Ecology

1.Chiappe, L. M. in Encyclopedia of Dinosaurs (eds Currie, P. J. & Padian, K.) 32–38 (Academic, 1997).2.Mayr, G. Avian Evolution: The Fossil Record of Birds and its Paleobiological Significance (Wiley, 2017).3.O’Connor, J. K. The trophic habits of early birds. Palaeogeogr. Palaeoclimatol. Palaeoecol. 513, 178–195 (2019).Article 

Google Scholar 
4.Benton, M. J. Vertebrate Palaeontology (Wiley, 2015).5.Chatterjee, S. The Rise of Birds: 225 Million Years of Evolution (Johns Hopkins Univ. Press, 2015).6.Chiappe, L. M. & Qingjin, M. Birds of Stone Chinese Avian Fossils from the Age of Dinosaurs (Johns Hopkins Univ. Press, 2016).7.Ksepka, D. T., Grande, L. & Mayr, G. Oldest finch-beaked birds reveal parallel ecological radiations in the earliest evolution of passerines. Curr. Biol. 29, 657–663 (2019).CAS 
PubMed 
Article 

Google Scholar 
8.O’Connor, J. K. & Zhou, Z. The evolution of the modern avian digestive system: insights from paravian fossils from the Yanliao and Jehol biotas. Palaeontology 63, 13–27 (2020).Article 

Google Scholar 
9.Zhou, Z., Barrett, P. M. & Hilton, J. An exceptionally preserved Lower Cretaceous ecosystem. Nature 421, 807–814 (2003).CAS 
PubMed 
Article 

Google Scholar 
10.Zhou, Z. & Zhang, F. A long-tailed, seed-eating bird from the Early Cretaceous of China. Nature 418, 405–409 (2002).CAS 
PubMed 
Article 

Google Scholar 
11.Zheng, X. et al. Fossil evidence of avian crops from the Early Cretaceous of China. Proc. Natl Acad. Sci. USA 108, 15904–15907 (2011).CAS 
PubMed 
Article 

Google Scholar 
12.Miller, C. V. et al. Disassociated rhamphotheca of fossil bird Confuciusornis informs early beak reconstruction, stress regime, and developmental patterns. Commun. Biol. 3, 519 (2020).PubMed 
PubMed Central 
Article 

Google Scholar 
13.Miller, C. & Pittman, M. The diet of early birds based on modern and fossil evidence and a new framework for its reconstruction. ESSOAr https://doi.org/10.1002/essoar.10504068.2 (2020).Article 

Google Scholar 
14.Wang, M., Wang, X., Wang, Y. & Zhou, Z. A new basal bird from China with implications for morphological diversity in early birds. Sci. Rep. 6, 19700 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
15.Zanno, L. E. & Makovicky, P. J. Herbivorous ecomorphology and specialization patterns in theropod dinosaur evolution. Proc. Natl Acad. Sci. USA 108, 232–237 (2011).CAS 
PubMed 
Article 

Google Scholar 
16.Karasov, W. H. & Douglas, A. E. Comparative digestive physiology. Compr. Physiol. 3, 741–783 (2013).PubMed 
PubMed Central 

Google Scholar 
17.Karasov, W. H., Martinez del Rio, C. & Caviedes-Vidal, E. Ecological physiology of diet and digestive systems. Annu. Rev. Physiol. 73, 69–93 (2011).CAS 
PubMed 
Article 

Google Scholar 
18.Miller, S. A. & Harley, J. P. Zoology (McGraw-Hill, 2016).19.Corring, T. The adaptation of digestive enzymes to the diet: its physiological significance. Reprod. Nutr. Dev. 20, 1217–1235 (1980).CAS 
PubMed 
Article 

Google Scholar 
20.German, D. P., Horn, M. H. & Gawlicka, A. Digestive enzyme activities in herbivorous and carnivorous prickleback fishes (Teleostei: Stichaeidae): ontogenetic, dietary, and phylogenetic effects. Physiol. Biochem. Zool. 77, 789–804 (2004).CAS 
PubMed 
Article 

Google Scholar 
21.Hidalgo, M., Urea, E. & Sanz, A. Comparative study of digestive enzymes in fish with different nutritional habits. Proteolytic and amylase activities. Aquaculture 170, 267–283 (1998).Article 

Google Scholar 
22.Karasov, W. H. & Diamond, J. M. Interplay between physiology and ecology in digestion: intestinal nutrient transporters vary within and between species according to diet. BioScience 38, 602–611 (1988).CAS 
Article 

Google Scholar 
23.Hecker, N., Sharma, V. & Hiller, M. Convergent gene losses illuminate metabolic and physiological changes in herbivores and carnivores. Proc. Natl Acad. Sci. USA 116, 3036–3041 (2019).CAS 
PubMed 
Article 

Google Scholar 
24.Schondube, J. E., Herrera-M, L. G. & del Rio, C. M. Diet and the evolution of digestion and renal function in phyllostomid bats. Zoology 104, 59–73 (2001).CAS 
PubMed 
Article 

Google Scholar 
25.Wang, Z. et al. Evolution of digestive enzyme genes associated with dietary diversity of crabs. Genetica 148, 87–99 (2020).CAS 
PubMed 
Article 

Google Scholar 
26.Wang, Z. et al. Evolution of digestive enzymes and RNASE1 provides insights into dietary switch of cetaceans. Mol. Biol. Evol. 33, 3144–3157 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
27.Mayo Clinic. Encyclopedia of Foods: a Guide to Healthy Nutrition (Academic, 2002).28.Chen, Y.-H. & Zhao, H. Evolution of digestive enzymes and dietary diversification in birds. PeerJ 7, e6840 (2019).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
29.Wu, Y. et al. Genomic bases underlying the adaptive radiation of core landbirds. Preprint at bioRxiv https://doi.org/10.1101/2020.07.29.222281 (2020).30.Wu, Y. & Wang, H. Convergent evolution of bird-mammal shared characteristics for adapting to nocturnality. Proc. Biol. Sci. 286, 20182185 (2019).PubMed 
PubMed Central 

Google Scholar 
31.Wu, Y., Wang, H. & Hadly, E. A. Invasion of ancestral mammals into dim-light environments inferred from adaptive evolution of the phototransduction genes. Sci. Rep. 7, 46542 (2017).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
32.Wu, Y., Wang, H., Wang, H. & Feng, J. Arms race of temporal partitioning between carnivorous and herbivorous mammals. Sci. Rep. 8, 1713 (2018).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
33.Yang, Z. PAML 4: phylogenetic analysis by maximum likelihood. Mol. Biol. Evol. 24, 1586–1591 (2007).CAS 
Article 

Google Scholar 
34.Naim, H. Y., Sterchi, E. & Lentze, M. Biosynthesis of the human sucrase-isomaltase complex. Differential O-glycosylation of the sucrase subunit correlates with its position within the enzyme complex. J. Biol. Chem. 263, 7242–7253 (1988).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
35.Boll, W., Wagner, P. & Mantei, N. Structure of the chromosomal gene and cDNAs coding for lactase-phlorizin hydrolase in humans with adult-type hypolactasia or persistence of lactase. Am. J. Hum. Genet. 48, 889–902 (1991).CAS 
PubMed 
PubMed Central 

Google Scholar 
36.Furuta, H. et al. Sequence of human hexokinase III cDNA and assignment of the human hexokinase III gene (HK3) to chromosome band 5q35. 2 by fluorescence in situ hybridization. Genomics 36, 206–209 (1996).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
37.Wright, E., Hirayama, B. & Loo, D. Active sugar transport in health and disease. J. Intern. Med. 261, 32–43 (2007).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
38.Cura, A. J. & Carruthers, A. Role of monosaccharide transport proteins in carbohydrate assimilation, distribution, metabolism, and homeostasis. Compr. Physiol. 2, 863–914 (2012).PubMed 
PubMed Central 

Google Scholar 
39.Douard, V. & Ferraris, R. P. Regulation of the fructose transporter GLUT5 in health and disease. Am. J. Physiol. Endocrinol. Metab. 295, E227–E237 (2008).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
40.Mueckler, M. & Thorens, B. The SLC2 (GLUT) family of membrane transporters. Mol. Asp. Med. 34, 121–138 (2013).CAS 
Article 

Google Scholar 
41.Li, Y. et al. N-myc downstream-regulated gene 2, a novel estrogen-targeted gene, is involved in the regulation of Na+/K+-ATPase. J. Biol. Chem. 286, 32289–32299 (2011).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
42.Pepino, M. Y., Kuda, O., Samovski, D. & Abumrad, N. A. Structure-function of CD36 and importance of fatty acid signal transduction in fat metabolism. Annu. Rev. Nutr. 34, 281–303 (2014).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
43.Izar, M. C., Tegani, D. M., Kasmas, S. H. & Fonseca, F. A. Phytosterols and phytosterolemia: gene–diet interactions. Genes Nutr. 6, 17–26 (2011).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
44.Takeuchi, K. & Reue, K. Biochemistry, physiology, and genetics of GPAT, AGPAT, and lipin enzymes in triglyceride synthesis. Am. J. Physiol. Endocrinol. Metab. 296, E1195–E1209 (2009).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
45.Mangaraj, M., Nanda, R. & Panda, S. Apolipoprotein AI a molecule of diverse function. Indian J. Clin. Biochem. 31, 253–259 (2016).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
46.Qu, J., Ko, C.-W., Tso, P. & Bhargava, A. Apolipoprotein A-IV: a multifunctional protein involved in protection against atherosclerosis and diabetes. Cells 8, 319 (2019).CAS 
PubMed Central 
Article 

Google Scholar 
47.Hazard, S. E. & Patel, S. B. Sterolins ABCG5 and ABCG8: regulators of whole body dietary sterols. Pflug. Arch. 453, 745–752 (2007).CAS 
Article 

Google Scholar 
48.Frølund, S., Holm, R., Brodin, B. & Nielsen, C. U. The proton‐coupled amino acid transporter, SLC36A1 (hPAT1), transports Gly‐Gly, Gly‐Sar and other Gly‐Gly mimetics. Br. J. Pharm. 161, 589–600 (2010).Article 
CAS 

Google Scholar 
49.Szabó, A., Pilsak, C., Bence, M., Witt, H. & Sahin-Tóth, M. Complex formation of human proelastases with procarboxypeptidases A1 and A2. J. Biol. Chem. 291, 17706–17716 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
50.Crisman, J. M., Zhang, B., Norman, L. P. & Bond, J. S. Deletion of the mouse meprin β metalloprotease gene diminishes the ability of leukocytes to disseminate through extracellular matrix. J. Immunol. 172, 4510–4519 (2004).CAS 
PubMed 
Article 

Google Scholar 
51.Erşahin, Ç., Szpaderska, A. M., Orawski, A. T. & Simmons, W. H. Aminopeptidase P isozyme expression in human tissues and peripheral blood mononuclear cell fractions. Arch. Biochem. Biophys. 435, 303–310 (2005).PubMed 
Article 
CAS 

Google Scholar 
52.Higuchi, Y. et al. Mutations in MME cause an autosomal‐recessive Charcot–Marie–Tooth disease type 2. Ann. Neurol. 79, 659–672 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
53.Lambeir, A.-M., Durinx, C., Scharpé, S. & De Meester, I. Dipeptidyl-peptidase IV from bench to bedside: an update on structural properties, functions, and clinical aspects of the enzyme DPP IV. Crit. Rev. Clin. Lab Sci. 40, 209–294 (2003).CAS 
PubMed 
Article 

Google Scholar 
54.Tipnis, S. R. et al. A human homolog of angiotensin-converting enzyme cloning and functional expression as a captopril-insensitive carboxypeptidase. J. Biol. Chem. 275, 33238–33243 (2000).CAS 
PubMed 
Article 

Google Scholar 
55.Yamamoto, K. K. et al. Isolation of a cDNA encoding a human serum marker for acute pancreatitis. Identification of pancreas-specific protein as pancreatic procarboxypeptidase B. J. Biol. Chem. 267, 2575–2581 (1992).CAS 
PubMed 
Article 

Google Scholar 
56.Liang, R. et al. Human intestinal H+/peptide cotransporter cloning, functional expression, and chromosomal localization. J. Biol. Chem. 270, 6456–6463 (1995).CAS 
PubMed 
Article 

Google Scholar 
57.Johansson, B. B. et al. The role of the carboxyl ester lipase (CEL) gene in pancreatic disease. Pancreatology 18, 12–19 (2018).CAS 
PubMed 
Article 

Google Scholar 
58.Shen, W.-J., Azhar, S. & Kraemer, F. B. SR-B1: a unique multifunctional receptor for cholesterol influx and efflux. Annu. Rev. Physiol. 80, 95–116 (2018).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
59.Stahl, A. et al. Identification of the major intestinal fatty acid transport protein. Mol. Cell 4, 299–308 (1999).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
60.Hussain, M. M., Rava, P., Walsh, M., Rana, M. & Iqbal, J. Multiple functions of microsomal triglyceride transfer protein. Nutr. Metab. 9, 14 (2012).CAS 
Article 

Google Scholar 
61.Ludvik, A. E. et al. HKDC1 is a novel hexokinase involved in whole-body glucose use. Endocrinology 157, 3452–3461 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
62.Wertheim, J. O., Murrell, B., Smith, M. D., Kosakovsky Pond, S. L. & Scheffler, K. RELAX: detecting relaxed selection in a phylogenetic framework. Mol. Biol. Evol. 32, 820–832 (2015).CAS 
PubMed 
Article 

Google Scholar 
63.Wang, N. & Tall, A. R. Regulation and mechanisms of ATP-binding cassette transporter A1-mediated cellular cholesterol efflux. Arterioscler. Thromb. Vasc. Biol. 23, 1178–1184 (2003).CAS 
PubMed 
Article 

Google Scholar 
64.Wang, G., Bonkovsky, H. L., de Lemos, A. & Burczynski, F. J. Recent insights into the biological functions of liver fatty acid binding protein 1. J. Lipid Res. 56, 2238–2247 (2015).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
65.Tousignant, K. D. et al. Lipid uptake is an androgen-enhanced lipid supply pathway associated with prostate cancer disease progression and bone metastasis. Mol. Cancer Res. 17, 1166–1179 (2019).CAS 
PubMed 
Article 

Google Scholar 
66.Cui, X.-L., Schlesier, A. M., Fisher, E. L., Cerqueira, C. & Ferraris, R. P. Fructose-induced increases in neonatal rat intestinal fructose transport involve the PI3-kinase/Akt signaling pathway. Am. J. Physiol. Gastrointest. Liver Physiol. 288, G1310–G1320 (2005).CAS 
PubMed 
Article 

Google Scholar 
67.Cappello, A. R., Curcio, R., Lappano, R., Maggiolini, M. & Dolce, V. The physiopathological role of the exchangers belonging to the SLC37 family. Front. Chem. 6, 122 (2018).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
68.Nesbitt, S. J. The early evolution of archosaurs: relationships and the origin of major clades. Bull. Am. Mus. Nat. Hist. 352, 1–292 (2011).Article 

Google Scholar 
69.Yahia, E. M. Fruit and Vegetable Phytochemicals: Chemistry and Human Health (Wiley, 2018).70.Caviedes-Vidal, E. et al. The digestive adaptation of flying vertebrates: high intestinal paracellular absorption compensates for smaller guts. Proc. Natl Acad. Sci. USA 104, 19132–19137 (2007).CAS 
PubMed 
Article 

Google Scholar 
71.Frei, S. et al. Comparative digesta retention patterns in ratites. Auk 132, 119–131 (2015).Article 

Google Scholar 
72.Price, E. R., Brun, A., Caviedes-Vidal, E. & Karasov, W. H. Digestive adaptations of aerial lifestyles. Physiology 30, 69–78 (2015).CAS 
PubMed 
Article 

Google Scholar 
73.Larson, D. W., Brown, C. M. & Evans, D. C. Dental disparity and ecological stability in bird-like dinosaurs prior to the end-Cretaceous mass extinction. Curr. Biol. 26, 1325–1333 (2016).CAS 
PubMed 
Article 

Google Scholar 
74.Matsukawa, M., Shibata, K., Sato, K., Xing, X. & Lockley, M. G. The Early Cretaceous terrestrial ecosystems of the Jehol Biota based on food-web and energy-flow models. Biol. J. Linn. Soc. 113, 836–853 (2014).Article 

Google Scholar 
75.Wolff, R. L. et al. Abietoid seed fatty acid composition—a review of the genera Abies, Cedrus, Hesperopeuce, Keteleeria, Pseudolarix, and Tsuga and preliminary inferences on the taxonomy of Pinaceae. Lipids 37, 17–26 (2002).CAS 
PubMed 
Article 

Google Scholar 
76.Wolff, R. L., Pédrono, F., Pasquier, E. & Marpeau, A. M. General characteristics of Pinus spp. Sseed fatty acid compositions, and importance of Δ5‐olefinic acids in the taxonomy and phylogeny of the genus. Lipids 35, 1–22 (2000).CAS 
PubMed 
Article 

Google Scholar 
77.Friis, E. M., Crane, P. R. & Pedersen, K. R. Early Flowers and Angiosperm Evolution (Cambridge Univ. Press, 2011).78.Clench, M. H. & Mathias, J. R. The avian cecum: a review. Wilson Bull. 107, 93–121 (1995).
Google Scholar 
79.Li, Z. et al. Ultramicrostructural reductions in teeth: implications for dietary transition from non-avian dinosaurs to birds. BMC Evol. Biol. 20, 46 (2020).PubMed 
PubMed Central 
Article 

Google Scholar 
80.Ma, W., Pittman, M., Lautenschlager, S., Meade, L. E. & Xu, X. in Pennaraptoran Theropod Dinosaurs: Past Progress and New Frontiers (eds Pittman, M. & Xu, X.) 229–249 (Scientific Publications of the American Museum of Natural History, 2020).81.Barrett, P. M. Paleobiology of herbivorous dinosaurs. Annu. Rev. Earth Planet Sci. 42, 207–230 (2014).CAS 
Article 

Google Scholar 
82.Zanno, L. E., Gillette, D. D., Albright, L. B. & Titus, A. L. A new North American therizinosaurid and the role of herbivory in ‘predatory’dinosaur evolution. Proc. R. Soc. B 276, 3505–3511 (2009).PubMed 
Article 

Google Scholar 
83.Cowen, R. History to Life (Wiley, 2013).84.You, H.-l et al. A nearly modern amphibious bird from the Early Cretaceous of northwestern China. Science 312, 1640–1643 (2006).CAS 
PubMed 
Article 

Google Scholar 
85.Xu, X. et al. An integrative approach to understanding bird origins. Science 346, 1253293 (2014).PubMed 
Article 
CAS 

Google Scholar 
86.Brusatte, S. L. Dinosaur Paleobiology (Wiley, 2012).87.Button, K., You, H., Kirkland, J. I. & Zanno, L. Incremental growth of therizinosaurian dental tissues: implications for dietary transitions in Theropoda. PeerJ 5, e4129 (2017).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
88.Han, G. et al. A new raptorial dinosaur with exceptionally long feathering provides insights into dromaeosaurid flight performance. Nat. Commun. 5, 4382 (2014).CAS 
PubMed 
Article 

Google Scholar 
89.O’Connor, J. et al. Microraptor with ingested lizard suggests non-specialized digestive function. Curr. Biol. 29, 2423–2429 (2019).PubMed 
Article 
CAS 

Google Scholar 
90.O’Connor, J., Zhou, Z. & Xu, X. Additional specimen of Microraptor provides unique evidence of dinosaurs preying on birds. Proc. Natl Acad. Sci. USA 108, 19662–19665 (2011).PubMed 
Article 

