Philippa Kaur

1.
Serre, D. & Paabo, S. Evidence for gradients of human genetic diversity within and among continents. Genome Res. 14, 1679–1685 (2004).
CAS  PubMed  PubMed Central  Article  Google Scholar 
2.
Ohta, T. Population size and rate of evolution. J. Mol. Evol. 1, 305–314 (1972).
PubMed  Article  PubMed Central  Google Scholar 

3.
Slatkin, M. Gene flow and selection in a cline. Genetics 75, 733–756 (1973).

4.
Potts, R. Variability selection in hominid evolution. Evol. Anthropol. 7, 81–96 (1998).
Article  Google Scholar 

5.
Potts, R. Hominin evolution in settings of strong environmental variability. Quat. Sci. Rev. 73, 1–13 (2013).
Article  Google Scholar 

6.
Prüfer, K. et al. The bonobo genome compared with the chimpanzee and human genomes. Nature 486, 527–531 (2012).
PubMed  PubMed Central  Article  CAS  Google Scholar 

7.
Hill, W. C. O. in The Nomenclature, Taxonomy and Distribution of Chimpanzees, Vol. 1 (ed. Bourne, G. H.) 22–49 (Karger, 1969).

8.
Pruetz, J. D. & Bertolani, P. Chimpanzee (Pan troglodytes verus) behavioral responses to stresses associated with living in a savannah-mosaic environment: implications for hominin adaptations to open habitats. Paleoanthropology 2009, 252–262 (2009).
Article  Google Scholar 

9.
Fünfstück, T. et al. The sampling scheme matters: Pan troglodytes troglodytes and P. t. schweinfurthii are characterized by clinal genetic variation rather than a strong subspecies break. Am. J. Phys. Anthropol. 156, 181–191 (2014).
PubMed  PubMed Central  Article  Google Scholar 

10.
Fischer, A., Pollack, J., Thalmann, O., Nickel, B. & Paabo, S. Demographic history and genetic differentiation in apes. Curr. Biol. 16, 1133–1138 (2006).
CAS  PubMed  Article  Google Scholar 

11.
Gonder, M. K. et al. A new west African chimpanzee subspecies? Nature 388, 337 (1997).
CAS  PubMed  Article  Google Scholar 

12.
Becquet, C., Patterson, N., Stone, A. C., Przeworski, M. & Reich, D. E. Genetic structure of chimpanzee populations. PLoS Genet. 3, e66 (2007).
PubMed  PubMed Central  Article  CAS  Google Scholar 

13.
Bowden, R. et al. Genomic tools for evolution and conservation in the chimpanzee: Pan troglodytes ellioti is a genetically distinct population. PLoS Genet. 8, e1002504 (2012).
CAS  PubMed  PubMed Central  Article  Google Scholar 

14.
Prado-Martinez, J. et al. Great ape genetic diversity and population history. Nature 499, 471–475 (2013).
CAS  PubMed  PubMed Central  Article  Google Scholar 

15.
de Manuel, M. et al. Chimpanzee genomic diversity reveals ancient admixture with bonobos. Science 354, 477–481 (2016).
PubMed  PubMed Central  Article  CAS  Google Scholar 

16.
Langergraber, K. E. et al. Genetic and ‘cultural’ similarity in wild chimpanzees. Proc. R. Soc. B. 278, 408–416 (2010).
PubMed  Article  PubMed Central  Google Scholar 

17.
Garcin, Y. et al. Early anthropogenic impact on Western Central African rainforests 2,600 y ago. Proc. Natl Acad. Sci. USA 115, 3261–3266 (2018).
CAS  PubMed  Article  PubMed Central  Google Scholar 

18.
Vicente, M. & Schlebusch, C. M. African population history: an ancient DNA perspective. Curr. Opin. Genet. Dev. 62, 8–15 (2020).
CAS  PubMed  Article  PubMed Central  Google Scholar 

19.
IUCN Red List. IUCN red list of threatened species. http://www.iucnredlist.org (2020).

20.
Wentworth, C. K. Natural bridges and glaciation. Am. J. Sci. 26, 577–584 (1933).
Article  Google Scholar 

21.
Maley, J. The African rainforest: main characteristics of changes in vegetation and climate from the Upper Cretaceous to the Quaternary. Proc. R. Soc. Edinb. 104B, 31–73 (1996).
Google Scholar 

22.
Langergraber, K. E. et al. Generation times in wild chimpanzees and gorillas suggest earlier divergence times in great ape and human evolution. Proc. Natl Acad. Sci. USA 109, 15716–15721 (2012).
CAS  PubMed  Article  Google Scholar 

23.
Shea, B. T. & Coolidge, H. J. Craniometric differentiation and systematics in the genus Pan. J. Hum. Evol. 13, 671–685 (1988).
Article  Google Scholar 

24.
Albrecht, G. H. & Miller, J. M. A. in Geographic Variation in Primates (eds Kimbel, W. H. & Martin, L. B.) 123–161 (Springer Science & Business Media, 2013).

25.
Shea, B. T., Leigh, S. R. & Groves, C. P. in Multivariate Craniometric Variation in Chimpanzees (eds Kimbel, W. H. & Martin, L. B.) 265–296 (Springer Science & Business Media, 2013).

26.
Kühl, H. S. et al. Chimpanzee accumulative stonethrowing. Sci. Rep. 6, 22219 (2016).

27.
Wright, S. Isolation by distance. Genetics 28, 114–138 (1943).
CAS  PubMed  PubMed Central  Google Scholar 

28.
Pritchard, J. K., Stephens, M. & Donnelly, P. Inference of population structure using multilocus genotype data. Genetics 155, 945–959 (2000).
CAS  PubMed  PubMed Central  Google Scholar 

29.
Pritchard, J. K., Wen, X. & Falush, D. Documentation for structure version 2.3 software: version 2.3. 1–39. http://pritchardlab.stanford.edu/structure_software/release_versions/v2.3.4/structure_doc.pdf (2009).

30.
Meirmans, P. G. The trouble with isolation by distance. Mol. Ecol. 21, 2839–2846 (2012).
PubMed  Article  Google Scholar 

31.
Perez, M. F. et al. Assessing population structure in the face of isolation by distance: are we neglecting the problem? Divers. Distrib. 24, 1883–1889 (2018).
Article  Google Scholar 

32.
Thalib, L., Kitching, R. L. & Bhatti, M. I. Principal component analysis for grouped data – a case study. Environmetrics 10, 565–574 (1999).
Article  Google Scholar 

33.
Fischer, A. et al. Bonobos fall within the genomic variation of chimpanzees. PLoS ONE 6, e21605 (2011).
CAS  PubMed  PubMed Central  Article  Google Scholar 

34.
Frantz, A. C., Cellina, S., Krier, A., Schley, L. & Burke, T. Using spatial Bayesian methods to determine the genetic structure of a continuously distributed population: clusters or isolation by distance? J. Appl. Ecol. 46, 493–505 (2009).
Article  Google Scholar 

35.
Kalinowski, S. T. The computer program STRUCTURE does not reliably identify the main genetic clusters within species: simulations and implications for human population structure. Heredity 106, 625–632 (2010).
PubMed  PubMed Central  Article  Google Scholar 

36.
Schwartz, M. K. & McKelvey, K. S. Why sampling scheme matters: the effect of sampling scheme on landscape genetic results. Conserv. Genet. 10, 441–452 (2008).
Article  Google Scholar 

37.
Meirmans, P. G. Seven common mistakes in population genetics and how to avoid them. Mol. Ecol. 24, 3223–3231 (2015).
PubMed  Article  PubMed Central  Google Scholar 

38.
Arandjelovic M, et al. Pan African Programme—The cultured chimpanzee. Guidelines for research and data collection. http://panafrican.eva.mpg.de/english/approaches_and_methods.php (2014).

39.
Arandjelovic, M. & Vigilant, L. Non-invasive genetic censusing and monitoring of primate populations. Am. J. Primatol. 80, e22743 (2018).
PubMed  Article  Google Scholar 

40.
Arthofer, W., Heussler, C., Krapf, P., Schlick-Steiner, B. C. & Steiner, F. M. Identifying the minimum number of microsatellite loci needed to assess population genetic structure: a case study in fly culturing. Fly 12, 13–22 (2018).

41.
Wenburg, J. K., Bentzen, P. & Foote, C. J. Microsatellite analysis of genetic population structure in an endangered salmonid: the coastal cutthroat trout (Oncorhyncus clarki clarki). Mol. Ecol. 7, 733–749 (1998).
CAS  Article  Google Scholar 

42.
Guo, X.-Z. et al. Phylogeography and populationgenetics of Schizothorax o’connori: strong subdivision in the Yarlung Tsangpo River inferred from mtDNA and microsatellite markers. Sci. Rep. 6, 29821 (2016).

43.
Kleinhans, C. & Willows-Munro, S. Low genetic diversity andshallow population structure inthe endangered vulture, Gyps copotheres. Sci. Rep. 9, 5536 (2019).
PubMed  PubMed Central  Article  CAS  Google Scholar 

44.
Bonato, L. et al. Diversity among peripheral populations: genetic and evolutionary differentiation of Salamandra atraat the southern edge of the Alps. J. Zool. Syst. Evol. Res. 56, 533–548 (2018).
Article  Google Scholar 

45.
Balkenhol, N. et al. A multi-method approach for analyzing hierarchical genetic structures: a case study with cougars Puma concolor. Ecography 37, 552–563 (2014).
Article  Google Scholar 

46.
Kobayashi, T. & Sota, T. Contrasting effects of habitat discontinuity on three closely related fungivorous beetle species with diverging host‐use patterns and dispersal ability. Ecol. Evol. 9, 2475–2486 (2019).
PubMed  PubMed Central  Article  Google Scholar 

47.
Rousset, F. Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance. Genetics 145, 1219–1228 (1997).

48.
Valdes, A. M., Slatkin, M. & Freimer, N. B. Allele frequencies at microsatellite loci: the stepwise mutation model revisited. Genetics 133, 737–749 (1993).
CAS  PubMed  PubMed Central  Article  Google Scholar 

49.
Goldstein, D. B., Ruiz Linares, A., Cavalli-Sforza, L. L. & Feldman, M. W. An evaluation of genetic distances for use with microsatellite loci. Genetics 139, 463–471 (1995).
CAS  PubMed  PubMed Central  Article  Google Scholar 

50.
Calabrese, P. P., Durrett, R. T. & Aquadro, C. F. Dynamics of microsatellite divergence under stepwise mutation and proportional slippage/point mutation models. Genetics 159, 839–852 (2001).
CAS  PubMed  PubMed Central  Google Scholar 

51.
Petkova, D., Novembre, J. & Stephens, M. Visualizing spatial population structure with estimated effective migration surfaces. Nat. Genet. 48, 94–100 (2015).
PubMed  PubMed Central  Article  CAS  Google Scholar 

52.
Rich, A. M., Wasserman, M. D., Hunt, K. D. & Kaestle, F. A. Chimpanzee (Pan troglodytes schweinfurthii) population spans multiple protected areas in the Albertine Rift. Folia. Primatol. 91, 595–609 (2020).

53.
Baldwin, P. J., McGrew, W. C. & Tutin, C. E. G. Wide-ranging chimpanzees at Mt. Assirik, Senegal. Int. J. Primatol. 3, 367–385 (1982).
Article  Google Scholar 

54.
Lemoine, S. et al. Group dominance increases territory size and reduces neighbour pressure in wild chimpanzees. R. Soc. Open Sci. 7, 200577 (2020).
PubMed  PubMed Central  Article  Google Scholar 

55.
Newton-Fisher, N. E. The home range of the Sonso community of chimpanzees from the Budongo Forest, Uganda. Afr. J. Ecol. 41, 150–156 (2003).
Article  Google Scholar 

56.
Allendorf, F. W. Genetic drift and the loss of alleles versus heterozygosity. Zoo. Biol. 5, 181–190 (1986).
Article  Google Scholar 

57.
Barratt, C. D., et al. Late Quaternary habitat suitability models for chimpanzees (Pan troglodytes) since the Last Interglacial (120,000 BP). Preprint at BioRxiv https://www.biorxiv.org/content/10.1101/2020.05.15.066662v1 (2019).

58.
Bertola, L. D. et al. Phylogeographic patterns in Africa and high resolution delineation of genetic clades in the lion (Panthera leo). Sci. Rep. 6, 30807 (2016).

59.
Marchesi, P., Marchesi, N., Fruth, B. & Boesch, C. Census and distribution of chimpanzees in Côte D’Ivoire. Primates 36, 591–607 (1995).
Article  Google Scholar 

60.
Sommer, V., Adanu, J., Faucher, I. & Fowler, A. Nigerian chimpanzees (Pan troglodytes vellerosus) at Gashaka: two years of habituation efforts. Folia Primatol. 75, 295–316 (2004).
Article  Google Scholar 

61.
Chancellor, R. L., Langergraber, K. E., Ramirez, S., Rundus, A. S. & Vigilant, L. Genetic sampling of unhabituated chimpanzees (Pan troglodytes schweinfurthii) in Gishwati Forest Reserve, an isolated forest fragment in western Rwanda. Int. J. Primatol. 33, 479–488 (2012).
Article  Google Scholar 

62.
Piel, A. K. et al. Population status of chimpanzees in the Masito-Ugalla Ecosystem, Tanzania. Am. J. Primatol. 77, 1027–1035 (2015).
PubMed  Article  Google Scholar 

63.
Wessling, E. G. et al. Seasonal variation in physiology challenges the notion of chimpanzees as a forest-adapted species. Front. Ecol. Evol. 6, 1–21 (2018).
Article  Google Scholar 

64.
Whiten, A. et al. Cultures in chimpanzees. Nature 399, 682–685 (1999).
CAS  PubMed  Article  Google Scholar 

65.
Kühl, H. S. et al. Human impact erodes chimpanzee behavioral diversity. Science 363, 1453–1455 (2019).
PubMed  Article  CAS  Google Scholar 

66.
Luncz, L. V., Mundry, R. & Boesch, C. Evidence for cultural differences between neighboring chimpanzee communities. Curr. Biol. 22, 922–926 (2012).
CAS  PubMed  Article  Google Scholar 

67.
Boesch, C., Marchesi, P., Marchesi, N., Fruth, B. & Joulian, F. Is nut cracking in wild chimpanzees a cultural behaviour? J. Hum. Evol. 26, 325–338 (1994).
Article  Google Scholar 

68.
Kalan, A. K. et al. Environmental variability supports chimpanzee behavioural diversity. Nat. Commun. 11, 4451 (2020).

