Ecology

1.
Falkowski, M. et al. Biogeochemical controls and feedbacks on ocean primary production. Science 281, 200–207 (1998).
CAS  PubMed  Article  Google Scholar 
2.
Worden, A. Z. et al. Rethinking the marine carbon cycle: Factoring in the multifarious lifestyles of microbes. Science (80–) 347, 1257594 (2015).
Article  CAS  Google Scholar 

3.
Legendre, L. The significance of microalgal blooms for fisheries and for the export of particulate organic carbon in oceans. J. Plankton Res. 12, 681–699 (1990).
CAS  Article  Google Scholar 

4.
Brander, K. M. Global fish production and climate change. Proc. Natl. Acad. Sci. USA 104, 19709–19714 (2007).
ADS  CAS  PubMed  Article  Google Scholar 

5.
Cardinale, B. J. Biodiversity improves water quality through niche partitioning. Nature 472, 86–89 (2011).
ADS  CAS  PubMed  Article  Google Scholar 

6.
Striebel, M., Singer, G., Stibor, H. & Andersen, T. ‘Trophic overyielding’: Phytoplankton diversity promotes zooplankton productivity. Ecology 93, 2719–2727 (2012).
PubMed  Article  Google Scholar 

7.
Irigoien, X., Huisman, J. & Harris, R. P. Global biodiversity patterns of marine phytoplankton and zooplankton. Nature 429, 863–867 (2004).
ADS  CAS  PubMed  Article  Google Scholar 

8.
Chust, G., Irigoien, X., Chave, J. & Harris, R. P. Latitudinal phytoplankton distribution and the neutral theory of biodiversity. Glob. Ecol. Biogeogr. 22, 531–543 (2013).
Article  Google Scholar 

9.
Righetti, D., Vogt, M., Gruber, N., Psomas, A. & Zimmermann, N. E. Global pattern of phytoplankton diversity driven by temperature and environmental variability. Sci. Adv. 5, eaau6253 (2019).
ADS  PubMed  PubMed Central  Article  Google Scholar 

10.
Della Penna, A. & Gaube, P. Overview of (sub)mesoscale ocean dynamics for the NAAMES field program. Front. Mar. Sci. 6, 1–7 (2019).
Article  Google Scholar 

11.
d’Ovidio, F., De Monte, S., Alvain, S., Dandonneau, Y. & Levy, M. Fluid dynamical niches of phytoplankton types. Proc. Natl. Acad. Sci. 107, 18366–18370 (2010).
ADS  PubMed  Article  Google Scholar 

12.
Villar, E. et al. Environmental characteristics of Agulhas rings affect interocean plankton transport. Science (80–) 348, 1261447–1261447 (2015).
Article  CAS  Google Scholar 

13.
Mousing, E. A., Richardson, K., Bendtsen, J., Cetinić, I. & Perry, M. J. Evidence of small-scale spatial structuring of phytoplankton alpha- and beta-diversity in the open ocean. J. Ecol. 104, 1682–1695 (2016).
Article  Google Scholar 

14.
Lévy, M., Franks, P. J. S. & Smith, K. S. The role of submesoscale currents in structuring marine ecosystems. Nat. Commun. 9, 4758 (2018).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

15.
Perruche, C., Rivière, P., Lapeyre, G., Carton, X. & Pondaven, P. Effects of surface quasi-geostrophic turbulence on phytoplankton competition and coexistence. J. Mar. Res. 69, 105–135 (2011).
Article  Google Scholar 

16.
Prairie, J. C., Sutherland, K. R., Nickols, K. J. & Kaltenberg, A. M. Biophysical interactions in the plankton: A cross-scale review. Limnol. Oceanogr. Fluids Environ. 2, 121–145 (2012).
Article  Google Scholar 

17.
Adjou, M., Bendtsen, J. & Richardson, K. Modeling the influence from ocean transport, mixing and grazing on phytoplankton diversity. Ecol. Modell. 225, 19–27 (2012).
CAS  Article  Google Scholar 

18.
Clayton, S., Dutkiewicz, S., Jahn, O. & Follows, M. J. Dispersal, eddies, and the diversity of marine phytoplankton. Limnol. Oceanogr. Fluids Environ. 3, 182–197 (2013).
Article  Google Scholar 

19.
Lévy, M., Jahn, O., Dutkiewicz, S., Follows, M. J. & d’Ovidio, F. The dynamical landscape of marine phytoplankton diversity. J. R. Soc. Interface 12, 20150481 (2015).
PubMed  PubMed Central  Article  Google Scholar 

20.
Cadier, M., Sourisseau, M., Gorgues, T., Edwards, C. A. & Memery, L. Assessing spatial and temporal variability of phytoplankton communities’ composition in the Iroise Sea ecosystem (Brittany, France): A 3D modeling approach: Part 2: Linking summer mesoscale distribution of phenotypic diversity to hydrodynamism. J. Mar. Syst. 169, 111–126 (2017).
Article  Google Scholar 

21.
Clayton, S., Lin, Y. C., Follows, M. J. & Worden, A. Z. Co-existence of distinct Ostreococcus ecotypes at an oceanic front. Limnol. Oceanogr. 62, 75–88 (2017).
ADS  Article  Google Scholar 

22.
Hill, A. E. et al. Thermohaline circulation of shallow tidal seas. Geophys. Res. Lett. 35, 5–9 (2008).
Google Scholar 

23.
Sharples, J. et al. Internal tidal mixing as a control on continental margin ecosystems. Geophys. Res. Lett. 36, 1–5 (2009).
Article  Google Scholar 

24.
Franks, P. J. S. Phytoplankton blooms at fronts: Patterns, scales, and physical forcing mechanisms. Rev. Aquat. Sci. 6, 121–137 (1992).
Google Scholar 

25.
Simpson, J. H. The shelf-sea fronts: Implications of their existence and behaviour. Philos. Trans. R. Soc. A 302, 531–546 (1981).
ADS  Google Scholar 

26.
Le Fèvre, J., Viollier, M., Le Corre, P., Dupouy, C. & Grall, J. R. Remote sensing observations of biological material by LANDSAT along a tidal thermal front and their relevancy to the available field data. Estuar. Coast. Shelf Sci. 16, 37–50 (1983).
ADS  Article  Google Scholar 

27.
Sverdrup, H. U. On conditions for the vernal bloom of phytoplankton. J. Cons. Perm. Int. Explor. Mer 18, 287–295 (1953).
Article  Google Scholar 

28.
Morin, P., Le Corre, P. & Le Févre, J. Assimilation and regeneration of nutrients off the west coast of brittany. J. Mar. Biol. Assoc. United Kingdom 65, 677–695 (1985).
Article  Google Scholar 

29.
Cloern, J. E. Phytoplankton bloom dynamics in coastal ecosystems: A review with some general lessons from sustained investigation of San Francisco Bay, California. Rev. Geophys. 34, 127 (1996).
ADS  CAS  Article  Google Scholar 

30.
Simpson, J. H. & Hunter, J. R. Fronts in the Irish Sea. Nature 250, 404–406 (1974).
ADS  Article  Google Scholar 

31.
Mariette, V. & Le Cann, B. Simulation of the formation of Ushant thermal front. Cont. Shelf Res. 4, 20 (1985).
Article  Google Scholar 

32.
Sharples, J. et al. Spring-neap modulation of internal tide mixing and vertical nitrate fluxes at a shelf edge in summer. Limnol. Oceanogr. 52, 1735–1747 (2007).
ADS  CAS  Article  Google Scholar 

33.
Le Fèvre, J. Aspects of the biology of frontal systems. Adv. Mar. Biol. 23, 163–299 (1986).
Article  Google Scholar 

34.
Maguer, J. F., L’Helguen, S. & Waeles, M. Effects of mixing-induced irradiance fluctuations on nitrogen uptake in size-fractionated coastal phytoplankton communities. Estuar. Coast. Shelf Sci. 154, 1–11 (2015).
ADS  CAS  Article  Google Scholar 

35.
Cadier, M., Gorgues, T., LHelguen, S., Sourisseau, M. & Memery, L. Tidal cycle control of biogeochemical and ecological properties of a macrotidal ecosystem. Geophys. Res. Lett. 44, 8453–8462 (2017).
ADS  Article  Google Scholar 

36.
Sharples, J. Potential impacts of the spring-neap tidal cycle on shelf sea primary production. J. Plankton Res. 30, 183–197 (2008).
CAS  Article  Google Scholar 

37.
Zhou, J. & Ning, D. Stochastic community assembly: Does it matter in microbial ecology?. Microbiol. Mol. Biol. Rev. 81, 1–32 (2017).
Article  Google Scholar 

38.
Hardin, G. The exclusion competitive principle. Am. Assoc. Adv. Sci. 131, 1292–1297 (1960).
CAS  Google Scholar 

39.
Barton, A. D., Dutkiewicz, S., Flierl, G., Bragg, J. & Follows, M. J. Patterns of Diversity in Marine Phytoplankton. Science (80–) 327, 1509–1512 (2010).
ADS  CAS  Article  Google Scholar 

40.
Charria, G. et al. Surface layer circulation derived from Lagrangian drifters in the Bay of Biscay. J. Mar. Syst. 109–110, S60–S76 (2013).
Article  Google Scholar 

41.
Ménesguen, A. et al. How to avoid eutrophication in coastal seas? A new approach to derive river-specific combined nitrate and phosphate maximum concentrations. Sci. Total Environ. 628–629, 400–414 (2018).
ADS  PubMed  Article  CAS  Google Scholar 

42.
Litchman, E. & Klausmeier, C. A. Trait-based community ecology of phytoplankton. Annu. Rev. Ecol. Evol. Syst. 39, 615–639 (2008).
Article  Google Scholar 

43.
Ramond, P. et al. Coupling between taxonomic and functional diversity in protistan coastal communities. Environ. Microbiol. 21, 730–749 (2019).
CAS  PubMed  Article  Google Scholar 

44.
Aminot, A. & Kérouel, R. Dosage Automatique des Nutriments Dans les Eaux Marines: Méthodes en Flux Continu. (2007).

45.
Stoeck, T. et al. Multiple marker parallel tag environmental DNA sequencing reveals a highly complex eukaryotic community in marine anoxic water. Mol. Ecol. 19, 21–31 (2010).
CAS  PubMed  Article  Google Scholar 

46.
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 

47.
de Vargas, C. et al. Eukaryotic plankton diversity in the sunlit ocean. Science (80–) 348, 1261605 (2015).
Article  CAS  Google Scholar 

48.
Guillou, L. et al. The Protist Ribosomal Reference database (PR2): A catalog of unicellular eukaryote Small Sub-Unit rRNA sequences with curated taxonomy. Nucleic Acids Res. 41, 597–604 (2013).
Article  CAS  Google Scholar 

49.
Mahé, F., Rognes, T., Quince, C., de Vargas, C. & Dunthorn, M. Swarm v2: Highly-scalable and high-resolution amplicon clustering. PeerJ 1420, 1–20 (2015).
Google Scholar 

50.
R Core Team. R: A Language and Environment for Statistical Computing. (2018). R version 3.5.0 (2018-04-23)—“Joy in Playing”. www.r-project.org.

51.
Mitra, A. The perfect beast. Sci. Am. 318, 26–33 (2018).
PubMed  Article  Google Scholar 

52.
Oksanen, J. et al. vegan: Community Ecology Package. (2018).

53.
Hsieh, T. C., Ma, K. H. & Chao, A. iNEXT: An R package for interpolation and extrapolation in measuring species diversity. 1–18 (2014). https://doi.org/10.1111/2041-210X.12613.