Google Scholar 
91.Xu, X., You, H., Du, K. & Han, F. An Archaeopteryx-like theropod from China and the origin of Avialae. Nature 475, 465–470 (2011).CAS 
PubMed 
Article 

Google Scholar 
92.Wang, S., Stiegler, J., Wu, P. & Chuong, C.-M. in Pennaraptoran Theropod Dinosaurs: Past Progress and New Frontiers (eds Pittman, M. & Xu, X.) 205–228 (Scientific Publications of the American Museum of Natural History, 2020).93.Farlow, J. O. & Holtz, T. R. The fossil record of predation in dinosaurs. Paleontol. Soc. Pap. 8, 251–266 (2002).Article 

Google Scholar 
94.Pittman, M. et al. in Pennaraptoran Theropod Dinosaurs: Past Progress and New Frontiers (eds Pittman, M. & Xu, X.) 37–95 (Scientific Publications of the American Museum of Natural History, 2020).95.Benson, R. B. et al. Rates of dinosaur body mass evolution indicate 170 million years of sustained ecological innovation on the avian stem lineage. PLoS Biol. 12, e1001853 (2014).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
96.Lee, M. S., Cau, A., Naish, D. & Dyke, G. J. Sustained miniaturization and anatomical innovation in the dinosaurian ancestors of birds. Science 345, 562–566 (2014).CAS 
PubMed 
Article 

Google Scholar 
97.O’Connor, J. & Zhou, Z. Early evolution of the biological bird: perspectives from new fossil discoveries in China. J. Ornithol. 156, 333–342 (2015).Article 

Google Scholar 
98.Zhou, Z. & Zhang, F. A precocial avian embryo from the Lower Cretaceous of China. Science 306, 653 (2004).CAS 
PubMed 
Article 

Google Scholar 
99.Mayr, G. Evolution of avian breeding strategies and its relation to the habitat preferences of Mesozoic birds. Evol. Ecol. 31, 131–141 (2017).Article 

Google Scholar 
100.Arendt, J. D. Adaptive intrinsic growth rates: an integration across taxa. Q. Rev. Biol. 72, 149–177 (1997).Article 

Google Scholar 
101.Jackson, B. E., Segre, P. & Dial, K. P. Precocial development of locomotor performance in a ground-dwelling bird (Alectoris chukar): negotiating a three-dimensional terrestrial environment. Proc. R. Soc. B 276, 3457–3466 (2009).PubMed 
Article 

Google Scholar 
102.Colquhoun, I. Comparing the impact of predators on the activity patterns of lemurids and ceboids. Folia Primatol. 77, 143–165 (2006).Article 

Google Scholar 
103.Maor, R., Dayan, T., Ferguson-Gow, H. & Jones, K. E. Temporal niche expansion in mammals from a nocturnal ancestor after dinosaur extinction. Nat. Ecol. Evol. 1, 1889–1895 (2017).PubMed 
Article 

Google Scholar 
104.Wu, Y. Evolutionary origin of nocturnality in birds. eLS 1, 483–489 (2020).Article 

Google Scholar 
105.Xu, X., Zhou, Z. & Wang, X. The smallest known non-avian theropod dinosaur. Nature 408, 705–708 (2000).CAS 
PubMed 
Article 

Google Scholar 
106.Xu, X. et al. Four-winged dinosaurs from China. Nature 421, 335–340 (2003).CAS 
PubMed 
Article 

Google Scholar 
107.Gong, E., Martin, L. D., Burnham, D. A. & Falk, A. R. The birdlike raptor Sinornithosaurus was venomous. Proc. Natl Acad. Sci. USA 107, 766–768 (2010).CAS 
PubMed 
Article 

Google Scholar 
108.Sullivan, C., Xu, X. & O’Connor, J. K. Complexities and novelties in the early evolution of avian flight, as seen in the Mesozoic Yanliao and Jehol Biotas of Northeast China. Palaeoworld 26, 212–229 (2017).Article 

Google Scholar 
109.Pei, R. et al. Potential for powered flight neared by most close avialan relatives, but few crossed its thresholds. Curr. Biol. 30, 4033–4046 (2020).CAS 
PubMed 
Article 

Google Scholar 
110.Turner, A. H., Pol, D., Clarke, J. A., Erickson, G. M. & Norell, M. A. A basal dromaeosaurid and size evolution preceding avian flight. Science 317, 1378–1381 (2007).CAS 
PubMed 
Article 

Google Scholar 
111.Carbone, C., Mace, G. M., Roberts, S. C. & Macdonald, D. W. Energetic constraints on the diet of terrestrial carnivores. Nature 402, 286–288 (1999).CAS 
PubMed 
Article 

Google Scholar 
112.Gittleman, J. L. Carnivore body size: ecological and taxonomic correlates. Oecologia 67, 540–554 (1985).PubMed 
Article 

Google Scholar 
113.Radloff, F. G. & Du Toit, J. T. Large predators and their prey in a southern African savanna: a predator’s size determines its prey size range. J. Anim. Ecol. 73, 410–423 (2004).Article 

Google Scholar 
114.Vézina, A. F. Empirical relationships between predator and prey size among terrestrial vertebrate predators. Oecologia 67, 555–565 (1985).PubMed 
Article 

Google Scholar 
115.Rezende, E. L., Bacigalupe, L. D., Nespolo, R. F. & Bozinovic, F. Shrinking dinosaurs and the evolution of endothermy in birds. Sci. Adv. 6, eaaw4486 (2020).PubMed 
PubMed Central 
Article 

Google Scholar 
116.Seebacher, F. Dinosaur body temperatures: the occurrence of endothermy and ectothermy. Paleobiology 29, 105–122 (2003).Article 

Google Scholar 
117.Chatterjee, S. & Templin, R. in Feathered Dragons: Studies on the Transition from Dinosaurs to Birds (eds Currie, P. J., Kopplehaus, E. B., Shugar, M. A. & Wright, J. L.) 251–281 (Indiana Univ. Press, 2004).118.Hedenström, A. How birds became airborne. Trends Ecol. Evol. 14, 375–376 (1999).PubMed 
Article 

Google Scholar 
119.Dudley, R. et al. Gliding and the functional origins of flight: biomechanical novelty or necessity? Annu. Rev. Ecol. Evol. Syst. 38, 179–201 (2007).Article 

Google Scholar 
120.Clemente, C. & Wilson, R. Speed and maneuverability jointly determine escape success during simulated games of escape behaviour. Behav. Ecol. 27, 45–54 (2016).Article 

Google Scholar 
121.Caro, T. Antipredator Defenses in Birds and Mammals (Univ. Chicago Press, 2005).122.Van den Hout, P. J., Mathot, K. J., Maas, L. R. & Piersma, T. Predator escape tactics in birds: linking ecology and aerodynamics. Behav. Ecol. 21, 16–25 (2010).Article 

Google Scholar 
123.Wright, N. A., Steadman, D. W. & Witt, C. C. Predictable evolution toward flightlessness in volant island birds. Proc. Natl Acad. Sci. USA 113, 4765–4770 (2016).CAS 
PubMed 
Article 

Google Scholar 
124.Wang, M., Zhou, Z. & Sullivan, C. A fish-eating enantiornithine bird from the Early Cretaceous of China provides evidence of modern avian digestive features. Curr. Biol. 26, 1170–1176 (2016).CAS 
PubMed 
Article 

Google Scholar 
125.Zheng, X. et al. New specimens of Yanornis indicate a piscivorous diet and modern alimentary canal. PLoS ONE 9, e95036 (2014).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
126.Zhou, Z., Zhang, F. & Li, Z. A new Lower Cretaceous bird from China and tooth reduction in early avian evolution. Proc. R. Soc. B 277, 219–227 (2010).PubMed 
Article 

Google Scholar 
127.Meredith, R. W., Zhang, G., Gilbert, M. T. P., Jarvis, E. D. & Springer, M. S. Evidence for a single loss of mineralized teeth in the common avian ancestor. Science 346, 1254390 (2014).PubMed 
Article 
CAS 

Google Scholar 
128.Lima, S. L. Maximizing feeding efficiency and minimizing time exposed to predators: a trade-off in the black-capped chickadee. Oecologia 66, 60–67 (1985).PubMed 
Article 

Google Scholar 
129.Lima, S. L., Valone, T. J. & Caraco, T. Foraging-efficiency-predation-risk trade-off in the grey squirrel. Anim. Behav. 33, 155–165 (1985).Article 

Google Scholar 
130.Verdolin, J. L. Meta-analysis of foraging and predation risk trade-offs in terrestrial systems. Behav. Ecol. Sociobiol. 60, 457–464 (2006).Article 

Google Scholar 
131.Yang, T.-R. & Sander, P. M. The origin of the bird’s beak: new insights from dinosaur incubation periods. Biol. Lett. 14, 20180090 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
132.Zhou, Y.-C., Sullivan, C. & Zhang, F. Negligible effect of tooth reduction on body mass in Mesozoic birds. Vert. Palas 57, 38–50 (2019).
Google Scholar 
133.Louchart, A. & Viriot, L. From snout to beak: the loss of teeth in birds. Trends Ecol. Evol. 26, 663–673 (2011).PubMed 
Article 

Google Scholar 
134.Randall, D., Burggren, W. & French, K. Eckert Animal Physiology: Mechanisms and Adaptations (W. H. Freeman, 1997).135.Davit‐Béal, T., Tucker, A. S. & Sire, J. Y. Loss of teeth and enamel in tetrapods: fossil record, genetic data and morphological adaptations. J. Anat. 214, 477–501 (2009).PubMed 
PubMed Central 
Article 

Google Scholar 
136.Gill, F. & Donsker, D. IOC World Bird List (v8.2). https://doi.org/10.14344/IOC.ML.8.2 (2018).137.Grabherr, M. G. et al. Full-length transcriptome assembly from RNA-Seq data without a reference genome. Nat. Biotechnol. 29, 644–652 (2011).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
138.Crawford, N. G. et al. A phylogenomic analysis of turtles. Mol. Phylogenet. Evol. 83, 250–257 (2015).PubMed 
Article 

Google Scholar 
139.Guillon, J.-M., Guéry, L., Hulin, V. & Girondot, M. A large phylogeny of turtles (Testudines) using molecular data. Contrib. Zool. 81, 147–158 (2012).Article 

Google Scholar 
140.Jønsson, K. A. & Fjeldså, J. A phylogenetic supertree of oscine passerine birds (Aves: Passeri). Zool. Scr. 35, 149–186 (2006).Article 

Google Scholar 
141.McKay, B. D., Barker, F. K., Mays, H. L. Jr, Doucet, S. M. & Hill, G. E. A molecular phylogenetic hypothesis for the manakins (Aves: Pipridae). Mol. Phylogenet. Evol. 55, 733–737 (2010).PubMed 
Article 
PubMed Central 

Google Scholar 
142.Oaks, J. R. A time‐calibrated species tree of Crocodylia reveals a recent radiation of the true crocodiles. Evolution 65, 3285–3297 (2011).PubMed 
Article 

Google Scholar 
143.Pyron, R. A., Burbrink, F. T. & Wiens, J. J. A phylogeny and revised classification of Squamata, including 4161 species of lizards and snakes. BMC Evol. Biol. 13, 93 (2013).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
144.Jarvis, E. D. et al. Whole-genome analyses resolve early branches in the tree of life of modern birds. Science 346, 1320–1331 (2014).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
145.Wilman, H. et al. EltonTraits 1.0: species‐level foraging attributes of the world’s birds and mammals. Ecology 95, 2027–2027 (2014).Article 

Google Scholar 
146.Brusatte, S. L., O’Connor, J. K. & Jarvis, E. D. The origin and diversification of birds. Curr. Biol. 25, R888–R898 (2015).CAS 
PubMed 
Article 

Google Scholar  More

Strains and mediaThe set of 16 strains used in this experiment contains environmental isolates along with strains from the ATCC collection (Supplementary Table 1). The strains were chosen based on two criteria: a distinct colony morphology that would enable visual identification when plated on an NB agar plate; and ability to coexist for ~60 generations with at least two other strains in our collection.All cultures were grown in M9 minimal salts media containing 1X M9 salts, 2 mM MgSO4, 0.1 mM CaCl2, 1X trace metal solution (Teknova), supplemented with 3 mM galacturonic acid (Sigma), 6.1 mM Serine (Sigma), and 9.1 mM sodium acetate as carbon sources, which correspond to 16.67 mM carbon atoms for each compound and 50 mM overall. We chose a combination of carbon sources representing three chemical groups—a carbohydrate, an amino acid, and a carboxylic acid—in order to promote the survival and coexistence of a diverse set of species. The media was prepared on the day of each transfer. A carbon source mixture was prepared ahead at 10X, and was kept in aliquots at 4 °C for up to four weeks.Evolution experimentFrozen stocks of individual species were streaked out on nutrient agar Petri plates and grown at 28 °C. After 48 h single colonies were picked and inoculated into 15 ml falcon tubes containing 3 ml nutrient broth (5 g/L peptone BD difco, BD Bioscience; 3 g/L yeast extract BD difco, BD Bioscience), and were grown overnight at 28 °C shaken at 250 rpm. Initial mixtures were prepared by diluting each species separately to an OD of ({10}^{-2}) and mixing the normalized cultures at equal volumes. OD measurements were done using a Epoch2 microplate reader (BioTek) and were recorded using the Gen5 v3.09 software (BioTek). After mixing, the cocultures were aliquoted to replicates and further diluted to a final OD of ({10}^{-4}), at which the evolutionary experiment was initialized. The number of replicates for each community varied between 3 and 18 (Supplementary Data 1).Communities were grown in 96-well plates containing 200 µl M9 at 28°C and were shaken at 900 rpm. Every 48 h cultures were diluted by a factor of 1500 into fresh M9 media, and OD600 was measured. For this dilution factor, each cycle corresponds to ~10.5 generations. As 1 OD600 ~ of ({10}^{9}) C.F.U/ml, and communities reached ~ 0.5 OD600 and were grown in 200 µl and was diluted by 1500, ~({10}^{5}) cells were transferred each dilution. To avoid cross contaminations, cultures were grown in a checkerboard formation, meaning that each community was surrounded by wells containing media but no bacteria.At transfers 0, 2, 5, 7, 10, 14, 19, 30, and 38 community composition was measured by plating on nutrient agar plates (5 g/L peptone BD difco, BD Bioscience; 3 g/L yeast extract BD difco, BD Bioscience, 15 g/L agar Bacto, BD Bioscience) and counting colonies. For that, the cultures were diluted to an OD of (2.4* {10}^{-8})− (1* {10}^{-8}) and 100 µl of the diluted culture was plated on NB plates and spread using glass beads. Plates were incubated at 28 °C for 48 h and colonies were counted manually. The distribution of the number of colonies counted at each plate to infer community composition is found in Supplementary Fig. 11.We chose the communities based on a preliminary experiment that was conducted by the same protocol for six transfers. In this experiment, 114 of 171 possible pairs of a set of 19 strains (3 strains were not included in the evolution experiment) were cocultured. Pairs that had coexisted for the duration of this experiment, and were confidently distinguishable by colony morphology, and trios that are composed of these pairs, were used for the coevolutionary experiment. We started the evolutionary experiment with 51 pairs and 51 trios, and removed communities that did not coexist for the first ~70 from the final analysis. If a replicate was suspected to be contaminated it was also excluded from further analysis.Ecological experimentsWe supplemented the data of the evolutionary experiment with two ecological competition experiments with the same experimental condition. In order to assess whether communities typically reach an ecological equilibrium within ~50–70 generations (Supplementary Fig. 3), we cultured eight of the pairs that were used in the evolutionary experiment. This experiment was initiated in the same way as the evolutionary experiment, only that after the species’ starters were normalized they were inoculated at the varying initial fractions – 9:1, 5:5, 1:9. Because the normalization depended on optical density, there is a variation in the actual initial fractions between different pairs. Community composition was then measured on six transfers during this experiment: 0, 1, 2, 4, 5, and 6.In order to assess whether changes in composition are due to heritable changes in species’ phenotypes, we used strains that were re-isolated from 31 evolved pairs, and 13 pairs of ancestral strains (Supplementary Figs. 6, 7). Strains were replicated from glycerol stocks into the experimental media and grown for 24 h. The starters were normalized to initiate the competition assay at ({rm{OD}}={10}^{-4}) in fresh M9 media. Species were mixed at equal volume and were propagated for five cycles. community composition was measured at initial conditions, and at the end of the final cycle (5).Quantification of repeatabilityIn order to quantify the qualitative repeatability of different replicate communities we first identified which species was the maximally increasing member at each replicate, that is, which species had increased its abundance by the largest factor between generation 70 and 400. Then, we quantified the frequency of the replicates that had the same maximally increasing member for each community. This measure always produces a value between 1 and 1/n where n is the number of species in the community. We checked the distribution of the repeatability scores against the null hypothesis that the factor by which a species’ abundance increases during evolution is independent of the species or the community. For this, we shuffled the factor of change in relative abundance across all samples, for pairs and trios separately, and quantified the new repeatability scores of the shuffled data. Data of the null hypothesis were generated over 2000 times, and the p value was given by the probability to get a mean equal or above the real data mean.We used the average Euclidean distance of replicates from the median replicate in order to quantify the variability between replicate communities. In order to check whether the distribution of variabilities is similar to what can be expected of random communities, in which each species in the community is just as likely to have any relative abundance, we replaced the real fractions with fractions drawn from a uniform Dirichlet distribution with (underline{{boldsymbol{alpha }}}=underline{1}). We then checked the statistical difference between the two distributions using one-sided Mann–Whitney U test.Trio composition predictionsWe used the formerly established method for predicting the composition of trios from the composition of pairs that was developed by Abreu et al.14 In this approach the fraction of a species when grown in a multispecies community is predicted as the weighted geometric mean of the fraction of the species in all pairwise cultures. The accuracy of the predictions was measured as the Euclidean distance between the prediction and the mean composition of the observed trio, normalized to the largest possible distance between each two communities, (sqrt{n}), where n is the number of species.We used the factors by which species increased their abundance during coevolution in pairs (between generations ~70 and ~400) to predict which species would increase by the largest factor in trios. The maximally increasing member in a given community was assigned to be the one that was the maximally increasing member in the most replicates of that community. If the same species was the maximally increasing member in both pairs it was a member of, then this species was predicted to be the maximally increasing member of the trio. If in every pair a different species was the maximally increasing member, then we predicted that the maximally increasing member of the trio would be the one with the highest mean increase. Only two trios had such transient topology, where in each pair a different species increases, thus we are unable to determine the general utility of the latter approach.Re-isolationEach ~50 generations all communities were frozen at −80 °C with 50% glycerol in a 96-deep well plate. In order to re-isolate strains, stocks were inoculated to a 96-well plate containing the experimental media using a 96-pin replicator, and grown for 24 h at 28 °C. After growth, cultures were diluted by a factor of (2.4* {10}^{-8}) and 100 µl were spread on a nutrient agar plate using glass beads. Plates were kept at room temperature for at least two days and no longer than a week before re-isolations. 5-15 colonies of each strain were picked using a sterile toothpick, and pooled together into 200 µl M9. Re-isolated strains were incubated at 28 °C and shaken at 900 rpm for 24 h and kept in 50% glycerol stock at −80 °C until further use.Growth rates and carrying capacities of individually evolved strainsRe-isolated strains were replicated from glycerol stocks into the experimental media and grown for 24 h. The starters were normalized to initiate the growth assay at (OD={10}^{-4}) in fresh M9 media. The optical density was measured in two automated plate readers simultaneously, Epoch2 microplate reader (BioTek) and Synergy microplate reader (BioTek), and was recorded using Gen5 v3.09 software (BioTek). Plates were incubated at 28 °C with a 1 °C gradient to avoid condensation on the lid, and were shaken at 250 cpm. OD was measured every 10 min. Each strain was measured in four technical replicates, evenly distributed between the two plates, and 2–3 evolutionary replicates were measured for each species (replicates that evolved separately for the duration of the experiment). Growth rates were quantified as the number of divisions it takes a strain to grow from the initial OD of ({10}^{-4}) to an OD of (8* {10}^{-2}) (({log }_{2}frac{0.08}{{10}^{-4}})) divided by the time it took the strain to reach this OD. This measure gives the average doubling time during the initial growth and also accounts for the lag times of the strain. The growth rates of evolutionary replicates were averaged after averaging technical replicates.Carrying capacity was defined as the OD a monoculture reached at the end of each growth cycle of the evolutionary experiment averaged across replicates. These measurements were done in an Epoch2 microplate reader (BioTek). In order to reduce noise, the trajectories of OD measurements were smoothed for each well using moving mean with an averaging window of three.Carrying capacities of coevolved strainsRe-isolated strains were replicated from glycerol stocks into the experimental media and grown for 48 h in M9 media at 28 °C. Cultures were then diluted by 1500 into 3 technical replicates in fresh M9-media, and were given another 48 h to reach carrying capacity. The strains used in this experiment were isolated from 1-3 evolutionary replicates (Supplementary Data 2).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

