Ecology

1.
Moen, R., Pastor, J., Cohen, Y. & Schwartz, C. C. Effects of moose movement and habitat use on GPS collar performance. J. Wildl. Manag. 60, 659–668 (1996).
Article  Google Scholar 
2.
Cain, J. W. III., Krausman, P. R., Jansen, B. D. & Morgart, J. R. Influence of topography and GPS fix interval on GPS collar performance. Wildl. Soc. Bull. 33, 926–934 (2005).
Article  Google Scholar 

3.
Graves, T. A. & Waller, J. S. Understanding the causes of missed global positioning system telemetry fixes. J. Wildl. Manag. 70, 844–851 (2006).
Article  Google Scholar 

4.
Moen, R., John, P. & Cohen, Y. Effects of animal activity on GPS telemetry location attempts. Alces 37, 207–216 (2001).
Google Scholar 

5.
D’Eon, R. G. Effects of a stationary GPS fix-rate bias on habitat-selection analyses. J. Wildl. Manag. 67, 858–863 (2003).
Article  Google Scholar 

6.
Dussault, C., Courtois, R., Ouellet, J. P. & Huot, J. Evaluation of GPS telemetry collar performance for habitat studies in the boreal forest. Wildl. Soc. Bull. 27, 965–972 (1999).
Google Scholar 

7.
Nielson, R. M., Manly, B. F. J., Mcdonald, L. L., Sawyer, H. & Mcdonald, T. L. Estimating habitat selection when GPS fix success is less than 100 %. Ecology 90, 2956–2962 (2009).
Article  PubMed  Google Scholar 

8.
Rempel, R. S., Rodgers, A. R. & Abraham, K. F. Performance of a GPS animal location system under boreal forest canopy. J. Wildl. Manag. 59, 543–551 (1995).
Article  Google Scholar 

9.
Bowman, J. L., Kochanny, C. O., Demarais, S. & Leopold, B. D. Evaluation of a GPS collar for white-tailed deer. Wildl. Soc. Bull. 28, 141–145 (2000).
Google Scholar 

10.
Jung, T. S. & Kuba, K. Performance of GPS collars on free-ranging bison (Bison bison) in north-western Canada. Wildl. Res. 42, 315–323 (2015).
Article  Google Scholar 

11.
Recio, M. R., Mathieu, R., Denys, P., Sirguey, P. & Seddon, P. J. Lightweight GPS-tags, one giant leap for wildlife tracking? An assessment approach. PLoS One 6, e28225 (2011).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

12.
Mattisson, J., Andrén, H., Persson, J. & Segerström, P. Effects of species behavior on global positioning system collar fix rates. J. Wildl. Manag. 74, 557–563 (2010).
Article  Google Scholar 

13.
Kaczensky, P., Ito, T. Y. & Walzer, C. Satellite telemetry of large mammals in Mongolia: What expectations should we have for collar function?. Wildl. Biol. Pract. 6, 108–126 (2010).
CAS  PubMed  PubMed Central  Google Scholar 

14.
Harris, R. B. et al. Tracking Wildlife by Satellite: Current systems and Performance. Fish and Wildlife Technical Report https://pubs.er.usgs.gov/publication/70185512 (1990).

15.
Schwartz, C. C. & Arthur, S. M. Radiotracking large wilderness mammals: Integration of GPS and argostechnology. Ursus 11, 261–274 (1999).
Google Scholar 

16.
Tomkiewicz, S. M., Fuller, M. R., Kie, J. G. & Bates, K. K. Global positioning system and associated technologies in animal behaviour and ecological research. Philos. Trans. R. Soc. B Biol. Sci. 365, 2163–2176 (2010).
Article  Google Scholar 

17.
Rodgers, A. R. Recent telemetry technology. In Radio Tracking and Animal Populations (eds Marzluff, J. M. & Millspaugh, J. J.) 79–121 (Elsevier, New York, 2001). https://doi.org/10.1016/B978-012497781-5/50005-0.
Google Scholar 

18.
Thomas, B., Holland, J. D. & Minot, E. O. Wildlife tracking technology options and cost considerations. Wildl. Res. 38, 653–663 (2011).
Article  Google Scholar 

19.
Margalida, A., Pérez-García, J. M., Afonso, I. & Moreno-Opo, R. Spatial and temporal movements in Pyrenean bearded vultures (Gypaetus barbatus): Integrating movement ecology into conservation practice. Sci. Rep. 6, 35746 (2016).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

20.
García-Jiménez, R., Pérez-García, J. M. & Margalida, A. Drivers of daily movement patterns affecting an endangered vulture flight activity. BMC Ecol. 18, 39 (2018).
Article  PubMed  PubMed Central  Google Scholar 

21.
BirdLife International. (2017). Gypaetus barbatus (Amended Version of 2017 Assessment). The IUCN Red List of Threatened Species 2017: e.T22695174A118590506. https://doi.org/10.2305/IUCN.UK.2017-3.RLTS.T22695174A118590506.en. Accessed: 12th Mar 2020.