69.
Hockings, K. J. in Chimpanzees of Bossou and Nimba, 221–219 (Springer Science & Business Media, 2011).

70.
McCarthy, M. S., Lester, J. D. & Stanford, C. B. Chimpanzees (Pan troglodytes) flexibly use introduced species for nesting and bark feeding in a human-dominated habitat. Int. J. Primatol. 38, 321–337 (2016).
PubMed  PubMed Central  Article  Google Scholar 

71.
McLennan, M. R. et al. Surviving at the extreme: chimpanzee ranging is not restricted in a deforested human‐dominated landscape in Uganda. Afr. J. Ecol. 8, e57872 (2020).
Google Scholar 

72.
Junker, J. et al. Recent decline in suitable environmental conditions for African great apes. Divers. Distrib. 18, 1077–1091 (2012).
Article  Google Scholar 

73.
Kühl, H. S. et al. The Critically Endangered western chimpanzee declines by 80%. Am. J. Primatol. 79, e22681 (2017).
Article  Google Scholar 

74.
Walsh, P. D., Breuer, T., Sanz, C., Morgan, D. B. & Doran-Sheehy, D. M. Potential for Ebola transmission between gorilla and chimpanzee social groups. Am. Nat. 169, 684–689 (2007).
PubMed  Article  Google Scholar 

75.
Baden, A. L. et al. Anthropogenic pressures drive population genetic structuring across a critically endangered lemur species range. Sci. Rep. 9, 16276 (2019).
PubMed  PubMed Central  Article  CAS  Google Scholar 

76.
Nsubuga, A. M. et al. Factors affecting the amount of genomic DNA extracted from ape faeces and the identification of an improved sample storage method. Mol. Ecol. 13, 2089–2094 (2004).
CAS  PubMed  Article  Google Scholar 

77.
Arandjelovic, M. et al. Two-step multiplex polymerase chain reaction improves the speed and accuracy of genotyping using DNA from noninvasive and museum samples. Mol. Ecol. Resour. 9, 28–36 (2009).
CAS  PubMed  Article  Google Scholar 

78.
Kalinowski, S. T., Taper, M. L. & Marshall, T. C. Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment. Mol. Ecol. 16, 1099–1106 (2007).
PubMed  Article  Google Scholar 

79.
Waits, L. P., Luikart, G. & Taberlet, P. Estimating the probability of identity among genotypes in natural populations: cautions and guidelines. Mol. Ecol. 10, 249–256 (2001).
CAS  PubMed  Article  Google Scholar 

80.
Meirmans, P. G. & Hedrick, P. W. Assessing population structure: FST and related measures. Mol. Ecol. Resour. 11, 5–18 (2010).
PubMed  Article  PubMed Central  Google Scholar 

81.
Mondol, S. et al. New evidence for hybrid zones of forest and savanna elephants in Central and West Africa. Mol. Ecol. 24, 6134–6147 (2015).
CAS  PubMed  Article  PubMed Central  Google Scholar  More

1.
Bindoff, N. L. et al. Changing Ocean, Marine Ecosystems, and Dependent Communities. in IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (eds. Pörtner, H.-O. et al.) 447–588 (IPCC, 2019).
2.
Collins, M. et al. Extremes, Abrupt Changes and Managing Risks. in IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (eds. Pörtner, H.-O. et al.) 589–656 (IPCC, 2019).

3.
Hoegh-Guldberg et al. The Ocean. in Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part B: Regional Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds. Barros, V. R. et al.) 1655–1731 (Cambridge University Press, 2014).

4.
Laufkotter, C., Zscheischler, J. & Frolicher, T. L. High-impact marine heatwaves attributable to human-induced global warming. Science 369, 1621–1625 (2020).
CAS  PubMed  PubMed Central  Google Scholar 

5.
Holbrook, N. J. et al. A global assessment of marine heatwaves and their drivers. Nat. Commun. 10, 1–13 (2019).
CAS  Article  Google Scholar 

6.
Oliver, E. C. J. et al. Longer and more frequent marine heatwaves over the past century. Nat. Commun. 9, 1–12 (2018).
CAS  Article  Google Scholar 

7.
Carr, M. & Kearns, E. J. Production regimes in four Eastern Boundary Current systems. Deep. Res. Part II 50, 3199–3221 (2003).
CAS  Article  Google Scholar 

8.
Castro, C. G. et al. Introduction to ‘ The 1997 – 8 El Nino Atlas of oceanographic conditions along the west coast of North America (23°N – 50°N)’. Prog. Oceanogr. 54, 503–511 (2002).
Article  Google Scholar 

9.
Kendrick, G. A. et al. A systematic review of how multiple stressors from an extreme event drove ecosystem-wide loss of resilience in an iconic seagrass community. Front. Mar. Sci. 6, 1–15 (2019).
Article  Google Scholar 

10.
Nohaïc, M. L. et al. Marine heatwave causes unprecedented regional mass bleaching of thermally resistant corals in northwestern Australia. Sci. Rep. 7, 1–11 (2017).
Article  CAS  Google Scholar 

11.
Smale, D. A. Impacts of ocean warming on kelp forest ecosystems. N. Phytol. 225, 1447–1454 (2020).
Article  Google Scholar 

12.
Smale, D. A. et al. Marine heatwaves threaten global biodiversity and the provision of ecosystem services. Nat. Clim. Chang. 9, 306–312 (2019).
Article  Google Scholar 

13.
Schiel, D. R. & Foster, M. S. The Biology and Ecology of Giant Kelp Forests (University of California Press, 2015).

14.
Wernberg, T., Krumhansl, K., Filbee-dexter, K. & Pedersen, M. F. in World Seas: An Environmental Evaluation (ed. Sheppard, C.) 57–78 (Elsevier Ltd., 2019).

15.
Wernberg, T. et al. An extreme climatic event alters marine ecosystem structure in a global biodiversity hotspot. Nat. Clim. Chang. 3, 78–82 (2012).
Article  Google Scholar 

16.
Wernberg, T. et al. Climate-driven regime shift of a temperate marine ecosystem. Science 353, 169–172 (2016).
CAS  PubMed  PubMed Central  Article  Google Scholar 

17.
Oliver, E. C. J. et al. The unprecedented 2015/16 Tasman Sea marine heatwave. Nat. Commun. 8, 1–12 (2017).
Article  Google Scholar 

18.
Thomsen, M. S. et al. Local extinction of bull kelp (Durvillaea spp.) due to a marine heatwave. Front. Mar. Sci. 6, 1–10 (2019).
Article  Google Scholar 

19.
Cavanaugh, K. C. et al. Spatial variability in the resistance and resilience of giant kelp in Southern and Baja California to a multiyear heatwave. Front. Mar. Sci. 6, 1–14 (2019).
Article  Google Scholar 

20.
Arafeh-dalmau, N., Montaño-moctezuma, G., Martínez, J. A. & Smale, D. A. Extreme marine heatwaves alter kelp forest community near its equatorward distribution limit. Front. Mar. Sci. 6, 1–18 (2019).
Article  Google Scholar 

21.
Filbee-Dexter, K., Feehan, C. J. & Scheibling, R. E. Large-scale degradation of a kelp ecosystem in an ocean warming hotspot. Mar. Ecol. Prog. Ser. 543, 141–152 (2016).

22.
Rogers-Bennett, L. & Catton, C. A. Marine heat wave and multiple stressors tip bull kelp forest to sea urchin barrens. Sci. Rep. 9, 1–9 (2019).
CAS  Article  Google Scholar 

23.
Sanford, E., Sones, J. L., García-reyes, M., Goddard, J. H. R. & Largier, J. L. Widespread shifts in the coastal biota of northern California during the 2014- 2016 marine heatwaves. Sci. Reportscientific Rep. 9, 1–14 (2019).
Article  CAS  Google Scholar 

24.
Beas-Luna, R. et al. Geographic variation in responses of kelp forest communities of the California current to recent climatic changes. Glob. Chang. Biol. https://doi.org/10.1111/gcb.15273 (2020).

25.
Filbee-Dexter, K. & Wernberg, T. Rise of turfs: a new battlefront for globally declining kelp forests. Bioscience 68, 64–76 (2018).
Article  Google Scholar 

26.
Filbee-Dexter, K. & Scheibling, R. E. Sea urchin barrens as alternative stable states of collapsed kelp ecosystems. Mar. Ecol. Prog. Ser. 495, 1–25 (2014).
Article  Google Scholar 

27.
Ling, S. D., Johnson, C. R., Frusher, S. D. & Ridgway, K. R. Overfishing reduces resilience of kelp beds to climate-driven catastrophic phase shift. Proc. Natl. Acad. Sci. USA 106, 22341–22345 (2009).

28.
Estes, J. A., Tinker, M. T., Williams, T. M. & Doak, D. F. Killer whale predation on sea otters linking oceanic and nearshore ecosystems. Science 282, 473–477 (1998).
CAS  PubMed  Article  PubMed Central  Google Scholar 

29.
Hamilton, S. L. & Caselle, J. E. Exploitation and recovery of a sea urchin predator has implications for the resilience of southern California kelp forests. Proc. R. Soc. B 282, 1–10 (2014).

30.
Jacox, M. G. et al. Forcing of multiyear extreme ocean temperatures that impacted California current living marine resources in 2016. Bull. Am. Meteorol. Soc. 99, 27–33 (2018).
Article  Google Scholar 

31.
Montecino-Latorre, D. et al. Devastating transboundary impacts of sea star wasting disease on subtidal asteroids. PLoS ONE 11, 1–21 (2016).
Article  CAS  Google Scholar 

32.
Eisaguirre, J. M., Davis, K., Carlson, P. M., Gaines, S. D. & Caselle, J. E. Trophic redundancy and predator size class structure drive differences in kelp forest ecosystem dynamics. Ecology 101, 1–11 (2020).
Article  Google Scholar 

33.
Harrold, C. & Reed, D. C. Food availability, sea urchin grazing, and kelp forest community structure. Ecology 66, 1160–1169 (1985).
Article  Google Scholar 

34.
Cowen, R. K. The effect of sheephead (Semicossyphus pulcher) predation on red sea urchin (Strongylocentrotus franciscanus) populations: an experimental analysis. Oecologia 58, 249–255 (1983).
PubMed  Article  Google Scholar 

35.
Burt, J. M. et al. Sudden collapse of a mesopredator reveals its complementary role in mediating rocky reef regime shifts. Proc. R. Soc. B 285, 1–9 (2018).

36.
Springer, Y. P., Hays, C., Carr, M. H. & Mackey, M. R. Toward ecosystem-based management of marine macroalgae-the bull kelp, Nereocystis luetkeana. Oceanogr. Mar. Biol. Annu. Rev. 48, 1–42 (2010).
Google Scholar 

37.
Springer, Y., Hays, C., Carr, M., Mackey, M. & Bloeser, J. Ecology and management of the bull kelp, Nereocystis luetkeana: a synthesis with recommendations for future research. Vol. 48, 1–45 (Lenfest Ocean Program at The Pew Charitable Trusts, 2006).

38.
Bell, T. W., Allen, J. G., Cavanaugh, K. C. & Siegel, D. A. Three decades of variability in California’s giant kelp forests from the Landsat satellites. Remote Sens. Environ. 238, 110811 (2020).

39.
Pfister, C. A., Berry, H. D. & Mumford, T. The dynamics of Kelp Forests in the Northeast Pacific Ocean and the relationship with environmental drivers. J. Ecol. https://doi.org/10.1111/1365-2745.12908 (2017).

40.
Griggs, G. B. & Hein, J. R. Sources, dispersal, and clay mineral composition of fine-grained sediment off Central and Northern California. J. Geol. 88, 541–566 (1979).
Article  Google Scholar 

41.
Harvell, C. D., Caldwell, J. M., Burt, J. M., Bosley, K. & Keller, A. Disease epidemic and a marine heat wave are associated with the continental-scale collapse of a pivotal predator (Pycnopodia helianthoides). Sci. Adv. 5, 1–9 (2019).
Article  Google Scholar 

42.
Okamoto, D. K., Schroeter, S. C. & Reed, D. C. Effects of ocean climate on spatiotemporal variation in sea urchin settlement and recruitment. Limnol. Oceanogr. https://doi.org/10.1002/lno.11440 (2020).

43.
Estes, J. A., Burdin, A. & Doak, D. F. Sea otters, kelp forests, and the extinction of Steller’s sea cow. Proc. Natl Acad. Sci. USA 113, 880–885 (2016).
CAS  PubMed  Article  PubMed Central  Google Scholar 

44.
Scheffer, M., Carpenter, S., Foley, J. A., Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001).
CAS  PubMed  Article  PubMed Central  Google Scholar 

45.
Ebert, T. A., Schroeter, S. C., Dixon, J. D. & Kalvass, P. Settlement patterns of red and purple sea urchins (Strongylocentrotus franciscanus and S. purpuratus) in California, USA. Mar. Ecol. Prog. Ser. 111, 41–52 (1994).
Article  Google Scholar 

46.
Frölicher, T. L., Fischer, E. M. & Gruber, N. Marine heatwaves under global warming. Nature 560, 360–366 (2018).
PubMed  Article  CAS  PubMed Central  Google Scholar 

47.
Steneck, R. S. et al. Kelp forest ecosystems: biodiversity, stability, resilience and future. Environ. Conserv. 29, 436–459 (2002).
Article  Google Scholar 

48.
Smith, J. G. et al. Behavioral responses across a mosaic of ecosystem states restructure a sea otter-urchin trophic cascade. Proc. Natl. Acad. Sci. USA 118, 202012493 (2020). https://doi.org/10.1073/pnas.2012493118.

49.
Eurich, J. G., Selden, R. L. & Warner, R. R. California spiny lobster preference for urchins from kelp forests: implications for urchin barren persistence. Mar. Ecol. Prog. Ser. 498, 217–225 (2014).
Article  Google Scholar 

50.
Graham, M. H. Effects of local deforestation on the diversity and structure of Southern California giant kelp forest food webs. Ecosystems 7, 341–357 (2004).
Article  Google Scholar 

51.
Babcock, R. C. et al. Decadal trends in marine reserves reveal differential rates of change in direct and indirect effects. Proc. Natl Acad. Sci. USA 107, 18256–18261 (2010).
CAS  PubMed  Article  PubMed Central  Google Scholar 

52.
Hewson, I., Bistolas, K. S. I., Cardé, E. M. Q. & Button, J. B. Investigating the complex association between viral ecology, environment, and Northeast Pacific Sea Star Wasting. Front. Mar. Sci. 5, 1–14 (2018).

53.
Pearse, J. S. & Hines, A. H. Expansion of a central California kelp forest following the mass mortality of sea urchins. Mar. Biol. 51, 83–91 (1979).

54.
Ebeling, A. W., Laur, D. R., Rowley, R. J. & Barbara, S. Severe storm disturbances and reversal of community structure in a southern California kelp forest. Mar. Biol. 294, 287–294 (1985).
Article  Google Scholar 

55.
Martínez, B. et al. Distribution models predict large contractions of forming seaweeds in response to ocean warming. Divers. Distrib. 24, 1350–1366 (2018).
Article  Google Scholar 

56.
DeYoung, B. et al. Regime shifts in marine ecosystems: detection, prediction and management. Trends Ecol. Evol. 23, 402–409 (2008).
PubMed  Article  Google Scholar 

57.
Crépin, A., Biggs, R., Polasky, S., Troell, M. & Zeeuw, A. De. Regime shifts and management. Ecol. Econ. 84, 15–22 (2012).
Article  Google Scholar 

58.
Roberts, D. A. et al. Mapping chaparral in the Santa Monica Mountains using multiple endmember spectral mixture models. Remote Sens. Environ. 65, 267–279 (1998).
Article  Google Scholar 

59.
Cavanaugh, K. C., Siegel, D. A., Reed, D. C. & Dennison, P. E. Environmental controls of giant-kelp biomass in the Santa Barbara Channel, California. Mar. Ecol. Prog. Ser. 429, 1–17 (2011).
Article  Google Scholar 

60.
Hobday, A. J. et al. A hierarchical approach to defining marine heatwaves. Prog. Oceanogr. 141, 227–238 (2016).
Article  Google Scholar 

61.
García-Reyes, M., Largier, J. L. & Sydeman, W. J. Progress in Oceanography Synoptic-scale upwelling indices and predictions of phyto- and zooplankton populations. Prog. Oceanogr. 120, 177–188 (2014).
Article  Google Scholar 

62.
McHugh, T., Abbott, D. & Freiwald, J. Phase shift from kelp forest to urchin barren along California’s North Coast. (Western Society of Naturalists, 2018).