1.Mendes, R. et al. Deciphering the rhizosphere microbiome for disease-suppressive bacteria. Science 32, 1097–1100 (2011).ADS 
Article 
CAS 

Google Scholar 
2.Bender, S. F., Wagg, C. & van der Heijden, M. G. A. An underground revolution: Biodiversity and soil ecological engineering for agricultural sustainability. Trends Ecol. Evol. 31, 440–452 (2016).PubMed 
Article 
PubMed Central 

Google Scholar 
3.Busby, P. E. et al. Research priorities for harnessing plant microbiomes in sustainable agriculture. PLOS Biol. 15, e2001793 (2017).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
4.Sergaki, C., Lagunas, B., Lidbury, I., Gifford, M. L. & Schäfer, P. Challenges and approaches in microbiome research: From fundamental to applied. Front Plant Sci. 9, 1205 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
5.Toju, H. et al. Core microbiomes for sustainable agroecosystems. Nat. Plants. 4, 247–257 (2018).PubMed 
Article 
PubMed Central 

Google Scholar 
6.Bonfante, P. & Anca, I.-A. Plants, mycorrhizal fungi, and bacteria: A network of interactions. Annu. Rev. Microbiol. 63, 363–383 (2009).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
7.Hiruma, K. et al. Root endophyte colletotrichum tofieldiae confers plant fitness benefits that are phosphate status dependent. Cell 165, 464–474 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
8.Calvo, P., Nelson, L. & Kloepper, J. W. Agricultural uses of plant biostimulants. Plant Soil 383, 3–41 (2014).CAS 
Article 

Google Scholar 
9.Vorholt, J. A., Vogel, C., Carlström, C. I. & Müller, D. B. Establishing causality: Opportunities of synthetic communities for plant microbiome research. Cell Host Microbe 22, 142–155 (2017).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
10.Howden, S. M. et al. Adapting agriculture to climate change. Proc. Natl. Acad. Sci. USA 104, 19691–19696 (2007).ADS 
CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
11.Robertson, G. P. & Vitousek, P. M. nitrogen in agriculture: Balancing the cost of an essential resource. Annu. Rev. Environ. Resour. 34, 97–125 (2009).Article 

Google Scholar 
12.Elser, J. & Bennett, E. Phosphorus cycle: A broken biogeochemical cycle. Nature 478, 29–31 (2011).ADS 
CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
13.Dangl, J. L., Horvath, D. M. & Staskawicz, B. J. Pivoting the plant immune system from dissection to deployment. Science 341, 746–751 (2013).ADS 
CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
14.Hassani, M. A., Durán, P. & Hacquard, S. Microbial interactions within the plant holobiont. Microbiome 6, 58 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
15.Qiu, Z., Egidi, E., Liu, H., Kaur, S. & Singh, B. K. New frontiers in agriculture productivity: Optimised microbial inoculants and in situ microbiome engineering. Biotechnol. Adv. 37, 107371 (2019).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
16.Wei, Z. et al. Initial soil microbiome composition and functioning predetermine future plant health. Sci. Adv. 5, eaaw0759 (2019).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
17.Xiong, W. et al. Rhizosphere protists are key determinants of plant health. Microbiome 8, 27 (2020).PubMed 
PubMed Central 
Article 

Google Scholar 
18.Shade, A. & Handelsman, J. Beyond the Venn diagram: The hunt for a core microbiome. Environ. Microbiol. 14, 4–12 (2012).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
19.Berendsen, R. L., Pieterse, C. M. J. & Bakker, P. A. H. M. The rhizosphere microbiome and plant health. Trends Plant Sci. 17, 478–486 (2012).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
20.Risely, A. Applying the core microbiome to understand host–microbe systems. J. Anim. Ecol. 89, 1549–1558 (2020).PubMed 
Article 

Google Scholar 
21.Lundberg, D. S. et al. Defining the core Arabidopsis thaliana root microbiome. Nature 488, 86–90 (2012).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
22.Bulgarelli, D. et al. Structure and function of the bacterial root microbiota in wild and domesticated barley. Cell Host Microbe 17, 392–403 (2015).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
23.Xu, J. et al. The structure and function of the global citrus rhizosphere microbiome. Nat. Commun. 9, 1–10 (2018).ADS 
Article 
CAS 

Google Scholar 
24.Walters, W. A. et al. Large-scale replicated field study of maize rhizosphere identifies heritable microbes. Proc. Natl. Acad. Sci. USA 115, 7368–7373 (2018).PubMed 
Article 

Google Scholar 
25.Pérez-Jaramillo, J. E. et al. Deciphering rhizosphere microbiome assembly of wild and modern common bean (Phaseolus vulgaris) in native and agricultural soils from Colombia. Microbiome 7, 114 (2019).PubMed 
PubMed Central 
Article 

Google Scholar 
26.Ofek-Lalzar, M. et al. Niche and host-associated functional signatures of the root surface microbiome. Nat. Commun. 5, 1–9 (2014).Article 
CAS 

Google Scholar 
27.Marasco, R., Rolli, E., Fusi, M., Michoud, G. & Daffonchio, D. Grapevine rootstocks shape underground bacterial microbiome and networking but not potential functionality. Microbiome 6, 3 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
28.Jin, T. et al. Taxonomic structure and functional association of foxtail millet root microbiome. Gigascience 6, 1–12 (2017).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
29.Gottel, N. R. et al. Distinct microbial communities within the endosphere and rhizosphere of Populus deltoides roots across contrasting soil types. Appl. Environ. Microbiol. 77, 5934–5944 (2011).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
30.Edwards, J. et al. Structure, variation, and assembly of the root-associated microbiomes of rice. Proc. Natl. Acad. Sci. USA 112, E911–E920 (2015).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
31.Mendes, L. W., Kuramae, E. E., Navarrete, A. A., Van Veen, J. A. & Tsai, S. M. Taxonomical and functional microbial community selection in soybean rhizosphere. ISME J. 8, 1577–1587 (2014).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
32.Hamonts, K. et al. Field study reveals core plant microbiota and relative importance of their drivers. Environ. Microbiol. 20, 124–140 (2018).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
33.Cheng, Z. et al. Revealing the Variation and Stability of Bacterial Communities in Tomato Rhizosphere Microbiota. Microorganisms 8, 170 (2020).CAS 
PubMed Central 
Article 

Google Scholar 
34.Donn, S., Kirkegaard, J. A., Perera, G., Richardson, A. E. & Watt, M. Evolution of bacterial communities in the wheat crop rhizosphere. Environ. Microbiol. 17, 610–621 (2015).PubMed 
Article 
PubMed Central 

Google Scholar 
35.Simonin, M. et al. Influence of plant genotype and soil on the wheat rhizosphere microbiome: Identification of a core microbiome across eight African and European soils. FEMS Microbiol. Ecol. 96, fiaa67 (2019).
Google Scholar 
36.Schlatter, D. C., Yin, C., Hulbert, S. & Paulitz, T. C. Core rhizosphere microbiomes of dryland wheat are influenced by location and land use history. Appl. Environ. Microbiol. 86, e02135-e2219 (2020).CAS 
PubMed 
PubMed Central 

Google Scholar 
37.Douglas, G. M. et al. PICRUSt2 for prediction of metagenome functions. Nat. Biotechnol. 38, 685–688 (2020).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
38.Kanehisa, M., Goto, S., Sato, Y., Furumichi, M. & Tanabe, M. KEGG for integration and interpretation of large-scale molecular data sets. Nucleic Acids Res. 40, D109–D114 (2012).CAS 
PubMed 
Article 

Google Scholar 
39.Lemanceau, P., Blouin, M., Muller, D. & Moënne-Loccoz, Y. Let the core microbiota be functional. Trends Plant Sci. 22, 583–595 (2017).CAS 
PubMed 
Article 

Google Scholar 
40.Klassen, J. L. Defining microbiome function. Nat. Microbiol. 3, 864–869 (2018).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
41.Ranjard, L. et al. Turnover of soil bacterial diversity driven by wide-scale environmental heterogeneity. Nat. Commun. 4, 1–10 (2013).Article 
CAS 

Google Scholar 
42.Haichar, F. E. Z. et al. Plant host habitat and root exudates shape soil bacterial community structure. ISME J. 2, 1221–1230 (2008).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
43.Bulgarelli, D. et al. Revealing structure and assembly cues for Arabidopsis root-inhabiting bacterial microbiota. Nature 488, 91–95 (2012).ADS 
CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
44.Turner, T. R., James, E. K. & Poole, P. S. The plant microbiome. Genome Biol. 14, 1–10 (2013).Article 
CAS 

Google Scholar 
45.Vandenkoornhuyse, P., Quaiser, A., Duhamel, M., Le Van, A. & Dufresne, A. The importance of the microbiome of the plant holobiont. New Phytol. 206, 1196–1206 (2015).PubMed 
Article 
PubMed Central 

Google Scholar 
46.Wu, Z. et al. Environmental factors shaping the diversity of bacterial communities that promote rice production. BMC Microbiol. 18, 51 (2018).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
47.Yan, Y., Kuramae, E. E., De Hollander, M., Klinkhamer, P. G. L. & Van Veen, J. A. Functional traits dominate the diversity-related selection of bacterial communities in the rhizosphere. ISME J. 11, 56–66 (2017).PubMed 
Article 
PubMed Central 

Google Scholar 
48.Schmidt, J. E., Kent, A. D., Brisson, V. L. & Gaudin, A. C. M. Agricultural management and plant selection interactively affect rhizosphere microbial community structure and nitrogen cycling. Microbiome 7, 146 (2019).PubMed 
PubMed Central 
Article 

Google Scholar 
49.van der Heijden, M. G. A. & Hartmann, M. Networking in the plant microbiome. PLoS Biol. 14, e1002378 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
50.Agler, M. T. et al. Microbial hub taxa link host and abiotic factors to plant microbiome variation. PLoS Biol. 14, e1002352 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
51.Louca, S. et al. Function and functional redundancy in microbial systems. Nat. Ecol. Evol. 2, 936–943 (2018).PubMed 
Article 
PubMed Central 

Google Scholar 
52.Lozupone, C. A., Stombaugh, J. I., Gordon, J. I., Jansson, J. K. & Knight, R. Diversity, stability and resilience of the human gut microbiota. Nature 489, 220–230 (2012).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
53.United Nations Food and Agriculture Organization (FAO) http://www.fao.org/faostat/en/#data/QC (2020).54.Stams, A. J. & Plugge, C. M. Electron transfer in syntrophic communities of anaerobic bacteria and archaea. Nat. Rev. Microbiol 7, 568–577 (2009).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
55.IPCC. IPCC Guidelines for National Greenhouse Gas Inventories Prepared by the National Greenhouse Gas Inventories Programme IGES (2019).56.Kuan, K. B., Othman, R., Rahim, K. A. & Shamsuddin, Z. H. Plant growth-promoting rhizobacteria inoculation to enhance vegetative growth, nitrogen fixation and nitrogen remobilisation of maize under greenhouse conditions. PLoS ONE 11, e0152478 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
57.Singh, R. P. & Jha, P. N. The multifarious PGPR Serratia marcescens CDP-13 augments induced systemic resistance and enhanced salinity tolerance of wheat (Triticum aestivum L.). PLoS ONE 11, e0155026 (2016).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
58.Sathya, A., Vijayabharathi, R. & Gopalakrishnan, S. Plant growth-promoting actinobacteria: A new strategy for enhancing sustainable production and protection of grain legumes. 3 Biotech 7, 102 (2017).PubMed 
PubMed Central 
Article 

Google Scholar 
59.Verbon, E. H. & Liberman, L. M. Beneficial microbes affect endogenous mechanisms controlling root development. Trends Plant Sci. 21, 218–229 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
60.Yang, P., Yu, S., Cheng, L. & Ning, K. Meta-network: Optimized species-species network analysis for microbial communities. BMC Genom. 20, 187 (2019).Article 

Google Scholar 
61.Smith, S. A. & Brown, J. W. Constructing a broadly inclusive seed plant phylogeny. Am. J. Bot. 105, 1–13 (2018).Article 

Google Scholar 
62.Bulgarelli, D., Schlaeppi, K., Spaepen, S., van Themaat, E. V. L. & Schulze-Lefert, P. Structure and functions of the bacterial microbiota of plants. Annu. Rev. Plant Biol. 64, 807–838 (2013).CAS 
PubMed 
Article 

Google Scholar 
63.Müller, D. B., Vogel, C., Bai, Y. & Vorholt, J. A. The plant microbiota: Systems-level insights and perspectives. Annu. Rev. Genet. 50, 211–234 (2016).PubMed 
Article 
CAS 

Google Scholar 
64.Grossmann, G. et al. The RootChip: An integrated microfluidic chip for plant science. Plant Cell 23, 4234–4240 (2011).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
65.Massalha, H., Korenblum, E., Malitsky, S., Shapiro, O. H. & Aharoni, A. Live imaging of root-bacteria interactions in a microfluidics setup. Proc. Natl. Acad. Sci. USA 114, 4549–4554 (2017).CAS 
PubMed 
Article 

Google Scholar 
66.Aßhauer, K. P., Wemheuer, B., Daniel, R. & Meinicke, P. Tax4Fun: Predicting functional profiles from metagenomic 16S rRNA data. Bioinformatics 31, 2882–2884 (2015).PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
67.Sun, S., Jones, R. B. & Fodor, A. A. Inference-based accuracy of metagenome prediction tools varies across sample types and functional categories. Microbiome 8, 46 (2020).PubMed 
PubMed Central 
Article 

Google Scholar 
68.Choi, J. et al. Strategies to improve reference databases for soil microbiomes. ISME J. 11, 829–834 (2017).PubMed 
Article 

Google Scholar 
69.Lopes, L. D., Pereira e Silva, M. C. & Andreote, F. D. Bacterial abilities and adaptation toward the rhizosphere colonization. Front. Microbiol. 7, 1341 (2016).PubMed 
PubMed Central 
Article 

Google Scholar 
70.Staley, C. et al. Core functional traits of bacterial communities in the Upper Mississippi River show limited variation in response to land cover. Front. Microbiol. 5, 414 (2014).PubMed 
PubMed Central 

Google Scholar 
71.Bolnick, D. I. et al. Individual diet has sex-dependent effects on vertebrate gut microbiota. Nat. Commun. 5, 4500 (2014).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
72.Goodrich, J. K. et al. Human genetics shape the gut microbiome. Cell 159, 789–799 (2014).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
73.Button, K. S. et al. Power failure: Why small sample size undermines the reliability of neuroscience. Nat. Rev. Neurosci. 14, 365 (2013).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
74.Jervis-Bardy, J. et al. Deriving accurate microbiota profiles from human samples with low bacterial content through post-sequencing processing of Illumina MiSeq data. Microbiome 3, 19 (2015).PubMed 
PubMed Central 
Article 

Google Scholar 
75.Schöler, A., Jacquiod, S., Vestergaard, G., Schulz, S. & Schloter, M. Analysis of soil microbial communities based on amplicon sequencing of marker genes. Biol. Fertil. Soils 53, 485–489 (2017).Article 
CAS 

Google Scholar 
76.Vestergaard, G., Schulz, S., Schöler, A. & Schloter, M. Making big data smart: How to use metagenomics to understand soil quality. Biol. Fertil. Soils 53, 479–484 (2017).Article 

Google Scholar 
77.Venturi, V. & Keel, C. Signaling in the rhizosphere. Trends Plant Sci. 21, 187–198 (2016).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
78.Boylen, E. et al. Reproducible, interactive, scalable, and extensible microbiome data science using QIIME 2. Nat. Biotechnol. 37, 852–857 (2019).Article 
CAS 

Google Scholar 
79.Callahan, B. J. et al. DADA2 paper supplementary information: High resolution sample inference from amplicon data. Nat. Methods. 13, 581–583 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
80.Quast, C. et al. The SILVA ribosomal RNA gene database project: Improved data processing and web-based tools. Nucleic Acids Res. 41, D590–D596 (2013).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
81.Bokulich, N. A. et al. Optimizing taxonomic classification of marker-gene amplicon sequences with QIIME 2’s q2-feature-classifier plugin. Microbiome 6, 90 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
82.Lozupone, C. & Knight, R. UniFrac: A new phylogenetic method for comparing microbial communities. Appl. Environ. Microbiol. 71, 8228–8235 (2005).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
83.Paradis, E. & Schliep, K. Phylogenetics ape 5.0: An environment for modern phylogenetics and evolutionary analyses in R. Bioinformatics 35, 526–528 (2018).Article 
CAS 

Google Scholar 
84.McMurdie, P. J. & Holmes, S. Waste not, want not: Why rarefying microbiome data is inadmissible. PLoS Comput. Biol. 10, e1003531 (2014).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
85.Caporaso, J. G. et al. QIIME allows analysis of high-throughput community sequencing data. Nat. Methods. 7, 335–336 (2010).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
86.Parks, D. H., Tyson, G. W., Hugenholtz, P. & Beiko, R. G. Genome analysis STAMP: Statistical analysis of taxonomic and functional profiles. Bioinformatics 30, 3123–3124 (2014).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
87.Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. R. Stat. Soc. B. 57, 289–300 (1995).MathSciNet 
MATH 

Google Scholar 
88.Yurgel, S. N., Nearing, J. T., Douglas, G. M. & Langille, M. G. I. Metagenomic functional shifts to plant induced environmental changes. Front. Microbiol. 10, 1682 (2019).PubMed 
PubMed Central 
Article 

Google Scholar 
89.Kimura, M. A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. J. Mol. Evol. 16, 111–120 (1980).ADS 
CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
90.Kumar, S., Stecher, G. & Tamura, K. MEGA7: Molecular evolutionary genetics analysis version 7.0 for bigger data sets. Mol. Biol. Evol. 33, 1870–1874 (2016).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
91.Brisson, V., Schmidt, J., Northen, T. R., Vogel, J. P. & Gaudin, A. A new method to correct for habitat filtering in microbial correlation networks. Front. Microbiol. 10, 585 (2019).PubMed 
PubMed Central 
Article 