22.
Houston D. C. Reintroduction programmes for vulture species. In Proceedings of the International Conference on Conservation and Management of Vulture populations 1, (eds Houston D. C. & Piper, S. E., 2006). Natural History Museum, University of Crete, Thessaloniki.

23.
Britten, M. W., Kennedy, P. L. & Ambrose, S. Performance and accuracy evaluation of small satellite transmitters. J. Wildl. Manag. 63, 1349–1358 (1999).
Article  Google Scholar 

24.
Soutullo, A., Cadahía, L., Urios, V., Ferrer, M. & Negro, J. J. Accuracy of lightweight satellite telemetry: A case study in the Iberian Peninsula. J. Wildl. Manag. 71, 1010–1015 (2007).
Article  Google Scholar 

25.
Silva, R., Afán, I., Gil, J. A. & Bustamante, J. Seasonal and circadian biases in bird tracking with solar GPS-tags. PLoS One 12, e0185344 (2017).
Article  CAS  PubMed  PubMed Central  Google Scholar 

26.
Byrne, M. E., Holland, A. E., Bryan, A. L. & Beasley, J. C. Environmental conditions and animal behavior influence performance of solar-powered GPS-GSM transmitters. Condor 119, 389–404 (2017).
Article  Google Scholar 

27.
Hofman, M. P. G. et al. Right on track? Performance of satellite telemetry in terrestrial wildlife research. PLoS One 14, 1–26 (2019).
Google Scholar 

28.
Aubrecht, C. et al. Vertical roughness mapping – ALS based classification of the vertical vegetation structure in forested areas. In Symposium A Quarterly Journal In Modern Foreign Literatures (eds. Wagner, W. & Székely, B.) XXXVIII, 35–40 (2010).

29.
Frair, J. L. et al. Resolving issues of imprecise and habitat-biased locations in ecological analyses using GPS telemetry data. Philos. Trans. R. Soc. B Biol. Sci. 365, 2187–2200 (2010).
Article  Google Scholar 

30.
Péron, G. et al. The challenges of estimating the distribution of flight heights from telemetry or altimetry data. Anim. Biotelemetry 8, 1–13 (2020).
Article  Google Scholar 

31.
Cargnelutti, B. et al. Testing global positioning system performance for wildlife monitoring using mobile collars and known reference points. J. Wildl. Manag. 71, 1380–1387 (2007).
Article  Google Scholar 

32.
Edenius, L. Field test of a GPS location system for moose Alces alces under Scandinavian boreal conditions. Wildl. Biol. 3, 39–43 (1997).
Article  Google Scholar 

33.
Jurdak, R., Corke, P., Dharman, D. & Salagnac, G. Adaptive GPS duty cycling and radio ranging for energy-efficient localization. In Proceedings of the 8th ACM Conference on Embedded Networked Sensor Systems-SenSys ’10 57–70 (ACM Press, 2010). https://doi.org/10.1145/1869983.1869990.

34.
Gau, R. J. et al. Uncontrolled field performance of Televilt GPS-SimplexTM collars on grizzly bears in western and northern Canada. Wildl. Soc. Bull. 32, 693–701 (2004).
Article  Google Scholar 

35.
Girard, I. et al. Feasibility of GPS use to locate wild ungulates in high mountain environment. Pirineos 157, 7–14 (2002).
Article  Google Scholar 

36.
Krüger, S., Reid, T. & Amar, A. Differential range use between age classes of Southern African bearded vultures Gypaetus barbatus. PLoS One 9, e114920 (2014).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

37.
Augustine, B. C., Crowley, P. H. & Cox, J. J. A mechanistic model of GPS collar location data: Implications for analysis and bias mitigation. Ecol. Modell. 222, 3616–3625 (2011).
Article  Google Scholar 

38.
Douglas, D. C. et al. Moderating Argos location errors in animal tracking data. Methods Ecol. Evol. 3, 999–1007 (2012).
Article  Google Scholar 

39.
Cuadrat, J. M. et al. El clima de los Pirineos. Base de datos y primeros resultados. Tiempo Clima 45, 38–41 (2010).
Google Scholar 