63.
Rogers-Bennett, L., Kashiwada, J. V., Taniguchi, I. K., Kawana, S. K. & Catton, C. A. Using density-based fishery management strategies to respond to mass mortality events. J. Shellfish Res. 38, 1–11 (2019).
Article  Google Scholar 

64.
Carrascal, L. M. & Galva, I. Partial least squares regression as an alternative to current regression methods used in ecology. Oikos 118, 681–690 (2009).
Article  Google Scholar 

65.
Vadas, R. L. Ecological implications of culture studies on nereocystis luetkeana. J. Phycol. 8, 196–203 (1972).
Google Scholar 

66.
Finger, D. J. I., McPherson, M. L., Houskeeper, H. F. & Kudela, R. M. Mapping bull kelp canopy in northern California using Landsat to enable long-term monitoring. Remote Sens. Environ. 254, 112243 (2021).
Article  Google Scholar  More

1.
Pringle, R. M. A mountain of ecological interactions. Nature 568, 38–39 (2019).
CAS  Article  ADS  Google Scholar 
2.
Sayre, R. et al. A new high-resolution map of world mountains and an online tool for visualizing and comparing characterizations of global mountain distributions. Mt Res Dev 38, 240–249. https://doi.org/10.1659/mrd-journal-d-17-00107.1 (2018).
Article  Google Scholar 

3.
Peters, M. K. et al. Climate-land-use interactions shape tropical mountain biodiversity and ecosystem functions. Nature 568, 88–92. https://doi.org/10.1038/s41586-019-1048-z (2019).
CAS  Article  PubMed  ADS  Google Scholar 

4.
Bian, J., Li, A., Lei, G., Zhang, Z. & Nan, X. Global high-resolution mountain green cover index mapping based on Landsat images and Google Earth Engine. ISPRS J Photogramm Remote Sens 162, 63–76. https://doi.org/10.1016/j.isprsjprs.2020.02.011 (2020).
Article  ADS  Google Scholar 

5.
Antonelli, A. et al. Geological and climatic influences on mountain biodiversity. Nat Geo 11, 718–725. https://doi.org/10.1038/s41561-018-0236-z (2018).
CAS  Article  ADS  Google Scholar 

6.
Price, M. F., Arnesen, T., Gløersen, E. & Metzger, M. J. Mapping mountain areas: learning from Global, European and Norwegian perspectives. J Mt Sci 16, 1–15. https://doi.org/10.1007/s11629-018-4916-3 (2019).
Article  Google Scholar 

7.
Körner, C., Paulsen, J. & Spehn, E. M. A definition of mountains and their bioclimatic belts for global comparisons of biodiversity data. Alp Bot 121, 73–78. https://doi.org/10.1007/s00035-011-0094-4 (2011).
Article  Google Scholar 

8.
Körner, C. et al. A global inventory of mountains for bio-geographical applications. Alp Bot 127, 1–15. https://doi.org/10.1007/s00035-016-0182-6 (2017).
Article  Google Scholar 

9.
Karagulle, D. et al. Modeling global Hammond landform regions from 250-m elevation data. Trans GIS 21, 1040–1060. https://doi.org/10.1111/tgis.12265 (2017).
Article  Google Scholar 

10.
Payne, D., Spehn, E. M., Snethlage, M. & Fischer, M. Opportunities for research on mountain biodiversity under global change. Curr Opin Environ Sustain 29, 40–47. https://doi.org/10.1016/j.cosust.2017.11.001 (2017).
Article  Google Scholar 

11.
Silveira, F. A. O. et al. Tropical mountains as natural laboratories to study global changes: A long-term ecological research project in a megadiverse biodiversity hotspot. Perspect Plant Ecol Evol Syst 38, 64–73. https://doi.org/10.1016/j.ppees.2019.04.001 (2019).
Article  Google Scholar 

12.
Elsen, P. R., Monahan, W. B. & Merenlender, A. M. Topography and human pressure in mountain ranges alter expected species responses to climate change. Nat Commun 11, 1974. https://doi.org/10.1038/s41467-020-15881-x (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

13.
Cheng, G. et al. Rebirth after death: forest succession dynamics in response to climate change on Gongga Mountain, Southwest China. J Mt Sci 15, 1671–1681. https://doi.org/10.1007/s11629-017-4435-7 (2018).
Article  Google Scholar 

14.
Trant, A., Higgs, E. & Starzomski, B. M. A century of high elevation ecosystem change in the Canadian Rocky Mountains. Sci Rep 10, 9698. https://doi.org/10.1038/s41598-020-66277-2 (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

15.
Strinella, E., Scridel, D., Brambilla, M., Schano, C. & Korner-Nievergelt, F. Potential sex-dependent effects of weather on apparent survival of a high-elevation specialist. Sci Rep 10, 8386. https://doi.org/10.1038/s41598-020-65017-w (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

16.
Durán-Romero, C., Medina-Sánchez, J. M. & Carrillo, P. Uncoupled phytoplankton-bacterioplankton relationship by multiple drivers interacting at different temporal scales in a high-mountain Mediterranean lake. Sci Rep 10, 350. https://doi.org/10.1038/s41598-019-57269-y (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

17.
Mair, D. et al. Fast long-term denudation rate of steep alpine headwalls inferred from cosmogenic 36Cl depth profiles. Sci Rep 9, 11023. https://doi.org/10.1038/s41598-019-46969-0 (2019).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

18.
Liu, H., Chen, Y., Ye, Z., Li, Y. & Zhang, Q. Recent lake area changes in Central Asia. Sci Rep 9, 16277. https://doi.org/10.1038/s41598-019-52396-y (2019).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

19.
Spandre, P. et al. Climate controls on snow reliability in French Alps ski resorts. Sci Rep 9, 8043. https://doi.org/10.1038/s41598-019-44068-8 (2019).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

20.
Tichavský, R., Ballesteros-Cánovas, J. A., Šilhán, K., Tolasz, R. & Stoffel, M. Dry spells and extreme precipitation are the main trigger of landslides in Central Europe. Sci Rep 9, 14560. https://doi.org/10.1038/s41598-019-51148-2 (2019).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

21.
Stoffel, M., Ballesteros Cánovas, J. A., Luckman, B. H., Casteller, A. & Villalba, R. Tree-ring correlations suggest links between moderate earthquakes and distant rockfalls in the Patagonian Cordillera. Sci Rep 9, 12112. https://doi.org/10.1038/s41598-019-48530-5 (2019).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

22.
de Haas, T., Nijland, W., de Jong, S. M. & McArdell, B. W. How memory effects, check dams, and channel geometry control erosion and deposition by debris flows. Sci Rep 10, 14024. https://doi.org/10.1038/s41598-020-71016-8 (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

23.
Yousefi, S. et al. A machine learning framework for multi-hazards modeling and mapping in a mountainous area. Sci Rep 10, 12144. https://doi.org/10.1038/s41598-020-69233-2 (2020).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar  More

Identification of the risk variables and their correlations with the COVID-19 damages
We have investigated a series of factors contributing to the risk of an epidemic diffusion and its impact on the population. Among many possible, we selected the following variables: mobility index, housing concentration, healthcare density, air pollution, average winter temperature and age of population. In paragraph 1 of Methods section we motivate our choice on such variables (mainly based on epidemics literature and features of the COVID-19 outbreak), show the related data (see Table 1) and explain the adopted normalization.
The first step is, of course, to estimate to what extent the chosen normalized variables individually correlate with the main impact indicators of the COVID-19 epidemic, i.e., total cases and total deaths detected in each Italian region, cumulated up to July 14, 20204, when the first epidemic wave seemed to have finished, and the intensive care occupancy recorded on April 2, 20204, when the epidemic peak was reached. In the first two rows of Fig. 2, from panel (a) to panel (f), the spatial distributions of the six risk indicators, multiplied by the population of each region, are reported as chromatic maps and thus can be visually compared with the analogous maps of the three impact indicators, panels (g), (h) and (i) in the third row. As detailed in Table 2, in paragraph 2 of Methods section, pairwise correlations between risk indicators are, with a few exceptions, quite weak; furthermore, in Table 3, results of the linear least squares fit of each individual risk indicator to damages are reported. We found correlation coefficients ranging from 0.71 to 0.96, always higher than those observed as a function of the population, which can be considered the null model; however, the relative quadratic errors stay quite high (from 0.26 to 0.62). This suggests that some opportune combination of risk indicators could better capture the risk associated to each region. In the next paragraph, we propose a risk assessment framework aimed to this.
Figure 2

The geographical distribution of the six risk factors (a–f) can be compared with the COVID-19 total cases (g), the total deaths (h) and the intensive care occupancy (i). Cases and deaths have been cumulated up to July 14, 2020, i.e. at the end of the first epidemic wave; the intensive care data have been recorded on April 2, 2020, i.e. just before the epidemic peak. The risk indicators have been multiplied for the population of each region and normalized between 0 and 1 (the color scale for temperature has been reversed, i.e. dark colors mean low temperatures, see Methods). A concentration of dark colors in the northern regions is roughly visible for almost all the indicators and the correlations between the single factors and the damages range from 0.70 to 0.95. Maps were realized with QGIS 3.10 (https://qgis.org/en/site/). (l) Crichton’s Risk Triangle. (m) Risk Index assessment framework: risk indicators (factors) are reported in red, risk components in black.

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Definition of a risk assessment framework and calibration with COVID-19 data
Conventional risk assessment theory relies on “Crichton’s Risk Triangle”24,25, shown in panel (l) of Fig. 2. In this framework, risk is evaluated as a function of three components: Hazard, Exposure and Vulnerability. Hazard is the potential for an event to cause harm (e.g., earthquake, flooding, epidemics); Exposure measures the amount of assets exposed to harm (e.g., buildings, infrastructures, population); Vulnerability is the harm proneness of assets if exposed to hazard events (e.g., building characteristics, drainage systems, age of population). The risk is present only when all of the three components co-exist in the same place. Used for the first time in the insurance industry24, this approach has been extended to assess spatially distributed risks in many fields of disaster management, such as those related to climate change impact27,28,29,30,31 and earthquakes32.
In the present paper, we consider Hazard as the degree of diffusion of the virus over the population of an Italian region (influenced by a set of factors, related to spatial and socio-economic characteristics of the region itself); Exposure is the amount of people who might potentially be infected by the virus as a consequence of the Hazard (it should coincide with the size of the population of the region); Vulnerability is the propensity of an infected person to become sick or die (in general, it is strongly related to the age and pre-existing health conditions prior to infection). The combination of Vulnerability and Exposure provides a measure of the absolute damage (i.e., the number of ill people due to pathologies related to the virus in the region), which we called Consequences.
In paragraph 3 of Methods section we propose two models that differ in the way the risk indicators are aggregated into the three components of the Crichton’s risk triangle. In particular, we consider the E_HV model, where the effect of Hazard and Vulnerability are combined in a single affine function of the six indicators, and the E_H_V model, where Hazard and Vulnerability are considered as affine functions of, respectively, mobility index, housing concentration and healthcare density, on one hand, and air pollution, average winter temperature and age of population on the other hand (see Fig. 2 (m) for a summary). In both models the Exposure is represented by the population of each region. Furthermore, two versions of each model have been considered: an optimized one, where the weights of the risk indicators are obtained through a least-square fitting versus real COVID-19 data, and an a-priori one, where all the weights are assumed to be equal.
As shown in Tables 4 and 5 of Methods section, models based on data fitting perform better, both in terms of relative mean quadratic error and correlation coefficient, as expected. In particular, the E_H_V model fits the best. Furthermore, in agreement with the strong correlation of the variables with the targets, most coefficients are positive. Indeed, all coefficients obtained by fitting the number of cases and the intensive care occupancy are positive, and only one negative coefficient appears in each model, when fitting the number of deceased. However, the numerical value of the coefficients strongly depends on both models and targets, making these models not very robust. On the other hand, the a-priori models are independent of the targets, depending only on the choice of the variables we decided to include in the risk evaluation.
Among the two considered a-priori models, where all coefficients assume the same value, we observe that the E_H_V model produces a smaller error with respect to real COVID-19 data and better correlation coefficients than the E_HV model, thus justifying the multiplicative approach which define the risk intensity in terms of the product between Hazard and Vulnerability (we used data at April 2, 2020 for this preliminary analysis but similar results would be obtained using data at July 14, 2020). Moreover, the aggregation of risk indicators in the three components of the E_H_V model follows better our motivations to choose those indicators (as explained in Methods, paragraph 1).
Validation of the a-priori E_H_V model on COVID-19 data
Once we established the robustness of the a-priori E_H_V model, let us now build the corresponding regional risk ranking and validate the model with the regional COVID-19 data as a case study. In particular, following the scheme of Fig. 2 (m), by multiplying Exposure and Vulnerability for the k-th region, we first calculate the Consequences ((C_{k} = E_{k} cdot V_{k}), k = 1,…,20). Then, by multiplying Hazard and Consequences, we obtain the global risk index (R_{k}) for each region ((R_{k} = H_{k} cdot C_{k}), k = 1,…, 20). In this respect, the risk index can be interpreted as the product of what is related to the occurrence of causes of the virus diffusion in a given region ((H_{k})) and what is related to the severity of effects on people ((C_{k})).
In Fig. 3a we can appreciate the predictive capability of our model by looking at the a-priori risk ranking of the Italian regions, compared with the COVID-19 data4, in terms of total cases (cumulated), deaths (cumulated) and intensive care occupancy (daily, not cumulated), updated both at April 2, 2020 and July 14, 2020. The values of (R_{k}) have been normalized to their maximum value, so that Lombardia results to have (R_{k}) = 1. The average of (R_{k}) over all the regions is (R_{av} = 0.15) and can be considered approximately a reference level for the Italian country (even if, of course, it has only a relative value).
Figure 3

(a) A-priori normalized risk ranking of Italian regions, emerging from our analysis of risk indicators, compared with the corresponding total cases, deaths and intensive care occupancy updated, respectively, at April 2, 2020 (just before the epidemic peak) and at July 14, 2020 (at the end of the first wave). Regions are organized in four risk groups, corresponding to different colors: very high, high, medium and low risk. The agreement with the observed effects Data referring to overestimations or underestimations of risk are also colored in green and red, respectively. (b–d) Comparison between the spatial distribution of COVID-19 total cases at July 14, 2020 (b), the most struck regions (in terms of severe cases and deaths) from 2019–2020 seasonal flu (d) according to the ISS data19 and our a-priori risk map (c). The geographical correlation with the risk map is evident for both kind of epidemic flus. Maps were realized with QGIS 3.10 (https://qgis.org/en/site/).