Google Scholar 
92.Reshef, D. N. et al. Detecting novel associations in large data sets. Science 334, 1518–1524 (2011).ADS 
CAS 
PubMed 
PubMed Central 
MATH 
Article 

Google Scholar 
93.Shannon, P. et al. Cytoscape: A software Environment for integrated models of biomolecular interaction networks. Genome Res. 13, 2498–2504 (2003).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
94.Banerjee, S., Thrall, P. H., Bissett, A., Heijden, M. G. A. & Richardson, A. E. Linking microbial co-occurrences to soil ecological processes across a woodland-grassland ecotone. Ecol. Evol. 8, 8217–8230 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
95.Gu, Y. et al. Long-term fertilization structures bacterial and archaeal communities along soil depth gradient in a paddy soil. Front. Microbiol. 8, 1516 (2017).PubMed 
PubMed Central 
Article 

Google Scholar  More

Data and data processingThe modeling tools described in the following sections are applied to the Italian COVID-19 epidemic at the scale of second-level administrative divisions, i.e., provinces and metropolitan cities (as of 2020, 107 spatial units). Official data about resident population at the provincial level are produced yearly by the Italian National Institute of Statistics (Istituto Nazionale di Statistica, ISTAT; data available at http://dati.istat.it/Index.aspx?QueryId=18460). The January 2019 update has been used to inform the spatial distribution of the population.The data to quantify nation-wide human mobility prior to the pandemic come from ISTAT (specifically, from the 2011 national census; data available online at https://www.istat.it/it/archivio/139381). Mobility fluxes, mostly reflecting commuting patterns related to work and study purposes, are provided at the scale of third-level administrative units (municipalities)53,54. These fluxes were upscaled to the provincial level following the administrative divisions of 2019, and used to evaluate the fraction pi of mobile people and the fraction qij of mobile people between i and all other administrative units j (see Supplementary Material in Gatto et al.7).Airport traffic data for year 2019, used to inform the simulation shown in Fig. 4c, d, are from the Italian Airports Association (Assaeroporti; data available at http://assaeroporti.com/statistiche_201912/). Note that airports have been assigned to the main Metropolitan Area they serve, rather than to the province where they are geographically located (e.g., Malpensa Airport has been assigned to the Metropolitan City of Milano, rather than to the neighboring Varese province, where it actually lies).Model parameters are taken from a paper by Bertuzzo et al.14, where they were inferred in a Bayesian framework on the basis of the official epidemiological bulletins released daily by Dipartimento della Protezione Civile55 (data available online at https://github.com/pcm-dpc/COVID-19) and the bulletins of Epicentro, at ISS51,56. The parameters estimated for the initial phase of the Italian COVID-19 epidemic14, during which SARS-CoV-2 was spreading unnoticed in the population, reflect a situation of unperturbed social mixing and human mobility, absent any effort devoted to disease control. This parameterization, in which all parameters (including the transmission rates) are spatially homogeneous, is reported in Table 2 and has been used to produce all the results presented in the main text, except for those of Fig. 6. In this case, to account for the containment measures put in place by the Italian authorities and their effects on transmission rates and mobility patterns during the first months of the pandemic, a time-varying parameterization14 for the period February 24 to May 1, 2020 has been used. In this parameterization, the transmission rates were allowed to take different values over different time windows, corresponding to the timing of the implementation of the main nation-wide restrictions, or lifting thereof. Specifically, the effect of the containment measures was parameterized by assuming that the transmission parameters had a sharp decrease after the containment measures announced at the end of February and the beginning of March, and that they were further reduced in the following weeks as the country was effectively entering full lockdown. As a by-product, these time-varying transmission rates can also at least partially account for seasonal effects on disease transmission. Due to the emerging nature of the pathogen, seasonality has not been given further consideration in this work; however, it may become a key component of future modeling efforts aimed at studying post-pandemic SARS-CoV-2 transmission dynamics3, i.e., if/when the pathogen establishes as endemic. Spatial connectivity too was modified with respect to the baseline scenario to reflect the disruption of mobility patterns induced by the pandemic and the associated containment measures14. Specifically, between-province mobility was progressively reduced as the epidemic unfolded according to estimates obtained through mobility data from mobile applications53,57.Spatially explicit SEPIAR with distributed controlsWe consider a set of n communities connected by human mobility fluxes. In each community, the human population is subdivided according to infection status into the epidemiological compartments of susceptible, exposed (latently infected), post-latent (incubating infectious, also termed pre-symptomatic7), symptomatic infectious, asymptomatic infectious (including paucisymptomatic), and recovered individuals. The present model utilizes previous work aimed to describe the first wave of COVID-19 infections7,14. In particular, it allows us to account for three widely adopted types of containment measures: reduction of local transmission (as a result of the use of personal protections, social distancing, and local mobility restriction), travel restriction, and isolation of infected individuals. To describe the effects of isolation, each infected compartment (exposed, post-latent, symptomatic and asymptomatic) is actually split into two, which allows keeping track of the abundances of infected individuals who are still in the community vs. those who are removed from it (i.e., either in isolation at a hospital, if symptomatic, or quarantined at home, if exposed, post-latent, or asymptomatic). The state variables of the model are summarized in Table 1. Supplementary Figure 1 recapitulates the structure of the model.COVID-19 transmission dynamics are thus described by the following set of ordinary differential equations:$${dot{S}}_{i} =mu ({N}_{i}-{S}_{i})-{lambda }_{i}{S}_{i}\ {dot{E}}_{i} ={lambda }_{i}{S}_{i}-(mu +{delta }^{E}+{chi }_{i}^{E}){E}_{i}\ {dot{P}}_{i} ={delta }^{E}{E}_{i}-(mu +{delta }^{P}+{chi }_{i}^{P}){P}_{i}\ {dot{I}}_{i} =sigma {delta }^{P}{P}_{i}-(mu +alpha +{gamma }^{I}+eta +{chi }_{i}^{I}){I}_{i}\ {dot{A}}_{i} =(1-sigma ){delta }^{P}{P}_{i}-(mu +{gamma }^{A}+{chi }_{i}^{A}){A}_{i}\ {dot{E}}_{i}^{{rm{q}}} ={chi }_{i}^{E}{E}_{i}-(mu +{delta }^{E}){E}_{i}^{{rm{q}}}\ {dot{P}}_{i}^{{rm{q}}} ={chi }_{i}^{P}{P}_{i}+{delta }^{E}{E}_{i}^{{rm{q}}}-(mu +{delta }^{P}){P}_{i}^{{rm{q}}}\ {dot{I}}_{i}^{{rm{h}}} =(eta +{chi }_{i}^{I}){I}_{i}+sigma {delta }^{P}{P}_{i}^{{rm{q}}}-(mu +alpha +{gamma }^{I}){I}_{i}^{{rm{h}}}\ {dot{A}}_{i}^{{rm{q}}} ={chi }_{i}^{A}{A}_{i}+(1-sigma ){delta }^{P}{P}_{i}^{{rm{q}}}-(mu +{gamma }^{A}){A}_{i}^{{rm{q}}}\ {dot{R}}_{i} ={gamma }^{I}({I}_{i}+{I}_{i}^{{rm{h}}})+{gamma }^{A}({A}_{i}+{A}_{i}^{{rm{q}}})-mu {R}_{i}.$$
(3)
Susceptible individuals are recruited into community i (i = 1…n) at a constant rate μNi, with μ and Ni being the average mortality rate of the population and the size of the community in the absence of disease, respectively, and die at rate μ. In this way, the equilibrium size of community i without disease amounts to Ni. Susceptible individuals get exposed to the pathogen at rate λi, corresponding to the force of infection for community i (detailed below), thus becoming latently infected (but not infectious yet). Exposed individuals die at rate μ and transition to the post-latent, infectious stage at rate δE. If containment measures including mass testing and preventive isolation of positive cases are in place, exposed individuals may be removed from the general population and quarantined at rate ({chi }_{i}^{E}). Post-latent individuals die at rate μ, progress to the next infectious classes at rate ηP, developing an infection that can be either symptomatic—with probability σ—or asymptomatic, including the case in which only mild symptoms are present—with probability 1 − σ, and may be tested and quarantined at rate ({chi }_{i}^{P}). Symptomatic infectious individuals die at rate μ + α, with α being an extra-mortality term associated with disease-related complications, recover from infection at rate γI, may spontaneously seek treatment at a hospital at rate η, and may be identified through mass screening and hospitalized at rate ({chi }_{i}^{I}). Asymptomatic individuals die at rate μ, recover at rate γA, and may be quarantined at rate ({chi }_{i}^{A}). Infected individuals who are either hospitalized or quarantined at home are subject to the same epidemiological dynamics as those who are still in the community, but are considered to be effectively removed from it, thus not contributing to disease transmission. Individuals who recover from the infection die at rate μ, and are assumed to have permanent immunity to reinfection. This last assumption is not fundamental, as loss of immunity can be easily included in the model. However, immunity to SARS-CoV-2 reinfection is reported to be relatively long-lasting (a few months at least), hence its loss cannot alter transmission dynamics over epidemic timescales14.The cornerstone of model (Eq. (3)) is the force of infection, λi, which in a spatially explicit setting must account not only for locally acquired infections but also for the role played by human mobility. We assume that, at the spatiotemporal scales of interest for our problem, human mobility mostly depicts daily commuting flows (also coherently with the data available for parameterization; see above) and does not actually entail a permanent relocation of individuals. We thus describe human mobility (and the associated social contacts possibly conducive to disease transmission) by means of instantaneous spatial-mixing matrices ({M}_{c,ij}^{X}) (with X ∈ {S, E, P, I, A, R}), i.e.,$${M}_{c,ij}^{X}=left{begin{array}{ll}{r}^{X}{p}_{i}{q}_{ij}(1-{xi }_{ij})hfill&,{text{if}},i,ne, jhfill\ (1-{p}_{i})+(1-{r}^{X}){p}_{i}+{r}^{X}{p}_{i}{q}_{ij}(1-{xi }_{ij})&,{text{if}},i=j,end{array}right.$$
(4)
where pi (0 ≤ pi ≤ 1 for all i’s) is the fraction of mobile people in community i, qij (0 ≤ qij ≤ 1 for all i’s and j’s) represents the fraction of people moving between i and j (including j = i, (mathop{sum }nolimits_{j = 1}^{n}{q}_{ij}=1) for all i’s), rX (0 ≤ rX ≤ 1 for all X’s) quantifies the fraction of contacts occurring while individuals in epidemiological compartment X are traveling, and ξij (0 ≤ ξij ≤ 1 for all i’s and j’s) represents the effects of travel restrictions that may be imposed between any two communities i and j as a part of the containment response. Therefore, the probability that residents from i have social contacts while being in j (independently of with whom) is assumed to be proportional to the fraction rX of the mobility-related contacts of the individuals in epidemiological compartment X, multiplied by the probability pi that people from i travel (independently of the destination) and the probability qij that the travel occurs between i and j, possibly reduced by a factor 1 − ξij accounting for travel restrictions. All other contacts contribute to mixing within the local community (i in this case). Note also that if ξij = 0 for all i’s and j’s, then ({M}_{c,ij}^{X}) reduces to ({M}_{ij}^{X}), i.e., to the mixing matrix in the absence of disease-containment measures. In this case, (mathop{sum }nolimits_{j = 1}^{n}{M}_{ij}^{X}=1) for all i’s and X’s. It is important to remark, though, that the epidemiologically relevant contacts between the residents of two different communities, say i and j, may not necessarily occur in either i or j; in fact, they could happen anywhere else, say in community k, between residents of i and j simultaneously traveling to k. On this basis, we define the force of infection as$${lambda }_{i}=mathop{sum }limits_{j=1}^{n}{M}_{c,ij}^{S}frac{(1-{epsilon }_{j})left({beta }_{j}^{P}mathop{sum }nolimits_{k = 1}^{n}{M}_{c,kj}^{P}{P}_{k}+{beta }_{j}^{I}mathop{sum }nolimits_{k = 1}^{n}{M}_{c,kj}^{I}{I}_{k}+{beta }_{j}^{A}mathop{sum }nolimits_{k = 1}^{n}{M}_{c,kj}^{A}{A}_{k}right)}{mathop{sum }nolimits_{k = 1}^{n}left({M}_{c,kj}^{S}{S}_{k}+{M}_{c,kj}^{E}{E}_{k}+{M}_{c,kj}^{P}{P}_{k}+{M}_{c,kj}^{I}{I}_{k}+{M}_{c,kj}^{A}{A}_{k}+{M}_{c,kj}^{R}{R}_{k}right)},$$
(5)
where the parameters ({beta }_{j}^{X}) (X ∈ {P, I, A}) are the community-dependent rates of disease transmission from the three infectious classes, ϵj (0 ≤ ϵj ≤ 1 for all j’s) represents the reduction of transmission induced by social distancing, the use of personal protective equipment, and local mobility restrictions if such containment measures are in fact in place, and the terms ({M}_{c,ij}^{X}) (with X ∈ {S, E, P, I, A, R}) describe the epidemiological effects of mobility between i and j in the presence of disease-containment measures. Note that transmission has been assumed to be frequency-dependent.The parameters μ, δX (X ∈ {E, P}), σ, α, η, γX (X ∈ {I, A}), and rX (X ∈ {S, E, P, I, A, R}) are assumed to be community-independent, for they pertain to population demography at the country scale or the clinical course of the disease. By contrast, the transmission rates ({beta }_{i}^{X}) (X ∈ {P, I, A}) and the control parameters, namely the isolation rates ({chi }_{i}^{X}) (X ∈ {E, P, I, A}), the reductions of transmission due to personal protection, social distancing, and local mobility restriction ϵi, and the travel restrictions ξij, are assumed to be possibly community-dependent, thereby reflecting spatial heterogeneities in disease transmission prior to the implementation of containment measures (({beta }_{i}^{X})), testing effort and/or strategy (({chi }_{i}^{X})), local transmission reduction (ϵi), and travel restriction (ξij).Derivation of the basic and control reproduction numbersClose to the DFE, a state in which all individuals are susceptible to the disease (Si = Ni, with Ni being the baseline population size of community i) and all the other epidemiological compartments are empty (({E}_{i}={P}_{i}={I}_{i}={A}_{i}={E}_{i}^{{rm{q}}}={P}_{i}^{{rm{q}}}={I}_{i}^{{rm{h}}}={A}_{i}^{{rm{q}}}={R}_{i}=0) for all i’s), the dynamics of model (Eq. (3)) is described by the linearized system (dot{{bf{x}}}={{bf{J}}}_{{bf{c}}}{bf{x}}), where ({bf{x}}={[{S}_{i},{E}_{i},{P}_{i},{I}_{i},{A}_{i},{E}_{i}^{{rm{q}}},{P}_{i}^{{rm{q}}},{I}_{i}^{{rm{h}}},{A}_{i}^{{rm{q}}},{R}_{i}]}^{T}) (where i = 1…n and the superscript T denotes matrix transposition) and Jc is the spatial Jacobian matrix$${{bf{J}}}_{{bf{c}}}=left[begin{array}{llllllllll}-mu {bf{I}}&{bf{0}}&-{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&-{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&-{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{delta }^{E}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&sigma {delta }^{P}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&(1-sigma ){delta }^{P}{bf{I}}&{bf{0}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{{boldsymbol{chi }}}^{{bf{E}}}&{bf{0}}&{bf{0}}&{bf{0}}&-(mu +{delta }^{E}){bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{{boldsymbol{chi }}}^{{bf{P}}}&{bf{0}}&{bf{0}}&{delta }^{E}{bf{I}}&-(mu +{delta }^{P}){bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&eta {bf{I}}+{{boldsymbol{chi }}}^{{bf{I}}}&{bf{0}}&{bf{0}}&sigma {delta }^{P}{bf{I}}&-(mu +alpha +{gamma }^{I}){bf{I}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{{boldsymbol{chi }}}^{{bf{A}}}&{bf{0}}&(1-sigma ){delta }^{P}{bf{I}}&{bf{0}}&-(mu +{gamma }^{A}){bf{I}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{gamma }^{I}{bf{I}}&{gamma }^{A}{bf{I}}&{bf{0}}&{bf{0}}&{gamma }^{I}{bf{I}}&{gamma }^{A}{bf{I}}&-mu {bf{I}}end{array}right],$$
(6)
where I and 0 are the identity and null matrices of size n, respectively, ({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{X}}}) (X ∈ {E, P, I, A}) are diagonal matrices whose non-zero elements are (mu +{delta }^{E}+{chi }_{i}^{E}) (for ({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}})), (mu +{delta }^{P}+{chi }_{i}^{P}) (for ({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}})), (mu +alpha +eta +{gamma }^{I}+{chi }_{i}^{I}) (for ({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}})), and (mu +{gamma }^{A}+{chi }_{i}^{A}) (for ({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}})), and the matrices ({{boldsymbol{theta }}}_{{bf{c}}}^{{bf{X}}}) (X ∈ {P, I, A}) are given by$${{boldsymbol{theta }}}_{{bf{c}}}^{{bf{X}}}={bf{N}}{{bf{M}}}_{{bf{c}}}^{{bf{S}}}({bf{I}}-{boldsymbol{epsilon }}){{boldsymbol{beta }}}^{{bf{X}}}{({{boldsymbol{Delta }}}_{{bf{c}}})}^{-1}{({{bf{M}}}_{{bf{c}}}^{{bf{X}}})}^{T},$$
(7)
where N is a diagonal matrix whose non-zero elements are the population sizes Ni, ({{bf{M}}}_{{bf{c}}}^{{bf{X}}}=[{M}_{c,ij}^{X}]) (X ∈ {S, P, I, A}) are sub-stochastic matrices representing the spatially explicit contact terms in the presence of containment measures, ϵ is a diagonal matrix whose non-zero entries are the transmission reductions ϵi, βX (X ∈ {P, I, A}) are diagonal matrices whose non-zero elements are the contact rates ({beta }_{i}^{X}), and Δc is a diagonal matrix whose non-zero entries are the elements of vector ({bf{u}}{bf{N}}{{bf{M}}}_{{bf{c}}}^{{bf{S}}}), with u being a unitary row vector of size n.Because of its block-triangular structure, it is immediate to see that Jc has 6n strictly negative eigenvalues, namely −μ, with multiplicity 2n, and −(μ + δE),−(μ + δP), −(μ + α + γI), and −(μ + γA), each with multiplicity n. Therefore, the asymptotic stability properties of the DFE of model (Eq. (3)), which determine whether long-term disease circulation in the presence of controls is possible, are linked to the eigenvalues of a reduced-order spatial Jacobian associated with the infection subsystem, i.e., the subset of state variables directly related to disease transmission, in this case {E1, …, En, P1, …, Pn, I1, …, In, A1, …, An}. Note that introducing waning immunity would not change the spectral properties of the Jacobian matrix evaluated at the DFE. The reduced-order Jacobian ({{bf{J}}}_{{bf{c}}}^{* }) thus reads$${{bf{J}}}_{{bf{c}}}^{* }=left[begin{array}{llll}-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}\ {delta }^{E}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}&{bf{0}}&{bf{0}}\ {bf{0}}&sigma {delta }^{P}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}}&{bf{0}}\ {bf{0}}&(1-sigma ){delta }^{P}{bf{I}}&{bf{0}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}}end{array}right].$$
(8)
The asymptotic stability properties of the DFE can be assessed through a NGM approach22,37. In fact, the spectral radius of the NGM provides an estimate of the so-called control reproduction number58, ({{mathcal{R}}}_{{rm{c}}}), which can be thought of as the average number of secondary infections produced by one infected individual in a completely susceptible population in the presence of disease-containment measures. Clearly, if ({{mathcal{R}}}_{{rm{c}}}, > , 1) the pathogen can invade the population in the long run, and endemic transmission will eventually be established despite the implementation of disease-containment measures. To evaluate ({{mathcal{R}}}_{{rm{c}}}) for model (Eq. (3)), the Jacobian of the infection subsystem can be decomposed into a spatial transmission matrix$${{bf{T}}}_{{bf{c}}}=left[begin{array}{llll}{bf{0}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}end{array}right],$$
(9)
and a transition matrix$${{boldsymbol{Sigma }}}_{{bf{c}}}=left[begin{array}{llll}-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}&{bf{0}}&{bf{0}}&{bf{0}}\ {delta }^{E}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}&{bf{0}}&{bf{0}}\ {bf{0}}&sigma {delta }^{P}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}}&{bf{0}}\ {bf{0}}&(1-sigma ){delta }^{P}{bf{I}}&{bf{0}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}}end{array}right],$$
(10)
so that Jc = Tc + Σc. The spatial NGM with large domain ({{bf{K}}}_{{bf{c}}}^{{bf{L}}}), including variables other than the states-at-infection59 (i.e., the exposed individuals Ei) thus reads$${{bf{K}}}_{{bf{c}}}^{{bf{L}}}=-{{bf{T}}}_{{bf{c}}}{({{mathbf{Sigma }}}_{{bf{c}}})}^{-1}=left[begin{array}{llll}{{bf{K}}}_{{bf{c}}}^{{bf{1}}}&{{bf{K}}}_{{bf{c}}}^{{bf{2}}}&{{bf{K}}}_{{bf{c}}}^{{bf{3}}}&{{bf{K}}}_{{bf{c}}}^{{bf{4}}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}end{array}right],$$
(11)
with$${{bf{K}}}_{{bf{c}}}^{{bf{1}}} ={delta }^{E}left[{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}+sigma {delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}})}^{-1}+(1-sigma ){delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}})}^{-1}right]{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}})}^{-1}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}})}^{-1}\ {{bf{K}}}_{{bf{c}}}^{{bf{2}}} =left[{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}+sigma {delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}})}^{-1}+(1-sigma ){delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}})}^{-1}right]{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}})}^{-1}\ {{bf{K}}}_{{bf{c}}}^{{bf{3}}} ={{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}})}^{-1}\ {{bf{K}}}_{{bf{c}}}^{{bf{4}}} ={{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}})}^{-1}.$$
(12)
Because of the peculiar block-triangular structure of ({{bf{K}}}_{{bf{c}}}^{{bf{L}}}), the spatial NGM with small domain (Kc, accounting only for Ei) is simply ({{bf{K}}}_{{bf{c}}}^{{bf{1}}}) (see again Diekmann et al.59). The control reproduction number can thus be found as the spectral radius of the NGM (with either large or small domain), i.e.,$${{mathcal{R}}}_{{rm{c}}}=rho ({{bf{K}}}_{{bf{c}}}^{{bf{L}}})=rho ({{bf{K}}}_{{bf{c}}})=rho ({{bf{G}}}_{{bf{c}}}^{{bf{P}}}+{{bf{G}}}_{{bf{c}}}^{{bf{I}}}+{{bf{G}}}_{{bf{c}}}^{{bf{A}}}),$$
(13)
where$${{bf{G}}}_{{bf{c}}}^{{bf{P}}} ={delta }^{E}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}})}^{-1}\ {{bf{G}}}_{{bf{c}}}^{{bf{I}}} =sigma {delta }^{E}{delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}})}^{-1}\ {{bf{G}}}_{{bf{c}}}^{{bf{A}}} =(1-sigma ){delta }^{E}{delta }^{P}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}{({{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}})}^{-1}$$
(14)
are three spatially explicit generation matrices describing the contributions of post-latent infectious people, infectious symptomatic people, and asymptomatic/paucisymptomatic infectious people to the next generation of infections in a neighborhood of the DFE in the presence of disease-containment measures.In the absence of controls, i.e., if the isolation rates ({chi }_{i}^{X}) (X ∈ {E, P, I, A}), the transmission reductions ϵi, and the travel restrictions ξij are equal to zero for all i’s and j’s, then the control reproduction number ({{mathcal{R}}}_{{rm{c}}}) reduces to the basic reproduction number ({{mathcal{R}}}_{0}), defined as the average number of secondary infections produced by one infected individual in a population that is completely susceptible to the disease and where no containment measures are in place. ({{mathcal{R}}}_{0}) can be evaluated as the spectral radius of matrix GP + GI + GA, where$${{bf{G}}}^{{bf{P}}} ={delta }^{E}{{boldsymbol{theta }}}^{{bf{P}}}{({{boldsymbol{phi }}}^{{bf{E}}}{{boldsymbol{phi }}}^{{bf{P}}})}^{-1}\ {{bf{G}}}^{{bf{I}}} =sigma {delta }^{E}{delta }^{P}{{boldsymbol{theta }}}^{{bf{I}}}{({{boldsymbol{phi }}}^{{bf{E}}}{{boldsymbol{phi }}}^{{bf{P}}}{{boldsymbol{phi }}}^{{bf{I}}})}^{-1}\ {{bf{G}}}^{{bf{A}}} =(1-sigma ){delta }^{E}{delta }^{P}{{boldsymbol{theta }}}^{{bf{A}}}{({{boldsymbol{phi }}}^{{bf{E}}}{{boldsymbol{phi }}}^{{bf{P}}}{{boldsymbol{phi }}}^{{bf{A}}})}^{-1}.$$
(15)
In the previous set of expressions, ϕX (X ∈ {E, P, I, A}) are diagonal matrices whose non-zero elements are μ + δE (for ϕE), μ + δP (for ϕP), μ + α + η + γI (for ϕI), and μ + γA (for ϕA), while matrices θX (X ∈ {P, I, A}) are given by ({bf{N}}{{bf{M}}}^{{bf{S}}}{{boldsymbol{beta }}}^{{bf{X}}}{({boldsymbol{Delta }})}^{-1}{({{bf{M}}}^{{bf{X}}})}^{T}), with ({{bf{M}}}^{{bf{X}}}=[{M}_{ij}^{X}]) (X ∈ {S, P, I, A}) and ({M}_{ij}^{X}={M}_{c,ij}^{X}) evaluated with ξij = 0 for all i’s and j’s, and Δ is a diagonal matrix whose non-zero entries are the elements of vector uNMS.Derivation of basic and control epidemicity indicesThe concept of epidemicity26 extends previous work24,25 where a reactivity index was defined and applied to study the transient dynamics of ecological systems characterized by steady-state behavior. To explain, in physical terms, the meaning of reactivity and of the Hermitian matrix used to derive it, consider a linear system dx/dt = Ax, where ({bf{x}}={({x}_{1},ldots ,{x}_{n})}^{T}) is the state vector and A is a n × n real state matrix. The system is subject to pulse perturbations x(0) = x0  > 0. Reactivity is defined as the gradient of the Euclidean norm (| | {bf{x}}| | =sqrt{{x}_{1}^{2}+cdots +{x}_{n}^{2}}=sqrt{{{bf{x}}}^{T}{bf{x}}}) of the state vector, evaluated for the fastest-growing initial perturbation, and corresponds to the spectral abscissa ({{{Lambda }}}_{max }^{{rm{Re}}}(cdot )) of the Hermitian part (A + AT)/2 of matrix A24. Following Mari et al.25, an asymptotically stable equilibrium is characterized by positive generalized reactivity if there exist small perturbations that can lead to a transient growth in the Euclidean norm of a suitable system output y = Wx, with matrix W describing a linear transformation of the system state.In epidemiological applications, W should include the variables of the infection subsystem26. Therefore, a suitable output transformation for the problem at hand is$${bf{W}}=left[begin{array}{llllllllll}{bf{0}}&{w}^{E}{bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{w}^{P}{bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{w}^{I}{bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}\ {bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{w}^{A}{bf{I}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}&{bf{0}}end{array}right],$$
(16)
where wE, wP, wI, wA are the weights assigned to the variables of the infection subsystem in the output ({bf{y}}=[{w}^{E}{E}_{1},ldots ,{w}^{E}{E}_{n},{w}^{P}{P}_{1},ldots ,{w}^{P}{P}_{n},{w}^{I}{I}_{1},ldots ,{w}^{I}{I}_{n},{w}^{A}{A}_{1},ldots ,{w}^{A}{A}_{n}]^{T}). Generalized reactivity for the DFE of system (Eq. (3)) is positive if the spectral abscissa of a suitable Hermitian matrix (either H0 or Hc, depending on whether the spread of disease is uncontrolled or some containment measures are in place) is also positive. In SEPIAR, the expressions of matrices H0 and Hc are far from trivial, as shown below, and the evaluation of spectral abscissae typically requires numerical techniques. Note also that, since recovered individuals are not accounted for in the system output, including waning immunity would not alter the epidemicity properties of the DFE.Let us consider the most general case of disease-containment measures being in place (which includes as a limit case also uncontrolled pathogen spread). If we note that (ker ({bf{W}})=ker ({bf{W}}{{bf{J}}}_{{bf{c}}})), with Jc being the Jacobian of SEPIAR at the DFE in the presence of controls, matrix Hc can be defined25,27 as the Hermitian part of WJc(W)+, i.e.,$${{bf{H}}}_{{bf{c}}}=H({bf{W}}{{bf{J}}}_{{bf{c}}}{({bf{W}})}^{+})=frac{1}{2}left{{bf{W}}{{bf{J}}}_{{bf{c}}}{({bf{W}})}^{+}+{[{({bf{W}})}^{+}]}^{T}{({{bf{J}}}_{{bf{c}}})}^{T}{({bf{W}})}^{T}right},$$
(17)
where (W)+ is the right pseudo-inverse (a generalization of the concept of inverse for non-square matrices) of W, and can be evaluated as$${({bf{W}})}^{+}={({bf{W}})}^{T}{[{bf{W}}{({bf{W}})}^{T}]}^{-1}.$$
(18)
Matrix$${{bf{H}}}_{{bf{c}}}=left[begin{array}{llll}-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{E}}}&frac{{w}^{P}}{2{w}^{E}}{delta }^{E}{bf{I}}+frac{{w}^{E}}{2{w}^{P}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&frac{{w}^{E}}{2{w}^{I}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&frac{{w}^{E}}{2{w}^{A}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}\ frac{{w}^{P}}{2{w}^{E}}{delta }^{E}{bf{I}}+frac{{w}^{E}}{2{w}^{P}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{P}}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{P}}}&frac{{w}^{I}}{2{w}^{P}}sigma {delta }^{P}{bf{I}}&frac{{w}^{A}}{2{w}^{P}}(1-sigma ){delta }^{P}{bf{I}}\ frac{{w}^{E}}{2{w}^{I}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{I}}}&frac{{w}^{I}}{2{w}^{P}}sigma {delta }^{P}{bf{I}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{I}}}&{bf{0}}\ frac{{w}^{E}}{2{w}^{A}}{{boldsymbol{theta }}}_{{bf{c}}}^{{bf{A}}}&frac{{w}^{A}}{2{w}^{P}}(1-sigma ){delta }^{P}{bf{I}}&{bf{0}}&-{{boldsymbol{phi }}}_{{bf{c}}}^{{bf{A}}}end{array}right]$$
(19)
is Hermitian, hence real and symmetric. Therefore all eigenvalues are real and the spectral abscissa ({e}_{{rm{c}}}={{{Lambda }}}_{max }^{{rm{Re}}}({{bf{H}}}_{{bf{c}}})) coincides with the largest eigenvalue, which corresponds to the fastest-growing perturbation in the system output. Thus, ec can be interpreted as a control epidemicity index: if ec  > 0, there must exist some small perturbations to the DFE that are temporarily amplified in the system output, thus generating a transient, subthreshold epidemic wave.Absent any containment measures, the control epidemicity index, ec, reduces to the basic epidemicity index, ({e}_{0}={{{Lambda }}}_{max }^{{rm{Re}}}({{bf{H}}}_{{bf{0}}})), where$${{bf{H}}}_{{bf{0}}}=H({bf{W}}{{bf{J}}}_{{bf{0}}}{({bf{W}})}^{+})=frac{1}{2}left{{bf{W}}{{bf{J}}}_{{bf{0}}}{({bf{W}})}^{+}+{[{({bf{W}})}^{+}]}^{T}{({{bf{J}}}_{{bf{0}}})}^{T}{({bf{W}})}^{T}right}$$
(20)
and the Jacobian matrix J0 can be obtained from Jc by setting equal to zero the isolation rates ({chi }_{i}^{X}) (X ∈ {E, P, I, A}), the transmission reductions ϵi, and the travel restrictions ξij for all i’s and j’s.The effective reproduction number and the effective epidemicity indexThe reproduction numbers and the epidemicity indices defined above can be rigorously applied only to characterize the spread of disease in a fully naïve population (Si = Ni ∀ i). As soon as the pathogen begins to circulate within the population, the state of the system gradually departs from the DFE. Under these circumstances, it is customary19,21 to define a time-dependent, effective reproduction number, ({mathcal{R}}(t)), to track the number of secondary infections caused by a single infectious individual in a population in which the pool of susceptible individuals is progressively depleted, and control measures are possibly in place58. Similarly, it is possible to define an effective epidemicity index, e(t), to evaluate the likelihood that transient epidemic waves may occur even if ({mathcal{R}}(t), More

