not account for the inertial forces due to the acceleration of the wing, and thus also neglecting the so-called inertial power. This inertial power was shown to be negligible in fast forward flight conditions, in comparison to the other contributions to actuation power24, and is thus systematically neglected in similar work10,11,25 since wing inertia is neglected.The body is thus modelled with a mass (m_b) and a rotational inertia (I_{yy}) about its center of mass. The equations of motion are expressed in the body frame (G(x’, y’, z’)) with unit vectors ((hat{textbf{e}}_{x’}, hat{textbf{e}}_{y’}, hat{textbf{e}}_{z’})), and an origin located at the center of mass, as pictured in Fig. 1a. The state space vector is thus$$begin{aligned} textbf{x} = {u, w, q, theta } end{aligned}$$where u and w are the body velocities along the (x’-) and (z’-)axis and (theta) and q are the pitch angle and its time derivative about the (y’-)axis, respectively. Consequently, the equations of motion read11,13,26$$begin{aligned} begin{aligned} dot{u}&= -qw – gsin theta + frac{1}{m_b}big ( {F_{x’}(textbf{x}(t), t)} \&quad + {F_{x’, t}(textbf{x}(t), t)} + D (textbf{x}(t), t) big )\ dot{w}&= qu + gcos theta +frac{1}{m_b} big ( F_{z’}(textbf{x}(t), t) + F_{z’, t}(textbf{x}(t), t) big ) \ dot{q}&=frac{1}{I_{yy}} big ( M_{y’}(textbf{x}(t), t) + M_{y’, t}(textbf{x}(t), t) big )\ dot{theta }&= q end{aligned} end{aligned}$$
(1)
Figure 1(a) Bird model for describing the flight dynamics in the longitudinal plane. The state variables are expressed with respect to the moving body-frame located at the flier’s center of mass (G(x’,z’)). These state variables are the component of forward flight velocity, u, the velocity component of local vertical velocity, w, the orientation of this body-centered moving frame with respect to the fixed frame, (theta) and its angular velocity, q. A second frame (O(x’_{w}, z’_{w})) is used to compute the position of the wing, relative to the body. The wings (dark gray) and the tail (red) are the surfaces of application of aerodynamic forces. (b) Top view of the bird model. The left wing emphasizes a cartoon model of the skeleton. The shoulder joint s connects the wing to the body via three rotational degrees of freedom (RDoF), the elbow joint e connects the arm with the forearm via one RDoF and the wrist joint w connects the forearm to the hand via two RDoF. Each feather is attached to a bone via two additional RDoF, except the most distal one ”1” which is rigidly aligned with the hand. The right wing further emphasizes the lifting line (red) which is computed as a function of the wing morphing. The aerodynamic forces generated on the wing are computed on the discretized elements (P_{i}). The tail is modelled as a triangular shape with fixed chord (c_{t}) and maximum width (b_{t}) that can be morphed as a function of its opening angle (beta). (c) Wing element i between two wing profiles, identifying a plane (Sigma) containing the lifting line (red). (d) Cross section of the wing element, containing the chord point (mathbf {P_i}) where the velocities are computed (Color figure online).Full size imageThe forcing terms in Eq. (1) are the aerodynamic forces and moments applied to the wing (namely (F_{x’}), (F_{z’}), and (M_{y’}) ) and to the tail ((F_{x’, t}), (F_{z’, t}), and (M_{y’, t})). The whole drag is captured by an extra force D that sums contributions due to the body (D_{b}), the skin friction of the wing (wing profile) (D_{p,w}), and the skin friction of the tail (tail profile) (D_{p,t}). These terms are described in detail in the next sections. Importantly, we accounted for the drag acting purely along (x’) direction, after proving that the projection of the drag forces along (z’)-axis is between two and three orders of magnitude smaller with respect to the aerodynamic forces produced by two other main lifting surfaces. This assumptions holds for the fast forward flight regime that are subject of our study, but such components of drag along (z’) axis should be accounted for other flight situations.Wing modelThe bird has two wings. Each wing is a rigid poly-articulated body, comprising the bird arm, forearm and hand, as pictured in Fig. 1b. Each segment is actuated by a joint to induce wing morphing. We refer to13,15 for a complete description of this wing kinematic model.Each joint is kinematically driven to follow a sinusoidal trajectory specified as:$$begin{aligned} q_{i}(t) = q_{0,i}(t) + A_{i} sin (omega t + phi _{0,i}) end{aligned}$$
(2)
with (omega = 2 pi f) and f being the flapping frequency which is identical for each joint, (q_{0,i}) being the mean angle over a period (or offset), (A_i) the amplitude, and (phi _{0,i}) the relative phase of joint i. A complete wingbeat cycle is therefore described through a set of 19 kinematic parameters, including the frequency f.We assume that the wing trajectory is rigidly constrained, and therefore we do not need to explicitly solve the wing dynamics. Under this assumption, the motion generation does not require the computation of joint torques. The model further embeds seven feathers of length (l_{ki}) in each wing. The feathers in the model have to be considered a representative sample of the real wing feathers. They thus have a limited biological relevance; their number is chosen so as to interpolate the planform satisfactorily and to smoothly capture the morphing generated by the bone movements. These feathers are attached to their respective wing bones via two rotational degrees of freedom allowing them to pitch and spread in the spanwise direction. These two degrees of freedom are again kinematically driven by relationships that depend on the angle between the wing segments13. This makes the feathers spreading and folding smoothly through the wingbeat cycle. In sum, the kinematic model of the wing yields the position of its bones and feathers at