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As already explained, due to the intrinsic limitations of the official COVID-19 data, it is convenient to make the comparison at the aggregate level of groups of regions, without expecting to predict the exact rank within each group. Let us therefore arrange the 20 regions in four risk groups, each one characterized by a different color and ordered according to decreasing values of the risk index: very high risk ((0.4 < R_{k} le 1), in red), high risk ((0.2 < R_{k} le 0.4), in brown), medium risk ((0.03 < R_{k} le 0.2), in beige) and low risk ((R_{k} le 0.03), in pink). With this choice, our model is clearly able to correctly identify the four northern regions where the epidemic effects have been far more evident, in terms of cases, deaths and intensive care occupancy: the first in the ranking, i.e. Lombardia (whose risk score is about three times the second classified) and the group of the three regions immediately after it, Veneto, Piemonte and Emilia Romagna (even if not in the exact order of damage). A quite good agreement can be observed also for the other two groups: only for Sardegna the effects on both total cases and deaths seem to have been slightly overestimated (its insularity might play a role), while for other two regions, Umbria and Valle d’Aosta, some impact indicators have been slightly underestimated. Notice that the proposed risk classification seems quite robust, since it holds both near to the peak of April and at the end of the first wave, in July, when the intensive care occupancy of the majority of the regions was zero. In Table 6 reported in Methods, a further analysis of the robustness of this classification has been performed by eliminating, one by one, single indicators from the risk index definition: results show that the position of some regions slightly changes inside each group, but the composition of the four risk groups remains for the mostly unchanged with just few exceptions worsening the agreement with the impact indicators shown in Fig. 3a. This confirms the advantage of including all indicators in the risk index. The clear separation between northern regions from central and southern ones is also confirmed in the bottom part of Fig. 3, where the a-priori risk color map, in panel (c), is compared with the map of COVID-19 total cases in July, panel (b), and the map of the serious cases and deaths of the seasonal flu 2019/20 in Italy, panel (d) (ISS data19). The agreement is clearly visible. In Fig. 4 we show the correlations between the a-priori risk index and the three main impact indicators related to the outbreak, i.e. the total number of cases (a) and the total number of deaths (b), cumulated up to July 14, 2020, and the intensive care occupancy (c), registered at April 2, 2020. For each plot, a linear regression has been performed, with Pearson correlation coefficients always taking values greater or equal to 0.97, indicating a strong positive correlation. On the right of each plot we report the corresponding percentages of damage observed in the three Italian macro-regions—North, Center and South, see the geographic map (d). Also in this case the correlation is evident, if compared with the percentage of cumulated a-priori risk associated to the same macro-regions (e). Figure 4 The three main impact indicators for COVID-19—the total number of cases (a) and the total number of deaths (b) cumulated up to July 14, 20204, and the intensive care occupancy (c) at April 2, 20204—are reported as function of the a-priori risk index for all the Italian regions. The size of the points is proportional to the risk index score. A linear regression has been performed for each plot. The Pearson correlation coefficients are very good, always greater or equal than 0.97. The corresponding percentages of damages, aggregated for the three Italian macro-regions (North, Center and South (d)) are also reported to the right and can be compared with the percentages of cumulated a-priori risk (e). It is clear that our a-priori risk index is able to explain the anomalous damage discrepancies between these different parts of Italy. Maps were realized with QGIS 3.10 (https://qgis.org/en/site/). Full size image Another interesting way to visualize these correlations is to represent the a-priori risk index through its two main aggregated components, Hazard and Consequences, and plotting each region as a point of coordinates ((H_{i} ,C_{i} )) in the plane (left{ {H times C} right}). This Risk Diagram is reported in Fig. 5a, where the points have been also characterized by the same color of the corresponding risk group of Fig. 3. It is evident that the iso-risk line described by the equation C = Rav/H (being Rav = 0.15 the average regional risk value) is correctly able to separate the four more damaged and highly risky, northern regions (plus Lazio) from all the others. The value of the risk index is reported in parentheses next to each region name. As shown in Fig. 5b, where the ranking of the Italian regions has been disaggregated for both Hazard and Consequences, it is interesting to notice that some regions (such as Friuli, Trentino or Valle d’Aosta) exhibit high values of Hazard and quite low values of Consequences, while for other regions (such as Campania or Piemonte) the opposite is true. See also the colored geographic maps in Fig. 5c,d for a visual comparison. This confirms that it is necessary to aggregate such two main components in a single global index to have a more reliable indication of the regional a-priori risk. Figure 5 (a) Risk Diagram. Each region is represented as a point in the plane (left{ {H times C} right}) while the color is proportional to the corresponding risk group updated at July 14, 2020 (see Fig. 3a). The most damaged regions lie with a good approximation above the C = Rav/H hyperbole (i.e. the iso-risk line related to the average regional risk index), while the less damaged ones lie below this line. The a-priori risk index score is also reported for each region. (b) The rankings of Italian regions according to either Hazard (on the left) or Consequences (on the right). The corresponding colored geographic maps are also shown in panels (c) and (d) for comparison. Maps were realized with QGIS 3.10 (https://qgis.org/en/site/). Full size image Let us close this paragraph by showing, in Fig. 6, three sequences of the geographic distribution of the total cases (a), total number of deaths (b) and current intensive care occupancy (c) as a function of time, from March 9 to July 14, 2020. These sequences are compared with the geographic map of the a-priori risk level (the bordered image on the right in each sequence), the latter being independent of time. In all the plots, damages seem to spread over the regions with a variable intensity (expressed by the color scale) quite correctly predicted by our a-priori risk analysis. The intensive care occupancy map compared with the risk map is dated April 2, since the occupancy on July 14 is zero almost everywhere (with the exception of Lombardia and a few other regions). Figure 6 The geographic distributions of damage in the various Italian regions—cumulated total cases (a), cumulated total deaths (b) and daily intensive care occupancy (c)—are reported as function of time, from March 9, 2020 to July 14, 2020 and compared with the geographic distribution of the a-priori risk. Obviously, the intensive care occupancy to compare with the risk map is that of April, since in July, at the end the epidemic wave, this variable is zero everywhere except for a few regions (among which only Lombardia has a score slightly higher than 25). Maps were realized with QGIS 3.10 (https://qgis.org/en/site/). Full size image In the next paragraph, the methodology proposed in this paper, and in particular this representation in terms of risk diagram, will be used to build a policy model aimed at mitigating damages in case of an epidemic outbreak similar to the COVID-19 one. A proposal for a policy protocol to reduce the epidemic risk We have seen how the risk can be thought as composed in two components, one related to the causes of the infection diffusion and the other to the consequences. In this paragraph we will interpret the consequences in terms of protection and required support to people with the goal of improving the social result and/or reducing the economic cost. It is evident that enhancing the capability of the healthcare system appears to be the most important action: basically, the insufficient carrying capacity creates the emergency. Beyond specific factors explained above, the epidemic crisis in Lombardia essentially showed a breakdown of its healthcare system, caused by high demand rate for hospital admissions, long permanence times in intensive care, insufficient health assistance (diagnosis equipment, staff, spaces, etc.). Previously illustrated data provide a positive analysis of an epidemic disease (i.e., how things are, in a given state of the world). The normative approach here described presents a viable framework to assess possible policy protocols. Several variables affecting the diffusion of an infection can be looked at as suitable policy instruments to manage both the spreading process and the stress level to the healthcare system of a given district (such as a country, a region, an urban area, etc.). Following the evidence suggested by data, we propose a theoretical model (whose details are presented in the Methods section, paragraph 4) based on two independent variables influencing the level of risk, namely the infection ratio, i.e., the proportion of infected individuals over the total population, and the number of per capita hospital beds, as a measure of the impact of consequences caused by the spreading of the disease. We adopt an approach based on a standard model of economic policy, in which a series of instruments explicitly affecting the infection ratio and the per capita hospital beds endowment can be used to approach the target, i.e., the minimization of the risk level. A similar rationale, covering other topics, can be found in Samuelson and Solow33 (1960) and builds upon a widely consolidated literature which dates back in time34,35,36,37,38,39 (among many others). Despite the analysis concerns a collective problem, the model here proposed describes elements of a possible decision process followed by an individual policy-maker, thus remaining microeconomic in nature. Panel (a) in Fig. 7 shows the risk function, while the right panel provides an illustration of the family of its convex contours, for a finite set of risk levels (limited for graphic convenience): Figure 7 (a,b) The Risk function and its convex contours: an example for (R = x^{0.5} b^{0.5}). (c,d) The carrying capacity function and effects of policy interventions on the supply-side. (e,f) Comparative statics of equilibrium and disequilibrium. (g,h) Two examples of model implementation, see the main text. Full size image Panel (b) in Fig. 7 replicates the meaning of Fig. 5a by translating the consequences indicated by data as the required per capita hospital beds, while explaining that the position of each iso-risk curve corresponds to the different actual composition of the scenario at hand. We assume a unique care strategy based on the structural carrying capacity of the healthcare system, defined as the available number of per capita hospital beds. Such a carrying capacity derives from the health expenditure (G_{H}), which is set to a level considered sufficient. Such a choice is based on political decisions and is reasonably inferred from past experience, structural elements of population, such as age and territorial density, etc. A part of the deliberated budget is dedicated to set up intensive care beds, as an advanced assistance service provision. During an emergency, possibly deriving from an epidemic spreading, the number of beds can suddenly reveal insufficient. In other words, it is possible that the amount of hospital beds required at a certain point is greater than the current availability. In the model, we assume the number of hospital beds, H, and the proportion of intensive care beds, (alpha), as exogenously determined by the policy-maker who fixes (G_{H}). The actual carrying capacity is shown as a function of the infection ratio, x, computed as the infected population over the total, as shown in panel (c) of Fig. 7, and detailed in paragraph 4 of Methods. Changes in the proportion of per capita intensive care hospital beds over the total, cause instead, a variation in the slope of the line (which becomes steeper for reduction in the proportion of intensive care beds). Finally, changes in the overall expenditure shift the line with the same slope (above for increments of the expenditure). In particular, it is worth to notice that the political choice of the ratio (alpha = HH/H) may imply that the overall capacity to assist the entire population is not guaranteed (i.e. the intercept on the (x) axis might be less than (1)). A direct comparison of elements contained in panels (a-b) and (c-d) of Fig. 7 provides a quick inspection of the policy problem, focused to control the epidemic spreading. The constraint should be considered as a dynamic law, but since the speed of adjustment is reasonably low, we will proceed by means of a comparative statics perspective, in which a comparison of different strategies can be presented, by starting from different, static, scenarios. Further, by definition, an emergency challenges the usual policy settings, since the speed of damages is greater than that of policy tools. In panel (e) of Fig. 7 a hypothetic country has a given carrying capacity to sustain the risk level represented by the iso-risk curve. Without an immediate availability of funds to increase the carrying capacity, the main policy target could easily be described as the transposition of the iso-risk curve to the bottom-left: the closer the curve to the origin, the higher the satisfaction for the community. Secondly, the meaning of the relationship between the curve and the line is that until the curve touches the line, the policy maker has a sort of measure of how much the problem is out of control, given by the distance between the curve and the constraint. Third, policies may try to transpose the curve to lower levels or, equivalently, the constraint upwards (with or without modification of the slope). A minimal result is reached if both are at least tangent, as depicted in panel (f) of Fig. 7. Whenever such a tangency condition has been reached, the highest infection rate that the given health care system can sustain has been found. Further policy actions are possible to approach a lower iso-risk curve or to save resources and/or re-allocate them differently. A policy can be considered satisfactory when any of points belonging to the arc TT’ is reached, e.g. the point L. Alternative policies are neither equivalent, nor requiring the same actions, and the policy-maker has to choose actions with reference to the actual data collected by its own Country. Points F and G, although carrying the same risk level as E, still represent out-of-control positions. Different regions of the plot have a different signaling power: at point F, the infection rate is low and, thus, very difficult to be further reduced. In such a case, for example, it would be advisable to suggest health protocols which improve people safety. On the contrary, at point G, the infection rate is so high that a limit on social interaction easily appears to be much more urgent than medical protocols. The right mix between a demand-side and a supply-side policy to adopt is a decision of political nature. A distinction can be made by saying that demand-side policies are devoted to reduce the number of newly infected people (by means of restrictions to movements, quarantine regulations, rules of conduct, etc.) and their effects are able to lower the iso-risk curves; supply-side policies are, instead, aimed at incrementing the carrying capacity of the system (by means of expenditure for the healthcare system, increments of dedicated personnel and intensive care beds, in-house medical protocols) and their effects can shift the constraint representing the carrying capacity of the system. Politics has, then, to decide when the risk is low enough or the constraint is sufficiently high. Specific calibration of the model will allow, in a forthcoming research, a detailed analysis of policy implications, by considering actual conditions and risk factors of specific districts, thus providing the policy-maker with a toolbox for normative directions. For instance, the model can be read to analyze differences in proposed actions in Lombardia and Veneto, and in other regions or countries. More

Photographs of crabs and backgrounds
We sampled crabs and backgrounds to obtain images for the game. The population used was located in Falmouth (50.141888, −5.063811) on the south coast of the UK, comprising a stretch of shoreline encompassing neighbouring Castle and Gyllyngvase beaches. The crab habitats at the site comprise rock pools with rocky crevices with stony or gravel substrates in the pools and, lower down on the shore, increasing abundance of seaweed21. Together these create visually variable textures and heterogeneity in crab habitat types.
Photographs of natural backgrounds (rock pools) were taken by Samsung NX1000 digital camera converted to full spectrum and attached with a Nikon EL 80 mm lens. Background sampling was conducted along three ~100 m long transects placed parallel to the shoreline across different tide-zones (i.e. low, middle, high) spaced evenly down the beach (following21). Each of the backgrounds photographed were at least 5 m apart from each other (i.e. transect was subdivided approximately into 5-m-intervals) ensuring the variability in background types across transect. These sampling quadrats were photographed during low-tide to avoid specular light reflecting back from the water. To obtain images that capture naturalistic colour variation, the images were taken in RAW format with manual white balance and a fixed aperture setting. For human visible photos as used here, we placed a UV and infra-red (IR) blocking filter in front of the lens, which transmits wavelengths only between 400–680 nm (Baader UV/IR Cut Filter). We have previously characterised the spectral sensitivity of our cameras39. For calibration purposes, each photograph included a grey reflectance standard, which reflects light equally at 7 and 93% between 300 and 750 nm.
Quadrats were searched for shore crabs for a period of ~5 min. We searched for crabs by raking gravel by hand, moving small boulders aside, turning seaweed over and checking crevices to ensure any crabs were unlikely to be missed. After crabs were found we transported them to laboratory facilities at the University of Exeter Penryn campus for standardised photography. During the transportation all crabs were kept on standard average grey buckets. Photographs of crabs were taken with the same camera set up as above. In the laboratory a bulb simulating D65 illuminant (Iwasaki eyeColor bulb) was used while crabs were photographed against grey standard background. We included grey standards and scale bars in the photographs. Images were then calibrated and converted to normalised reflectance images (relative to the grey standard)39,40.
Crab images were scaled into the same pixel/mm aspect ratio to show crabs against the background images in natural size with respect to the background scale. Following past work25, crab outlines were cut out from the image by custom software was designed (called ‘autocrab’) to automate the process of background subtraction. This software allowed us to step through hundreds of images, automatically loading, thresholding and flood filling background areas, saving them with an appropriate transparency channel in the correct format and resolution needed for the game. This created usable crab images for 80% of the photographs easily, with some additional cleaning up required for the rest using GIMP2 image manipulation software (https://zenodo.org/record/1101057; DOI for the source code: https://doi.org/10.5281/zenodo.1099634). The crab images were PNGs (portable network graphic) with a variable alpha level to ensure there were no jagged edges visible.
Selection of crabs
We aimed to ensure that we had an ecologically relevant range of crab phenotypes used in the game. We also sought to test how different types or ‘morphs’ of crab would affect search image formation and detection. Therefore, we used a procedure to categorise crabs into one of six categories prior the experiment. Note that, statistically crab variation may be more continuous rather than falling into true morphs, but there are a number of common crab patterns and features that frequently arise in the wild20, potentially reflecting ‘modules’ of development and pattern expression. We emphasise that our aim here was not to test specifically whether shore crabs occur in discrete morphs, but rather to capture some of the variation and common features that exist in this species in order to explore the effects of different pattern types on search image formation and whether effects differ among common categories of appearance.
Game design
The design of the experiment generally followed the approach of previous citizen science camouflage games24. Ethical approval was granted by Exeter University (ID: 2015/736). Subjects were recruited via social media and word of mouth. On loading the webpage, subjects were taken to a start screen and informed that the game was an experiment and that by playing they consented to their data being used. They were free to leave the game at any time and no personal or identifying data were collected. Subjects also asked if they had played the game before.
The game was programmed in HTML5 (including JavaScript, CSS and PHP), and was available to play on all standard internet browsers. Upon loading the game each participant was shown a series of photographs of 24 natural rock pool backgrounds (randomly sampled from 105 natural background images) with a single crab (randomly sampled from 155 natural crab images) in each image (Fig. 1). Participants were asked to detect the crab (by clicking on it) as quickly as possible, which would progress them to the next slide. If the crab was not found within 15 s the crab was highlighted with a circle for 1 s, and then the participant progressed to the next slide. During the experiment, the probability of being shown the same individual crab phenotype in the next slide was always 80% (although the crab’s position and rotation, and the background image were all randomised), meaning that subjects were likely to have runs of the same individual crab in succession, often up to 10 encounters (the median run length for each crab being ~5 encounters). This approach mimicked a situation where there is no intraspecific variation in pattern, and allowed us to test which aspects of crab/morph appearance affected search image formation and switching.
Analysis of crab appearance and camouflage
Following our previous work testing how different types of camouflage metric predict detection26, we analysed a large number of metrics linked to camouflage efficacy, these include edge disruption, colour, luminance (lightness), and pattern metrics. The metrics included crab-only appearance measures (such as the crab’s intrinsic colour, brightness, and dominant marking size), and also comparative metrics where each crab is compared to its local surroundings (within a radius of one body-length, where body length is described as the diameter of a circle which best fits the crab’s outline), and also the crab compared to the entire background image. In total there were 45 metrics, all described in Supplementary Data 1. All image analysis was performed using ImageJ v1.5041, code available on request.
Images were converted from sRGB to CIELAB colour space before measuring them given that humans were the participants used in this study. Each crab was measured by recreating its exact position and rotation on each background for image analysis.
Luminance distribution difference was measured from the CIE L channel in 100 bins following the methods described in Troscianko et al.26, effectively the sum of absolute differences between the crab’s luminance histogram and the background or surrounding’s luminance histogram. The highly variable nature of the crab’s colour and background colours mean that calculating a mean colour for the background or crab may not be appropriate because it creates intermediate colours which do not represent the scene as a whole. Therefore, a colour equivalent of the luminance distribution difference method was also developed, where pixel CIE A and B values were plotted in a two-dimensional histogram to create a proportional frequency “map”. Each axis had 200 bins ranging from −100 to 100, meaning the bins are smaller than the human colour discrimination threshold in CIE LAB space. The absolute differences in the crab’s colour map and its background or surround colour maps were used as a non-parametric method for describing background colour matching. Edge disruption was also measured following the GabRat approach described in Troscianko et al. (2017), however in addition to measuring the CIE L image, the chromatic opponent channel images (CIE A and B images) were also measured (i.e. as a measure of chromatic edge disruption). Pattern energy difference was measured by creating a series of bandpass images, filtering each crab and surround into different spatial scales, then measuring the degree of “energy” standard deviation in pixel values) at each spatial scale to create an energy spectrum. Pattern energy difference calculates the absolute sum of energy differences at each spatial scale between the crab and its background following Troscianko et al.26.
Statistics and reproducibility
Survival models were used to determine how crab capture times were affected by experimental treatments and camouflage variables. Survival models offer the ability to count crabs reaching “timeout” (where participants still could not find the crab after 15 s) as surviving up to this point (termed censored in survival models). Mixed effects survival models (coxme version 2.2–1027) were used to reflect the fact that within-session data are not independent. All statistical analyses were performed in R (version 3.4.4), with the raw data and R script available as supplementary material (“Supplementary Data 2”, and “Supplementary Data 3” respectively). We used four different models to test each of our key predictions: (i) models ranking each of the camouflage metrics in order to find the best predictor of human performance, within each camouflage strategy the best predictor was selected and used in the subsequent tests; (ii) models testing the rate of improvement in capture time for each phenotype; (iii) models comparing the capture time and appearance of each crab relative to those of the previously encountered crab; (iv) models comparing the capture time of each crab given its morph, and the morph of the previous crab (i.e. interaction between individual phenotype and overall morph). We describe each in turn here:
First, based on our metrics of camouflage, we worked out the best predictor of human performance within each of these metrics. An example of the survival model is:
coxme(Surv(cTime, hit) ~ screenScale + playedBefore + poly(crab_circular_fit_centre_x,2) + poly(crab_circular_fit_centre_y,2) + L_GabRat_sig2.0 + crab_area + (1|sessionID), data).
This model takes into account the screen resolution, whether subjects have played before, the slide number (learning within session), the screen coordinates of the crabs (crabs in the corners of the screen take longer to find), the camouflage metric (GabRat luminance edge disruption in this example), the size of the crab (bigger crabs are easier to find), and session ID as a random factor. From these models we could calculate the metrics that were most effective in predicting detection times26, and narrowed the metrics down to the best predictors of luminance, colour, pattern and edge disruption.
Second, we tested how the number of previous encounters with the current crab phenotype affected capture times. This is testing for speed-of-improvement within each phenotype, and how different types of camouflage (determined above) affect this. An example survival model is:
coxme(Surv(cTime, hit) ~ screenScale + playedBefore + slide + poly(crab_circular_fit_centre_x,2) + poly(crab_circular_fit_centre_y,2) + L_GabRat_sig2.0 * encounters + crab_area + (1|sessionID), data). Where ‘encounters’ codes for the number of previous encounters with the current phenotype.
Third, we tested capture time differences when switching between crabs, comparing the camouflage of the previous crab with the current one (note the previously encountered crab was sometimes the same phenotype, and sometimes would switch to a new one). The dependent variable (timeDiff) was log(current crab capture time) – log(previous crab capture time). The camouflage variables are calculated in the same manner, e.g. the current level of disruption minus the previous level of disruption. Here, an interaction with the number of prior encounters with the current crab phenotype shows how switching is affected by prior experience of this camouflage type. An example model is:
lmer(timeDiff ~ crab_area + pArea + playedBefore + slide + poly(crab_circular_fit_centre_x,2) + poly(crab_circular_fit_centre_y,2) + poly(pX,2) + poly(pY,2) + drpLDiff*novelCrab + (1|sessionID), diffData). The values pArea, pX and pY denote the size and screen location of the previous crab.
Finally, we analysed capture time differences when switching between each of the six crab morphs (rather than comparing camouflage metric differences), using the timeDiff value as above. An example model is:
lmer(timeDiff ~ crab_area + pArea + slide + poly(crab_circular_fit_centre_x,2) + poly(crab_circular_fit_centre_y,2) + poly(pX,2) + poly(pY,2) + slide + morphSwitch*novelCrab + (1|sessionID), morphData). Here ‘morphSwitch’ has two levels which describe whether a switch event was to the same, or a different morph. The random factor ‘sessionID’ explained almost zero variance in this dataset, and where this occurred the models were cross-validated with GLMs (see Supplementary Data 3).
Selection of crab phenotypes
We asked 10 naïve participants (who had no prior experience of crab phenotype discrimination) to subjectively sort images of crabs into distinct categories. People were not instructed on how many groups they should form – they were simply asked to group crabs based on their colour and patterning (i.e. phenotypic variation). This resulted in six categories (the actual numbers of the crab images representing that phenotype are given in brackets as follows): Black (22), Disruptive (15), Green (50), Mottled (28), Pale (20) and Spotted (20). Although this is subjective, we subsequently analysed the appearance of crabs from these categories and showed that ‘crab morph’ is a significant predictor of a range of appearance metrics, including colour, luminance, mean pattern energy, and dominant marking size (P  More