The area of study (Fig. 6) was the Greater North Sea ecoregion, which includes the EEZs of six countries (England, Scotland, the Netherlands, Denmark, Norway and Germany). The Kattegat area, the English Channel, and the Belgium EEZ were omitted from the study area. The North Sea Marine Ecosystem is a large semi-closed continental sea situated on the continental shelf of North-western Europe, with a dominant physical division between the comparatively deep northern part (50–200 m, with the Norwegian Trench dropping to 700 m) and the shallower southern part (20–50 m)48. The North Sea is one of the most varied coastal regions in the world, which is characterised by, among others, rocky, fjord and mountainous shores as well as sandy beaches with dunes48. Apart from the marine seabirds feeding primarily in the coastal areas, under 5 km from the coast (e.g., terns, sea-ducks, grebes), the North Sea basin also hosts pelagic birds feeding further offshore, with some also diving for food (guillemot, razorbill, etc.). The North Sea basin is also a major habitat for four marine mammal species, of which the harbour porpoise and harbour seal are the most common. Moreover, fish ecology has been a widely studied topic, especially for commercial species, due to evidence of a decline in the fish stock, such as sprat, whiting, bib, and mackerel. Fish communities, and in particular the small pelagic fish group (such as European sprat, European pilchard), play also a key ecologic role, constituting the main pray for most piscivorous fishes, cetacean and seabirds49, Based on early surveys, the predominant species divided by the three North Sea fish communities are: saithe (43.6% in the shelf edge), haddock (42.4% in the central North Sea, 11.6% in the shelf edge), whiting (21.6% in the eastern North Sea, 13.9% central North Sea), and dab (21.8% in the eastern North Sea)34. More recent assessments of North Sea fish community are emphasizing the clear geographical distinction between the fish species living in the southern part of the North Sea, a shallow area with high primary production and pronounced seasonality, and northern part, a deeper area with lower primary production and lower seasonal variation in temperature and salinity. The southern North Sea fish community is represented by fish species such as lesser weever, while the northern North Sea fish community is represented by species such as saithe, with species like whitting, haddock representative for the North–West subdivision, and the European plaice having the highest abundance in the South–East community50. The future fish stock and spatial distribution is however uncertain due to impacts of climate change related factors (e.g., growing temperatures)49 and overexploitation.Figure 6Offshore wind farm prospects (existing/authorised/planned) in the North Sea basin.Full size imageThe most prominent human activities in the North Sea basin are fishing, coastal construction, maritime transport, oil and gas exploration and production, tourism, military, and OWF construction38. Within this list, the construction of OWFs has seen a rapid increase, aiming to reach a total cumulative installed capacity of 61.8–66.8 GW by 203051. As indicated in Fig. 6, the new designated/search/scoping areas for the location of future OWFs will significantly increase the current space reserved for the offshore production of renewable energy in the North Sea basin.Spatio-temporal database of OWF developments in the North Sea basinFor the input of the geo-spatial layers with the location of OWF areas we compiled a comprehensive spatial data repository in QGIS containing the shapefiles of analysed OWF, from 1999 to 2027 (last year of available official information on OWF development, Appendix D). The analysis was performed for the North Sea geographic area, referred here as the basin scale, taking into account the cumulative pressures from individual OWF projects (project scale). The main data sources for geospatial information for OWF, for the entire North Sea basin, are EMODnet (Human Activities data portal) and OSPAR, which were complemented by data on the country level, where needed; i.e. from Crown Estate Scotland (Energy infrastructure, Legal Agreements), Rijkswaterstaat for the Netherlands. From the available geo-spatial data for OWF, we selected the OWF in our area of study (Fig. 6) with the status of consent-authorised, authorised, pre-construction, under construction, or fully commissioned (operational). Therefore, planned OWF such as Vesterhavet Syd and Vesterhavet Nord, for which the start date of construction is still unknown, were not included in the analysis. Similarly, for the Horns Rev 3 OWF no geo-referenced spatial footprint was available in the open-access data sets, and therefore it was not included in the analysis.The collected OWF geospatial data was aggregated to create a geospatial database, for the studied period of 1999–2050, composed by the following attributes: code name, country, name, production capacity (MW), area (({mathrm{km}}^{2})), number of turbines, start operation (year), installation time, and status in the period 1999–2050 (construction, operation, decommissioning). The created geospatial dataset was additionally cross-checked for integrity with the information provided through the online platform 4coffshore.com.The lack of data regarding the construction time was complemented with the methodology proposed by Lacal-Arántegui et al.36. Based on this research, we calculated the time required for OWF construction phase related activities multiplying 1.06 days by the known production capacity (total MW) for each analysed OWF.The average time of operation is considered to be 20 years, probably profitably extendable to 25 years, as stated in a number of studies on the cycle of offshore wind farms52. For this case study, the operation time considered is 20 years (subject to change). Since there is little experience with the decommissioning of offshore wind farms (only a few OWFs have so far been decommissioned in the UK and Denmark), the decommissioning time is not yet clear. There are a number of parameters that influence the decommissioning time, which are: the number of turbines, the foundation type, the distance to port, etc. It is estimated that the time taken for decommissioning should be around 50–60% less than the installation time37. Our study considers the decommissioning time as 50% of the construction time.Time-aware cumulative effects assessmentIn this study, Tools4MSP53,54, a Python-based Free and Open Source Software (FOSS) for geospatial analysis in support of Maritime Spatial Planning and marine environmental management, was used for the assessment of the impacts of OWFs on the marine ecosystem, in the three development stages. We applied the Tools4MSP CEA module to the OWF of the North Sea basin for the period 1999–2050, taking into account the full life cycle of the OWF development, namely the construction, operation and decommissioning phases. The modified methodology from Menegon et al.31 and subsequent implementation55, proposes to calculate the CEA score for each cell of analysis as follows (Eqs. 1, 2):$$CEA=sum_{k=1}^{n}d({E}_{k}) sum_{j=1}^{m}{s}_{i,j} eff({P}_{j}{E}_{k})$$
(1)
where eff is the effect of pressure P over the environmental component E and is defined as follows:$$eff left({P}_{j}{E}_{k}right)=(sum_{i=1}^{l}{w}_{i,j} i({U}_{i},{M}_{i,j,k})){^{prime}}$$
(2)
whereas,

({U}_{i}) defines the human activity, namely the OWF activity in the study area

({E}_{k}) defines the environmental components of the study area described in the Table 1

({d(E}_{k})) defines intensity or presence/absence of the k-th environmental component

({P}_{j}) defines the pressures exerted by human activities dependent on the three different OWF development phases (Annex B)

({w}_{i,j}) refers to the specific pressure weight according to the OWF phase

({s(P}_{j}, {E}_{k})) is the sensitivity of the k-th environmental component to the j-th pressure

({i({U}_{i, }M({U}_{i, }P}_{j}, {E}_{k}))) is the distance model propagating j-th pressure caused by i-th activity over the k-th environmental component

({M(U}_{i}, {P}_{j})) is the 2D Gaussian kernel function used for convolution, which considers buffer distances at 1 km, 5 km, 10 km, 20 km, and 50 km56.