54.
Csárdi, G. & Nepusz, T. The igraph software package for complex network research. J. Comput. Appl. https://doi.org/10.3724/SP.J.1087.2009.02191 (2014).
Article  Google Scholar 

55.
Stegen, J. C. et al. Quantifying community assembly processes and identifying features that impose them. ISME J. 7, 2069–2079 (2013).
PubMed  PubMed Central  Article  Google Scholar 

56.
Bruggeman, J. A phylogenetic approach to the estimation of phytoplankton traits. J. Phycol. 65, 52–65 (2011).
Article  Google Scholar 

57.
Callahan, B. J., Sankaran, K., Fukuyama, J. A., McMurdie, P. J. & Holmes, S. P. Bioconductor workflow for microbiome data analysis: From raw reads to community analyses [version 1; referees: 3 approved]. F1000Research 5, 1–49 (2016).
Article  Google Scholar 

58.
Kembel, S. W. et al. Picante: R tools for integrating phylogenies and ecology. Bioinformatics 26, 1463–1464 (2010).
CAS  PubMed  Article  Google Scholar 

59.
Chase, J. M., Kraft, N. J. B., Smith, K. G., Vellend, M. & Inouye, B. D. Using null models to disentangle variation in community dissimilarity from variation in α-diversity. Ecosphere 2, 20 (2011).
Article  Google Scholar 

60.
Stegen, J. C., Lin, X., Fredrickson, J. K. & Konopka, A. E. Estimating and mapping ecological processes influencing microbial community assembly. Front. Microbiol. 6, 1–15 (2015).
Article  Google Scholar 

61.
Maire, E., Grenouillet, G., Brosse, S. & Villéger, S. How many dimensions are needed to accurately assess functional diversity? A pragmatic approach for assessing the quality of functional spaces. Glob. Ecol. Biogeogr. 24, 728–740 (2015).
Article  Google Scholar 

62.
Legendre, P. & Legendre, L. Numerical Ecology. Third English. (Elsevier, Oxford, 2012).
Google Scholar 

63.
Massana, R. Eukaryotic picoplankton in surface oceans. Annu. Rev. Microbiol. 65, 91–110 (2011).
CAS  PubMed  Article  Google Scholar 

64.
Litchman, E., Klausmeier, C. A., Schofield, O. M. & Falkowski, P. G. The role of functional traits and trade-offs in structuring phytoplankton communities: Scaling from cellular to ecosystem level. Ecol. Lett. 10, 1170–1181 (2007).
PubMed  Article  Google Scholar 

65.
Margalef, R. Life-forms of phytoplankton as survival alternatives in an unstable environment. Oceanologia 1, 493–509 (1978).
Google Scholar 

66.
Thingstad, T. F., Øvreas, L., Egge, J. K., Løvdal, T. & Heldal, M. Use of non-limiting substrates to increase size; a generic strategy to simultaneously optimize uptake and minimize predation in pelagic osmotrophs?. Ecol. Lett. 8, 675–682 (2005).
Article  Google Scholar 

67.
Marañón, E. Cell size as a key determinant of phytoplankton metabolism and community structure. Ann. Rev. Mar. Sci. 7, 241–264 (2015).
PubMed  Article  Google Scholar 

68.
Raven, J. A. Small is beautiful: The picophytoplankton. Funct. Ecol. 12, 503–513 (1998).
Article  Google Scholar 

69.
Castaing, P. et al. Relationship between hydrology and seasonal distribution of suspended sediments on the continental shelf of the Bay of Biscay. Deep. Res. Part II Top. Stud. Oceanogr. 46, 1979–2001 (1999).
ADS  Article  Google Scholar 

70.
Schultes, S., Sourisseau, M., Le, E., Lunven, M. & Marié, L. Influence of physical forcing on mesozooplankton communities at the Ushant tidal front. J. Mar. Syst. 109–110, S191–S202 (2013).
Article  Google Scholar 

71.
Cabello, A. M., Latasa, M., Forn, I., Morán, X. A. G. & Massana, R. Vertical distribution of major photosynthetic picoeukaryotic groups in stratified marine waters. Environ. Microbiol. 18, 1578–1590 (2016).
CAS  PubMed  Article  Google Scholar 

72.
Simo-Matchim, A.-G., Gosselin, M., Poulin, M., Ardyna, M. & Lessard, S. Summer and fall distribution of phytoplankton in relation to environmental variables in Labrador fjords, with special emphasis on Phaeocystis pouchetii. Mar. Ecol. Prog. Ser. 572, 19–42 (2017).
ADS  CAS  Article  Google Scholar 

73.
Vallina, S. M. et al. Global relationship between phytoplankton diversity and productivity in the ocean. Nat. Commun. 5, 4299 (2014).
ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

74.
Connell, J. Diversity in tropical rain forests and coral reefs. Science 199, 1302–1310 (1978).
ADS  CAS  Article  Google Scholar 

75.
Reynolds, C. S., Padisak, J. & Sommer, U. Intermediate disturbance in the ecology of phytoplankton and the maintenance of species diversity : A synthesis. Hydrobiologia 249, 183–188 (1993).
Article  Google Scholar 

76.
Fox, J. W. The intermediate disturbance hypothesis should be abandoned. Trends Ecol. Evol. 28, 86–92 (2013).
PubMed  Article  Google Scholar 

77.
Chevallier, C. et al. Observations of the Ushant front displacements with MSG/SEVIRI derived sea surface temperature data. Remote Sens. Environ. 146, 3–10 (2014).
ADS  Article  Google Scholar 

78.
Raes, E. J. et al. Oceanographic boundaries constrain microbial diversity gradients in the South Pacific Ocean. Proc. Natl. Acad. Sci. https://doi.org/10.1073/pnas.1719335115 (2018).
Article  PubMed  Google Scholar 

79.
Ribalet, F. et al. Unveiling a phytoplankton hotspot at a narrow boundary between coastal and offshore waters. Proc. Natl. Acad. Sci. 107, 16571–16576 (2010).
ADS  CAS  PubMed  Article  Google Scholar 

80.
Villa Martín, P., Buček, A., Bourguignon, T. & Pigolotti, S. Ocean currents promote rare species diversity in protists. Sci. Adv. 6, eaaz9037 (2020).
ADS  PubMed  PubMed Central  Article  Google Scholar 

81.
Reynolds, C. S. Scales of disturbance and their role in plankton ecology. Hydrobiologia 249, 157–171 (1993).
Article  Google Scholar 

82.
Marañon, E. et al. Unimodal size scaling of phytoplankton growth and the size dependence of nutrient uptake and use. Ecol. Lett. 16, 371–379 (2013).
PubMed  Article  Google Scholar 

83.
Mouillot, D., Gaham, N. A. J., Villéger, S., Mason, N. W. H. & Bellwood, D. R. A functional approach reveals community responses to disturbances. Trends Ecol. Evol. 28, 167–177 (2013).
PubMed  Article  Google Scholar 

84.
Kruk, C. et al. Functional redundancy increases towards the tropics in lake phytoplankton. J. Plankton Res. 39, 518–530 (2017).
Google Scholar 

85.
Leruste, A., Villéger, S., Malet, N., De Wit, R. & Bec, B. Complementarity of the multidimensional functional and the taxonomic approaches to study phytoplankton communities in three Mediterranean coastal lagoons of different trophic status. Hydrobiologia https://doi.org/10.1007/s10750-018-3565-4 (2018).
Article  Google Scholar 

86.
Pauly, D. & Christensen, V. Primary production required to sustain global fisheries. Nature 374, 255–257 (1995).
ADS  CAS  Article  Google Scholar 

87.
Ayata, S. D., Stolba, R., Comtet, T. & Thiébaut, E. Meroplankton distribution and its relationship to coastal mesoscale hydrological structure in the northern Bay of Biscay (NE Atlantic). J. Plankton Res. 33, 1193–1211 (2011).
Article  Google Scholar  More

1.
Settele, J. et al. in Climate Change 2014 Impacts, Adaptation and Vulnerability: Part A: Global and Sectoral Aspects. https://doi.org/10.1017/CBO9781107415379.009 (2015).
2.
Pecl, G. T. et al. Biodiversity redistribution under climate change: impacts on ecosystems and human well-being. Science 355, eaai9214 (2017).
PubMed  Article  CAS  PubMed Central  Google Scholar 

3.
Li, Y., Cohen, J. M. & Rohr, J. R. Review and synthesis of the effects of climate change on amphibians. Integr. Zool. 8, 145–161 (2013).
PubMed  Article  PubMed Central  Google Scholar 

4.
Barnosky, A. D. et al. Has the Earth’s sixth mass extinction already arrived? Nature 471, 51–57 (2011).
CAS  PubMed  Article  PubMed Central  Google Scholar 

5.
IUCN. IUCN Red List of Threatened Species. Version 2019-3. http://www.iucnredlist.org (IUCN, 2019).

6.
Hoffmann, M. et al. The impact of conservation on the status of the world’s vertebrates. Science 330, 1503–1509 (2010).
CAS  PubMed  Article  PubMed Central  Google Scholar 

7.
Warren, R. et al. Quantifying the benefit of early climate change mitigation in avoiding biodiversity loss. Nat. Clim. Chang. 3, 678–682 (2013).
Article  Google Scholar 

8.
Kiesecker, J. M. Global stressors and the global decline of amphibians: tipping the stress immunocompetency axis. Ecol. Res. 26, 897–908 (2011).
PubMed  Article  PubMed Central  Google Scholar 

9.
Collins, J. P. & Storfer, A. Global amphibian declines: sorting the hypotheses. Diversity Distrib. 9, 89–98 (2003).
Article  Google Scholar 

10.
Stebbins, R. C. & Cohen, N. W. A Natural History of Amphibians (Princeton University Press, 1997).

11.
Wells, K. D. The Ecology and Behavior of Amphibians (University of Chicago Press, 2010).

12.
Flato, G. et al. in Climate Change 2013 the Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al.) Vol. 9781107057, 741–866 (Cambridge University Press, 2013).

13.
Kriegler, E., Hall, J. W., Held, H., Dawson, R. & Schellnhuber, H. J. Imprecise probability assessment of tipping points in the climate system. Proc. Natl Acad. Sci. USA 106, 5041–5046 (2009).
CAS  PubMed  Article  PubMed Central  Google Scholar 

14.
Lenton, T. M. et al. Climate tipping points—too risky to bet against. Nature 575, 592–595 (2019).
CAS  PubMed  Article  PubMed Central  Google Scholar 

15.
Collins, M. et al. in Climate Change 2013—The Physical Science Basis: Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change Vol. 9781107057, 1029–1136 (2013).

16.
Lenton, T. M. et al. Tipping elements in the Earth’s climate system. Proc. Natl Acad. Sci. USA 105, 1786–93 (2008).
CAS  PubMed  Article  PubMed Central  Google Scholar 

17.
Collins, M. & Sutherland, M. Extremes, Abrupt Changes and Managing Risks. IPCC Special Report on the Ocean and Cryosphere in a Changing Climate. https://report.ipcc.ch/srocc/pdf/SROCC_FinalDraft_Chapter6.pdf (2019).

18.
Sgubin, G., Swingedouw, D., Drijfhout, S., Mary, Y. & Bennabi, A. Abrupt cooling over the North Atlantic in modern climate models. Nat. Commun. 8, 14375 (2017).
CAS  PubMed Central  Article  Google Scholar 

19.
Vellinga, M. & Wood, R. A. Global climatic impacts of a collapse of the atlantic thermohaline circulation. Clim. Change 54, 251–267 (2002).
Article  Google Scholar 

20.
Jackson, L. C. et al. Global and European climate impacts of a slowdown of the AMOC in a high resolution GCM. Clim. Dyn. 45, 3299–3316 (2015).
Article  Google Scholar 

21.
Swingedouw, D. Oceanography: fresh news from the Atlantic. Nat. Clim. Change 5, 411–412 (2015).
Article  Google Scholar 

22.
Gregory, J. M. et al. A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration. Geophys. Res. Lett. 32, 1–5 (2005).
Article  CAS  Google Scholar 

23.
Thornalley, D. J. R. et al. Anomalously weak Labrador Sea convection and Atlantic overturning during the past 150 years. Nature 556, 227–230 (2018).
CAS  PubMed  Article  PubMed Central  Google Scholar 

24.
Taylor, K. E., Stouffer, R. J. & Meehl, G. A. An overview of CMIP5 and the experiment design. Bull. Am. Meteorological Soc. 93, 485–498 (2012).
Article  Google Scholar 

25.
Cheng, W. et al. Atlantic meridional overturning circulation (AMOC) in CMIP5 models: RCP and historical simulations. J. Clim. 26, 7187–7197 (2013).
Article  Google Scholar 

26.
Jourdain, N. et al. A protocol for calculating basal melt rates in the ISMIP6 Antarctic ice sheet projections. Cryosph. Discuss. 1–33, https://doi.org/10.5194/tc-2019-277 (2019).