1.
Tsukamoto, K. Discovery of the spawning area for Japanese eel. Nature 356, 789–791 (1992).
ADS  Article  Google Scholar 
2.
Tsukamoto, K. Spawning of eels near a seamount. Nature 439, 929 (2006).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

3.
Chow, S. et al. Discovery of mature freshwater eels in the open ocean. Fish. Sci. 75, 257–259 (2009).
CAS  Article  Google Scholar 

4.
Kurogi, H. et al. First capture of post-spawning female of the Japanese eel Anguilla japonica at the southern West Mariana Ridge. Fish. Sci. 77, 199–205 (2011).
CAS  Article  Google Scholar 

5.
Tsukamoto, K. et al. Positive buoyancy in eel leptocephali: an adaptation for life in the ocean surface layer. Mar. Biol. 156, 835–846 (2009).
Article  Google Scholar 

6.
Cheng, P. W. & Tzeng, W. N. Timing of metamorphosis and estuarine arrival across the dispersal range of the Japanese eel Anguilla japonica. Mar. Ecol. Prog. Ser. 131, 87–96 (1996).
ADS  Article  Google Scholar 

7.
Chen, J. Z., Huang, S. L. & Han, Y. S. Impact of long-term habitat loss on the Japanese eel Anguilla japonica. Estuar. Coast. Shelf Sci. 151, 361–369 (2014).
ADS  CAS  Article  Google Scholar 

8.
Tanaka, E. Stock assessment of Japanese eels using Japanese abundance indices. Fish. Sci. 80, 1129–1144 (2014).
CAS  Article  Google Scholar 

9.
Jacoby, D. & Gollock, M. Anguilla anguilla. The IUCN red list of threatened species, version 2014.2. IUCN 2014 e.T60344A45833138. https://doi.org/10.1108/ICS-04-2017-0025 (2014).

10.
Onda, H. et al. Vertical distribution and assemblage structure of leptocephali in the North Equatorial Current region of the western Pacific. Mar. Ecol. Prog. Ser. 575, 119–136 (2017).
ADS  Article  Google Scholar 

11.
Saijo, Y., Iizuka, S. & Asaoka, O. Chlorophyll maxima in Kuroshio and adjacent area. Mar. Biol. 4, 190–196 (1969).
CAS  Article  Google Scholar 

12.
Furuya, K. Subsurface chlorophyll maximum in the tropical and subtropical western Pacific Ocean: Vertical profiles of phytoplankton biomass and its relationship with chlorophylla and particulate organic carbon. Mar. Biol. 107, 529–539 (1990).
CAS  Article  Google Scholar 

13.
Otake, T., Nogami, K. & Maruyama, K. Dissolved and particulate organic matter as possible food sources for eel leptocephali. Mar. Ecol. Prog. Ser. 92, 27–34 (1993).
ADS  Article  Google Scholar 

14.
Mochioka, N. & Iwamizu, M. Diet of anguilloid larvae: Leptocephali feed selectively on larvacean houses and fecal pellets. Mar. Biol. 125, 447–452 (1996).
Google Scholar 

15.
Miller, M. J., Otake, T. & Aoyama, J. Observations of gut contents of leptocephali in the North Equatorial current and Tomini Bay Indonesia. Coast. Mar. Sci. 35, 277–288 (2012).
Google Scholar 

16.
Tomoda, T. et al. Observations of gut contents of anguilliform leptocephali collected in the western North Pacific. Nippon Suisan Gakkaishi 84, 32–44 (2018).
Article  Google Scholar 

17.
Deibel, D., Parrish, C. C., Grønkjær, P., Munk, P. & GisselNielsen, T. Lipid class and fatty acid content of the leptocephalus larva of tropical eels. Lipids 47, 623–634 (2012).
CAS  PubMed  Article  PubMed Central  Google Scholar 

18.
Liénart, C. et al. Geographic variation in stable isotopic and fatty acid composition of anguilliform leptocephali and particulate organic matter in the South Pacific. Mar. Ecol. Prog. Ser. 544, 225–241 (2016).
ADS  Article  CAS  Google Scholar 

19.
Miller, M. J. et al. A low trophic position of Japanese eel larvae indicates feeding on marine snow. Biol. Lett. 9, 20120826 (2013).
PubMed  PubMed Central  Article  Google Scholar 

20.
Miyazaki, S. et al. Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region. Mar. Biol. 158, 2555–2564 (2011).
CAS  Article  Google Scholar 

21.
Chow, S. et al. Japanese eel Anguilla japonica do not assimilate nutrition during the oceanic spawning migration: evidence from stable isotope analysis. Mar. Ecol. Prog. Ser. 402, 233–238 (2010).
ADS  CAS  Article  Google Scholar 

22.
Chow, S. et al. Onboard rearing attempts for the Japanese eel leptocephali using POM-enriched water collected in the Western North Pacific. Aquat. Living Resour. 30, 1–7 (2017).
Article  CAS  Google Scholar 

23.
Miller, M. J., Hanel, R., Feunteun, E. & Tsukamoto, K. The food source of Sargasso Sea leptocephali. Mar. Biol. 167, 57 (2020).
CAS  Article  Google Scholar 

24.
Pompanon, F. et al. Who is eating what: Diet assessment using next generation sequencing. Mol. Ecol. 21, 1931–1950 (2012).
CAS  PubMed  Article  PubMed Central  Google Scholar 

25.
Wang, M. & Jeffs, A. G. Nutritional composition of potential zooplankton prey of spiny lobster larvae: a review. Rev. Aquac. 6, 270–299 (2014).
Article  Google Scholar 

26.
Ho, T. W., Hwang, J. S., Cheung, M. K., Kwan, H. S. & Wong, C. K. Dietary analysis on the shallow-water hydrothermal vent crab Xenograpsus testudinatus using Illumina sequencing. Mar. Biol. 162, 1787–1798 (2015).
CAS  Article  Google Scholar 

27.
Chow, S. et al. Molecular diet analysis of Anguilliformes leptocephalus larvae collected in the western North Pacific. PLoS ONE 14, e0225610 (2019).
CAS  PubMed  PubMed Central  Article  Google Scholar 

28.
Riemann, L. et al. Qualitative assessment of the diet of European eel larvae in the Sargasso Sea resolved by DNA barcoding. Biol. Lett. 6, 819–822 (2010).
CAS  PubMed  PubMed Central  Article  Google Scholar 

29.
Ayala, D. J. et al. Gelatinous plankton is important in the diet of European eel (Anguilla anguilla) larvae in the Sargasso Sea. Sci. Rep. 8, 6156 (2018).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

30.
Estrada, M. et al. Phytoplankton across tropical and subtropical regions of the Atlantic Indian and Pacific Oceans. PLoS ONE 11, e0151699 (2016).
PubMed  PubMed Central  Article  CAS  Google Scholar 

31.
Lundgreen, R. B. C. et al. Eukaryotic and cyanobacterial communities associated with marine snow particles in the oligotrophic Sargasso Sea. Sci. Rep. 9, 1–12 (2019).
CAS  Article  Google Scholar 

32.
Ayala, D., Riemann, L. & Munk, P. Species composition and diversity of fish larvae in the Subtropical Convergence Zone of the Sargasso Sea from morphology and DNA barcoding. Fish. Oceanogr. 25, 85–104 (2016).
Article  Google Scholar 

33.
Arai, M. N. Active and passive factors affecting aggregations of hydromedusae: a review. Sci. Mar. 56, 99–108 (1992).
Google Scholar 

34.
Boero, F. et al. Gelatinous plankton: Irregularities rule the world (sometimes). Mar. Ecol. Prog. Ser. 356, 299–310 (2008).
ADS  Article  Google Scholar 

35.
Purcell, J. E. Feeding and growth of the siphonophore Muggiaea atlantica (Cunningham 1893). J. Exp. Mar. Bio. Ecol. 62, 39–54 (1982).
Article  Google Scholar 

36.
Alldredge, A. Particle aggregation dynamics. In Encyclopedia of Ocean Sciences, 2nd edn, 330–337 (Elsevier Inc., 2008). https://doi.org/10.1016/B978-012374473-9.00468-9

37.
Hosia, A. & Bamstedt, U. Seasonal abundance and vertical distribution of siphonophores in western Norwegian fjords. J. Plankton Res. 30, 951–962 (2008).
Article  Google Scholar 

38.
Lo, W. T., Yu, S. F. & Hsieh, H. Y. Effects of summer mesoscale hydrographic features on epipelagic siphonophore assemblages in the surrounding waters of Taiwan, western North Pacific Ocean. J. Oceanogr. 69, 495–509 (2013).
Article  Google Scholar 

39.
Lo, W.-T., Yu, S.-F. & Hsieh, H.-Y. Hydrographic processes driven by seasonal monsoon system affect siphonophore assemblages in tropical-subtropical waters (Western North Pacific Ocean). PLoS ONE 9, e100085 (2014).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

40.
Li, K. Z., Yin, J. Q., Huang, L. M. & Song, X. Y. Comparison of siphonophore distributions during the southwest and northeast monsoons on the northwest continental shelf of the South China Sea. J. Plankton Res. 34, 636–641 (2012).
Article  Google Scholar 

41.
López-López, L., Molinero, J. C., Tseng, L.-C., Chen, Q.-C. & Hwang, J.-S. Seasonal variability of the gelatinous carnivore zooplankton community in Northern Taiwan. J. Plankton Res. 35, 677–683 (2013).
Article  Google Scholar 

42.
Price, J. F. Upper ocean response to a hurricane. J. Phys. Ocean. 11, 153–175 (1981).
ADS  Article  Google Scholar 

43.
Toratani, M. Primary production enhancement by typhoon Ketsana in 2003 in western North Pacific. In Remote Sensing of Inland, Coastal, and Oceanic Waters (eds. Frouin, R. J. et al.) 7150, 715013 (SPIE, 2008).