Table 1 Primary sources for the environmental component data sets.Full size tableIn Eq. (3), the CEA 1999–2050 describes the modelling over the time frame 1999–2050, whereas ({CEA}_{t}) is the cumulative effect of year t within the timeframe 1999–2050:$${CEA}_{1999-2050}= sum_{t=1999}^{2050}{CEA}_{t}$$In this study, each final CEA score was normalised. To normalise the value of each initial CEA score obtained using the Eq. (1), we calculated its percentage of the sum of all CEA scores for all OWFs in the three development phases, period spanning the period 1999–2050 (({CEA}_{1999-2050})).Environmental componentsThe selection of the environmental components (receptors) impacted by the identified pressures is an essential part of the scoping phase for OWF location, as monitoring the status (distribution, abundance) of different identified species represents a relevant indicator for the ecosystem status. For the evaluation of the habitats and species that can be affected by the cumulative ecological effects of OWF, we adapted the methodology of Meissl et al.14. Therefore, we selected the environmental components based first on their: (1) ecological value, supported by legal documents identifying species protected by law or through various national and international agreements (e.g. EU Habitats Directive, Wild Mammals (Protection) Act (UK), see Table 1 in Appendix E), to which we added species with (2) commercial value, but also with a (3) broad geographic-scale habitat occurrence of the species in the studied area, based on previous studies35 and on 35 EIA studies for OWF in the North Sea basin.Among the five fish species selected, sprat and sandeel play key roles in the marine food web (small pelagic fish), as prey source for piscivorous fish, cetacean and birds. The ecological value of sandeel, sprat, whiting and saither is also highlighted through EU or national protection agreements such as Priority Marine Features—PMF or Scottish/UK Biodiversity list (see Appendix E, Table 2). The list is completed by haddock, one of the fish species with commercial importance, highly dominant in the Central North Sea. With regards to the spatial occurrence at the basin level, the fish species selected are representative for both of the two distinct North Sea communities50, the southern part of the North Sea (sprat), and the northern and north-west part (haddock, whiting, saithe).The three selected seabird species are of ecological importance for the marine ecosystem, as indicated through the European, national and international protection agreements, such as the EU Birds Directive Migratory Species or the IUCN Red List (see Appendix E, Table 1). While razorbill and guillemot have similar feeding and flying patterns (low flight, catch pray underwater), there is evidence of different behaviors towards OWFs, with relatively more avoidance from razorbill compared to guillemot. In relation to the spatial distribution of the three selected species, there is a clear distinction between razorbill, highly present in the coastal areas of west North Sea basin, guillemot, with a relatively even distribution across the marine basin, and fulmar, one of the 4 most common seabirds in the studied area, in particular in the central and N–E parts.In the marine mammals category we selected the harbor porpoise, indicated to be one of the most impacted species in this category57, with a high occurrence in the North Sea basin. Its ecological value is emphasized by its presence in European and international lists for habitat protection, such as EU Habitats Directive58, OSPAR List of Threatened and/or Declining Species59, the Agreement on the Conservation of Small Cetaceans in the Baltic and the North Seas (ASCOBANS)60. The harbor porpoise is the protected species in numerous Natura 2000 areas in the North Sea basin, such as the Spatial Area of Conservation Southern North Sea61 (British EEZ) or The Special area of Protection Kleverbank62 (Dutch EEZ).Among the selected fish species, sandeel had the highest occurrence in EIA studies of OWF developments (23 out of 35), while guillemot had the highest occurrence among seabird species (25 out of 35). With an occurrence of 26 out of the 35 analysed EIA document, the harbour porpoise is the most studied mammal in relation to the impact of OWF.As a result, we selected three EUNIS marine seabed habitat types (European Union Nature Information System)58 (Appendix E, Table 2), three seabird species, one mammal species and five fish species (Appendix E, Table 1). The list can be extended; however, for this exercise we considered it sufficient.The data sets used to represent the spatial distribution (presence/absence, intensity) of the environmental components in the studied area were obtained from multiple sources and were used in the Tools4MSP model either directly (EUNIS habitats, marine mammals, seabirds) or further processed using a predictive distribution model (fish species). In the case of EUNIS marine habitats, the data source was the online geo-portal EMODnet, through the Seabed Habitat service (Table 1), which provided GIS polygon layers for each habitat type and was further used to indicate presence/absence of a specific habitat.For the distribution of the selected mammal species, the harbour porpoise, we used the modelling results of Waggit et al.16, translated into maps for the prediction of densities (nr. animals/({mathrm{km}}^{2})). The mapping approach starts with collating data from available surveys, which are further standardised with regards to transect length, number of platform sides, and the effective strip width. Finally, the standardised data sets were used in a binomial and a Poisson model, in association with environmental conditions (Table 1), in order to deliver a homogenous cover of species distribution maps, on 10 km × 10 km spatial resolution grid16.For the distribution of the selected seabird species (razorbill, fulmar, guillemot), we used the results of the SEAPOP program (http://www.seapop.no/en/distribution-status/), through the open-source data portal (https://www2.nina.no/seapop/seapophtml/). The proposed methodology for creating the occurrence density prediction maps, on a 10 × 10 km spatial resolution grid, starts with the modelling of the presence/absence of birds using a binomial distribution and “logit link”. This was followed by the modelling of the number of birds using a Gamma distribution with a “log link” function, which also took into account geographically fixed explanatory variables (geographic position, water depth, and distance to coast).The predictive model for the spatial distribution of fish species biomass (haddock, sandeel, whiting, saithe, sprat) was developed using AI4Blue software, an open-source, python-based library for Artificial Intelligence based geospatial analysis of Blue Growth settings (AI4Blue, 2021)63. The model was based on two types of inputs: (1) the observation data on the presence of species and (2) data on the absence of species (absence data) for the period 2000–2019. Both data types were extracted by the ICES North Sea International Bottom Trawl Survey (NSI-IBTS, extracted survey year 2000–2019 including all available quarters) for commercial fish species, which was accessed on the online ICES-DATRAS database64. Data was extracted using two DATRAS web service Application Programming Interfaces (APIs): (1) the HHData, that returns detailed haul-based meta-data of the survey (e.g. haul position, sampling method etc.) and (2) the CPUEPerLengthPerHaulPerHour for the catch/unit of effort per length of sampled species.The presence data were represented by the catch/unit of effort (CPUE), expressed in kg of biomass of the specified species per one hour of hauling. The biomass was estimated by using the SAMLK (sex-maturity-age-length keys) dataset for ICES standard species. This approach is a viable alternative to presence-only data models, as it tackles the biased outcomes resulting from an non-uniform marine coverage of the data sets (mainly along the shipping routes)65. The absence data were estimated using the methodology presented by Coro et al.65, which detects absence location for the chosen species as the locations in which repeated surveys (with the selected species on the survey’s species target list) report information only on other species.Additionally, the predictive model automatically correlates the presence/absence data with environmental conditions (Appendix E, Table 3) data to more accurately estimate the likelihood of species presence in the North Sea basin. Intersecting a large number of surveys containing observation data on the presence of selected species can return the true absence data locations, which represent a valuable indicator for geographical areas with unsuitable habitat (see methodology by Coro et al.65). Those locations were estimated from abiotic and biotic parameters and differed to the sampling absences which were estimated from surveys without presence data65. The environmental conditions (Appendix E, Table 2) data were accessed through direct queries using the MOTU Client option from the Marine Copernicus database. In order to input the layers to the CEA calculation, the input layer for the biomass was transformed using log[x + 1] to avoid an over-dominance of extreme values and all datasets rescaled from 0 to 1 in order to allow direct comparison on a single, unit-less scale55.The rescaled special distribution of biomass for the selected species are presented in Appendix F (Fig. a–j).OWF pressures and relative weightsA systematic literature review was conducted to reach a first quantification of the OWF pressure weights (({w}_{i,j}),) in the construction, operation, and decommissioning phases (({U}_{i})). The OWF-related pressures specific to each of the phases of the OWF life cycle were based on the comprehensive analysis of all the existing Environmental Impact Assessment (EIA) methodologies used in the North Sea countries14. The review enabled the collection of 18 pressures that were subsequently compared and merged with the pressures established in the Marine Strategy Framework Directive, applied by the EU countries in the assessment of environmental impacts66. Figure 7 illustrates the impact chain linking the three OWF development phases with the exerted 18 pressures and the 12 selected environmental components impacted.Figure 7Impact chain defining OWF phases-pressure-environmental components analysed in the North Sea (the strength of the link between pressures and environmental components is proportional to the sensitivity scores. The order is descending from the pressures with highest impact, as well as from the environmental components most affected).Full size imageSensitivity in this research is defined as the likelihood of change when a pressure is applied to a receptor (environmental component) and is a function of the ability of the receptor to adapt, tolerate or resist change and its ability to recover from the impact67. The criteria for assessing the sensitivities of environmental components is based on MarLIN (Marine Life Information Network) detailed criteria (https://www.marlin.ac.uk/sensitivity/sensitivity_rationale).We validated the weights of pressures (({w}_{i,j}) from 0 to 5) and scores of environmental components sensitivities (({s(P}_{j}, {E}_{k})) from 0 to 5), as well as the distance of pressure propagation (≤1000 m to ≥ 25,000 m), through a series of 4 questionnaires for the marine mammals, seabirds, fish and seabed habitats. The compiled questionnaires were further validated through semi-interviews of 9 experts in the field of marine ecology, spatial planning, environmental impact assessment and offshore wind energy development. The expert-based questionnaires also included a confidence level for the proposed scores, which ranged between 0.2 (very low confidence: based on expert judgement; proxy assessment) and 1 (very high confidence: based on peer reviewed papers, report, assessment on the same receptor). The confidence level was used in determining the final scores for the pressure weights and species sensitivities. The final scores for weights and sensitivity scores were identified either by calculating the mean value (for cases where literature review scores and expert scores differed by  > 2 units) or selecting the higher value—precautionary principle (for cases where scores from different sources differed by  More

1.Capella-Gutiérrez, S., Marcet-Houben, M. & Gabaldon, T. Phylogenomics supports microsporidia as the earliest diverging clade of sequenced fungi. BMC Biol. 10, 47. https://doi.org/10.1186/1741-7007-10-47 (2012).Article 
PubMed 
PubMed Central 

Google Scholar 
2.Corsaro, D. et al. Filling gaps in the microsporidian tree: rDNA phylogeny of Chytridiopsis typographi (Microsporidia: Chytridiopsida). Parasitol. Res. 118, 169–180. https://doi.org/10.1007/s00436-018-6130-1 (2019).Article 
PubMed 

Google Scholar 
3.Corsaro, D. et al. Molecular identification of Nucleophaga terricolae sp. nov. (Rozellomycota), and new insights on the origin of the Microsporidia. Parasitol. Res. 115, 3003–3011 (2016).Article 

Google Scholar 
4.James, T. Y. et al. Reconstructing the early evolution of Fungi using a six-gene phylogeny. Nature 443, 818–822 (2006).ADS 
CAS 
Article 

Google Scholar 
5.Sprague, V. & Becnel, J. J. in The Microsporidia and Microsporidiosis (eds M. Wittner & L. M. Weiss) 517–530 (ASM Press, 1999).6.Dunn, A. M., Terry, R. S. & Smith, J. E. Transovarial transmission in the microsporidia. Adv. Parasitol. 48, 57–100. https://doi.org/10.1016/S0065-308X(01)48005-5 (2001).CAS 
Article 
PubMed 

Google Scholar 
7.Goertz, D. & Hoch, G. Vertical transmission and overwintering of Microsporidia in the gypsy moth, Lymantria dispar. J. Invertebr. Pathol. 99, 43–48. https://doi.org/10.1016/j.jip.2008.03.008 (2008).Article 
PubMed 

Google Scholar 
8.Becnel, J. J. & Andreadis, T. G. in Microsporidia: Pathogens of Opportunity (eds L. M. Weiss & J. J. Becnel) 521–570 (Wiley, 2014).9.Kellen, W. R. & Lindegren, J. E. Modes of transmission of Nosema plodiae Kellen and Lindegren, a pathogen of Plodia interpunctella (Hübner). J. Stored Prod. Res. 7, 31–34. https://doi.org/10.1016/0022-474X(71)90035-X (1971).Article 

Google Scholar 
10.Vávra, J. & Larsson, R. J. in Microsporidia: Pathogens of Opportunity (eds L. M. Weiss & J. J. Becnel) 1–70 (Wiley, 2014).11.Mudasar, M., Mathivanan, V., Shah, G. N., Mir, G. M. & Selvisabhanayakam, M. Nosemosis and its effect on performance of honey bees: A review. Int. J. Pharm. Bio. Sci. 4, 923–937 (2013).
Google Scholar 
12.Wolf, S. et al. So near and yet so far: Harmonic radar reveals reduced homing ability of Nosema infected honeybees. PLoS ONE 9, e103989. https://doi.org/10.1371/journal.pone.0103989 (2014).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
13.Naug, D. & Gibbs, A. Behavioral changes mediated by hunger in honeybees infected with Nosema ceranae. Apidologie 40, 595–599 (2009).Article 

Google Scholar 
14.Dussaubat, C. et al. Flight behavior and pheromone changes associated to Nosema ceranae infection of honey bee workers (Apis mellifera) in field conditions. J. Invertebr. Pathol. 113, 42–51 (2013).CAS 
Article 

Google Scholar 
15.Goblirsch, M., Huang, Z. Y. & Spivak, M. Physiological and behavioral changes in honey bees (Apis mellifera) induced by Nosema ceranae infection. PLoS ONE 8, 6 (2013).
Google Scholar 
16.Lipsitch, M., Nowak, M. A., Ebert, D. & May, R. M. The population dynamics of vertically and horizontally transmitted parasites. Proc. R. Soc. Lond. B 260, 321–327. https://doi.org/10.1098/rspb.1995.0099 (1995).ADS 
CAS 
Article 

Google Scholar 
17.Goertz, D., Solter, L. F. & Linde, A. Horizontal and vertical transmission of a Nosema sp. (Microsporidia) from Lymantria dispar (L.) (Lepidoptera: Lymantriidae). J. Invertebr. Pathol. 95, 9–16. https://doi.org/10.1016/j.jip.2006.11.003 (2007).Article 
PubMed 

Google Scholar 
18.Kellen, W. R., Chapman, H. C., Clark, T. B. & Lindegren, J. E. Host-parasite relationships of some Thelohania from mosquitoes (Nosematidae: Microsporidia). J. Invertebr. Pathol. 7, 161–166. https://doi.org/10.1016/0022-2011(65)90030-3 (1965).CAS 
Article 
PubMed 

Google Scholar 
19.Dunn, A. M. & Smith, J. E. Microsporidian life cycles and diversity: the relationship between virulence and transmission. Microbes Infect. 3, 381–388. https://doi.org/10.1016/S1286-4579(01)01394-6 (2001).CAS 
Article 
PubMed 

Google Scholar 
20.Terry, R. S. et al. Widespread vertical transmission and associated host sex–ratio distortion within the eukaryotic phylum Microspora. Proc. R. Soc. Lond. B 271, 1783–1789. https://doi.org/10.1098/rspb.2004.2793 (2004).Article 

Google Scholar 
21.Mercer, C. & Wigley, P. A microsporidian pathogen of the poroporo stem borer, Sceliodes cordalis (Dbld)(Lepidoptera: Pyralidae): Effects on adult reproductive success. J. Invertebr. Pathol. 49, 108–115. https://doi.org/10.1016/0022-2011(87)90132-7 (1987).Article 

Google Scholar 
22.Bauer, L. S. & Nordin, G. L. Effect of Nosema fumiferanae (Microsporida) on fecundity, fertility, and progeny performance of Choristoneura fumiferana (Lepidoptera: Tortricidae). Environ. Entomol. 18, 261–265. https://doi.org/10.1093/ee/18.2.261 (1989).Article 

Google Scholar 
23.Futerman, P. et al. Fitness effects and transmission routes of a microsporidian parasite infecting Drosophila and its parasitoids. Parasitology 132, 479–492. https://doi.org/10.1017/S0031182005009339 (2006).CAS 
Article 
PubMed 

Google Scholar 
24.Goertz, D., Golldack, J. & Linde, A. Two different and sublethal isolates of Nosema lymantriae (Microsporidia) reduce the reproductive success of their host, Lymantria dispar. Biocontrol Sci. Technol. 18, 419–430. https://doi.org/10.1080/09583150801993212 (2008).Article 

Google Scholar 
25.Lockwood, J. A., Bomar, C. R. & Ewen, A. B. The history of biological control with Nosema locustae: Lessons for locust management. Int. J. Trop. Insect Sci. 19, 333–350. https://doi.org/10.1017/S1742758400018968 (1999).Article 

Google Scholar 
26.Kiritani, K. & Yamamura, K. in Invasive Species: Vectors and Management Strategies. (ed J. Carlton) 44–67 (Island Press, 2003).27.Walsh, D. B. et al. Drosophila suzukii (Diptera: Drosophilidae): invasive pest of ripening soft fruit expanding its geographic range and damage potential. J. Integr. Pest Manage. 2, G1–G7. https://doi.org/10.1603/IPM10010 (2011).Article 

Google Scholar 
28.Cini, A., Ioriatti, C. & Anfora, G. A review of the invasion of Drosophila suzukii in Europe and a draft research agenda for integrated pest management. Bull. Insectol. 65, 149–160 (2012).
Google Scholar 
29.Tochen, S. et al. Temperature-related development and population parameters for Drosophila suzukii (Diptera: Drosophilidae) on cherry and blueberry. Environ. Entomol. 43, 501–510. https://doi.org/10.1603/en13200 (2014).Article 
PubMed 

Google Scholar 
30.Chabert, S., Allemand, R., Poyet, M., Eslin, P. & Gibert, P. Ability of European parasitoids (Hymenoptera) to control a new invasive Asiatic pest, Drosophila suzukii. Biol. Control 63, 40–47. https://doi.org/10.1016/j.biocontrol.2012.05.005 (2012).Article 

Google Scholar 
31.Gabarra, R., Riudavets, J., Rodríguez, G., Pujade-Villar, J. & Arnó, J. Prospects for the biological control of Drosophila suzukii. Biocontrol 60, 331–339. https://doi.org/10.1007/s10526-014-9646-z (2015).Article 

Google Scholar 
32.Cuthbertson, A. G. S. & Audsley, N. Further screening of entomopathogenic fungi and nematodes as control agents for Drosophila suzukii. Insects 7, 24. https://doi.org/10.3390/insects7020024 (2016).Article 
PubMed Central 