40.
Margalida, A., Bertran, J. & Heredia, R. Diet and food preferences of the endangered Bearded Vulture Gypaetus barbatus: A basis for their conservation. Ibis (Lond. 1859) 151, 235–243 (2009).
Google Scholar 

41.
del Hoyo, J., Elliott, A., Sargatal, J., Christie, D. A. & Kirwan, G. Handbook of the Birds of the World,2 (Lynx Edicions, Barcelona, 1994).
Google Scholar 

42.
Antor, R. J. et al. First breeding age in captive and wild bearded vultures Gypaetus barbatus. Acta Ornithol. 42, 114–118 (2007).
Article  Google Scholar 

43.
Gil, J. A. et al. Home ranges and movements of non-breeding bearded vultures tracked by satellite telemetry in the Pyrenees. Ardeola 61, 379–387 (2014).
Article  Google Scholar 

44.
Sunyer, C. El periodo de emancipación en el Quebrantahuesos (Gypaetus barbatus): Consideraciones sobre su conservación. In El quebrantahuesos (Gypaetus barbatus) en los Pirineos. Características Ecológicas y Biología (eds Heredia, R. & Heredia, B.) 47–65 (ICONA, Turin, 1991).
Google Scholar 

45.
Margalida, A. et al. Uneven large-scale movement patterns in wild and reintroduced pre-adult Bearded Vultures: Conservation implications. PLoS One 8, e65857 (2013).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

46.
Ellergren, H. First gene on the avian W chromosome (CHD) provides a tag for universal sexing of non-ratite birds. Proc. R Soc. Lond. Ser. B Biol. Sci. 263, 1635–1641 (1996).
ADS  Article  Google Scholar 

47.
Cruz, S., Proaño, C. B., Anderson, D., Huyvaert, K. & Wikelski, M. Data from: The Environmental-Data Automated Track Annotation (Env-DATA) System: Linking animal tracks with environmental data. (2013). https://doi.org/10.5441/001/1.3hp3s250.

48.
Dodge, S. et al. The environmental-data automated track annotation (Env-DATA) system: Linking animal tracks with environmental data. Mov. Ecol. 1, 3 (2013).
Article  PubMed  PubMed Central  Google Scholar 

49.
Cuscó, F., Cardador, L., Bota, G., Morales, M. B. & Mañosa, S. Inter-individual consistency in habitat selection patterns and spatial range constraints of female little bustards during the non-breeding season. BMC Ecol. 18, 1–12 (2018).
Article  Google Scholar 

50.
Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods Ecol. Evol. 4, 133–142 (2013).
Article  Google Scholar 

51.
Anadón, J. D. et al. Factors determining the distribution of the spur-thighed tortoise Testudo graeca in south-east Spain: A hierarchical approach. Ecography (Cop.) 29, 339–346 (2006).
Article  Google Scholar 

52.
R Foundation for Statistical Computing. R Core Team. R: A Language and Environment for Statistical Computing. https://www.R-project.org/ (2019).

53.
Bates, D., Maechler, M. & Dai, B. lme4: Linear mixed-effects models using S4 classes. 2009. R package version 0.999375-31. https://CRAN.R-project.org/package=lme4 (2009).

54.
Burnham, K. P. & Anderson, D. R. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach Vol 2 (Springer, Berlin, 2002).
Google Scholar 

55.
Zuur, A., Ieno, E. N., Walker, N., Saveliev, A. A. & Smith, G. M. Mixed Effects Models and Extensions in Ecology with R (Springer, Berlin, 2009).
Google Scholar 

56.
Barton, K. Package ‘MuMIn’. R package version 1.43. 15. https://CRAN.R-project.org/package=MuMIn (2019).

57.
Fox, J. & Weisberg, S. An R Companion to Applied Regression (Sage publications, Thousand Oaks, 2018).
Google Scholar 

58.
Mitchell, L. J., White, P. C. & Arnold, K. E. The trade-off between fix rate and tracking duration on estimates of home range size and habitat selection for small vertebrates. PLoS One 14, e0219357 (2019).
CAS  Article  PubMed  PubMed Central  Google Scholar  More

1.
Hughes, T. P. et al. Global warming and recurrent mass bleaching of corals. Nature 543, 373–377 (2017).
ADS  CAS  PubMed  PubMed Central  Google Scholar 
2.
Bellwood, D. R., Hughes, T. P., Folke, C. & Nyström, M. Confronting the coral reef crisis. Nature 429, 827–833 (2004).
ADS  CAS  PubMed  PubMed Central  Google Scholar 