44.
Lin, I. I. Typhoon-induced phytoplankton blooms and primary productivity increase in the western North Pacific subtropical ocean. J. Geophys. Res. Ocean. 117, C03039 (2012).
ADS  Article  Google Scholar 

45.
Ishida, H., Furusawa, K., Makino, T., Ishizaka, J. & Watanabe, Y. The effect of typhoons on phytoplankton communities and settling particle flux in the western North Pacific subtropical region. Oceanogr. Jpn. 25, 17–41 (2016).
Article  Google Scholar 

46.
Siswanto, E., Ishizaka, J., Yokouchi, K., Tanaka, K. & Tan, C. K. Estimation of interannual and interdecadal variations of typhoon-induced primary production: a case study for the outer shelf of the East China Sea. Geophys. Res. Lett. 34, L03604 (2007).
ADS  Article  Google Scholar 

47.
Chen, Y. L. L., Houng-Yung, C., Jan, S. & Tuo, S. H. Phytoplankton productivity enhancement and assemblage change in the upstream Kuroshio after typhoons. Mar. Ecol. Prog. Ser. 385, 111–126 (2009).
ADS  CAS  Article  Google Scholar 

48.
Tsuchiya, K. et al. Typhoon-induced response of phytoplankton and bacteria in temperate coastal waters. Estuar. Coast. Shelf Sci. 167, 458–465 (2015).
ADS  CAS  Article  Google Scholar 

49.
Typhoon information. Japan Meteorological Agency. https://www.data.jma.go.jp/fcd/yoho/typhoon/index.html. Accessed 10 Dec 2020.

50.
Miller, M. J. et al. Morphology and gut contents of anguillid and marine eel larvae in the Sargasso Sea. Zool. Anz. 279, 138–151 (2019).
Article  Google Scholar 

51.
Singh, P., Liu, Y., Li, L. & Wang, G. Ecological dynamics and biotechnological implications of thraustochytrids from marine habitats. Appl. Microbiol. Biotechnol. 98, 5789–5805 (2014).
CAS  PubMed  Article  Google Scholar 

52.
Tanaka, H., Kagawa, H., Ohta, H., Unuma, T. & Nomura, K. The first production of glass eel in captivity: fish reproductive physiology facilitates great progress in aquaculture. Fish Physiol. Biochem. 28, 493–497 (2003).
Article  Google Scholar 

53.
Stenly, W. et al. Ingestion by Japanese eel Anguilla japonica larvae on various minute zooplanktons. Aquac. Sci. 61, 341–347 (2013).
Google Scholar 

54.
Butts, I. A. E., Sørensen, S. R., Politis, S. N. & Tomkiewicz, J. First-feeding by European eel larvae: a step towards closing the life cycle in captivity. Aquaculture 464, 451–458 (2016).
Article  Google Scholar 

55.
Tsukamoto, K. & Miller, M. J. The mysterious feeding ecology of leptocephali: a unique strategy of consuming marine snow materials. Fish. Sci. 87, 11–29 (2020).
Article  CAS  Google Scholar 

56.
Bouilliart, M., Tomkiewicz, J., Lauesen, P., De Kegel, B. & Adriaens, D. Musculoskeletal anatomy and feeding performance of pre-feeding engyodontic larvae of the European eel (Anguilla anguilla). J. Anat. 227, 325–340 (2015).
PubMed  PubMed Central  Article  Google Scholar 

57.
Westeberg, H. A proposal regarding the source of nutrition of leptocephalus larvae. Int. Rev. Hydrobiol. Hydrogr. 75, 863–864 (1990).
Article  Google Scholar 

58.
Miller, M. Ecology of anguilliform leptocephali: remarkable transparent fish larvae of the ocean surface layer. Aqua-BioScience Monogr. https://doi.org/10.1093/gbe/evy021 (2009).
ADS  Article  Google Scholar 

59.
Strom, S., Bright, K., Fredrickson, K. & Brahamsha, B. The Synechococcus cell surface protein SwmA increases vulnerability to predation by flagellates and ciliates. Limnol. Oceanogr. 62, 784–794 (2017).
ADS  Article  Google Scholar 

60.
Benner, R. & Kaiser, K. Abundance of amino sugars and peptidoglycan in marine particulate and dissolved organic matter. Limnol. Oceanogr. 48, 118–128 (2003).
ADS  CAS  Article  Google Scholar 

61.
Seymour, J., Ahmed, T., Durham, W. & Stocker, R. Chemotactic response of marine bacteria to the extracellular products of Synechococcus and Prochlorococcus. Aquat. Microb. Ecol. 59, 161–168 (2010).
Article  Google Scholar 

62.
Biller, S. J. et al. Bacterial vesicles in marine ecosystems. Science (80-) 343, 183–186 (2014).
ADS  CAS  Article  Google Scholar 

63.
Scanlan, D. Bacterial vesicles in the ocean. Science 343, 143–144 (2014).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

64.
Cisternas-Novoa, C., Lee, C. & Engel, A. Transparent exopolymer particles (TEP) and Coomassie stainable particles (CSP): Differences between their origin and vertical distributions in the ocean. Mar. Chem. 175, 56–71 (2015).
CAS  Article  Google Scholar 

65.
Long, R. A. & Azam, F. Abundant protein-containing particles in the sea. Aquat. Microb. Ecol. 10, 213–221 (1996).
Article  Google Scholar 

66.
Tanoue, E., Ishii, M. & Midorikawa, T. Discrete dissolved and particulate proteins in oceanic waters. Limnol. Oceanogr. 41, 1334–1343 (1996).
ADS  CAS  Article  Google Scholar 

67.
Simon, M., Alldredge, A. L. & Azam, F. Bacterial carbon dynamics on marine snow. Mar. Ecol. Prog. Ser. 65, 205–211 (1990).
ADS  CAS  Article  Google Scholar 

68.
Godhe, A. et al. Quantification of diatom and dinoflagellate biomasses in coastal marine seawater samples by real-time PCR. Appl. Environ. Microbiol. 74, 7174–7182 (2008).
CAS  PubMed  PubMed Central  Article  Google Scholar 

69.
Zhu, F., Massana, R., Not, F., Marie, D. & Vaulot, D. Mapping of picoeucaryotes in marine ecosystems with quantitative PCR of the 18S rRNA gene. FEMS Microbiol. Ecol. 52, 79–92 (2005).
CAS  PubMed  Article  PubMed Central  Google Scholar 

70.
Gong, W. & Marchetti, A. Estimation of 18S gene copy number in marine eukaryotic plankton using a next-generation sequencing approach. Front. Mar. Sci. 6, 219 (2019).
Article  Google Scholar 

71.
Furuya, K. & Marumo, R. The structure of the phytoplankton community in the subsurface chlorophyll maxima in the western North Pacific Ocean. J. Plankton Res. 5, 393–406 (1983).
Article  Google Scholar 

72.
Kuroki, M., Okamura, A., Yamada, Y., Hayasaka, S. & Tsukamoto, K. Evaluation of optimum temperature for the early larval growth of Japanese eel in captivity. Fish. Sci. 85, 801–809 (2019).
CAS  Article  Google Scholar 

73.
Okamura, A. et al. Effects of water temperature on early development of Japanese eel Anguilla japonica. Fish. Sci. 73, 1241–1248 (2007).
CAS  Google Scholar 

74.
Kurokawa, T. et al. Influence of water temperature on morphological deformities in cultured larvae of Japanese eel, Anguilla japonica, at completion of yolk resorption. J. World Aquac. Soc. 39, 726–735 (2008).
Article  Google Scholar 

75.
Tsukamoto, K. et al. Oceanic spawning ecology of freshwater eels in the western North Pacific. Nat. Commun. 2, 179 (2011).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

76.
Shirai, K. et al. Temperature and depth distribution of Japanese eel eggs estimated using otolith oxygen stable isotopes. Geochim. Cosmochim. Acta 236, 373–383 (2018).
ADS  CAS  Article  Google Scholar 

77.
Ichikawa, T. Particulate organic carbon and nitrogen in the adjacent seas of the Pacific Ocean. Mar. Biol. 68, 49–60 (1982).
CAS  Article  Google Scholar 

78.
Hebel, D. V. & Karl, D. M. Seasonal, interannual and decadal variations in particulate matter concentrations and composition in the subtropical North Pacific Ocean. Deep Sea Res Part II Top. Stud. Oceanogr. 48, 1669–1695 (2001).
ADS  CAS  Article  Google Scholar 

79.
MacIntyre, S., Alldredge, A. L. & Gotschalk, C. C. Accumulation of marines now at density discontinuities in the water column. Limnol. Oceanogr. 40, 449–468 (1995).
ADS  Article  Google Scholar 

80.
Tomas, C. R. & Hasle, G. R. Identifying Marine Phytoplankton (Academic Press, New York, 1997).
Google Scholar 

81.
Suzuki, K. et al. Responses of phytoplankton and heterotrophic bacteria in the northwest subarctic Pacific to in situ iron fertilization as estimated by HPLC pigment analysis and flow cytometry. Prog. Oceanogr. 64, 167–187 (2005).
ADS  Article  Google Scholar 

82.
Nagai, S. et al. Influences of diurnal sampling bias on fixed-point monitoring of plankton biodiversity determined using a massively parallel sequencing-based technique. Gene 576, 667–675 (2016).
CAS  PubMed  Article  PubMed Central  Google Scholar 

83.
Tanabe, A. S. et al. Comparative study of the validity of three regions of the 18S-rRNA gene for massively parallel sequencing-based monitoring of the planktonic eukaryote community. Mol. Ecol. Resour. 16, 402–414 (2016).
CAS  PubMed  Article  PubMed Central  Google Scholar 

84.
Dzhembekova, N., Moncheva, S., Ivanova, P., Slabakova, N. & Nagai, S. Biodiversity of phytoplankton cyst assemblages in surface sediments of the Black Sea based on metabarcoding. Biotechnol. Biotechnol. Equip. 32, 1507–1513 (2018).
CAS  Article  Google Scholar 

85.
Dzhembekova, N., Urusizaki, S., Moncheva, S., Ivanova, P. & Nagai, S. Applicability of massively parallel sequencing on monitoring harmful algae at Varna Bay in the Black Sea. Harmful Algae 68, 40–51 (2017).
PubMed  Article  PubMed Central  Google Scholar 

86.
Bolger, A. M., Lohse, M. & Usadel, B. Trimmomatic: a flexible trimmer for Illumina sequence data. Bioinformatics 30, 2114–2120 (2014).
CAS  PubMed  PubMed Central  Article  Google Scholar 

87.
Schloss, P. D., Gevers, D. & Westcott, S. L. Reducing the effects of PCR amplification and sequencing artifacts on 16S rRNA-based studies. PLoS ONE 6, e27310 (2011).
ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

88.
Edgar, R. C., Haas, B. J., Clemente, J. C., Quince, C. & Knight, R. UCHIME improves sensitivity and speed of chimera detection. Bioinformatics 27, 2194–2200 (2011).
CAS  PubMed  PubMed Central  Article  Google Scholar 

89.
Cheung, K. L. Y., Huen, J., Houry, W. A. & Ortega, J. Comparison of the multiple oligomeric structures observed for the Rvb1 and Rvb2 proteins. Biochem. Cell Biol. 88, 77–88 (2010).
CAS  PubMed  PubMed Central  Article  Google Scholar 

90.
Camacho, C. et al. BLAST+: architecture and applications. BMC Bioinform. 10, 421 (2009).
Article  CAS  Google Scholar 

91.
Horton, T. et al. World register of marine species (WoRMS) (2018).

92.
R Core team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing , Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/ (2017). https://doi.org/10.2788/95827.

93.
Bray, J. R. & Curtis, J. T. An ordination of the upland forest communities of southern Wisconsin. Ecol. Monogr. 27, 325–349 (1957).
Article  Google Scholar 

94.
Anderson, M. J. A new method for non-parametric multivariate analysis of variance. Aust. Ecol. 26, 32–46 (2001).
Google Scholar 

95.
Oksanen, J. et al. vegan: Community ecology package. R package version 2.5-2. CRAN R (2018). ISBN 0-387-95457-0. More

The “consumer first” pattern of spatial self-organization is the minority pattern
We first determined which of the two patterns of spatial self-organization (i.e., the “producer first” or “consumer first” pattern (Fig. 1B, C)) is the minority pattern. We reasoned that the minority pattern is the one likely to be caused by genetic or nongenetic variants. When we performed range expansion experiments using equivalent initial cell densities of the producer and consumer (i.e., initial producer and consumer proportions of 0.5), the “consumer first” pattern was clearly the minority pattern (Fig. 1B). Among nine independent replicates, we observed mean numbers of 64 “producer first” patterns (SD = 9, n = 9) and 20 “consumer first” patterns per range expansion (SD = 4, n = 9), and the mean number of “producer first” patterns was significantly greater than the mean number of “consumer first“ patters (two-sample two-sided t test; P = 1 × 10−6, n = 9). Overall, “consumer first” patterns accounted for 24% (SD = 4%, n = 9) of the total number of patterns per range expansion. We therefore conclude that the “consumer first” pattern is indeed the minority pattern, and thus the pattern likely to be caused by genetic or phenotypic variants.
The number of “consumer first” patterns depends on initial cell densities
If the “consumer first” pattern were caused by genetic variants, then the number of “consumer first” patterns that emerge per range expansion should depend on the initial cell densities of the producer or consumer. For example, if a genetic variant of the consumer causes the emergence of the “consumer first” pattern, then increasing the initial cell density of the consumer should increase the number of the causative variants of the consumer, and thus promote the emergence of more “consumer first” patterns.
To test this, we varied the initial producer proportion while holding the total initial cell density of the producer and consumer constant, thus allowing us to avoid potential confounding effects that may result from modifying the total initial cell density. We then quantified the mean number of “consumer first” patterns that emerged per range expansion as a function of the initial producer proportion. When we tested an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5), we observed the characteristic emergence of the two different patterns, where the “consumer first” pattern was the minority pattern (Fig. 2B). When we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), the “consumer first” pattern completely disappeared while the “producer first” pattern occupied the entire expansion area (Fig. 2A). In contrast, when we tested an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999), the “producer first” pattern completely disappeared while the “consumer first” pattern occupied the entire expansion area (Fig. 2C). We then repeated the experiment across a range of initial producer proportions and observed a decreasing monotonic relationship between the mean number of “consumer first” patterns that emerged per range expansion and the initial producer proportion (Fig. 3). We could model the decreasing relationship with a Poisson regression using the natural logarithm as the link function (intercept = 3.76, slope = −4.15, P for both parameters = 2 × 10−16, n = 9) (black line; Fig. 3). Thus, the number of “consumer first” patterns that emerge per range expansion does indeed depend on the initial cell densities of the producer and consumer.
Fig. 2: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

The producer expressed the cyan fluorescent protein-encoding ecfp gene (blue) while the consumer expressed the green fluorescent protein-encoding egfp gene (green). Initial producer proportions include (A) 0.98, (B) 0.5, and (C) 0.001. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions.

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Fig. 3: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

Each data point is the number of “consumer first” patterns that emerged for an independent range expansion. The black line is the fit of a Poisson regression model to the data. The gray area is the 95% confidence interval of Poisson distributions with λ = predicted value of the Poisson regression fit. The green line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the consumer. The blue line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the producer. The total initial cell densities of producer and consumer were identical across all of the tested initial proportions.