27.
Swingedouw, D. et al. Decadal fingerprints of freshwater discharge around Greenland in a multi-model ensemble. Clim. Dyn. 41, 695–720 (2013).
Article  Google Scholar 

28.
Anthoff, D., Estrada, F. & Tol, R. S. J. Shutting down the thermohaline circulation. Am. Econ. Rev. 106, 602–606 (2016).
Article  Google Scholar 

29.
Defrance, D. et al. Consequences of rapid ice sheet melting on the Sahelian population vulnerability. Proc. Natl Acad. Sci. USA 114, 6533–6538 (2017).
CAS  PubMed  Article  PubMed Central  Google Scholar 

30.
Ritchie, P. D. L. et al. Shifts in national land use and food production in Great Britain after a climate tipping point. Nat. Food 1, 76–83 (2020).
Article  Google Scholar 

31.
Kuhlbrodt, T. et al. An integrated assessment of changes in the thermohaline circulation. Clim. Change 96, 489–537 (2009).
CAS  Article  Google Scholar 

32.
Osman, M. B. et al. Industrial-era decline in subarctic Atlantic productivity. Nature 569, 551–555 (2019).
CAS  PubMed  Article  PubMed Central  Google Scholar 

33.
Schmittner, A. Decline of the marine ecosystem caused by a reduction in the Atlantic overturning circulation. Nature 434, 628–633 (2005).
CAS  PubMed  Article  PubMed Central  Google Scholar 

34.
Schenk, F. et al. Warm summers during the Younger Dryas cold reversal. Nat. Commun. 9, 1–13 (2018).
CAS  Article  Google Scholar 

35.
Gunderson, L. H. Ecological resilience—in theory and application. Annu. Rev. Ecol. Syst. 31, 425–439 (2000).
Article  Google Scholar 

36.
Lockwood, J. L. & McKinney, M. L. Biotic Homogenization (Kluwer Academic/Plenum Publishers, 2001).

37.
Devictor, V. et al. Spatial mismatch and congruence between taxonomic, phylogenetic and functional diversity: the need for integrative conservation strategies in a changing world. Ecol. Lett. 13, 1030–1040 (2010).
PubMed  PubMed Central  Google Scholar 

38.
Araújo, M. B., Thuiller, W. & Pearson, R. G. Climate warming and the decline of amphibians and reptiles in Europe. J. Biogeogr. 33, 1712–1728 (2006).
Article  Google Scholar 

39.
Lemoine, D. & Traeger, C. P. Economics of tipping the climate dominoes. Nat. Clim. Chang. 6, 514–519 (2016).
Article  Google Scholar 

40.
Stern, N. The structure of economic modeling of the potential impacts of climate change: grafting gross underestimation of risk onto already narrow science models. J. Econ. Lit. 51, 838–859 (2013).
Article  Google Scholar 

41.
Fick, S. E. & Hijmans, R. J. WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas. Int. J. Climatol. 37, 4302–4315 (2017).
Article  Google Scholar 

42.
Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G. & Jarvis, A. Very high resolution interpolated climate surfaces for global land areas. Int. J. Climatol. 25, 1965–1978 (2005).
Article  Google Scholar 

43.
Zurell, D., Graham, C. H., Gallien, L., Thuiller, W. & Zimmermann, N. E. Long-distance migratory birds threatened by multiple independent risks from global change. Nat. Clim. Chang. 8, 992–996 (2018).
PubMed  PubMed Central  Article  Google Scholar 

44.
Munguía, M., Rahbek, C., Rangel, T. F., Diniz-Filho, J. A. F. & Araújo, M. B. Equilibrium of global amphibian species distributions with climate. PLoS ONE 7, e34420 (2012).
PubMed  PubMed Central  Article  CAS  Google Scholar 

45.
Hof, C., Araújo, M. B., Jetz, W. & Rahbek, C. Additive threats from pathogens, climate and land-use change for global amphibian diversity. Nature 480, 516–519 (2011).
CAS  PubMed  Article  PubMed Central  Google Scholar 

46.
Hof, C. et al. Bioenergy cropland expansion may offset positive effects of climate change mitigation for global vertebrate diversity. Proc. Natl Acad. Sci. USA 115, 13294–13299 (2018).
CAS  PubMed  Article  PubMed Central  Google Scholar 

47.
Biber, M. F., Voskamp, A., Niamir, A., Hickler, T. & Hof, C. A comparison of macroecological and stacked species distribution models to predict future global terrestrial vertebrate richness. J. Biogeogr. https://doi.org/10.1111/jbi.13696 (2019).

48.
Thuiller, W., Guéguen, M., Renaud, J., Karger, D. N. & Zimmermann, N. E. Uncertainty in ensembles of global biodiversity scenarios. Nat. Commun. 10, 1446 (2019).
PubMed  PubMed Central  Article  CAS  Google Scholar 

49.
Fourcade, Y. Comparing species distributions modelled from occurrence data and from expert-based range maps. Implication for predicting range shifts with climate change. Ecol. Inform. 36, 8–14 (2016).
Article  Google Scholar 

50.
Alhajeri, B. H. & Fourcade, Y. High correlation between species-level environmental data estimates extracted from IUCN expert range maps and from GBIF occurrence data. J. Biogeogr. 46, 1329–1341 (2019).
Google Scholar 

51.
Ficetola, G. F. et al. An evaluation of the robustness of global amphibian range maps. J. Biogeogr. https://doi.org/10.1111/jbi.12206 (2014).

52.
Olson, D. M. et al. Terrestrial ecoregions of the world: a new map of life on Earth. Bioscience 51, 933–938 (2001).
Article  Google Scholar 

53.
Araújo, M. B. et al. Quaternary climate changes explain diversity among reptiles and amphibians. Ecography 31, 8–15 (2008).
Article  Google Scholar 

54.
Ochoa-Ochoa, L. M., Mejía-Domínguez, N. R., Velasco, J. A., Marske, K. A. & Rahbek, C. Amphibian functional diversity is related to high annual precipitation and low precipitation seasonality in the New World. Glob. Ecol. Biogeogr. 28, 1219–1229 (2019).
Article  Google Scholar 

55.
Oliveira, B. F., Sheffers, B. R. & Costa, G. C. Decoupled erosion of amphibians’ phylogenetic and functional diversity due to extinction. Glob. Ecol. Biogeogr. 29, 309–319 (2020).
Article  Google Scholar 

56.
Naimi, B. & Araújo, M. B. Sdm: a reproducible and extensible R platform for species distribution modelling. Ecography https://doi.org/10.1111/ecog.01881 (2016).

57.
Di Cola, V. et al. ecospat: an R package to support spatial analyses and modeling of species niches and distributions. Ecography https://doi.org/10.1111/ecog.02671 (2017).

58.
Fielding, A. H. & Bell, J. F. A review of methods for the assessment of prediction errors in conservation presence/absence models. Environ. Conserv. https://doi.org/10.1017/S0376892997000088 (1997).

59.
Allouche, O., Tsoar, A. & Kadmon, R. Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS). J. Appl. Ecol. https://doi.org/10.1111/j.1365-2664.2006.01214.x (2006).

60.
Peterson, A. T. et al. Ecological Niches and Geographic Distributions (MPB-49). Ecological Niches and Geographic Distributions (MPB-49) https://doi.org/10.23943/princeton/9780691136868.001.0001 (Princeton University Press, 2011).

61.
Barve, N. et al. The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecol. Modell. https://doi.org/10.1016/j.ecolmodel.2011.02.011 (2011).

62.
Guisan, A., Thuiller, W. & Zimmermann, N. E. Habitat Suitability and Distribution Models: with Applications in R. Habitat Suitability and Distribution Models: with Applications in R. https://doi.org/10.1017/9781139028271 (2017).

63.
Liu, C., Berry, P. M., Dawson, T. P. & Pearson, R. G. Selecting thresholds of occurrence in the prediction of species distributions. Ecography https://doi.org/10.1111/j.0906-7590.2005.03957.x (2005).

64.
Diniz-Filho, J. A. F. et al. Partitioning and mapping uncertainties in ensembles of forecasts of species turnover under climate change. Ecography https://doi.org/10.1111/j.1600-0587.2009.06196.x (2009).

65.
Velasco, J. et al. Synergistic impacts of global warming and thermohaline circulation collapse on amphibians. https://doi.org/10.6084/m9.figshare.13280951.v1 (2020). More

In this study we were able to obtain estimates of parameters that had been missing for the southwest subpopulation, including survival probabilities of younger stages of manatees, recovery rates of manatee carcasses, and abundance in years before and between abundance surveys.
Survival probabilities of younger animals are key parameters in population viability analyses of Florida manatees11,23,25. But these probabilities have long been extrapolated from one study of manatees in a small management unit on Florida’s east coast26. The average probabilities of juvenile survival estimated here are lower than those obtained from that extrapolation (Fig. 8). Independent estimates of the younger manatee survival probabilities for the southwest management unit will soon be available from genetic mark–recapture–recovery modeling, but such data are not forthcoming for the other three Florida manatee management units, making the approach used here for estimating these probabilities more readily applicable.
In addition, our model provided estimates of the effects of red tide and cold events on the population. The red tide event of 2013, during which 353 carcasses were recovered in the southwest (of which at least 268 were killed by red tide), contributed to an estimated net drop in the population of 331 (217–459) manatees (Fig. 5) for an annual population growth rate of 0.89 (0.85–0.93; Fig. 4). Our results support the finding that such red tide events (classified as intense) affect calves particularly (Supplementary Fig. S13, online)11. In contrast, the cold event of 2010, which led to 247 recovered carcasses in the southwest region, did not appear to lead to a net drop in population, according to our model. This may be in part because our prior estimate of adult survival that year was relatively high (Fig. 7), and the model assumes (and estimates) a fixed ratio between age-class survival rates across years (Supplementary Table S1, online). These new estimates can be helpful in communicating the impact these disturbance events had on the population. Unusual mortality events that lead to high carcass counts often attract a lot of attention from the press and the public. The IPM provides a way to put such mortality events in perspective and to answer questions such as “What was the impact of a particular mortality event on the population?” In addition, the average population growth rate (1.02, 1.01–1.03) estimated from our data supports the hypothesis that the manatee population was increasing from 1997 to 2016 (Figs. 3 and 4). This is the first rigorous estimate of historical (realized) population growth rate for this population. This information is complementary to and consistent with the projected population growth rate obtained from the CBM projections11.
Our model also provided more precise estimates of many parameters estimated earlier, such as adult survival and abundance for years in which abundance surveys were carried out (Figs. 3 and 7). In some cases, our approach may reduce bias, although it is also possible for IPMs to introduce or increase bias27. Possible biases in some input estimates to our model, such as abundance28,29 and end-of-time-series survival probabilities30, have been noted28,29,30. In some cases, the median estimates obtained from the IPM were substantially different from the original estimates (compare prior abundance survey and posterior estimates in Figs. 3 and 7). The IPM might correct for biases in abundance and end-of-time-series survival estimates, although this idea needs to be further evaluated. Because it includes a recovery model for carcass data, the IPM does not hindcast impossible numbers of deaths, unlike the simulation-based hindcast model (Supplementary Fig. S3, online). The IPM results suggest that these results from the simulation-based hindcast model were off both because the 2011 abundance estimate input was too low and because the survival estimate inputs for juveniles (s1–s4) were too high. By integrating multiple sources of information, we are synthesizing the best available information but also hedging our bets by not relying on just one source of data in estimating critical demographic parameters.
Many of our posterior estimates are consistent with other published results for Florida manatees. Our estimates of realized population growth rates (Fig. 4) are similar to the projected population growth estimates from the CBM and consistent with general trends of growth in synoptic and carcass counts. Our estimates of age structure (Fig. 6), although variable over time, are consistent with the asymptotic stable age structure that projecting from a simple matrix model would provide. Our estimates of the mortality effects of the 2013 red tide (Supplementary Fig. S13, online) are similar to those from the CBM. The pattern of our estimated recovery probabilities by coarse stage (Supplementary Fig. S5, online) is consistent with an earlier estimate of age-specific recovery rates relative to (unknown) adult recovery probability31, although our estimates of subadult and adult recovery probabilities are closer to 1 than we expected. The high estimates of recovery probability may be due to the IPM attempting to harmonize partially incompatible model components (Supplementary Fig. S3, online). When model components generate incompatible results, either due to model misspecification or not referencing exactly the same populations, an IPM must reconcile those results. This reconciliation can generate bias in some estimates, although the generally higher precision of IPM estimates may still mean higher accuracy. Ground truthing or other research may be needed to determine whether FWC is actually recovering such a high proportion of manatee carcasses.
The results of this study are relevant to the management of Florida manatee populations. The manatee recovery plan used by the USFWS under the Endangered Species Act relies on several metrics that can be obtained from the IPM, such as realized population growth rates and population size. The IPM provides one of the most rigorous assessments to date for these quantities and may be used by natural resource managers in assessing the status of the manatee population. It can also be used to update key model parameters of the CBM, which at present is the primary population assessment tool for managers.
Another important regulatory framework relevant to marine mammal conservation in the United States is the Marine Mammal Protection Act. Here again, an IPM can help in addressing some of the act’s requirements. Indeed, the act specifies a formula for computing potential biological removal (PBR; the maximum number of animals that can be removed from a stock while allowing it to reach or remain at its optimum sustainable population)32,33,34,35