Google Scholar 
33.Woltz, J. M., Donahue, K. M., Bruck, D. J. & Lee, J. C. Efficacy of commercially available predators, nematodes and fungal entomopathogens for augmentative control of Drosophila suzukii. J. Appl. Entomol. 139, 759–770. https://doi.org/10.1111/jen.12200 (2015).Article 

Google Scholar 
34.Haye, T. et al. Current SWD IPM tactics and their practical implementation in fruit crops across different regions around the world. J. Pest. Sci. 89, 643–651. https://doi.org/10.1007/s10340-016-0737-8 (2016).Article 

Google Scholar 
35.Biganski, S., Jehle, J. A. & Kleespies, R. G. Bacillus thuringiensis serovar israelensis has no effect on Drosophila suzukii Matsumura. J. Appl. Entomol. 142, 33–36. https://doi.org/10.1111/jen.12415 (2018).CAS 
Article 

Google Scholar 
36.Carrau, T., Hiebert, N., Vilcinskas, A. & Lee, K.-Z. Identification and characterization of natural viruses associated with the invasive insect pest Drosophila suzukii. J. Invertebr. Pathol. 154, 74–78. https://doi.org/10.1016/j.jip.2018.04.001 (2018).CAS 
Article 
PubMed 

Google Scholar 
37.Medd, N. C. et al. The virome of Drosophila suzukii, an invasive pest of soft fruit. BioRxiv 4, 190322. https://doi.org/10.1093/ve/vey009 (2017).Article 

Google Scholar 
38.Kaur, R., Siozios, S., Miller, W. J. & Rota-Stabelli, O. Insertion sequence polymorphism and genomic rearrangements uncover hidden Wolbachia diversity in Drosophila suzukii and D. subpulchrella. Sci. Rep. 7, 14815. https://doi.org/10.1038/s41598-017-13808-z (2017).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
39.Biganski, S. et al. Molecular and morphological characterisation of a novel microsporidian species, Tubulinosema suzukii, infecting Drosophila suzukii (Diptera: Drosophilidae). J. Invertebr. Pathol. 107440 (2020).40.Anderson, R. M. & May, R. M. Coevolution of hosts and parasites. Parasitology 85, 411–426. https://doi.org/10.1017/S0031182000055360 (1982).Article 
PubMed 

Google Scholar 
41.Aigaki, T. & Ohba, S. Effect of mating status on Drosophila virilis lifespan. Exp. Gerontol. 19, 267–278. https://doi.org/10.1016/0531-5565(84)90022-6 (1984).CAS 
Article 
PubMed 

Google Scholar 
42.Partridge, L., Green, A. & Fowler, K. Effects of egg-production and of exposure to males on female survival in Drosophila melanogaster. J. Insect Physiol. 33, 745–749. https://doi.org/10.1016/0022-1910(87)90060-6 (1987).Article 

Google Scholar 
43.Bretman, A., Westmancoat, J. D., Gage, M. J. & Chapman, T. Costs and benefits of lifetime exposure to mating rivals in male Drosophila melanogaster. Evolution 67, 2413–2422. https://doi.org/10.1111/evo.12125 (2013).Article 
PubMed 

Google Scholar 
44.Armstrong, E. & Bass, L. K. Nosema kingi: Effects on fecundity, fertility, and longevity of Drosophila melanogaster. J. Exp. Zool. 250, 82–86. https://doi.org/10.1002/jez.1402500111 (1989).Article 

Google Scholar 
45.Armstrong, E. Transmission and infectivity studies on Nosema kingi in Drosophila willistoni and other Drosophilids. Z. Parasitenkd. 50, 161–165. https://doi.org/10.1007/BF00380520 (1976).Article 

Google Scholar 
46.Armstrong, E., Bass, L., Staker, K. & Harrell, L. A comparison of the biology of a Nosema in Drosophila melanogaster to Nosema kingi in Drosophila willistoni. J. Invertebr. Pathol. 48, 124–126. https://doi.org/10.1016/0022-2011(86)90151-5 (1986).Article 

Google Scholar 
47.Vijendravarma, R. K., Godfray, H. C. J. & Kraaijeveld, A. R. Infection of Drosophila melanogaster by Tubulinosema kingi: Stage-specific susceptibility and within-host proliferation. J. Invertebr. Pathol. 99, 239–241. https://doi.org/10.1016/j.jip.2008.02.014 (2008).Article 
PubMed 

Google Scholar 
48.Niehus, S., Giammarinaro, P., Liégeois, S., Quintin, J. & Ferrandon, D. Fly culture collapse disorder: Detection, prophylaxis and eradication of the microsporidian parasite Tubulinosema ratisbonensis infecting Drosophila melanogaster. Fly 6, 193–204. https://doi.org/10.4161/fly.20896 (2012).CAS 
Article 
PubMed 

Google Scholar 
49.Franchet, A., Niehus, S., Caravello, G. & Ferrandon, D. Phosphatidic acid as a limiting host metabolite for the proliferation of the microsporidium Tubulinosema ratisbonensis in Drosophila flies. Nat Microbiol 4, 645–655 (2019).CAS 
Article 

Google Scholar 
50.Robertson, F. W. & Sang, J. H. The ecological determinants of population growth in a Drosophila culture. I. Fecundity of adult flies. Proc. R. Soc. Lond. B 132, 258–277. https://doi.org/10.1098/rspb.1944.0017 (1944).ADS 
Article 

Google Scholar 
51.Vijendravarma, R. K., Kraaijeveld, A. R. & Godfray, H. C. J. Experimental evolution shows Drosophila melanogaster resistance to a microsporidian pathogen has fitness costs. Evolution 63, 104–114. https://doi.org/10.1111/j.1558-5646.2008.00516.x (2009).Article 
PubMed 

Google Scholar 
52.Rousset, F., Bouchon, D., Pintureau, B., Juchault, P. & Solignac, M. Wolbachia endosymbionts responsible for various alterations of sexuality in arthropods. Proc. R. Soc. Lond. B 250, 91–98. https://doi.org/10.1098/rspb.1992.0135 (1992).ADS 
CAS 
Article 

Google Scholar 
53.Saeed, N., Battisti, A., Martinez-Sañudo, I. & Mori, N. Combined effect of temperature and Wolbachia infection on the fitness of Drosophila suzukii. Bull. Insectol. 71, 161–169 (2018).
Google Scholar 
54.Hamm, C. A. et al. Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella. Mol. Ecol. 23, 4871–4885. https://doi.org/10.1111/mec.12901 (2014).Article 
PubMed 
PubMed Central 

Google Scholar 
55.Mazzetto, F., Gonella, E. & Alma, A. Wolbachia infection affects female fecundity in Drosophila suzukii. Bull. Insectol. 68, 153–157 (2015).
Google Scholar 
56.Hurst, G. D., Johnson, A. P., vd Schulenburg, J. H. G. & Fuyama, Y. Male-killing Wolbachia in Drosophila: a temperature-sensitive trait with a threshold bacterial density. Genetics 156, 699–709 (2000).57.Markow, T. A. Parents without partners: Drosophila as a model for understanding the mechanisms and evolution of parthenogenesis. G3 3, 757–762. https://doi.org/10.1534/g3.112.005421 (2013).CAS 
Article 
PubMed 

Google Scholar 
58.Wolfner, M. F. The gifts that keep on giving: physiological functions and evolutionary dynamics of male seminal proteins in Drosophila. Heredity 88, 85–93. https://doi.org/10.1038/sj.hdy.6800017 (2002).CAS 
Article 
PubMed 

Google Scholar 
59.Blaser, M. & Schmid-Hempel, P. Determinants of virulence for the parasite Nosema whitei in its host Tribolium castaneum. J. Invertebr. Pathol. 89, 251–257. https://doi.org/10.1016/j.jip.2005.04.004 (2005).Article 
PubMed 

Google Scholar 
60.Solter, L. F. in Microsporidia: Pathogens of Opportunity (eds L. M. Weiss & J. J. Becnel) 165–194 (Wiley, 2014).61.Eberle, K. E., Wennmann, J. T., Kleespies, R. G. & Jehle, J. A. in Manual of Techniques in Invertebrate Pathology (ed L. A. Lacey) 15–74 (Academic Press, 2012).62.Hughes, P. & Wood, H. A synchronous peroral technique for the bioassay of insect viruses. J. Invertebr. Pathol. 37, 154–159. https://doi.org/10.1016/0022-2011(81)90069-0 (1981).Article 

Google Scholar 
63.Abbott, W. A method of computing the effectiveness of an insecticide. J. Econ. Entomol. 18, 265–267 (1925).CAS 
Article 

Google Scholar 
64.Software for the statistical analysis of biotests (ToxRat GmbH, Alsdorf, Germany, 2003).65.Pan, G. et al. Invertebrate host responses to microsporidia infections. Dev. Comp. Immunol. 83, 104–113. https://doi.org/10.1016/j.dci.2018.02.004 (2018).Article 
PubMed 

Google Scholar 
66.Roxström-Lindquist, K., Terenius, O. & Faye, I. Parasite-specific immune response in adult Drosophila melanogaster: A genomic study. EMBO Rep. 5, 207–212. https://doi.org/10.1038/sj.embor.7400073 (2004).CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
67.Kraaijeveld, A. R. & Godfray, H. C. J. Selection for resistance to a fungal pathogen in Drosophila melanogaster. Heredity 100, 400–406. https://doi.org/10.1038/sj.hdy.6801092 (2008).CAS 
Article 
PubMed 

Google Scholar  More

1.Seeley, T. D. Honey bee colonies are group-level adaptive units. Am. Nat. 150, S22–S41 (1997).PubMed 
Article 

Google Scholar 
2.Negroni, M. A., Jongepier, E., Feldmeyer, B., Kramer, B. H. & Foitzik, S. Life history evolution in social insects: A female perspective. Curr. Opin. Insect Sci. 16, 51–57 (2016).PubMed 
Article 

Google Scholar 
3.Wilson, E. O. The Insect Societies. (Belknap Press, 1971).4.Boomsma, J. J., Huszár, D. B. & Pedersen, J. S. The evolution of multiqueen breeding in eusocial lineages with permanent physically differentiated castes. Anim. Behav. 92, 241–252 (2014).Article 

Google Scholar 
5.Ratnieks, F. L. W., Vetter, R. S. & Visscher, P. K. A polygynous nest of Vespula pensylvanica from California with a discussion of possible factors influencing the evolution of polygyny in Vespula. Insect. Soc. 43, 401–410 (1996).Article 

Google Scholar 
6.Wilson, E. E., Mullen, L. M. & Holway, D. A. Life history plasticity magnifies the ecological effects of a social wasp invasion. Proc. Natl. Acad. Sci. USA. 106, 12809–12813 (2009).ADS 
CAS 
PubMed 
Article 

Google Scholar 
7.Gambino, P. Reproductive plasticity of Vespula pensylvanica (Hymenoptera: Vespidae) on Maui and Hawaii Islands, USA. N. Z. J. Zool. 18, 139–149 (1991).Article 

Google Scholar 
8.Hanna, C. et al. Colony social structure in native and invasive populations of the social wasp Vespula pensylvanica. Biol. Invasions 16, 283–294 (2014).Article 

Google Scholar 
9.Ross, K. G. & Matthews, R. W. Two polygynous overwintered Vespula squamosa colonies from the southeastern US (Hymenoptera: Vespidae). Florida Entomol. 65, 176–184 (1982).Article 

Google Scholar 
10.Visscher, P. K. & Vetter, R. S. Annual and multi-year nests of the western yellowjacket, Vespula pensylvanica, in California. Insect. Soc. 50, 160–166 (2003).Article 

Google Scholar 
11.Plunkett, G. M., Moller, H., Hamilton, C., Clapperton, B. K. & Thomas, C. D. Overwintering colonies of German (Vespula germanica) and common wasps (Vespula vulgaris) (Hymenoptera: Vespidae) in New Zealand. N. Z. J. Zool. 16, 345–353 (1989).Article 

Google Scholar 
12.Goodisman, M. A., Matthews, R. W., Spradbery, J. P., Carew, M. E. & Crozier, R. H. Reproduction and recruitment in perennial colonies of the introduced wasp Vespula germanica. J. Hered. 92, 346–349 (2001).CAS 
PubMed 
Article 

Google Scholar 
13.Gambino, P. & Loope, L. L. Yellowjacket (Vespula pensylvanica): Biology and abatement in the National Parks of Hawaii.  Technical report of the Cooperatuve National Parks Resources Study Unit, Honolulu (1992).14.Wilson, E. E. & Holway, D. A. Multiple mechanisms underlie displacement of solitary Hawaiian Hymenoptera by an invasive social wasp. Ecology 91, 3294–3302 (2010).CAS 
PubMed 
Article 

Google Scholar 
15.Wilson Rankin, E. E. Diet subsidies and climate may contribute to Vespula invasion impacts. In 17th Congress of the International Union for the Study of Social Insects (IUSSI), Cairns, Australia, 13-18 July 2014 (2014).16.Seeley, T. D. & Tarpy, D. R. Queen promiscuity lowers disease within honeybee colonies. Proc. R. Soc. B Biol. Sci. 274, 67–72 (2007).Article 

Google Scholar 
17.Berthoud, H., Imdorf, A., Haueter, M., Radloff, S. & Neumann, P. Virus infections and winter losses of honey bee colonies (Apis mellifera). J. Apic. Res. 49, 60–65 (2010).Article 

Google Scholar 
18.Otti, O. & Schmid-Hempel, P. A field experiment on the effect of Nosema bombi in colonies of the bumblebee Bombus terrestris. Ecol. Entomol. 33, 577–582 (2008).Article 

Google Scholar 
19.Cremer, S., Pull, C. D. & Fürst, M. A. Social immunity: Emergence and evolution of colony-level disease protection. Annu. Rev. Entomol. 63, 105–123 (2018).CAS 
PubMed 
Article 

Google Scholar 
20.Graystock, P., Yates, K., Darvill, B., Goulson, D. & Hughes, W. O. H. Emerging dangers: Deadly effects of an emergent parasite in a new pollinator host. J. Invertebr. Pathol. 114, 114–119 (2013).PubMed 
Article 

Google Scholar 
21.Fürst, M. A., McMahon, D. P., Osborne, J. L., Paxton, R. J. & Brown, M. J. F. Disease associations between honeybees and bumblebees as a threat to wild pollinators. Nature 506, 364–366 (2014).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
22.McMahon, D. P. et al. A sting in the spit: widespread cross-infection of multiple RNA viruses across wild and managed bees. J. Anim. Ecol. 84, 615–624 (2015).PubMed 
PubMed Central 
Article 

Google Scholar 
23.Alger, S. A., Alexander Burnham, P., Boncristiani, H. F. & Brody, A. K. RNA virus spillover from managed honeybees (Apis mellifera) to wild bumblebees (Bombus spp.). PLoS One 14, 1–13 (2018).24.Dobelmann, J. et al. Fitness in invasive social wasps: The role of variation in viral load, immune response and paternity in predicting nest size and reproductive output. Oikos 126, 1208–1218 (2017).CAS 
Article 

Google Scholar 
25.Torchin, M. E., Lafferty, K. D., Dobson, A. P., McKenzie, V. J. & Kuris, A. M. Introduced species and their missing parasites. Nature 421, 628–630 (2003).ADS 
CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
26.Lester, P. J. et al. No evidence of enemy release in pathogen and microbial communities of common wasps (Vespula vulgaris) in their native and introduced range. PLoS One 10, e0121358 (2015).27.Mordecai, G. J. et al. Moku virus; a new Iflavirus found in wasps, honey bees and Varroa. Sci. Rep. 6, srep34983 (2016).28.Loope, K. J., Baty, J. W., Lester, P. J. & Wilson Rankin, E. E. Pathogen shifts in a honeybee predator following the arrival of the Varroa mite. Proc. R. Soc. B Biol. Sci. 286 (2019).29.Brettell, L. E., Schroeder, D. C. & Martin, S. J. RNAseq analysis reveals virus diversity within hawaiian apiary insect communities. Viruses 11 (2019).30.Moret, Y. & Schmid-Hempel, P. Immune responses of bumblebee workers as a function of individual and colony age: Senescence versus plastic adjustment of the immune function. Oikos 118, 371–378 (2009).Article 

Google Scholar 
31.Budge, G. E. et al. Identifying bacterial predictors of honey bee health. J. Invertebr. Pathol. 141, 41–44 (2016).PubMed 
Article 

Google Scholar 
32.Schmid-Hempel, R. & Tognazzo, M. Molecular divergence defines two distinct lineages of Crithidia bombi (Trypanosomatidae), parasites of bumblebees. J. Eukaryot. Microbiol. 57, 337–345 (2010).CAS 
PubMed 
Article 

Google Scholar 
33.Akre, R. D., Hill, W. B., Donald, J. F. M. & Garnett, W. B. Foraging distances of Vespula pensylvanica workers (Hymenoptera: Vespidae). J. Kansas Entomol. Soc. 48, 12–16 (1975).
Google Scholar 
34.Seeley, T. D. & Smith, M. L. Crowding honeybee colonies in apiaries can increase their vulnerability to the deadly ectoparasite Varroa destructor. Apidologie 46, 716–727 (2015).Article 

Google Scholar 
35.McArt, S. H., Koch, H., Irwin, R. E. & Adler, L. S. Arranging the bouquet of disease: Floral traits and the transmission of plant and animal pathogens. Ecol. Lett. 17, 624–636 (2014).PubMed 
Article 

Google Scholar 
36.Peck, D. T. & Seeley, T. D. Mite bombs or robber lures? The roles of drifting and robbing in Varroa destructor transmission from collapsing honey bee colonies to their neighbors. PLoS ONE 14, 1–14 (2019).Article 
CAS 

Google Scholar 
37.Yañez, O. et al. Bee viruses: Routes of infection in Hymenoptera. Front. Microbiol. 11, 1–22 (2020).Article 

Google Scholar 
38.Malham, J. P., Rees, J. S., Alspach, P. A., Beggs, J. R. & Moller, H. Traffic rate as an index of colony size in Vespula wasps. N. Z. J. Zool. 18, 105–109 (1991).Article 

Google Scholar 
39.Brettell, L. et al. A comparison of deformed wing virus in deformed and asymptomatic honey bees. Insects 8, 28 (2017).PubMed Central 
Article 
PubMed 

Google Scholar 
40.Garigliany, M. et al. Moku virus in invasive Asian Hornets, Belgium, 2016. Emerg. Infect. Dis. 23, 2109–2112 (2017).PubMed 
PubMed Central 
Article 

Google Scholar 
41.Garigliany, M., El Agrebi, N., Franssen, M., Hautier, L. & Saegerman, C. Moku virus detection in honey bees, Belgium, 2018. Transbound. Emerg. Dis. 66, 43–46 (2019).PubMed 
Article 

Google Scholar 
42.Highfield, A. et al. Detection and replication of Moku virus in honey bees and social wasps. Viruses 12, 607 (2020).CAS 
PubMed Central 
Article 
PubMed 

Google Scholar 
43.Felden, A. et al. Viral and fungal pathogens associated with Pneumolaelaps niutirani (Acari: Laelapidae): A mite found in diseased nests of Vespula wasps. Insect. Soc. 67, 83–93 (2020).Article 

Google Scholar 
44.Lindström, A., Korpela, S. & Fries, I. Horizontal transmission of Paenibacillus larvae spores between honey bee (Apis mellifera) colonies through robbing. Apidologie 39, 515–522 (2008).Article 