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Genetic variants as a cause of the observed pattern diversification
While we found that the number of “consumer first” patterns that emerge per range expansion depends on the initial cell densities of the producer and consumer (Fig. 3), the log-linear form of the decreasing relationship is inconsistent with the “consumer first” pattern being caused by genetic variants. Consider initial producer proportions of 0.02. 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9). At these initial producer proportions, the initial cell density of the consumer is approximately twofold greater (1.96-, 1.90-, and 1.8-fold, respectively) than that for an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). If genetic variants of the consumer cause the emergence of the “consumer first” pattern, we would therefore expect approximately twofold more “consumer first” patterns to emerge per range expansion. More generally, we would expect the number of “consumer first” patterns that emerge per range expansion to decrease linearly as the initial producer proportion increases (i.e., as the initial consumer proportion decreases) (Fig. 3, green line) (see the Supplementary Text for the formulation of this expectation). We did not observe either of these expectations. First, at initial producer proportions of 0.02, 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9), the number of “consumer first” patterns was not approximately twofold greater than at an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). Instead, it was three to fivefold greater (Fig. 3) (one-sample two-sided t test; P = 6 × 10−5, n = 3). Second, we experimentally observed a decreasing log-linear relationship (black line; Fig. 3) rather than the expected decreasing linear relationship (green line; Fig. 3) between the number of “consumer first” patterns that emerged per range expansion and the initial producer proportion. Thus, we conclude that genetic variants of the consumer are unlikely to cause the emergence of the two patterns of spatial self-organization.
Our analysis above assumes that the “consumer first” pattern is caused by genetic variants of the consumer. However, it is plausible that the “consumer first” pattern is instead caused by genetic variants of the producer. The form of the relationship between the number of “consumer first” patterns that emerged per range expansion and the initial cell densities of the producer and consumer, however, is again inconsistent with this hypothesis (Fig. 3). If genetic variants of the producer cause the emergence of the “consumer first” pattern, then we would expect the number of “consumer first” patterns that emerge per range expansion to increase as the initial producer proportion increases (blue line; Fig. 3). Stated alternatively, increasing the initial producer proportion will increase the abundance of the causative variants of the producer, and thus increase the number of “consumer first” patterns that emerge. However, we observed the opposite outcome, where the number of “consumer first” patterns that emerged per range expansion decreased as the initial producer proportion increased (black line; Fig. 3). Thus, we conclude that genetic variants of the producer are also unlikely to cause the emergence of the two different patterns of spatial self-organization.
While the above analyses provide circumstantial evidence that genetic variants do not cause the simultaneous emergence of the two different patterns of spatial self-organization, we sought to provide more conclusive evidence of this by testing whether the “consumer first” pattern is heritable. To achieve this, we obtained a collection of isolates purified from prior “consumer first” patterns. We then mixed the isolates together (one producer with one consumer; initial producer and consumer proportions of 0.5) and repeated the range expansion experiment. Finally, we counted the numbers of “consumer first” patterns that emerged during the second range expansion and compared the numbers to those for pairs of the ancestral strains (producer and consumer). If the emergence of the “consumer first” pattern were heritable, we would expect more “consumer first” patterns when using pairs of isolates purified from prior “consumer first” patterns.
We found that pairs of isolates (producer and consumer) purified from prior “consumer first” patterns do not behave differently when compared to pairs of the ancestral strains (producer and consumer). Among ten independent range expansions for a pair of isolates (producer and consumer) purified from a prior “consumer first” pattern, we found that the “consumer first” pattern completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3a). However, among ten independent range expansions for the pair of ancestral strains (producer and consumer), we found that the “consumer first” pattern also completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3b). Overall, among the remaining nine independent range expansions, we did not detect more “consumer first” patterns per range expansion for the pair of isolates (producer and consumer) purified from a prior “consumer first” pattern than for the pair of ancestral strains (producer and consumer) (two-sample two-sided t test; P = 0.27, n = 9). Moreover, we sequenced the genomes of four producer isolates and four consumer isolates purified from prior “consumer first” patterns and found only one putative genetic difference in a single consumer isolate when compared to their respective ancestors (Supplementary Text and Supplementary Table S3). Thus, the “consumer first” pattern is not heritable, and its emergence is therefore not caused by genetic variants.
Neighborhood effects as a cause for the observed pattern diversification
If the simultaneous emergence of the two different patterns of spatial self-organization is not caused by genetic variants, what then could be the cause? We argue that one plausible cause is neighborhood effects that emerge due to local differences in the initial spatial positionings of otherwise identical individuals. Consider random initial distributions of producer and consumer cells across a surface (initial producer and consumer proportions of 0.5; Fig. 4B). At some spatial locations, producer cells may initially lie sufficiently close to the expansion frontier such that the consumer cells do not physically impede their expansion (white arrow; Fig. 4B). The producer cells would then expand first while the consumer cells would expand afterwards, giving rise to the “producer first” pattern (white arrow; Fig. 4B). However, at other spatial locations, producer cells may initially lie behind a cluster of consumer cells such that the consumer cells physically impede the expansion of the producer cells (green arrow; Fig. 4B). Indeed, we observed this experimentally at an intermediate timepoint of expansion (Supplementary Fig. S4). These clusters of consumer cells can occur purely as a consequence of the random initial spatial positionings of those cells, a process known as Poisson clumping [55]. The producer cells would then shove the consumer cells forward as they expand, giving rise to the “consumer first” pattern (green arrow; Fig. 4B). This hypothesis assumes that cell shoving is the dominant form of cell movement in the densely packed expanding microbial colonies produced by our synthetic microbial community, which is an assumption supported by numerous experimental and theoretical investigations [17, 53, 56,57,58,59,60].
Fig. 4: Conceptual model for how local differences in the initial spatial positionings of individual cells could promote diversification in patterns of spatial self-organization.

The producer is blue while the consumer is green. The initial producer proportion is (A) approximating to 1, (B) 0.5, or (C) approximating to 0. White arrows indicate “producer first” patterns and green arrows indicate “consumer first” patterns. The horizontal panels from left to right depict pattern formation over time.

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Importantly, this hypothesis is qualitatively consistent with our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). If producer cells initially far outnumber consumer cells, then the “consumer first” pattern should become less numerous (Fig. 4A). This is because there are fewer consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells can therefore expand immediately giving rise to the “producer first” pattern (Fig. 4A). In contrast, if the consumer cells initially far outnumber producer cells, then the “consumer first” pattern should become more numerous (Fig. 4C). This is because there are more consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells must therefore shove the consumer cells forward giving rise to the “consumer first” pattern (Fig. 4C).
This hypothesis is also consistent with quantitative features of our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). The initial spatial distributions of producer and consumer cells can be thought of as realizations of a Poisson point process. Such a process by chance produces clusters of consumer cells whose occurrence is described by a Poisson distribution with mean and variance λ. The mean number of consumer clusters and variance depend on the initial proportion of the consumer in a log-linear manner. As the initial proportion of the consumer increases, the probability for a consumer cluster to occur also increases. This, in turn, increases the probability that a “consumer first” pattern will form and increases the variance in the expected number of “consumer first” patterns. We found that this Poisson process accurately captures key features of our experimental data. First, the relationship between the number of “consumer first” patterns and the initial consumer proportion is modeled very well by a Poisson regression (Fig. 3). Second, the variance in the number of “consumer first” patterns increases as the experimentally observed number of “consumer first” patterns increases (Fig. 3). Third, the 95% confidence intervals of the Poisson distributions with λ equal to the predicted value of the Poisson regression matches the spread of the experimentally observed number of “consumer first” patterns (Fig. 3). In summary, the log-linear shape and the increasing variance of the data are thus consistent with our hypothesis that Poisson clumping due to the random initial spatial positionings of individuals causes the ‘consumer first’ pattern and promotes the observed diversification in patterns of spatial self-organization.
To provide further evidence that neighborhood effects due to local differences in the initial spatial positionings of individuals can promote diversification in patterns of spatial self-organization, we performed mathematical simulations with an individual-based model that accounts for cell shoving during range expansion. The original model and its adaptions to range expansion are described in detail elsewhere [17, 53]. We further adapted the model to simulate the emergence of spatial self-organization during expansion of our own synthetic microbial community [20]. In this study, we applied the model for two purposes. First, we asked whether the model could simulate the simultaneous emergence of the two different patterns of spatial self-organization in the absence of spatial heterogeneity in the initial abiotic environment. Second, we varied the initial producer proportion and evaluated the consequences on the number of “consumer first” patterns that emerge during range expansion. Note that our implementation of the model does not incorporate genetic or stochastic phenotypic heterogeneity or demographic effects. However, our implementation does account for heterogeneity in the initial spatial positionings of individuals, as we randomly distributed individuals of the producer and consumer across the inoculation area prior to the onset of community expansion.
Our simulations revealed three important outcomes. First, when we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), we found rare localized spatial areas where consumer cells were pushed forward by producer cells (Fig. 5A and Supplementary Movie S1). These cells maintained a spatial position at the expansion frontier for a prolonged period of time and formed a characteristic “consumer first” pattern (Fig. 5A and Supplementary Movie S1). Second, at this initial producer proportion, both “producer first” and “consumer first” patterns emerged simultaneously, from the very origin of expansion, and at the same length scale, even though the initial abiotic environment was spatially homogeneous and all individuals were subject the same deterministic rules (Fig. 5A and Supplementary Movie S1). Finally, when we decreased the initial producer proportion to 0.02 (i.e., an initial consumer proportion of 0.98), the number of consumer cells that maintained a position at the expansion frontier increased, thus indicating the formation of more “consumer first” patterns (Fig. 5B and Supplementary Movie S2). All three of these observations are consistent with our experimental observations and, importantly, did not require the consideration of heterogeneity in the initial abiotic environment, genetic or stochastic phenotypic heterogeneity within populations, or demographic effects. Thus, neighborhood effects due to local differences in the initial spatial positionings of individuals are sufficient alone to promote pattern diversification and result in the emergence of two different patterns of spatial self-organization.
Fig. 5: Individual-based modeling simulations of the effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion.

The producer is blue while the consumer is green. Initial producer proportions are (A) 0.98 (see Supplementary Movie S1) and (B) 0.02 (see Supplementary Movie S2). The initial abiotic environment was spatially homogeneous and genetic heterogeneity, stochastic phenotypic heterogeneity, and demographic effects were not incorporated into the model. Producer and consumer cells were distributed randomly around the center prior to the onset of expansion and the total initial cell densities of producer and consumer were identical across all of the simulations. The white arrows indicate “producer first” patterns and the green arrow indicates a “consumer first” pattern.

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The different patterns of spatial self-organization have different community properties
We finally asked whether the different patterns of spatial self-organization have different community-level properties. More specifically, we tested whether the different patterns have different expansion speeds. Two features of our previous experimental observations already point towards this being the case. First, the “consumer first” patterns (green arrows; Fig. 1C) extend further in the radial direction of expansion than do the “producer first” patterns (white arrows; Fig. 1C). This is readily observed at the expansion frontier, where the “consumer first” patterns tend to protrude outwards in the radial direction (Fig. 1C). Second, the “consumer first” patterns increase in width in the direction of expansion (green arrows; Fig. 1C). Both of these features are consistent with faster expansion speeds [61, 62].
To further test this, we varied the initial producer proportion, and thus varied the ratio of “consumer first” to “producer first” patterns (Fig. 3), and quantified the expansion radii over time. We found that the initial expansion speeds were significantly faster for an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999) than for 0.98 (i.e., an initial consumer proportion of 0.02) (F-test; P = 1 × 10−5) (Fig. 6A). Thus, smaller initial producer proportions that promote the emergence of more ‘consumer first’ patterns result in faster expansion speeds. Moreover, when we varied the initial producer proportion between 0.02 and 0.98 (i.e., initial consumer proportions between 0.98 and 0.02), we found a decreasing relationship between the final expansion radius and the initial producer proportion (linear model: final expansion radius ~ initial producer proportion; slope = −263, R2 = 0.42, P = 2 × 10−4, n = 9) (Fig. 6B). Thus, smaller initial producer proportions that promote the emergence of more “consumer first” patterns result in a greater extent of community expansion over the time-course of the experiment. Together, our data demonstrate that the different patterns of spatial self-organization do indeed have different expansion speeds.
Fig. 6: Effect of the initial producer proportion on expansion properties.

A Effect on the initial expansion speed. B Effect on the final expansion radius. Each data point is the expansion radius for an independent range expansion. The lines are linear models and the gray areas are the 95% confidence intervals. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions. The final expansion radii were measured after 4 weeks of incubation.

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1.
Rosati, A. G. & Cognition, F. Reviving the ecological intelligence hypothesis. Trends Cognit. Sci. 21(9), 691–702. https://doi.org/10.1016/j.tics.2017.05.011 (2017) (ISSN 1879307X).
Article  Google Scholar 
2.
Kuhn, S. L., Raichlen, D. A. & Clark, A. E. What moves us? How mobility and movement are at the center of human evolution. Evolut. Anthropol. 25(3), 86–97. https://doi.org/10.1002/evan.21480 (2016).
Article  Google Scholar 

3.
Pacheco-Cobos, L. et al. Nahua mushroom gatherers use area-restricted search strategies that conform to marginal value theorem predictions. Proc. Natl. Acad. Sci. USA 116(21), 10339–10347. https://doi.org/10.1073/pnas.1814476116 (2019) (ISSN 10916490).
CAS  Article  PubMed  Google Scholar 

4.
Viswanathan, G. M. et al. Optimizing the success of random searches. Nature 401(6756), 911–914. https://doi.org/10.1038/44831 (1999) (ISSN 00280836).
CAS  Article  PubMed  ADS  Google Scholar 

5.
Bartumeus, F. Lévy processes in animal movement: an evolutionary hypothesis. Fractals 15(2), 151–162. https://doi.org/10.1142/S0218348X07003460 (2007).
Article  Google Scholar 

6.
Bartumeus, F. et al. Foraging success under uncertainty: search tradeoffs and optimal space use. Ecol. Lett. 19(11), 1299–1313. https://doi.org/10.1111/ele.12660 (2016).
Article  PubMed  Google Scholar 

7.
Sims, D. W. et al. Scaling laws of marine predator search behaviour. Nature 451(7182), 1098–1102. https://doi.org/10.1038/nature06518 (2008).
CAS  Article  PubMed  ADS  Google Scholar 

8.
Bartumeus, F., Peters, F., Pueyo, S., Marrasé, C. & Catalan, J. Helical Lévy walks: adjusting searching statistics to resource availability in microzooplankton. Proc. Natl. Acad. Sci. USA 100(22), 12771–12775. https://doi.org/10.1073/pnas.2137243100 (2003).
CAS  Article  PubMed  ADS  Google Scholar 

9.
Boyer, D., Crofoot, M. C. & Walsh, P. D. Non-random walks in monkeys and humans. J. R. Soc. Interface 9(70), 842–847. https://doi.org/10.1098/rsif.2011.0582 (2012) (ISSN 17425662).
Article  PubMed  Google Scholar 

10.
Brown, C. T., Liebovitch, L. S. & Glendon, R. Lévy flights in dobe Ju/’hoansi foraging patterns. Hum. Ecol. 35(1), 129–138. https://doi.org/10.1007/s10745-006-9083-4 (2007) (ISSN 03007839).
Article  Google Scholar 

11.
Raichien, D. A. et al. Evidence of Lévy walk foraging patterns inhuman hunter-gatherers. Proc. Natl. Acad. Sci. USA 111(2), 728–733. https://doi.org/10.1073/pnas.1318616111 (2014).
CAS  Article  ADS  Google Scholar 

12.
Kölzsch, A. et al. Experimental evidence for inherent lévy search behaviour in foraging animals. Proc. R. Soc. B Biol. Sci. 282(1807), 20150424. https://doi.org/10.1098/rspb.2015.0424 (2005).
Article  Google Scholar 

13.
Kramer, D. L. & McLaughlin, R. L. The behavioral ecology of intermittent locomotion. Am. Zool. 41(2), 137–153. https://doi.org/10.1093/icb/41.2.137 (2001).
Article  Google Scholar 

14.
Bartumeus, F. & Levin, S.A. Fractal reorientation clocks: Linking animal behavior to statistical patterns of search. Technical Report 49, (2008). https://www.pnas.org/content/pnas/105/49/19072.full.pdf.

15.
Bazazi, S., Bartumeus, F., Hale, J. J. & Couzin, I. D. Intermittent motion in desert locusts: behavioural complexity in simple environments. PLoS Comput. Biol. 8(5), e1002498. https://doi.org/10.1371/journal.pcbi.1002498 (2012).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

16.
Reynolds, A. Liberating Lévy walk research from the shackles of optimal foraging (2015). ISSN 15710645.

17.
Grove, M., Lycett, S.J. & Chauhan, P.R. The Quantitative Analysis of Mobility: Ecological Techniques and Archaeological Extensions. https://doi.org/10.1007/978-1-4419-6861-6 (2010). ISBN 9781441968609.