$$begin{aligned} PBR & = N_{min} frac{{R_{max} }}{2}F_{r} \ N_{min} & = frac{{hat{N}}}{{exp left( {0.842sqrt {log left( {1 + {text{CV}} left( {hat{N}} right)^{2} } right)} } right)}} \ end{aligned}$$
(1)

where Nmin is the minimum population abundance estimate (20th percentile of abundance estimate distribution), Rmax is the theoretical maximum rate of increase for the stock, Fr is a recovery factor (generally 0.5 for threatened species, but see Moore et al.35), and (hat{N}) is the point estimate of population abundance. Based on our estimate from the last year of the analysis (2016), Nmin for the southwest population of Florida manatees is about 2780. This is lower than Nmin would be based on the abundance survey (prior) estimate from the same year (about 3140); (CVleft(hat{N}right)) from the IPM posterior was lower than from the prior (Supplementary Fig. S2, online) but (hat{N}) was as well (Fig. 3). Estimation of Rmax requires extrapolating growth rates to conditions of low population density and absence of anthropogenic mortality; our IPM is not designed for that purpose, but future extensions could be developed to address this need. A merging of our IPM, or other matrix model approach, with an allometric approach to estimating Rmax would allow a more accurate estimate of this parameter36. Both matrix model (individual population) and allometric (cross population) approaches to estimating Rmax are strongly affected by biases caused by using empirical estimates of adult survival instead of what adult survival would be under ideal conditions; however, these biases run in opposite directions, so an integration of these approaches greatly reduces any bias in Rmax36.
Another benefit of the IPM is its usefulness for planning monitoring activities, including how to allocate resources to various aspects of the monitoring program, such as aerial surveys, photo-identification, genetic sampling, and carcass recovery. Various sampling scenarios (e.g., 40% of carcasses recovered; 200 genetic samples per year; one aerial survey every 5 years) can be combined with simulated data generated under those scenarios to see how the accuracy of model parameter estimates differs among scenarios. Trade-offs between parameter accuracy/precision and budget allocation can then be examined to improve monitoring efficiency. Optimizing the sampling with an IPM also makes sense in the context of targeted monitoring for adaptive management37. In such applications, the IPM can be used to estimate state variables (e.g., abundance) that keep track of system changes, allow managers to implement state-dependent decisions, and update beliefs about which model is the best approximation of reality (through Bayes theorem)37,38. A now classic example of an implementation of this adaptive management process is for the sustainable harvesting of waterfowl in North America37, where the optimal state-dependent harvest policies are driven, at least partially, by waterfowl abundance. IPMs are now being used to increase precision of abundance and other state variables in adaptive management of waterfowl39,40.
A monitoring component that could be streamlined is the carcass-recovery and necropsy program. The present protocol is that almost all carcasses reported must be recovered and necropsied, which, along with the growth in the manatee population, is making this program increasingly labor-intensive and expensive. The IPM gives us the first true estimates of carcass recovery probabilities for Florida manatees. These estimates are now being used by FWC in evaluating and improving the efficiency of these programs.
Monitoring populations of marine mammals involves special challenges, such as the difficulty, cost, and risk to researchers involved in counting the population, often through aerial surveys. Several other studies that involved the development of IPM for marine mammals16,41,42,43 had at least one thing in common with ours: population surveys were not conducted every year, which differs from most IPMs used for terrestrial birds and mammals. Our approach, like those applied to other marine mammals, could be valuable for filling in abundance estimates for other sirenians and small cetaceans, where estimating survival and reproductive probabilities from mark–recapture data is often easier than obtaining abundance estimates. As explained earlier, the IPM can then be used to determine the optimal frequency of surveys and optimal spatial sampling effort (e.g., how much area to survey and how many survey visits at each location to estimate detection)28.
Studies of other marine mammals16,41,42,43 collected explicit data on age or stage structure, while for manatees, reliable data were not available for these parameters. We were able to estimate age class structure for the years 2002–2016 using neither stage structure data nor particularly informed priors (Fig. 6). This is likely because of the weak ergodic theorem of demography, which shows that the initial stage structure becomes less relevant with more years of known (or, in our case, estimated) survival and reproductive probabilities3,44. Our approach may be useful for other marine species without reliable stage structure information. Modeling stage structure and transient dynamics can be important to improving understanding of the dynamics of wild populations and can have important management implications. For instance, Johnson et al.45 found that the initial stage structure could have substantial policy consequences for the management of an invasive species.
Our IPM and the associated input models are based on a series of assumptions (Supplementary Table S1, online). One of the assumptions of the IPM is the independence of the data sources for the input analyses. This assumption is violated in our case; the adult survival analysis shares carcass data with the recovery analysis and mark–recapture data with the reproductive analysis. Two simulation studies17,46 found that violating this assumption had little effect, but as their analyses were not identical to ours, this assumption violation still might diminish the accuracy of our estimates. Simulations by Rieke et al.47 show that assumption violations in one of the model components can dramatically reduce the accuracy of estimates of latent parameters. Therefore, in our case, the estimates of juvenile survival, recovery probabilities, and abundance in years without abundance surveys should all be interpreted cautiously.
There are several possible extensions of this model, for example for use in the other three Florida manatee management units (Fig. 1). Because we are uncertain about winter within-coast manatee distribution29, two coast-wide IPMs that each jointly model the two management units on that coast might be most appropriate. With an initial abundance distribution and yearly vital rate estimates for each management unit (possibly including movement rates between regions, if they become available), subsequent coast-wide abundance estimates could be shared between them. This would allow relaxation of the assumption that the proportion of the winter population in each of the two management units remains fixed over time.
Possible extensions could demonstrate whether and to what extent the IPM decreases bias in input estimates, through simulating estimates with known biases and carcass data, running the IPM with the simulated data, and repeating this process many times. One could similarly test the model’s robustness to different assumption violations.
Preliminary analyses suggest that our use of earlier analyses as priors in the integrated model does not bias results but that it might reduce precision. Therefore, it may be useful to estimate more parameters from data directly within a future version of this IPM. In addition, incorporating additional data sources (such as genetic mark–recapture and age estimates using tympanoperiotic ear bones) could improve parameter estimation. Since each parameter can have only one prior, this too requires performing more of the data analysis within the IPM.
Despite these limitations, we believe that this manatee IPM is the most rigorous means of retrospective assessment of the population dynamics of the Florida manatee. Because the model is modular (e.g., abundance module, survival module), as each module is improved, the model as a whole is improved. This offers a compelling framework within which to synthesize and update information about population dynamics. We have shown here that an IPM can be used: (1) to infer historical trends in abundance, improving our understanding of population dynamics and therefore our ability to forecast; (2) to model the transient dynamics of stage distribution, which can be important to some populations; (3) to assess the conservation status of wild populations and to communicate that information to stakeholders (e.g., we can now quantify the impact of the 2013 red tide event on the manatee population); and (4) to improve allocation of effort in complex monitoring programs.
Our modeling frameworks are relevant to population status assessment protocols for management and conservation, such as recovery plans under the Endangered Species Act and potential biological removal under the Marine Mammal Protection Act. Other marine mammal conservation programs, such as that of the Hawaiian monk seal, also have complex monitoring components48. We hope that our ideas can inform other programs that focus on the conservation of marine mammals. More

1.
Lubchenco, J., Palumbi, S. R., Gaines, S. D. & Andelman, S. Plugging a hole in the ocean: the emerging science of marine reserves. Ecol. Appl. 13, 3–7 (2003).
Article  Google Scholar 
2.
Di Franco, A. et al. Five key attributes can increase marine protected areas performance for small-scale fisheries management. Sci. Rep. 6, 38135 (2016).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

3.
Sala, E. & Giakoumi, S. No-take marine reserves are the most effective protected areas in the ocean. ICES J. Mar. Sci. 75, 1166–1168 (2018).
Article  Google Scholar 

4.
Lester, S. E. & Halpern, B. S. Biological responses in marine no-take reserves versus partially protected areas. Mar. Ecol. Prog. Ser. 367, 49–56 (2008).
ADS  Article  Google Scholar 

5.
Lester, S. E. et al. Biological effects within no-take marine reserves: A global synthesis. Mar. Ecol. Prog. Ser. 384, 33–46 (2009).
ADS  Article  Google Scholar 

6.
Edgar, G. J. et al. Global conservation outcomes depend on marine protected areas with five key features. Nature 506, 216–220 (2014).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

7.
Gaines, S. D., White, C., Carr, M. H. & Palumbi, S. R. Designing marine reserve networks for both conservation and fisheries management. Proc. Nat. Acad. Sci. 107, 18286–18293 (2010).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

8.
Sala, E. et al. A general business model for marine reserves. PLoS ONE 8, e58799 (2013).
ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

9.
Lynham, J. et al. Impact of two of the world’s largest protected areas on longline fishery catch rates. Nat. Commun. 11, 1–9 (2020).
MathSciNet  Article  CAS  Google Scholar 

10.
Cudney-Bueno, R., Lavín, M. F., Marinone, S. G., Raimondi, P. T. & Shaw, W. W. Rapid effects of marine reserves via larval dispersal. PLoS ONE 4, e4140 (2009).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

11.
Pelc, R. A., Warner, R. R., Gaines, S. D. & Paris, C. B. Detecting larval export from marine reserves. Proc. Nat. Acad. Sci. 107, 18266–18271 (2010).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

12.
Gell, F. R. & Roberts, C. M. Benefits beyond boundaries: The fishery effects of marine reserves. Trends Ecol. Evol. 18, 448–455 (2003).
Article  Google Scholar 

13.
Roberts, C. M., Hawkins, J. P. & Gell, F. R. The role of marine reserves in achieving sustainable fisheries. Philso. Trans. R. Soc. B Biol. Sci. 360, 123–132 (2005).
Article  Google Scholar 

14.
Russ, G. R. & Alcala, A. C. Enhanced biodiversity beyond marine reserve boundaries: The cup spillith over. Ecol. Appl. 21, 241–250 (2011).
PubMed  Article  PubMed Central  Google Scholar 

15.
Di Lorenzo, M., Guidetti, P., Di Franco, A., Calò, A. & Claudet, J. Assessing spillover from marine protected areas and its drivers: A meta-analytical approach. Fish Fish. 21, 906–915 (2020).
Article  Google Scholar 