every time step. This provides a certain wing morphing from which the wing envelope (leading edge and trailing edge) can be computed (see Fig. 1b). From the wing envelope, the aerodynamic chord and the lifting line are computed. The lifting line is the line passing through the quarter of chord, which is itself defined as the segment connecting the leading edge to the trailing edge and orthogonal to the lifting line (Fig. 1b). This extraction algorithm is explained in detail in15.In order to calculate the aerodynamic forces, the angle of attack of the wing profile has to be evaluated. Each wing element defines a plane containing the lifting line and the aerodynamic chord as pictured in Fig. 1c. The orientation of the plane is identified by the orthogonal unit vectors ((hat{textbf{e}}_n, hat{textbf{e}}_t, hat{textbf{e}}_b)), where (hat{textbf{e}}_n) is the vector perpendicular to the plane and (hat{textbf{e}}_t) is the tangent to the lifting line. To compute the effective angle of attack, the velocity perceived by the wing profile is computed as the sum of the velocities due to the body and wing motion, and the velocity induced by the wake. The first contribution, (textbf{U}), accounts for$$begin{aligned} textbf{U} = textbf{U}_{infty } – textbf{v}_{kin} – textbf{v}_{q}end{aligned}$$where (textbf{U}_{infty } = u hat{textbf{e}}_{x’} + w hat{textbf{e}}_{z’}) is the actual flight velocity, (textbf{v}_{kin}) is the relative velocity of the wing due to its motion, and (textbf{v}_{q}) is the component induced by the angular velocity of the body q and calculated as$$begin{aligned} textbf{v}_{q} = qhat{textbf{e}}_{y’} wedge (textbf{P}_{i} – textbf{G})end{aligned}$$This velocity vector (textbf{U}) defines the angle (alpha), as pictured in Fig. 1d.The second contribution is due to the induced velocity field by the wake, i.e. the downwash velocity (w_{d}), and acting along the normal unit vector (-w_{d}hat{textbf{e}}_n). The resulting effective angle of attack, (alpha _{r}), is thus$$begin{aligned} alpha _{r} = alpha – frac{w_{d}}{|textbf{U}|}end{aligned}$$The downwash velocity (w_d) is computed according to the Biot-Savart law23, assuming the wake being shed backwards in the form of straight and infinitely long vortex filaments at each time step of the simulation13,15. This quasi-steady approximation is justified a posteriori by ensuring that our reduced frequency, inversely proportional to the unknown airspeed, never exceeds the value of 0.2, below which the effects of time-dependent wake shapes on wing circulation are negligible (e.g. see discussion in27). Once the downwash is evaluated, it is possible to evaluate the circulation, and consequently the aerodynamic force and moment acting at the element (P_i), i.e. (F_{x’, i}(textbf{x}(t), t), F_{z’, i}(textbf{x}(t), t), M_{y’, i}(textbf{x}(t), t)), as explained in detail in13. We use the thin airfoil theory for the estimation of the lift coefficient, with a slope of (2pi) that saturates at an effective angle of attack (alpha _{r}) of (pm 15^{circ }).Drag production by body and wingThe main body and the wings induce drag that should be accounted for in a model aiming at characterizing energetic performance. Body-induced drag is named parasitic because the body itself does not contribute to lift generation, and only induces skin friction and pressure drag around its envelope28. The total body drag is$$begin{aligned} D_{b} = frac{1}{2}rho C_{d, b} S_{b}|textbf{U}_{infty }|^{2} end{aligned}$$
(3)
where (rho) is the air density. We implemented the model described by Maybury28 to compute the body drag coefficient (C_{d, b}). This depends on the morphology of the bird and the Reynolds number Re according to$$begin{aligned} C_{d,b} = 66.6m_{b}^{-0.511}FR_{t}^{0.9015}S_{b}^{1.063}Re^{-0.197} end{aligned}$$
(4)
with (S_{b}) and (FR_{t}) are respectively the frontal area of the body and the fitness ratio of the bird, and both of them can be estimated from other allometric formulas i.e.28,29.$$begin{aligned} S_{b}= & {} 0.00813m_{b}^{2/3} end{aligned}$$
(5)
$$begin{aligned} FR_{t}= & {} 6.0799m_{b}^{0.1523} end{aligned}$$
(6)
The Reynolds number (Re = rho |textbf{U}_{infty }| overline{c} / mu) is calculated with the reference length of the mean aerodynamic chord (overline{c}), with (mu) being the dynamic viscosity. This model is found to be suitable for Reynolds number in the range (10^{4}-10^{5})28. Another source of drag is the profile drag due to friction between the air and the feathers on the wings. It is the sum of the profile drag at each section along the wingspan, i.e.$$begin{aligned} D_{p,w} = frac{1}{2} rho C_{d, pro} sum _{i=1}^{n} c_{i}|textbf{U}_{r,i}|^{2} ds_{i} end{aligned}$$
(7)
with (c_{i}) the chord length, (ds_{i}) the length of the lifting line element along the wingspan, and (textbf{U}_{r,i}) the velocity at the wing section i accounting for the body velocity, the kinematics velocity of the wing and the downwash velocity (Fig. 1c,d). We used a value of profile drag of (C_{d, pro} = 0.02) and this is assumed to be constant over the wingspan and throughout the flapping cycle30. In reality, due to the wing motion, this value should be gait dependent. However, the aforementioned assumption has been largely used in previous works31,32.Tail modelSince the span of the tail is of the same magnitude as its aerodynamic chord, here the lifting line approach cannot be used23. Therefore, the tail is modelled according to the slender delta wing theory, as a triangular planform33. Its morphology is illustrated in Fig. 1b and characterized by the opening angle (beta) and the chord (c_t). This latter parameter is kept constant, thus the tail span is controlled via (beta) from the trigonometrical relationship$$begin{aligned} b_{t} = 2c_{t}tan frac{beta }{2}end{aligned}$$The main limitation of this framework is the low range of angles of attack ((alpha _{tail} More