18.
Bond, A. B. & Kamil, A. C. Spatial heterogeneity, predator cognition, and the evolution of color polymorphism in virtual prey. Proc. Natl. Acad. Sci. USA 103(9), 3214–3219. https://doi.org/10.1073/pnas.0509963103 (2006) (ISSN 00278424).
CAS  Article  PubMed  ADS  Google Scholar 

19.
Spaethe, J., Tautz, J. & Chittka, L. Do honeybees detect colour targets using serial or parallel visual search?. J. Exp. Biol. 209(6), 987–993. https://doi.org/10.1242/jeb.02124 (2006) (ISSN 00220949).
Article  PubMed  Google Scholar 

20.
de Froment, A. J., Rubenstein, D. I. & Levin, S. A. An extra dimension to decision-making in animals: the three-way trade-off between speed, effort per-unit-time and accuracy. PLoS Comput. Biol. 10(12), e1003937. https://doi.org/10.1371/journal.pcbi.1003937 (2014).
Article  PubMed  PubMed Central  Google Scholar 

21.
Campos, D., Méndez, V. & Bartumeus, F. Optimal intermittence in search strategies under speed-selective target detection. Phys. Rev. Lett. 108(2), 028102. https://doi.org/10.1103/PhysRevLett.108.028102 (2012) (ISSN 00319007).
CAS  Article  PubMed  ADS  Google Scholar 

22.
Bogacz, R., Brown, E., Moehlis, J., Holmes, P. & Cohen, J. D. The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychol. Rev. 113(4), 700–765. https://doi.org/10.1037/0033-295X.113.4.700 (2006).
Article  PubMed  Google Scholar 

23.
Chittka, L., Skorupski, P. & Raine, N. E. Speed-accuracy tradeoffs in animal decision making. Trends Ecol. Evol. 24(7), 400–407. https://doi.org/10.1016/j.tree.2009.02.010 (2009) (ISSN 01695347).
Article  PubMed  Google Scholar 

24.
Nityananda, V. & Chittka, L. Modality-specific attention in foraging bumblebees. R. Soc. Open Sci.https://doi.org/10.1098/rsos.150324 (2015).
Article  PubMed  PubMed Central  Google Scholar 

25.
Chittka, L. & Raine, N.E. Recognition of flowers by pollinators, 8 (2006). ISSN 13695266.

26.
Zhang, M. et al. Finding any Waldo with zero-shot invariant and efficient visual search. Nat. Commun. 9(1), 1–15. https://doi.org/10.1038/s41467-018-06217-x (2018).
CAS  Article  ADS  Google Scholar 

27.
Viswanathan, G. M., Da Luz, M. G. E., Raposo, E. P. & Eugene Stanley, H. The Physics of Foraging: An Introduction to Random Searches and Biological Encounters Vol. 9781107006 (Cambridge University Press, Cambridge, 2011). https://doi.org/10.1017/CBO9780511902680.
Google Scholar 

28.
Wilson, R. P., Quintana, F. & Hobson, V. J. Construction of energy landscapes can clarify the movement and distribution of foraging animals. Proc. R. Soc. B Biol. Sci. 279(1730), 975–980. https://doi.org/10.1098/rspb.2011.1544 (2012).
Article  Google Scholar 

29.
Ross, C. T. & Winterhalder, B. Sit-and-wait versus active-search hunting: a behavioral ecological model of optimal search mode. J. Theor. Biol. 387, 76–87. https://doi.org/10.1016/j.jtbi.2015.09.022 (2015) (ISSN 10958541).
MathSciNet  Article  PubMed  MATH  Google Scholar 

30.
Gameiro, R. R., Kaspar, K., König, S. U., Nordholt, S. & König, P. Exploration and exploitation in natural viewing behavior. Sci. Rep. 7(1), 1–23. https://doi.org/10.1038/s41598-017-02526-1 (2017) (ISSN 20452322).
CAS  Article  Google Scholar 

31.
LaScala-Gruenewald, D. E., Mehta, R. S., Liu, Yu. & Denny, M. W. Sensory perception plays a larger role in foraging efficiency than heavy-tailed movement strategies. Ecol. Model. 404(October 2018), 69–82. https://doi.org/10.1016/j.ecolmodel.2019.02.015 (2019) (ISSN 03043800).
Article  Google Scholar 

32.
Mugan, U. & MacIver, M. A. Spatial planning with long visual range benefits escape from visual predators in complex naturalistic environments. Nat. Commun. 11(1), 1–14. https://doi.org/10.1038/s41467-020-16102-1 (2020) (ISSN 20411723).
CAS  Article  Google Scholar 

33.
Kerster, B. E., Rhodes, T. & Kello, C. T. Spatial memory in foraging games. Cognition 148, 85–96. https://doi.org/10.1016/j.cognition.2015.12.015 (2016) (ISSN 18737838).
Article  PubMed  Google Scholar 

34.
Martínez-García, R., Calabrese, J. M. & López, C. Online games: a novel approach to explore how partial information influences human random searches. Sci. Rep. 7(1), 40029. https://doi.org/10.1038/srep40029 (2017).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

35.
Kalff, C. & Hills, T. Human foraging behavior: a virtual reality investigation on area restricted search in humans. Search 32(32), 168–173 (2006).
Google Scholar 

36.
Kamil, A. C., Krebs, J. R. & Pulliam, H. R. Foraging Behavior. https://doi.org/10.1007/978-1-4613-1839-2 (1987). ISBN 9781461290278.

37.
Korn, C. W. & Bach, D. R. Heuristic and optimal policy computations in the human brain during sequential decision-making. Nat. Commun. 9(1), 1–15. https://doi.org/10.1038/s41467-017-02750-3 (2018).
CAS  Article  Google Scholar 

38.
Zollner, P.A. & Lima, S.L. Search Strategies for Landscape-Level Interpatch Movements. Technical Report 3 (1999).

39.
Zurick, D., Valli, É., Farkas, R. & Troyer, H. Land of pure vision: The sacred geography of Tibet and the Himalaya. University Press of Kentucky (2014). ISBN 9780813145594.

40.
Kaushal, M. Divining the landscape-the Gaddi and his land. India Int. Centre Q. 27, 31–40 (2001).
Google Scholar 

41.
Minetti, A. E., Moia, C., Roi, G. S., Susta, D. & Ferretti, G. Energy cost of walking and running at extreme uphill and downhill slopes. J. Appl. Physiol. 93(3), 1039–1046. https://doi.org/10.1152/japplphysiol.01177.2001 (2002).
Article  PubMed  Google Scholar 

42.
Reynolds, A. M. Optimal random Lévy-loop searching: New insights into the searching behaviours of central-place foragers. Epl 82(2), 20001. https://doi.org/10.1209/0295-5075/82/20001 (2008).
CAS  Article  ADS  Google Scholar 

43.
Ydenberg, R. C., Welham, C. V. J., Schmid-hempel, R., Schmid-hempel, P. & Beauchamp, G. Time and energy constraints and the relationships between currencies in foraging theory. Technical Report1, (1994).

44.
Bracis, C., Gurarie, E., Van Moorter, B. & Andrew Goodwin, R. Memory effects on movement behavior in animal foraging. PLoS ONE 10(8), e0136057. https://doi.org/10.1371/journal.pone.0136057 (2015).
CAS  Article  PubMed  PubMed Central  Google Scholar 

45.
Spencer, W. D. Home ranges and the value of spatial information. J. Mammal. 93(4), 929–947. https://doi.org/10.1644/12-mamm-s-061.1 (2012).
Article  Google Scholar 

46.
Sims, D. W., Humphries, N. E., Hu, N., Medan, V. & Berni, J. Optimal searching behaviour generated intrinsically by the central pattern generator for locomotion. eLife 8, 1–31. https://doi.org/10.7554/eLife.50316 (2019).
Article  Google Scholar 

47.
Reynolds, A., Ceccon, E., Baldauf, C., Medeiros, T. K. & Miramontes, O. Lévy foraging patterns of rural humans. PLoS ONE 13(6), e0199099. https://doi.org/10.1371/journal.pone.0199099 (2018).
CAS  Article  PubMed  PubMed Central  Google Scholar 

48.
Seuront, L. & Eugene Stanley, H. Anomalous diffusion and multifractality enhance mating encounters in the ocean. Proc. Natl. Acad. Sci. USA 111(6), 2206–2211. https://doi.org/10.1073/pnas.1322363111 (2014).
CAS  Article  PubMed  ADS  Google Scholar 

49.
Wearmouth, V. J. et al. Scaling laws of ambush predator “waiting” behaviour are tuned to a common ecology. Proc. R. Soc. B Biol. Sci.https://doi.org/10.1098/rspb.2013.2997 (2014).

50.
Reynolds, A. M., Ropert-Coudert, Y., Kato, A., Chiaradia, A. & MacIntosh, A. J. J. A priority-based queuing process explanation for scale-free foraging behaviours. Anim. Behav. 108, 67–71. https://doi.org/10.1016/j.anbehav.2015.07.022 (2015) (ISSN 00033472).
Article  Google Scholar 

51.
Raposo, E. P. et al. Dynamical robustness of lévy search strategies. Phys. Rev/. Lett. 91, 24. https://doi.org/10.1103/PhysRevLett.91.240601 (2003).
CAS  Article  Google Scholar 

52.
Vazquez, A. Impact of memory on human dynamics. Physica A Stat. Mech. Its Appl. 373, 747–752. https://doi.org/10.1016/j.physa.2006.04.060 (2007) (ISSN 03784371).
Article  ADS  Google Scholar 

53.
Stephens, D. W. Decision ecology: foraging and the ecology of animal decision making. Cognit. Affect. Behav. Neurosci. 8(4), 475–484. https://doi.org/10.3758/CABN.8.4.475 (2008) (ISSN 15307026).
Article  Google Scholar 

54.
Bell, W.J. Searching Behavior: the Behavioral Ecology of Finding Resources. https://doi.org/10.1093/aesa/85.1.108 (1990). ISBN 9789401053723.

55.
Pyke, G.H. Animal Movements—An Optimal Foraging Theory Approach, Vol. 2. 2nd edn Elsevier, (2019). ISBN 9780128132517. https://doi.org/10.1016/B978-0-12-809633-8.90160-2

56.
Namboodiri, V. M. K., Levy, J. M., Mihalas, S., Sims, D. W. & Hussain Shuler, M. G. Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework. Proc. Natl. Acad. Sci. USA 113(31), 8747–8752. https://doi.org/10.1073/pnas.1601664113 (2016).
CAS  Article  PubMed  Google Scholar 

57.
Humphries, N. E. & Sims, D. W. Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions. J. Theor. Biol. 358, 179–193. https://doi.org/10.1016/j.jtbi.2014.05.032 (2014).
Article  PubMed  MATH  Google Scholar 

58.
Bartumeus, F. et al. Superdiffusion and encounter rates in diluted, low dimensional worlds. Eur. Phys. J. Spec. Top. 157(1), 157–166. https://doi.org/10.1140/epjst/e2008-00638-6 (2008).
Article  Google Scholar 

59.
Nurzaman, S.G., Matsumoto, Y., Nakamura, Y., Shirai, K., Koizumi, S. & Ishiguro, H. An adaptive switching behavior between levy and brownian random search in a mobile robot based on biological fluctuation. In IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems, IROS 2010 – Conference Proceedings, pages 1927–1934. IEEE, 10 https://doi.org/10.1109/IROS.2010.5651671 (2010). ISBN 9781424466757. http://ieeexplore.ieee.org/document/5651671/.

60.
Mason, W. & Suri, S. Conducting behavioral research on Amazon’s Mechanical Turk. Behav. Res. Methods 44(1), 1–23. https://doi.org/10.3758/s13428-011-0124-6 (2012).
Article  PubMed  ADS  Google Scholar 

61.
Ross, J., Irani, L., Six Silberman, M., Zaldivar, A. & Tomlinson, B. Who are the crowdworkers? Shifting demographics in mechanical turk. In Conference on Human Factors in Computing Systems – Proceedings, pages 2863–2872, New York, New York, USA, https://doi.org/10.1145/1753846.1753873 (2010). ACM Press. ISBN 9781605589312. http://portal.acm.org/citation.cfm?doid=1753846.1753873.

62.
Hamilton, M. J., Lobo, J., Rupley, E., Youn, H. & West, G. B. The ecological and evolutionary energetics of hunter-gatherer residential mobility. Evolut. Anthropol. 25(3), 124–132. https://doi.org/10.1002/evan.21485 (2016) (ISSN 15206505).
Article  Google Scholar 

63.
Sakiyama, T. & Gunji, Y. P. Emergent weak home-range behaviour without spatial memory. R. Soc. Open Sci.https://doi.org/10.1098/rsos.160214 (2016).
Article  PubMed  PubMed Central  Google Scholar 

64.
Bénichou, O., Coppey, M., Moreau, M., Suet, P. H. & Voituriez, R. Optimal search strategies for hidden targets. Phys. Rev. Lett.https://doi.org/10.1103/PhysRevLett.94.198101 (2005).
Article  PubMed  Google Scholar 

65.
Nathan, R., Getz, W.M., Revilla, E., Holyoak, M., Kadmon, R., Saltz, D. & Smouse, P.E. A movement ecology paradigm for unifying organismal movement research, 12 (2008). ISSN 00278424. http://www.ncbi.nlm.nih.gov/pubmed/19060196, http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC2614714.

66.
Hills, T. Animal foraging and the evolution of goal-directed cognition. Cognit. Sci. 30(1), 3–41. https://doi.org/10.1207/s15516709cog0000_50 (2006).
MathSciNet  Article  Google Scholar 

67.
Purcell, B. A. & Kiani, R. Hierarchical decision processes that operate over distinct timescales underlie choice and changes in strategy. Proc. Natl. Acad. Sci. USA 113(31), E4531–E4540. https://doi.org/10.1073/pnas.1524685113 (2016) (ISSN 10916490).
CAS  Article  PubMed  Google Scholar 

68.
Jeffrey Brantingham, P. et al. Measuring forager mobility. Curr. Anthropol. 47(3), 435–459. https://doi.org/10.1086/503062 (2006).
Article  Google Scholar 

69.
Farnsworth, K. D. & Beecham, J. A. How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks. Am. Nat. 153(5), 509–526. https://doi.org/10.1086/303192 (1999) (ISSN 00030147).
CAS  Article  PubMed  Google Scholar 

70.
Wilke, A. & Barrett, H. C. The hot hand phenomenon as a cognitive adaptation to clumped resources. Evol. Hum. Behav. 30(3), 161–169. https://doi.org/10.1016/j.evolhumbehav.2008.11.004 (2009) (ISSN 10905138).
Article  Google Scholar 

71.
Hills, T. T. Animal foraging and the evolution of goal-directed cognition. Cognit. Sci. 30(1), 3–41. https://doi.org/10.1207/s15516709cog0000_50 (2006).
MathSciNet  Article  Google Scholar 

72.
Rhodes, T., Kello, C. T. & Kerster, B. Intrinsic and extrinsic contributions to heavy tails in visual foraging. Vis. Cognit. 22(6), 809–842. https://doi.org/10.1080/13506285.2014.918070 (2014).
Article  Google Scholar 

73.
Levin, S. A. The problem of pattern and scale in ecology. Ecology 73(6), 1943–1967. https://doi.org/10.2307/1941447 (1992) (ISSN 00129658).
Article  Google Scholar 

74.
Mobbs, D., Trimmer, P.C., Blumstein, D.T. & Dayan, P. Foraging for foundations in decision neuroscience: Insights from ethology. Technical Report 7, (2018). www.nature.com/nrn.

75.
Schulz, E., Wu, C. M., Huys, Q. J. M., Krause, A. & Speekenbrink, M. Generalization and search in risky environments. Cognit. Sci. 42(8), 2592–2620. https://doi.org/10.1111/cogs.12695 (2018) (ISSN 15516709).
Article  Google Scholar 

76.
Hart, Y. et al. Creative exploration as a scale-invariant search on a meaning landscape. Nat. Commun. 9(1), 5411. https://doi.org/10.1038/s41467-018-07715-8 (2018).
CAS  Article  PubMed  PubMed Central  ADS  Google Scholar 

77.
Shlesinger, M. F. Mathematical physics: search research. Nature 443(7109), 281–282. https://doi.org/10.1038/443281a (2006).
CAS  Article  PubMed  ADS  Google Scholar 

78.
Clauset, A., Shalizi, C. R. & Newman, M. E. J. Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703. https://doi.org/10.1137/070710111 (2009).
MathSciNet  Article  MATH  ADS  Google Scholar  More