16.
Dayton, P. K., Sala, E., Tegner, M. J. & Thrush, S. Marine reserves: parks, baselines, and fishery enhancement. Bull. Mar. Sci. 6, 617–634 (2000).
Google Scholar 

17.
Roberts, C. M., Bohnsack, J. A., Gell, F. J., Hawkins, J. P. & Goodridge, R. Effects of marine reserves on adjacent fisheries. Science 294, 1920–1923 (2001).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

18.
Russ, G. R. et al. Marine reserve benefits local fisheries. Ecol. Appl. 14, 597–606 (2004).
Article  Google Scholar 

19.
Goñi, R., Badalamenti, F. & Tupper, M. H. Fisheries—effects of marine protected areas on local fisheries: Evidence from empirical studies. In Marine Protected Areas: A Multidisciplinary Approach (Cambridge Univ (ed. Claudet, J.) 73–102 (Press, Cambridge, 2011).
Google Scholar 

20.
Abesamis, R. A. & Russ, G. R. Density-dependent spillover from a marine reserve: Long-term evidence. Ecol. Appl. 15, 1798–1812 (2005).
Article  Google Scholar 

21.
Kay, M. C. et al. Collaborative assessment of California spiny lobster population and fishery responses to a marine reserve network. Ecol. Appl. 22, 322–335 (2012).
PubMed  Article  Google Scholar 

22.
Kellner, J. B., Tetreault, I., Gaines, S. D. & Nisbet, R. M. Fishing the line near marine reserves in single and multispecies fisheries. Ecol. Appl. 17, 1039–1054 (2007).
PubMed  Article  Google Scholar 

23.
Edgar, G. J. et al. Bias in evaluating the effects of marine protected areas: The importance of baseline data for the Galapagos Marine Reserve. Envir. Conserv. 31, 212–218 (2004).
Article  Google Scholar 

24.
Edgar, G. J., Barrett, N. S. & Morton, A. J. Biases associated with the use of underwater visual census techniques to quantify the density and size-structure of fish populations. J. Exp. Mar. Biol. Ecol. 308, 269–290 (2004).
Article  Google Scholar 

25.
Sale, P. F. et al. Critical science gaps impede use of no-take fishery reserves. Trends Ecol. Evol. 20, 74–80 (2005).
PubMed  Article  Google Scholar 

26.
Forcada, A. et al. Effects of habitat on spillover from marine protected areas to artisanal fisheries. Mar. Ecol. Prog. Ser. 379, 197–211 (2009).
ADS  Article  Google Scholar 

27.
Hovel, K. A., Neilson, D. J., & Parnell, E. Baseline characterization of California spiny lobster (Panulirus interruptus) in South Coast marine protected areas: A report to California Sea Grant and the California Ocean Science Trust. 172 p. (COPC, 2015).

28.
Di Lorenzo, M., Claudet, J. & Guidetti, P. Spillover from marine protected areas to adjacent fisheries has an ecological and a fishery component. J. Nat. Conserv. 32, 62–66 (2016).
Article  Google Scholar 

29.
Eggleston, D. B. & Parsons, D. M. Disturbance-induced ‘spill-in’ of Caribbean spiny lobster to marine reserves. Mar. Ecol. Prog. Ser. 371, 213–220 (2008).
ADS  Article  Google Scholar 

30.
Goñi, R., Hilborn, R., Díaz, D., Mallol, S. & Adlerstein, S. Net contribution of spillover from a marine reserve to fishery catches. Mar. Ecol. Prog. Ser. 400, 233–243 (2010).
ADS  Article  Google Scholar 

31.
Moland, E. et al. Lobster and cod benefit from small-scale northern marine protected areas: Inference from an empirical before-after control-impact study. Proc. Royal Soc. B 280, 20122679 (2013).
Article  Google Scholar 

32.
Hilborn, R. K. et al. When can marine reserves improve fisheries management?. Ocean Coast. Manage. 47, 197–205 (2004).
Article  Google Scholar 

33.
Saarman, E. T. & Carr, M. H. The California Marine Life Protection Act: A balance of top down and bottom up governance in MPA planning. Mar. Pol. 41, 41–49 (2013).
Article  Google Scholar 

34.
Hamilton, S. L., Caselle, J. E., Malone, D. P. & Carr, M. H. Incorporating biogeography into evaluations of the Channel Islands marine reserve network. Proc. Natl. Acad. Sci. 107, 18272–18277 (2010).
ADS  CAS  PubMed  Article  Google Scholar 

35.
Caselle, J. E., Rassweiler, A., Hamilton, S. L. & Warner, R. R. Recovery trajectories of kelp forest animals are rapid yet spatially variable across a network of temperate marine protected areas. Sci. Rep. 5, 14102 (2015).
ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

36.
Kay, M. C., Lenihan, H. S., Kotchen, M. J. & Miller, C. J. Effects of marine reserves on California spiny lobster are robust and modified by fine-scale habitat features and distance from reserve borders. Mar. Ecol. Prog. Ser. 451, 137–150 (2012).
ADS  Article  Google Scholar 

37.
Koslow, J. A., Rogers-Bennett, L. & Neilson, D. J. A time series of California spiny lobster (Panulirus interruptus) phyllosoma from 1951 to 2008 links abundance to warm oceanographic conditions in southern California. CalCOFI Rep. 53, 132–139 (2012).
Google Scholar 

38.
Guenther, C., López-Carr, D. & Lenihan, H. S. Differences in lobster fishing effort before and after MPA establishment. Appl. Geog. 59, 78–87 (2015).
Article  Google Scholar 

39.
Peters, J. R., Reed, D. C. & Burkepile, D. E. Climate and fishing drive regime shifts in consumer-mediated nutrient cycling in kelp forests. Glob. Change Biol. 25, 3179–3192 (2019).
ADS  Article  Google Scholar 

40.
Fitzgerald, S. P. Collaborative Research and Data-Limited Assessment of Small-Scale Trap Fisheries in the Santa Barbara Channel (Doctoral dissertation, UC Santa Barbara). 165 p. (2019).

41.
Iacchei, M., Robinson, P. & Miller, K. A. Direct impacts of commercial and recreational fishing on spiny lobster, Panulirus interruptus, populations at Santa Catalina Island, California, United States. N. Z. J. Mar. Fresh. Res. 39, 1201–1214 (2005).
Article  Google Scholar 

42.
Lafferty, K. D. Fishing for lobsters indirectly increases epidemics in sea urchins. Ecol. Appl. 14, 1566–1573 (2004).
Article  Google Scholar 

43.
Castorani, M. C., Reed, D. C. & Miller, R. J. Loss of foundation species: Disturbance frequency outweighs severity in structuring kelp forest communities. Ecology 99, 2442–2454 (2018).
PubMed  Article  PubMed Central  Google Scholar 

44.
Berriman, J. S. et al. Shifts in attack behavior of an important kelp forest predator within marine reserves. Mar. Ecol. Prog. Series 522, 193–201 (2015).
ADS  Article  Google Scholar 

45.
Withy-Allen, K. R. & Hovel, K. A. California spiny lobster (Panulirus interruptus) movement behaviour and habitat use: Implications for the effectiveness of marine protected areas. Mar. Fresh. Res. 64, 359–371 (2013).
Article  Google Scholar 

46.
Hart, D. R. When do marine reserves increase fishery yield?. Can. J. Fish. Aquat. Sci. 63, 1445–1449 (2006).
Article  Google Scholar 

47.
Buxton, C. D., Hartmann, K. R., Kearney, R. & Gardner, C. When is spillover from marine reserves likely to benefit fisheries?. PLoS ONE 9, e107032 (2014).
ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

48.
Goñi, R. S. et al. Spillover from six western Mediterranean marine protected areas: Evidence from artisanal fisheries. Mar. Ecol. Prog. Ser. 366, 159–174 (2008).
ADS  Article  Google Scholar 

49.
Nillos-Kleiven, P. J. et al. Fishing pressure impacts the abundance gradient of European lobsters across the borders of a newly established marine protected area. Proc. R. Soc. B 286, 20182455 (2019).
PubMed  Article  PubMed Central  Google Scholar 

50.
Halpern, B. S., Lester, S. E. & Kellner, J. B. Spillover from marine reserves and the replenishment of fished stocks. Environ. Conserv. 36, 268–276 (2009).
Article  Google Scholar 

51.
Woodcock, P., O’Leary, B. C., Kaiser, M. J. & Pullin, A. S. Your evidence or mine? Systematic evaluation of reviews of marine protected area effectiveness. Fish Fish. 18, 668–681 (2017).
Article  Google Scholar 

52.
Hilborn, R. Are MPAs effective?. ICES J. Mar. Sci. 75, 1160–1162 (2018).
Article  Google Scholar 

53.
Ojeda-Martínez, C. et al. Review of the effects of protection in marine protected areas: Current knowledge and gaps. Anim. Biodiv. Conserv. 34, 191–203 (2011).
Google Scholar 

54.
Kerwath, S. E., Winker, H., Götz, A. & Attwood, C. G. Marine protected area improves yield without disadvantaging fishers. Nat. Commun. 4, 1–6 (2013).
Article  Google Scholar 

55.
Rassweiler, A., Costello, C., Hilborn, R. & Siegel, D. A. Integrating scientific guidance into marine spatial planning. Proc. R. Soc. B Biol. Sci. 281, 20132252 (2014).
Article  Google Scholar 

56.
Selkoe, K. A. et al. Taking the chaos out of genetic patchiness: Seascape genetics reveals ecological and oceanographic drivers of genetic patterns in three temperate reef species. Mol. Ecol. 19, 3708–3726 (2010).
PubMed  Article  PubMed Central  Google Scholar 

57.
Starr, R. M. et al. Variation in responses of fishes across multiple reserves within a network of marine protected areas in temperate waters. PLoS ONE 10, e118502 (2015).
Article  CAS  Google Scholar 

58.
Jones, N., McGinlay, J. & Dimitrakopoulos, P. G. Improving social impact assessment of protected areas: A review of the literature and directions for future research. Envir. Impact Assess. Rev. 64, 1–7 (2017).
Article  Google Scholar 

59.
CDFW. South Coast Fishery Spotlight: California Spiny Lobster. State of the California South Coast Supplemental Report: California Spiny Lobster. 7 pp. https://nrm.dfg.ca.gov/FileHandler.ashx?DocumentID=141295&inline (2017)

60.
Reed, D. C. SBC LTER: reef: abundance, size and fishing effort for California Spiny Lobster (Panulirus interruptus), ongoing since 2012. Environ. Data Initiat. https://doi.org/10.6073/pasta/a593a675d644fdefb736750b291579a0 (2019).
Article  Google Scholar 

61.
Reed, D. C., Nelson, J. C., Harrer, S. L. & Miller, R. J. Estimating biomass of benthic kelp forest invertebrates from body size and percent cover data. Mar. Biol. 163, 1–6 (2017).
Google Scholar  More