Google Scholar 
45.Smith, M. L. The honey bee parasite Nosema ceranae: Transmissible via food exchange?. PLoS ONE 7, 1–6 (2012).
Google Scholar 
46.Folly, A. J., Koch, H., Stevenson, P. C. & Brown, M. J. F. Larvae act as a transient transmission hub for the prevalent bumblebee parasite Crithidia bombi. J. Invertebr. Pathol. 148, 81–85 (2017).PubMed 
PubMed Central 
Article 

Google Scholar 
47.Loope, K. J., Millar, J. G. & Wilson Rankin, E. E. Weak nestmate discrimination behavior in native and invasive populations of a yellowjacket wasp (Vespula pensylvanica). Biol. Invasions 20, 3431–3444 (2018).48.Yañez, O., Gauthier, L., Chantawannakul, P. & Neumann, P. Endosymbiotic bacteria in honey bees: Arsenophonus spp. are not transmitted transovarially. FEMS Microbiol. Lett. 363, fnw147 (2016).49.McNally, L. C. & Schneider, S. S. Spatial distribution and nesting biology of colonies of the African honey bee Apis mellifera scutellata (Hymenoptera: Apidae) in Botswana, Africa. Environ. Entomol. 25, 643–652 (1996).Article 

Google Scholar 
50.Seeley, T. D. Honey bees of the Arnot forest: A population of feral colonies persisting with Varroa destructor in the northeastern United States. Apidologie 38, 19–29 (2007).Article 

Google Scholar 
51.Arundel, J., Oldroyd, B. P. & Winter, S. Modelling estimates of honey bee (Apis spp.) colony density from drones. Ecol. Model. 267, 1–10 (2013).52.Graystock, P., Goulson, D. & Hughes, W. O. H. Parasites in bloom: Flowers aid dispersal and transmission of pollinator parasites within and between bee species. Proc. R. Soc. B Biol. Sci. 282, 20151371 (2015).Article 

Google Scholar 
53.Graystock, P., Meeus, I., Smagghe, G., Goulson, D. & Hughes, W. O. H. The effects of single and mixed infections of Apicystis bombi and deformed wing virus in Bombus terrestris. Parasitology 143, 358–365 (2016).PubMed 
Article 

Google Scholar 
54.Benaets, K. et al. Covert deformed wing virus infections have long-term deleterious effects on honeybee foraging and survival. Proc. R. Soc. B Biol. Sci. 284, 20162149 (2017).Article 

Google Scholar 
55.Natsopoulou, M. E. et al. The virulent, emerging genotype B of deformed wing virus is closely linked to overwinter honeybee worker loss. Sci. Rep. 7, 5242 (2017).ADS 
PubMed 
PubMed Central 
Article 
CAS 

Google Scholar 
56.Gambino, P., Medeiros, A. C. & Loope, L. L. Invasion and colonization of upper elevations on East Maui (Hawaii) by Vespula pensylvanica (Hymenoptera: Vespidae). Ann. Entomol. Soc. Am. 83, 1088–1095 (1990).Article 

Google Scholar 
57.Akre, R. D. & Reed, H. C. Population cycles of yellowjackets (Hymenoptera: Vespinae) in the Pacific Northwest. Environ. Entomol. 10, 267–274 (1981).Article 

Google Scholar 
58.Giambelluca, T. W. et al. Online rainfall atlas of Hawai’i. Bull. Am. Meteorol. Soc. 94, 313–316 (2013).ADS 
Article 

Google Scholar 
59.Marion, G. M. et al. Open-top designs for manipulating field temperature in high-latitude ecosystems. Glob. Chang. Biol. 3, 20–32 (1997).Article 

Google Scholar 
60.de Miranda, J. R. et al. Standard methods for virus research in Apis mellifera. J. Apic. Res. 52, 1–56 (2013).ADS 
Article 
CAS 

Google Scholar 
61.Johnson, D. H. Estimating nest success : The Mayfield method and an alternative. Auk 96, 651–661 (1979).
Google Scholar 
62.R Core Team. R: A Language and Environment for Statistical Computing. (2020).63.Therneau, T. A Package for Survival Analysis in S. (2015).64.Bivand, R. S. & Wong, D. W. S. Comparing implementations of global and local indicators of spatial association. TEST 27, 716–748 (2018).MathSciNet 
MATH 
Article 

Google Scholar 
65.Kahle, D. & Wickham, H. ggmap: Spatial visualization with ggplot2. R J. 5, 144–161 (2013).Article 

Google Scholar  More

1.Croston, R., Branch, C. L., Kozlovsky, D. Y., Dukas, R. & Pravosudov, V. V. The importance of heritability estimates for understanding the evolution of cognition: A response to comments on Croston et al. Behav. Ecol. 26, 1463–1464 (2015).Article 

Google Scholar 
2.Langley, E. J. G. et al. Heritability and correlations among learning and inhibitory control traits. Behav. Ecol. 1, 1–9 (2020).
Google Scholar 
3.Boogert, N. J., Madden, J. R., Morand-Ferron, J. & Thornton, A. Measuring and understanding individual differences in cognition. Philos. Trans. R. Soc. B. 373, 2017080 (2018).
Google Scholar 
4.Sonnenberg, B. R., Branch, C. L., Pitera, A. M., Bridge, E. & Pravosudov, V. V. Natural selection and spatial cognition in wild food-caching mountain chickadees. Curr. Biol. 29, 1–7 (2019).Article 
CAS 

Google Scholar 
5.Benedict, L. M. et al. Elevation-related differences in annual survival of adult food-caching mountain chickadees are consistent with natural selection on spatial cognition. Behav. Ecol. Sociobiol. 74, 2817 (2020).Article 

Google Scholar 
6.Shaw, R. C., MacKinlay, R. D., Clayton, N. S. & Burns, K. C. Memory performance influences male reproductive success in a wild bird. Curr. Biol. 29, 1498–1502 (2019).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
7.Cauchoix, M. & Chaine, A. S. How can we study the evolution of animal minds?. Front. Psychol. 7, 1–18 (2016).Article 

Google Scholar 
8.Janmaat, K. R. L. et al. Spatio-temporal complexity of chimpanzee food: How cognitive adaptations can counteract the ephemeral nature of ripe fruit. Am. J. Primatol. 78, 626–645 (2016).PubMed 
Article 
PubMed Central 

Google Scholar 
9.Collett, M., Chittka, L. & Collett, T. S. Spatial memory in insect navigation. Curr. Biol. 23, R789–R800 (2013).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
10.Hampton, R. R. & Shettleworth, S. J. Hippocampus and memory in a food-storing and in a nonstoring bird species. Behav. Neurosci. 110, 946–964 (1996).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
11.LaDage, L. D., Roth, T. C., Cerjanic, A. M., Sinervo, B. & Pravosudov, V. V. Spatial memory: Are lizards really deficient?. Biol. Lett. 8, 939–941 (2012).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
12.Milton, K. Distribution patterns of tropical plant foods as an evolutionary stimulus to primate mental development. Am. Anthropol. 83, 534–548 (1981).Article 

Google Scholar 
13.Thornton, A. & Boogert, N. J. Animal cognition: The benefits of remembering. Curr. Biol. 29, R324–R327 (2019).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
14.Pravosudov, V. V. & Clayton, N. S. A test of the adaptive specialization hypothesis: Population differences in caching, memory, and the hippocampus in black-capped chickadees (Poecile atricapilla). Behav. Neurosci. 116, 515–522 (2002).PubMed 
Article 
PubMed Central 

Google Scholar 
15.Morand-Ferron, J., Hermer, E., Jones, T. B. & Thompson, M. J. Environmental variability, the value of information, and learning in winter residents. Anim. Behav. 147, 137–145 (2019).Article 

Google Scholar 
16.Hermer, E., Cauchoix, M., Chaine, A. S. & Morand-Ferron, J. Elevation-related difference in serial reversal learning ability in a nonscatter hoarding passerine. Behav. Ecol. 29, 840–847 (2018).Article 

Google Scholar 
17.Boyle, A. W., Sandercock, B. K. & Martin, K. Patterns and drivers of intraspecific variation in avian life history along elevational gradients: A meta-analysis. Biol. Rev. 91, 469–482 (2016).Article 

Google Scholar 
18.Roth, T. C. II. & Pravosudov, V. V. Hippocampal volumes and neuron numbers increase along a gradient of environmental harshness: A large-scale comparison. Proc. R. Soc. B 276, 401–405 (2009).PubMed 
Article 
PubMed Central 

Google Scholar 
19.Körner, C. The use of ‘altitude’ in ecological research. Trends Ecol. Evol. 22, 569–574 (2007).PubMed 
Article 
PubMed Central 

Google Scholar 
20.Roth, T. C. II., LaDage, L. D. & Pravosudov, V. V. Learning capabilities enhanced in harsh environments: A common garden approach. Proc. R. Soc. B 277, 3187–3193 (2010).PubMed 
Article 
PubMed Central 

Google Scholar 
21.Tello-Ramos, M. C., Branch, C. L., Kozlovsky, D. Y., Pitera, A. M. & Pravosudov, V. V. Spatial memory and cognitive flexibility trade-offs: to be or not to be flexible, that is the question. Anim. Behav. 1, 1–8 (2018).
Google Scholar 
22.Gonzalez, R. C., Behrend, E. R. & Bitterman, M. E. Reversal learning and forgetting in bird and fish. Science 158, 519–521 (1967).CAS 
PubMed 
Article 
ADS 
PubMed Central 

Google Scholar 
23.Strang, C. G. & Sherry, D. F. Serial reversal learning in bumblebees (Bombus impatiens). Anim. Cogn. 17, 723–734 (2014).PubMed 
Article 
PubMed Central 

Google Scholar 
24.Herszage, J. & Censor, N. Modulation of learning and memory: A shared framework for interference and generalization. Neuroscience 392, 270–280 (2018).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
25.Squier, L. H. Reversal learning improvement in the fish Astronotus ocellatus (Oscar). Psychon. Sci. 14, 143–144 (1969).Article 

Google Scholar 
26.Miyashita, Y., Nakajima, S. & Imada, H. Differential outcome effect in the horse. J. Exp. Anal. Behav. 74, 245–253 (2000).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
27.Missaire, M. et al. Long-term effects of interference on short-term memory performance in the rat. PLoS ONE 12, 1–18 (2017).Article 
CAS 

Google Scholar 
28.Bublitz, A., Weinhold, S. R., Strobel, S., Dehnhardt, G. & Hanke, F. D. Reconsideration of serial visual reversal learning in octopus (Octopus vulgaris) from a methodological perspective. Front. Physiol. 8, 1–11 (2017).Article 

Google Scholar 
29.Chittka, L. Sensorimotor learning in bumblebees: Long-term retention and reversal training. J. Exp. Biol. 201, 515–524 (1998).Article 

Google Scholar 
30.Chrobak, J. J., Hinman, J. R. & Sabolek, H. R. Revealing past memories: Proactive interference and ketamine-induced memory deficits. J. Neurosci. 28, 4512–4520 (2008).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
31.Malleret, G. et al. Bidirectional regulation of hippocampal long-term synaptic plasticity and its influence on opposing forms of memory. J. Neurosci. 30, 3813–3825 (2010).CAS 
PubMed 
PubMed Central 
Article 

Google Scholar 
32.Joseph, M. A. et al. Differential involvement of the dentate gyrus in adaptive forgetting in the rat. PLoS ONE 10, 1–17 (2015).
Google Scholar 
33.Shiflett, M. W., Rankin, A. Z., Tomaszycki, M. L. & DeVoogd, T. J. Cannabinoid inhibition improves memory in food-storing birds, but with a cost. Proc. R. Soc. B. 271, 2043–2048 (2004).CAS 
PubMed 
Article 

Google Scholar 
34.Meck, W. H. & Williams, C. L. Choline supplementation during prenatal development reduces proactive interference in spatial memory. Dev. Brain Res. 118, 51–59 (1999).CAS 
Article 

Google Scholar 
35.Clayton, N. S. & Krebs, J. R. One-trial associative memory: Comparison of food-storing and nonstoring species of birds. Anim. Learn. Behav. 22, 366–372 (1994).Article 

Google Scholar 
36.McGregor, A. & Healy, S. D. Spatial accuracy in food-storing and nonstoring birds. Anim. Behav. 58, 727–734 (1999).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
37.Healy, S. D. Memory for objects and positions: Delayed non-matching-to-sample in storing and non-storing tits. Q. J. Exp. Psychol. Sect. B 48, 179–191 (1995).
Google Scholar 
38.Healy, S. D. & Krebs, J. R. Delayed-matching-to-sample by marsh tits and great tits. Q. J. Exp. Psychol. B 45, 33–47 (1992).CAS 
PubMed 
PubMed Central 

Google Scholar 
39.Hampton, R. R., Shettleworth, S. J. & Westwood, R. P. Proactive interference, recency, and associative strength: Comparisons of black-capped chickadees and dark-eyed juncos. Anim. Learn. Behav. 26, 475–485 (1998).Article 

Google Scholar 
40.Tello-Ramos, M. C. et al. Memory in wild mountain chickadees from different elevations: Comparing first-year birds with older survivors. Anim. Behav. 137, 149–160 (2018).Article 

Google Scholar 
41.Croston, R. et al. Predictably harsh environment is associated with reduced cognitive flexibility in wild food-caching mountain chickadees. Anim. Behav. 123, 139–149 (2017).Article 

Google Scholar 
42.Careau, V. & Wilson, R. S. Of uberfleas and krakens: Detecting trade-offs using mixed models. Integr. Comp. Biol. 57, 362–371 (2017).PubMed 
Article 
PubMed Central 

Google Scholar 
43.Niemelä, P. T. & Dingemanse, N. J. On the usage of single measurements in behavioural ecology research on individual differences. Anim. Behav. 145, 99–105 (2018).Article 

Google Scholar 
44.Gosler, A. G. The Great Tit (Hamlyn, 1993).
Google Scholar 
45.Lejeune, L. et al. Environmental effects on parental care visitation patterns in blue tits Cyanistes caeruleus. Front. Ecol. Evol. 7, 1–15 (2019).Article 

Google Scholar 
46.Bründl, A. C. et al. Experimentally induced increases in fecundity lead to greater nestling care in blue tits. Proc. R. Soc. B. 286, 20191013 (2019).PubMed 
Article 
CAS 
PubMed Central 

Google Scholar 
47.Thompson, M. J. & Morand-Ferron, J. Food caching in city birds: Urbanization and exploration do not predict spatial memory in scatter hoarders. Anim. Cogn. 22, 743–756 (2019).PubMed 
Article 
PubMed Central 

Google Scholar 
48.Roth, T. C. II., LaDage, L. D., Freas, C. A. & Pravosudov, V. V. Variation in memory and the hippocampus across populations from different climates: A common garden approach. Proc. R. Soc. B 279, 402–410 (2012).PubMed 
Article 
PubMed Central 

Google Scholar 
49.Griffin, A. S., Guillette, L. M. & Healy, S. D. Cognition and personality: An analysis of an emerging field. Trends Ecol. Evol. 30, 207–214 (2015).PubMed 
Article 
PubMed Central 

Google Scholar 
50.Ashton, B. J., Thornton, A. & Ridley, A. R. An intraspecific appraisal of the social intelligence hypothesis. Philos. Trans. R. Soc. B. 373, 20170288 (2018).Article 

Google Scholar 
51.Croston, R., Branch, C. L., Kozlovsky, D. Y., Dukas, R. & Pravosudov, V. V. Heritability and the evolution of cognitive traits. Behav. Ecol. 26, 1447–1459 (2015).Article 

Google Scholar 
52.Bründl, A. C. et al. Elevational gradients as a model for understanding associations among temperature, breeding phenology and success. Front. Ecol. Evol. 8, 56377 (2020).Article 

Google Scholar 
53.Freas, C. A., LaDage, L. D., Roth, T. C. II. & Pravosudov, V. V. Elevation-related differences in memory and the hippocampus in mountain chickadees, Poecile gambeli. Anim. Behav. 84, 121–127 (2012).Article 

Google Scholar 
54.Pravosudov, V. V. & Roth, T. C. II. Cognitive ecology of food hoarding: The evolution of spatial memory and the hippocampus. Annu. Rev. Ecol. Evol. Syst. 44, 173–193 (2013).Article 

Google Scholar 
55.Croston, R. et al. Potential mechanisms driving population variation in spatial memory and the hippocampus in food-caching chickadees. Integr. Comp. Biol. 55, 354–371 (2015).PubMed 
Article 
PubMed Central 

Google Scholar 
56.Kozlovsky, D. Y., Weissgerber, E. A. & Pravosudov, V. V. What makes specialized food-caching mountain chickadees successful city slickers?. Proc. R. Soc. B 284, 20162613 (2017).PubMed 
Article 
PubMed Central 

Google Scholar 
57.Izquierdo, A., Brigman, J. L., Radke, A. K., Rudebeck, P. H. & Holmes, A. The neural basis of reversal learning: An updated perspective. Neuroscience 345, 12–26 (2017).CAS 
PubMed 
Article 
PubMed Central 

Google Scholar 
58.Cauchoix, M. et al. The repeatability of cognitive performance: A meta-analysis. Neuroscience 373, 20170281 (2018).
Google Scholar 
59.Croston, R. et al. Individual variation in spatial memory performance in wild mountain chickadees from different elevations. Anim. Behav. 111, 225–234 (2016).Article 

Google Scholar 
60.Svensson, L. Identification Guide to European Passerines (British Trust for Ornithology, 1992).
Google Scholar 
61.Friard, O. & Gamba, M. BORIS: A free, versatile open-source event-logging software for video/audio coding and live observations. Methods Ecol. Evol. 7, 1325–1330 (2016).Article 

Google Scholar 
62.Tillé, Y., Newman, J. A. & Healy, S. D. New tests for departures from random behavior in spatial memory experiments. Anim. Learn. Behav. 24, 327–340 (1996).Article 

Google Scholar 
63.Bates, D. et al. Linear Mixed-Effects using ‘Eigen’ and S4 1–113 (Springer, 2016).
Google Scholar 
64.Kuznetsova, A. & Christensen, R. H. B. lmerTest package: Tests in linear mixed effects models. J. Stat. Softw. 82, 1–26 (2017).Article 

Google Scholar 
65.R Core Team. A Language and Environment for Statistical Computing. (R Foundation for Statistical Computing, 2020).66.Warton, D. I., Lyons, M., Stoklosa, J. & Ives, A. R. Three points to consider when choosing a LM or GLM test for count data. Methods Ecol. Evol. 7, 882–890 (2016).Article 

Google Scholar 
67.Wilson, A. J. How should we interpret estimates of individual repeatability?. Evol. Lett. 2, 4–8 (2018).PubMed 
PubMed Central 
Article 

Google Scholar 
68.Stoffel, M. A., Nakagawa, S. & Schielzeth, H. rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models. Methods Ecol. Evol. 8, 1639–1644 (2017).Article 

Google Scholar 
69.Hadfield, J. D. MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package. J. Stat. Softw. 33, 1–22 (2010).Article 

Google Scholar 
70.Houslay, T. M. & Wilson, A. J. Avoiding the misuse of BLUP in behavioural ecology. Behav. Ecol. 28, 948–952 (2017).PubMed 
PubMed Central 
Article 

Google Scholar 
71.Kilkenny, C., Browne, W. J., Cuthill, I. C., Emerson, M. & Altman, D. G. Improving bioscience research reporting: The arrive guidelines for reporting animal research. PLoS Biol. 8, 6–10 (2010).Article 
CAS 

Google Scholar  More