Neighbor GWAS
Basic model
We analyzed neighbor effects in GWAS as an inverse problem of the two-dimensional Ising model, named “neighbor GWAS” hereafter (Fig. 1). We considered a situation where a plant accession has one of two alleles at each locus, and a number of accessions occupied a finite set of field sites, in a two-dimensional lattice. The allelic status at each locus was represented by x, and so the allelic status at each locus of the ith focal plant and the jth neighboring plants was designated as xi(j)∈{−1, +1}. Based on a two-dimensional Ising model, we defined a phenotype value for the ith focal individual plant yias:

$$y_i = beta _1x_i + beta _2mathop {sum }limits_{ < i,j > } x_ix_j$$
(1)

where β1 and β2 denoted self-genotype and neighbor effects, respectively. If two neighboring plants shared the same allele at a given locus, the product xixj turned into (−1) × (−1) = +1 or (+1) × (+1) = +1. If two neighbors had different alleles, the product xixj became (−1) × (+1) = −1 or (+1) × (−1) = −1. Accordingly, the effects of neighbor genotypic identity on a particular phenotype depended on the coefficient β2 and the number of the two alleles in a neighborhood. If the numbers of identical and different alleles were the same near a focal plant, these neighbors offset the sum of the products between the focal plant i and all j neighbors (mathop {sum }nolimits_{ < i,j > } x_ix_j) and exerted no effects on a phenotype. When we summed up the phenotype values for the total number of plants n and replaced it as E = −β2, H = −β1 and εI = Σyi, Eq. 1 could be transformed into ({it{epsilon }}_I = – {E}mathop {sum }nolimits_{ < i,j > } x_ix_j – {H}mathop {sum }x_i), which defined the interaction energy of a two-dimensional ferromagnetic Ising model (McCoy and Maillard 2012). The neighbor effect β2 and self-genotype effect β1 were interpreted as the energy coefficient E and external magnetic effects H, respectively. An individual plant represented a spin and the two allelic states of each locus corresponded to a north or south dipole. The positive or negative value of Σxixj indicated a ferromagnetism or paramagnetism, respectively. In this study, we did not consider the effects of allele dominance because this model was applied to inbred plants. However, heterozygotes could be processed if the neighbor covariate xixj was weighted by an estimated degree of dominance in the self-genotypic effects on a phenotype.
Association tests
For association mapping, we needed to determine β1 and β2 from the observed phenotypes and considered a confounding sample structure as advocated by previous GWAS (e.g., Kang et al. 2008; Korte and Farlow 2013). Extending the basic model (Eq. (1)), we described a linear mixed model at an individual level as:

$$y_i = beta _0 + beta _1x_i + frac{{beta _2}}{L}mathop {sum }limits_{ < i,j > }^L x_ix_j^{(s)} + u_i + e_i$$
(2)

where β0 indicated the intercept; the term β1xi represented fixed self-genotype effects as tested in standard GWAS; and β2 was the coefficient of fixed neighbor effects. The neighbor covariate (mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}) indicated a sum of products for all combinations between the ith focal plant and the jth neighbor at the sth spatial scale from the focal plant i, and was scaled by the number of neighboring plants, L. The number of neighboring plants L was dependent on the spatial scale s to be referred. Variance components due to the sample structure of self and neighbor effects were modeled by a random effect (u_i in {boldsymbol{u}}) and ({boldsymbol{u}}sim {mathrm{Norm}}(textbf{0},sigma _1^2{boldsymbol{K}}_1 + sigma _2^2{boldsymbol{K}}_2)). The residual was expressed as (e_i in {boldsymbol{e}}) and ({boldsymbol{e}}sim {mathrm{Norm}}(textbf{0},sigma _e^2{boldsymbol{I}})), where I represented an identity matrix.
Variation partitioning
To estimate the proportion of phenotypic variation explained (PVE) by the self and neighbor effects, we utilized variance component parameters in linear mixed models. The n × n variance-covariance matrices represented the similarity in self-genotypes (i.e., kinship) and neighbor covariates among n individual plants as ({boldsymbol{K}}_1 = frac{1}{{q – 1}}{boldsymbol{X}}_1^{mathrm{T}}{boldsymbol{X}}_1) and ({boldsymbol{K}}_2 = frac{1}{{q – 1}}{boldsymbol{X}}_2^{mathrm{T}}{boldsymbol{X}}_2), where the elements of n plants × q markers matrix X1 and X2 consisted of explanatory variables for the self and neighbor effects as X1 = (xi) and ({boldsymbol{X}}_2 = (frac{{mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}}}{L})). As we defined (x_{i(j)} in){+1, −1}, the elements of the kinship matrix K1 were scaled to represent the proportion of marker loci shared among n × n plants such that ({boldsymbol{K}}_1 = left( {frac{{k_{ij}, + ,1}}{2}} right));(sigma _1^2)and (sigma _2^2) indicated variance component parameters for the self and neighbor effects.
The individual-level formula Eq. (2) could also be converted into a conventional matrix form as:

$${boldsymbol{y}} = {boldsymbol{X}}{boldsymbol{beta }} + {boldsymbol{Zu}} + {boldsymbol{e}}$$
(3)

where y was an n × 1 vector of the phenotypes; X was a matrix of fixed effects, including a unit vector, self-genotype xi, neighbor covariate (({mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}})/{L}), and other confounding covariates for n plants; β was a vector that represents the coefficients of the fixed effects; Z was a design matrix allocating individuals to a genotype, and became an identity matrix if all plants were different accessions; u was the random effect with Var(u) =(sigma _1^2{boldsymbol{K}}_1 + sigma _2^2{boldsymbol{K}}_2); and e was residual as Var(e) = (sigma _e^2{boldsymbol{I}}).
Because our objective was to test for neighbor effects, we needed to avoid the detection of false positive neighbor effects. The self-genotype value xi and neighbor genotypic identity (mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}) would become correlated explanatory variables in a single regression model (sensu colinear) due to the minor allele frequency (MAF) and the spatial scale of s. When MAF is low, neighbors (x_j^{(s)}) are unlikely to vary in space and most plants will have similar values for neighbor identity (mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}). Furthermore, if the neighbor effects range was broad enough to encompass an entire field (i.e., s→∞), the neighbor covariate and self-genotype xiwould become colinear according to the equation: (left(mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}right)/L = x_ileft( {mathop {sum }nolimits_{j = 1}^L x_j^{left( s right)}} right)/L = x_ibar x_j), where (bar x_j) indicates a population-mean of neighbor genotypes and corresponds to a population-mean of self-genotype values (bar x_i), if s→∞. The standard GWAS is a subset of the neighbor GWAS and these two models become equivalent at s = 0 and (sigma _2^2) = 0. When testing the self-genotype effect β1, we recommend that the neighbor effects and its variance component (sigma _2^2) should be excluded; otherwise, the standard GWAS fails to correct a sample structure because of the additional variance component at (sigma _2^2, ne ,0). To obtain a conservative conclusion, the significance of β2 and (sigma _2^2) should be compared using the standard GWAS model based on self-effects alone.
Given the potential collinearity between the self and neighbor effects, we defined different metrics for the proportion of phenotypic variation explained (PVE) based on self or neighbor effects. Using a single-random effect model, we calculated PVE for either the self or neighbor effects as follows:
‘single’ PVEself = (sigma _1^2/(sigma _1^2 + sigma _e^2))when s and (sigma _2^2) were set at 0, or
‘single’ PVEnei = (sigma _2^2/(sigma _2^2 + sigma _e^2))when (sigma _1^2) was set at 0.
Using a two-random effect model, we could focus on one variable while considering relationships between two variables (sensu partial out) for either of the two variance components. We defined such a partial PVE as:
‘partial’ PVEself = (sigma _1^2/(sigma _1^2 + sigma _2^2 + sigma _e^2)) and
‘partial’ PVEnei = (sigma _2^2/(sigma _1^2 + sigma _2^2 + sigma _e^2)).
As the partial PVEself was equivalent to the single PVEself when s was set at 0, the net contribution of neighbor effects at s ≠ 0 was given as
‘net’ PVEnei = (partial PVEself + partial PVEnei) − single PVEself,
which indicated the proportion of phenotypic variation that could be explained by neighbor effects, but not by the self-genotype effects.
Simulation
To examine the model performance, we applied the neighbor GWAS to simulated phenotypes. Phenotypes were simulated using a subset of the actual A. thaliana genotypes. To evaluate the performance of the simple linear model, we assumed a complex ecological form of neighbor effects with multiple variance components controlled. The model performance was evaluated in terms of the causal variant detection and accuracy of estimates. All analyses were performed using R version 3.6.0 (R Core Team 2019).
Genotype data
To consider a realistic genetic structure in the simulation, we used part of the A. thaliana RegMap panel (Horton et al. 2012). The genotype data for 1307 accessions were downloaded from the Joy Bergelson laboratory website (http://bergelson.uchicago.edu/?page_id=790 accessed on February 9, 2017). We extracted data for chromosomes 1 and 2 with MAF at >0.1, yielding a matrix of 1307 plants with 65,226 single nucleotide polymorphisms (SNPs). Pairwise linkage disequilibrium (LD) among the loci was r2 = 0.003 [0.00–0.06: median with upper and lower 95 percentiles]. Before generating a phenotype, genotype values at each locus were standardized to a mean of zero and a variance of 1. Subsequently, we randomly selected 1,296 accessions (= 36 × 36 accessions) without any replacements for each iteration and placed them in a 36 × 72 checkered space, following the Arabidopsis experimental settings (see Fig. S1).
Phenotype simulation
To address ecological issues specific to plant neighborhood effects, we considered two extensions, namely asymmetric neighbor effects and spatial scales. Previous studies have shown that plant–plant interactions between accessions are sometimes asymmetric under herbivory (e.g., Bergvall et al. 2006; Verschut et al. 2016; Sato and Kudoh 2017) and height competition (Weiner 1990); where one focal genotype is influenced by neighboring genotypes, while another receives no neighbor effects. Such asymmetric neighbor effects can be tested by statistical interaction terms in a linear model (Bergvall et al. 2006; Sato and Kudoh 2017). Several studies have also shown that the strength of neighbor effects depends on spatial scales (Hambäck et al. 2014), and that the scale of neighbors to be analyzed relies on the dispersal ability of the causative organisms (see Hambäck et al. 2009; Sato and Kudoh 2015; Verschut et al. 2016; Ida et al. 2018 for insect and mammal herbivores; Rieux et al. 2014 for pathogen dispersal) or the size of the competing plants (Weiner 1990). We assumed the distance decay at the sth sites from a focal individual i with the decay coefficient α as (wleft( {s,alpha } right) = {mathrm{e}}^{ – alpha (s – 1)}), since such an exponential distance decay has been widely adopted in empirical studies (Devaux et al. 2007; Carrasco et al. 2010; Rieux et al. 2014; Ida et al. 2018). Therefore, we assumed a more complex model for simulated phenotypes than the model for neighbor GWAS as follows:

$$y_i = beta _0 + beta _1x_i + frac{{beta _2}}{L}mathop {sum }limits_{ < i,j > }^L w(s,alpha )x_ix_j^{(s)} + beta _{12}frac{{x_i}}{L}mathop {sum }limits_{ < i,j > }^L w(s,alpha )x_ix_j^{(s)} + u_i + e_i$$
(4)

where β12 was the coefficient for asymmetry in neighbor effects. By incorporating an asymmetry coefficient, the model (Eq. (4)) can deal with cases where neighbor effects are one-sided or occur irrespective of a focal genotype (Fig. 2). Total variance components resulting from three background effects (i.e., the self, neighbor, and self-by-neighbor effects) were defined as (u_i in {boldsymbol{u}}) and ({boldsymbol{u}}sim {mathrm{Norm}}(textbf{0},sigma _1^2{boldsymbol{K}}_1 + sigma _2^2{boldsymbol{K}}_2 + sigma _{12}^2{boldsymbol{K}}_{12})). The three variance component parameters (sigma _1^2), (sigma _2^2), and (sigma _{12}^2), determined the relative importance of the self-genotype, neighbor, and asymmetric neighbor effects in ui. Given the elements of n plants × q marker explanatory matrix with ({boldsymbol{X}}_{12} = (frac{{x_i}}{L}mathop {sum }nolimits_{ < i,j > }^L w(s,alpha )x_ix_j^{(s)})), the similarity in asymmetric neighbor effects was calculated as ({boldsymbol{K}}_{12} = frac{1}{q-1}{boldsymbol{X}}_{12}^{mathrm{T}}{boldsymbol{X}}_{12}). To control phenotypic variations, we further partitioned the proportion of phenotypic variation into those explained by the major-effect genes and variance components PVEβ + PVEu, major-effect genes alone PVEβ, and residual error PVEe, where PVEβ + PVEu + PVEe = 1. The optimize function in R was used to adjust the simulated phenotypes to the given amounts of PVE.
Fig. 2: Numerical examples of the symmetric and asymmetric neighbor effects.

The intercept, distance decay, random effects, and residual errors are neglected, to simplify this scheme. a Symmetric neighbor effects represent how neighbor genotype similarity (or dissimilarity) affects the trait value of a focal individual yi regardless of its own genotype. b Asymmetric neighbor effects can represent a case in which one genotype experiences neighbor effects while the other does not (b) and a case in which the direction of the neighbor effects depends on the genotypes of a focal individual (c). The case b was considered in our simulation as it has been empirically reported (e.g., Bergvall et al. 2006; Verschut et al. 2016; Sato & Kudoh 2017).

Full size image

Parameter setting
Ten phenotypes were simulated with varying combination of the following parameters, including the distance decay coefficient α, the proportion of phenotypic variation explained by the major-effect genes PVEβ, the proportion of phenotypic variation explained by major-effect genes and variance components PVEβ + PVEu, and the relative contributions of self, symmetric neighbor, and asymmetric neighbor effects, i.e., PVEself:PVEnei:PVEs×n. We ran the simulation with different combinations, including α = 0.01, 1.0, or 3.0; PVEself:PVEnei:PVEs×n = 8:1:1, 5:4:1, or 1:8:1; and PVEβ and PVEβ + PVEu = 0.1 and 0.4, 0.3 and 0.4, 0.3 and 0.8, or 0.6 and 0.8. The maximum reference scale was fixed at s = 3. The line of simulations was repeated for 10, 50, or 300 causal SNPs to examine cases of oligogenic and polygenic control of a trait. The non-zero coefficients (i.e., signals) for the causal SNPs were randomly sampled from −1 or 1 digit and then assigned, as some causal SNPs were responsible for both the self and neighbor effects. Of the total number of causal SNPs, 15% had self, neighbor, and asymmetric neighbor effects (i.e.,β1 ≠ 0 and β2 ≠ 0 and β12 ≠ 0); another 15% had both the self and neighbor effects, but no asymmetry in the neighbor effects (β1 ≠ 0 and β2 ≠ 0 and β12 ≠ 0); another 35% had self-genotypic effects only (β1 ≠ 0); and the remaining 35% had neighbor effects alone (β2 ≠ 0). Given its biological significance, we assumed that some loci having neighbor signals possessed asymmetric interactions between the neighbors (β2 ≠ 0 and β12 ≠ 0), while the others had symmetric interactions (β2 ≠ 0 and β12 ≠ 0). Therefore, the number of causal SNPs in β12 was smaller than that in the main neighbor effects β2. According to this assumption, the variance component (sigma _{12}^2) was also assumed to be smaller than (sigma _2^2). To examine extreme conditions and strong asymmetry in neighbor effects, we additionally analyzed the cases with PVEself:PVEnei:PVEs×n = 1:0:0, 0:1:0, or 1:1:8.
Summary statistics
The simulated phenotypes were fitted by Eq. (2) to test the significance of coefficients β1 and β2, and to estimate single or partial PVEself and PVEnei. To deal with potential collinearity between xi and neighbor genotypic identity (mathop {sum }nolimits_{ < i,j > }^L x_ix_j^{(s)}), we performed likelihood ratio tests between the self-genotype effect model and the model with both self and neighbor effects, which resulted in conservative tests of significance for β2 and (sigma _2^2). The simulated phenotype values were standardized to have a mean of zero and a variance of 1, where true β was expected to match the estimated coefficients (hat beta) when multiplied by the standard deviation of non-standardized phenotype values. The likelihood ratio was calculated as the difference in deviance, i.e., −2 × log-likelihood, which is asymptotically χ2 distributed with one degree of freedom. The variance components, (sigma _1^2) and (sigma _2^2), were estimated using a linear mixed model without any fixed effects. To solve the mixed model with the two random effects, we used the average information restricted maximum likelihood (AI-REML) algorithm implemented in the lmm.aireml function in the gaston package of R (Perdry and Dandine-Roulland 2018). Subsequently, we replaced the two variance parameters (sigma _1^2) and (sigma _2^2) in Eq. (2) with their estimates (hat sigma _1^2) and (hat sigma _2^2) from the AI-REML, and performed association tests by solving a linear mixed model with a fast approximation, using eigenvalue decomposition (implemented in the lmm.diago function: Perdry and Dandine-Roulland 2018). The model likelihood was computed using the lmm.diago.profile.likelihood function. We evaluated the self and neighbor effects for association mapping based on the forward selection of the two fixed effects, β1 and β2, as described below:
1.
Computed the null likelihood with (sigma _1^2, ne ,0) and (sigma _2^2 = 0) in Eq. (2).

2.
Tested the self-effect, β1, by comparing with the null likelihood.

3.
Computed the self-likelihood with (hat sigma _1^2), (hat sigma _2^2), and β1 using Eq. (2).

4.
Tested the neighbor effects, β2, by comparing with the self-likelihood.

We also calculated PVE using the mixed model (Eq. (3)) without β1 and β2 as follows:
1.
Calculated single PVEself or single PVEnei by setting either (sigma _1^2) or (sigma _2^2) at 0.

2.
Tested the single PVEself or single PVEnei using the likelihood ratio between the null and one-random effect model.

3.
Calculated the partial PVEself and partial PVEnei by estimating (sigma _1^2) and (sigma _2^2) simultaneously.

4.
Tested the partial PVEself and partial PVEnei using the likelihood ratio between the two- and one-random effect model.

We inspected the model performance based on causal variant detection, PVE estimates, and effect size estimates. The true or false positive rates between the causal and non-causal SNPs were evaluated using ROC curves and area under the ROC curves (AUC) (Gage et al. 2018). An AUC of 0.5 would indicate that the GWAS has no power to detect true signals, while an AUC of 1.0 would indicate that all the top signals predicted by the GWAS agree with the true signals. In addition, the sensitivity to distinguish self or neighbor signals (i.e., either β1 ≠ 0 or β2 ≠ 0) was evaluated using the true positive rate of the ROC curves (i.e., y-axis of the ROC curve) at a stringent specificity level, where the false positive rate (x-axis of the ROC curve) = 0.05. The roc function in the pROC package (Robin et al. 2011) was used to calculate the ROC and AUC from −log10(p value). Factors affecting the AUC or sensitivity were tested by analysis-of-variance (ANOVA) for the self or neighbor effects (AUCself or AUCnei; self or neighbor sensitivity). The AUC and PVE were calculated from s = 1 (the first nearest neighbors) to s = 3 (up to the third nearest neighbors) cases. The AUC was also calculated using standard linear models without any random effects, to examine whether the linear mixed models were superior to the linear models. We also tested the neighbor GWAS model incorporating the neighbor phenotype (y_j^{(s)}) instead of (x_j^{(s)}). The accuracy of the total PVE estimates was defined as PVE accuracy = (estimated total PVE − true total PVE) / true total PVE. The accuracy of the effect size estimates was evaluated using mean absolute errors (MAE) between the true and estimated β1 or β2 for the self and neighbor effects (MAEself and MAEnei). Factors affecting the accuracy of PVE and effect size estimates were also tested using ANOVA. Misclassifications between self and neighbor signals were further evaluated by comparing p value scores between zero and non-zero coefficients. If −log10(p value) scores of zero β are the same or larger than non-zero β, it infers a risk of misspecification of the true signals.
Arabidopsis herbivory data
We applied the neighbor GWAS to field data of Arabidopsis herbivory. The procedure for this field experiment followed that of our previous experiment (Sato et al. 2019). We selected 199 worldwide accessions (Table S1) from 2029 accessions sequenced by the RegMap (Horton et al. 2012) and 1001 Genomes project (Alonso-Blanco et al. 2016). Of the 199 accessions, most were overlapped with a previous GWAS of biotic interactions (Horton et al. 2014) and half were included by a GWAS of glucosinolates (Chan et al. 2010). Eight replicates of each of the 199 accessions were first prepared in a laboratory and then transferred to the outdoor garden at the Center for Ecological Research, Kyoto University, Japan (Otsu, Japan: 35°06′N, 134°56′E, alt. ca. 200 m: Fig. S1a). Seeds were sown on Jiffy-seven pots (33-mm diameter) and stratified at a temperature of 4 °C for a week. Seedlings were cultivated for 1.5 months under a short-day condition (8 h light: 16 h dark, 20 °C). Plants were then separately potted in plastic pots (6 cm in diameter) filled with mixed soil of agricultural compost (Metro-mix 350, SunGro Co., USA) and perlite at a 3:1 ratio. Potted plants were set in plastic trays (10 × 40 cells) in a checkered pattern (Fig. S1b). In the field setting, a set of 199 accessions and an additional Col-0 accession were randomly assigned to each block without replacement (Fig. S1c). Eight replicates of these blocks were set >2 m apart from each other (Fig. S1c). Potted plants were exposed to the field environment for 3 weeks in June 2017. At the end of the experiment, the percentage of foliage eaten was scored as: 0 for no visible damage, 1 for ≤10%, 2 for >10% and ≤25%, 3 for >25% and ≤50%, 4 for >50% and ≤75%, and 5 for >75%. All plants were scored by a single person to avoid observer bias. The most predominant herbivore in this field trial was the diamond back moth (Plutella xylostella), followed by the small white butterfly (Pieris rapae). We also recorded the initial plant size and the presence of inflorescence to incorporate them as covariates. Initial plant size was evaluated by the length of the largest rosette leaf (mm) at the beginning of the field experiment and the presence of inflorescence was recorded 2 weeks after transplanting.
We estimated the variance components and performed the association tests for the leaf damage score with the neighbor covariate at s = 1 and 2. These two scales corresponded to L = 4 (the nearest four neighbors) and L = 12 (up to the second nearest neighbors), respectively, in the Arabidopsis dataset. The variation partitioning and association tests were performed using the gaston package, as mentioned above. To determine the significance of the variance component parameters, we compared the likelihood between mixed models with one or two random effects. For the genotype data, we used an imputed SNP matrix of the 2029 accessions studied by the RegMap (Horton et al. 2012) and 1001 Genomes project (Alonso-Blanco et al. 2016). Missing genotypes were imputed using BEAGLE (Browning and Browning 2009), as described by Togninalli et al. (2018) and updated on the AraGWAS Catalog (https://aragwas.1001genomes.org). Of the 10,709,466 SNPs from the full imputed matrix, we used 1,242,128 SNPs with MAF at >0.05 and LD of adjacent SNPs at r2  More

1.
Cox, P. M. et al. Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability. Nature 494, 341–344 (2013).
ADS  CAS  PubMed  Article  Google Scholar 
2.
Guimberteau, M. et al. Impacts of future deforestation and climate change on the hydrology of the Amazon Basin: a multi-model analysis with a new set of land-cover change scenarios. Hydrol. Earth Syst. Sci. 21, 1455–1475 (2017).
ADS  Article  Google Scholar 

3.
Marengo, J. A. & Espinoza, J. C. Extreme seasonal droughts and floods in Amazonia: causes, trends and impacts. Int. J. Climatol. 36, 1033–1050 (2016).
Article  Google Scholar 

4.
Jimenez, J. C. et al. Spatio-temporal patterns of thermal anomalies and drought over tropical forests driven by recent extreme climatic anomalies. Philos. Trans. R. Soc. B Biol. Sci. 373, 20170300 (2018).
Article  Google Scholar 

5.
Phillips, O. L. et al. Drought sensitivity of the Amazon rainforest. Science 323, 1344–1347 (2009).
ADS  CAS  PubMed  Article  Google Scholar 

6.
Kumar, J., Hoffman, F. M., Hargrove, W. W. & Collier, N. Understanding the representativeness of FLUXNET for upscaling carbon flux from eddy covariance measurements. Earth Syst. Sci. Data Discuss. 1–25 (2016). https://doi.org/10.5194/essd-2016-36

7.
Baldocchi, D. et al. FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull. Am. Meteorol. Soc. 82, 2415–2434 (2001).
ADS  Article  Google Scholar 

8.
Girardin, C. A. J. et al. Seasonal trends of Amazonian rainforest phenology, net primary productivity, and carbon allocation. Glob. Biogeochem. Cycles 30, 700–715 (2016).
ADS  CAS  Article  Google Scholar 

9.
Running, S. W. et al. A continuous satellite-derived measure of global terrestrial primary production. Bioscience 54, 547–560 (2004).
Article  Google Scholar 

10.
Malhi, Y. & Wright, J. Spatial patterns and recent trends in the climate of tropical rainforest regions. Philos. Trans. R. Soc. B Biol. Sci. 359, 311–329 (2004).
Article  Google Scholar 

11.
Huete, A. R. et al. Amazon rainforests green-up with sunlight in dry season. Geophys. Res. Lett. 33, L06405 (2006).
ADS  Article  Google Scholar 

12.
Morton, D. C. et al. Amazon forests maintain consistent canopy structure and greenness during the dry season. Nature 506, 221–224 (2014).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

13.
Myneni, R. B. et al. Large seasonal swings in leaf area of Amazon rainforests. Proc. Natl Acad. Sci. USA 104, 4820–4823 (2007).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

14.
Morton, D. C. et al. Morton et al. reply. Nature 531, E6–E6 (2016).
CAS  PubMed  Article  PubMed Central  Google Scholar 

15.
Saleska, S. R. et al. Dry-season greening of Amazon forests. Nature 531, E4–E5 (2016).
CAS  PubMed  Article  PubMed Central  Google Scholar 

16.
Saleska, S. R., Didan, K., Huete, A. R. & Da Rocha, H. R. Amazon forests green-up during 2005 drought. Science 318, 612 (2007).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

17.
Samanta, A. et al. Amazon forests did not green-up during the 2005 drought. Geophys. Res. Lett. 37, LG05401 (2010).
ADS  Article  Google Scholar 

18.
Samanta, A. et al. Comment on ‘Drought-induced reduction in global terrestrial net primary production from 2000 through 2009’. Science 333, 1093 (2011).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

19.
Xu, L. et al. Widespread decline in greenness of Amazonian vegetation due to the 2010 drought. Geophys. Res. Lett. 38, L07402 (2011).
ADS  Article  Google Scholar 

20.
Atkinson, P. M., Dash, J. & Jeganathan, C. Amazon vegetation greenness as measured by satellite sensors over the last decade. Geophys. Res. Lett. 38, L19105 (2011).
ADS  Article  Google Scholar 

21.
Zhao, M. & Running, S. W. Drought-induced reduction in global terrestrial net primary production from 2000 through 2009. Science 329, 940–943 (2010).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

22.
Samanta, A., Ganguly, S., Vermote, E., Nemani, R. R. & Myneni, R. B. Why is remote sensing of Amazon forest greenness so challenging? Earth Interact. 16, 1–14 (2012).
Article  Google Scholar 

23.
Lyapustin, A., Wang, Y., Laszlo, I. & Korkin, S. Improved cloud and snow screening in MAIAC aerosol retrievals using spectral and spatial analysis. Atmos. Meas. Tech. 5, 843–850 (2012).
Article  Google Scholar 

24.
Hilker, T. et al. Vegetation dynamics and rainfall sensitivity of the Amazon. Proc. Natl Acad. Sci. USA 111, 16041–16046 (2014).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

25.
Schmit, T. J. et al. A closer look at the ABI on the GOES-R series. Bull. Am. Meteorol. Soc. 98, 681–698 (2017).
ADS  Article  Google Scholar 

26.
Wu, J. et al. Leaf development and demography explain photosynthetic seasonality in Amazon evergreen forests. Science 351, 972–976 (2016).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

27.
Chave, J. et al. Regional and seasonal patterns of litterfall in tropical South America. Biogeosciences 7, 43–55 (2010).
ADS  Article  Google Scholar 

28.
Samanta, A. et al. Seasonal changes in leaf area of Amazon forests from leaf flushing and abscission. J. Geophys. Res. Biogeosci. 117, G01015 (2012).
ADS  Article  Google Scholar 

29.
Brando, P. M. et al. Seasonal and interannual variability of climate and vegetation indices across the Amazon. Proc. Natl Acad. Sci. USA 107, 14685–14690 (2010).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

30.
Myneni, R. B., Nemani, R. R. & Running, S. W. Estimation of global leaf area index and absorbed PAR using radiative transfer models. IEEE Trans. Geosci. Remote Sens. 35, 1380–1393 (1997).
ADS  Article  Google Scholar 

31.
Hilker, T. et al. On the measurability of change in Amazon vegetation from MODIS. Remote Sens. Environ. 166, 233–242 (2015).
ADS  Article  Google Scholar 

32.
Araújo, A. C. et al. Comparative measurements of carbon dioxide fluxes from two nearby towers in a central Amazonian rainforest: The Manaus LBA site. J. Geophys. Res. 107, 8090 (2002).
Article  Google Scholar 

33.
Holben, B. N. Characteristics of maximum-value composite images from temporal AVHRR data. Int. J. Remote Sens. 7, 1417–1434 (1986).
ADS  Article  Google Scholar 

34.
Galvão, L. S., Ponzoni, F. J., Epiphanio, J. C. N., Rudorff, B. F. T. & Formaggio, A. R. Sun and view angle effects on NDVI determination of land cover types in the Brazilian Amazon region with hyperspectral data. Int. J. Remote Sens. 25, 1861–1879 (2004).
ADS  Article  Google Scholar 

35.
Fensholt, R., Huber, S., Proud, S. R. & Mbow, C. Detecting canopy water status using shortwave infrared reflectance data from polar orbiting and geostationary platforms. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens 3, 271–285 (2010).
ADS  Article  Google Scholar 

36.
Gao, F., Jin, Y., Li, X., Schaaf, C. B. & Strahler, A. H. Bidirectional NDVI and atmospherically resistant BRDF inversion for vegetation canopy. IEEE Trans. Geosci. Remote Sens. 40, 1269–1278 (2002).
ADS  Article  Google Scholar 

37.
Kruijt, B. et al. The robustness of eddy correlation fluxes for Amazon rain forest conditions. Ecol. Appl. 14, 101–113 (2004).
Article  Google Scholar 

38.
Galvão, L. S. et al. On intra-annual EVI variability in the dry season of tropical forest: A case study with MODIS and hyperspectral data. Remote Sens. Environ. 115, 2350–2359 (2011).
ADS  Article  Google Scholar 

39.
NOAA National Centers for Environmental Information. State of the Climate: Global Climate Report for Annual 2018. (2019). Available at: https://www.ncdc.noaa.gov/sotc/global/201813. (Accessed: 18th June 2019)

40.
Andreae, M. O. et al. The Amazon Tall Tower Observatory (ATTO): Overview of pilot measurements on ecosystem ecology, meteorology, trace gases, and aerosols. Atmos. Chem. Phys. 15, 10723–10776 (2015).
ADS  CAS  Article  Google Scholar 

41.
Kobayashi, H. & Dye, D. G. Atmospheric conditions for monitoring the long-term vegetation dynamics in the Amazon using normalized difference vegetation index. Remote Sens. Environ. 97, 519–525 (2005).
ADS  Article  Google Scholar 

42.
Xu, L. et al. Satellite observation of tropical forest seasonality: spatial patterns of carbon exchange in Amazonia. Environ. Res. Lett. 10, 084005 (2015).
ADS  Article  CAS  Google Scholar 

43.
Doughty, R. et al. TROPOMI reveals dry-season increase of solar-induced chlorophyll fluorescence in the Amazon forest. Proc. Natl Acad. Sci. USA 116, 22393–22398 (2019).
CAS  PubMed  Article  PubMed Central  Google Scholar 

44.
Bi, J. et al. Sunlight mediated seasonality in canopy structure and photosynthetic activity of Amazonian rainforests. Environ. Res. Lett. 10, 064014 (2015).
ADS  Article  Google Scholar 

45.
Nemani, R. R. et al. Climate-driven increases in global terrestrial net primary production from 1982 to 1999. Science 300, 1560–1563 (2003).
ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

46.
Wu, J. et al. Biological processes dominate seasonality of remotely sensed canopy greenness in an Amazon evergreen forest. N. Phytol. 217, 1507–1520 (2018).
Article  Google Scholar 

47.
Tang, H. & Dubayah, R. Light-driven growth in Amazon evergreen forests explained by seasonal variations of vertical canopy structure. Proc. Natl Acad. Sci. USA 114, 2640–2644 (2017).
CAS  PubMed  Article  Google Scholar 

48.
Huete, A. et al. Overview of the radiometric and biophysical performance of the MODIS vegetation indices. Remote Sens. Environ. 83, 195–213 (2002).
ADS  Article  Google Scholar 

49.
Justice, C. O., Townshend, J. R. G., Holben, A. N. & Tucker, C. J. Analysis of the phenology of global vegetation using meteorological satellite data. Int. J. Remote Sens. 6, 1271–1318 (1985).
ADS  Article  Google Scholar 

50.
Badgley, G., Anderegg, L. D., Berry, J. A. & Field, C. B. Terrestrial gross primary production: Using NIRv to scale from site to globe. Glob. Chang. Biol. 25, 3731–3740 (2019).
ADS  PubMed  Article  PubMed Central  Google Scholar 

51.
Piao, S. et al. Evidence for a weakening relationship between interannual temperature variability and northern vegetation activity. Nat. Commun. 5, 1–7 (2014).
Article  CAS  Google Scholar 

52.
Myneni, R. B., Hall, F. G., Sellers, P. J. & Marshak, A. L. The interpretation of spectral vegetation indexes. IEEE Trans. Geosci. Remote Sens. 33, 481–486 (2019).
ADS  Article  Google Scholar 

53.
Sellers, P. J. Canopy reflectance, photosynthesis and transpiration. Int. J. Remote Sens 6, 1335–1372 (1985).
ADS  Article  Google Scholar 

54.
Smith, M. N. et al. Seasonal and drought‐related changes in leaf area profiles depend on height and light environment in an Amazon forest. N. Phytol. 222, 1284–1297 (2019).
Article  Google Scholar 

55.
Goward, S. N. & Huemmrich, K. F. Vegetation canopy PAR absorptance and the normalized difference vegetation index: An assessment using the SAIL model. Remote Sens. Environ. 39, 119–140 (1992).
ADS  Article  Google Scholar 

56.
Miura, T., Nagai, S., Takeuchi, M., Ichii, K. & Yoshioka, H. Improved characterisation of vegetation and land surface seasonal dynamics in central Japan with Himawari-8 hypertemporal data. Sci. Rep. 9, 1–12 (2019).
Article  CAS  Google Scholar 

57.
Da Rocha, H. R. et al. Patterns of water and heat flux across a biome gradient from tropical forest to savanna in Brazil. J. Geophys. Res. Biogeosci. 114, G00B12 (2009).
Article  Google Scholar 

58.
Wang, W. et al. An introduction to the Geostationary-NASA Earth Exchange (GeoNEX) Products: 1. Top-of-atmosphere reflectance and brightness temperature. Remote Sens. 12, 1267 (2020).
ADS  Article  Google Scholar 

59.
Lyapustin, A., Martonchik, J., Wang, Y., Laszlo, I. & Korkin, S. Multiangle implementation of atmospheric correction (MAIAC): 1. Radiative transfer basis and look-up tables. J. Geophys. Res. 116, D03210 (2011).
ADS  Google Scholar 

60.
de Moura, Y. M. et al. Spectral analysis of Amazon canopy phenology during the dry season using a tower hyperspectral camera and MODIS observations. ISPRS J. Photogramm. Remote Sens. 131, 52–64 (2017).
ADS  Article  Google Scholar 

61.
Friedl, M. A. et al. MODIS Collection 5 global land cover: Algorithm refinements and characterization of new datasets. Remote Sens. Environ. 114, 168–182 (2010).
ADS  Article  Google Scholar 

62.
Sorooshian, S. et al. Evaluation of PERSIANN system satellite-based estimates of tropical rainfall. Bull. Am. Meteorol. Soc. 81, 2035–2046 (2000).
ADS  Article  Google Scholar 

63.
Sinyuk, A. et al. The AERONET Version 3 aerosol retrieval algorithm, associated uncertainties and comparisons to Version 2. Atmos. Meas. Tech. 13, 3375–3411 (2020).
CAS  Article  Google Scholar 

64.
Virtanen, P. et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).
CAS  PubMed  PubMed Central  Article  Google Scholar  More