3.
Hughes, T. P. et al. Spatial and temporal patterns of mass bleaching of corals in the Anthropocene. Science 359, 80–83 (2018).
ADS  CAS  PubMed  PubMed Central  Google Scholar 

4.
Van Hooidonk, R., Maynard, J. A. & Planes, S. Temporary refugia for coral reefs in a warming world. Nat. Clim. Chang. 3, 508–511 (2013).
ADS  Google Scholar 

5.
Costanza, R. et al. Changes in the global value of ecosystem services. Glob. Environ. Chang. 26, 152–158 (2014).
Google Scholar 

6.
Moberg, F. & Folke, C. Ecological goods and services of coral reef ecosystems. Ecol. Econ. 29, 215–233 (1999).
Google Scholar 

7.
Hughes, T. P. et al. Ecological memory modifies the cumulative impact of recurrent climate extremes. Nat. Clim. Change 9, 40–43 (2019).
ADS  Google Scholar 

8.
Krueger, T. et al. Common reef-building coral in the northern red sea resistant to elevated temperature and acidification. R. Soc. Open Sci. 4, 170038 (2017).
ADS  PubMed  PubMed Central  Google Scholar 

9.
Penin, L., Vidal-Dupiol, J. & Adjeroud, M. Response of coral assemblages to thermal stress: are bleaching intensity and spatial patterns consistent between events?. Environ. Monit. Assess. 185, 5031–5042 (2013).
PubMed  PubMed Central  Google Scholar 

10.
Thompson, D. M. & van Woesik, R. Corals escape bleaching in regions that recently and historically experienced frequent thermal stress. Proc. Biol. Sci. 276, 2893–2901 (2009).
CAS  PubMed  PubMed Central  Google Scholar 

11.
Sully, S., Burkepile, D. E., Donovan, M. K., Hodgson, G. & van Woesik, R. A global analysis of coral bleaching over the past two decades. Nat. Commun. 10, 1–5 (2019).
CAS  Google Scholar 

12.
Thomas, L. et al. Mechanisms of thermal tolerance in reef-building corals across a fine-grained environmental mosaic: lessons from Ofu, American Samoa. Front. Mar. Sci. 4, 434 (2018).
Google Scholar 

13.
Bay, R. A. & Palumbi, S. R. Multilocus adaptation associated with heat resistance in reef-building corals. Curr. Biol. 24, 2952–2956 (2014).
CAS  PubMed  PubMed Central  Google Scholar 

14.
Wilson, K. L., Tittensor, D. P., Worm, B. & Lotze, H. K. Incorporating climate change adaptation into marine protected area planning. Glob. Chang. Biol. 26, 3251–3267 (2020).
ADS  PubMed  PubMed Central  Google Scholar 

15.
Baums, I. B. et al. Considerations for maximizing the adaptive potential of restored coral populations in the western Atlantic. Ecol. Appl. 29, (2019).

16.
Matz, M. V., Treml, E. & Haller, B. C. Predicting coral adaptation to global warming in the Indo-West-Pacific. BioRxiv https://doi.org/10.1101/722314 (2019).
Article  Google Scholar 

17
Selmoni, O., Rochat, E., Lecellier, G., Berteaux-Lecellier, V. & Joost, S. Seascape genomics as a new tool to empower coral reef conservation strategies: an example on north-western Pacific Acropora digitifera. Evol. Appl. https://doi.org/10.1101/588228 (2020).
Article  PubMed  PubMed Central  Google Scholar 

18
Riginos, C., Crandall, E. D., Liggins, L., Bongaerts, P. & Treml, E. A. Navigating the currents of seascape genomics: how spatial analyses can augment population genomic studies. Curr. Zool. https://doi.org/10.1093/cz/zow067 (2016).
Article  PubMed  PubMed Central  Google Scholar 

19.
Maina, J., Venus, V., McClanahan, T. R. & Ateweberhan, M. Modelling susceptibility of coral reefs to environmental stress using remote sensing data and GIS models. Ecol. Modell. 212, 180–199 (2008).
Google Scholar 

20.
Liu, G., Strong, A. E. & Skirving, W. Remote sensing of sea surface temperatures during 2002 Barrier Reef coral bleaching. Eos Trans. Am. Geophys. Union 84, 137–141 (2003).
ADS  Google Scholar 

21
Rochat, E. & Joost, S. Spatial areas of genotype probability (SPAG): predicting the spatial distribution of adaptive genetic variants under future climatic conditions. BioRxiv. https://doi.org/10.1101/2019.12.20.884114 (2019).
Article  Google Scholar 

22
Boulanger, E., Dalongeville, A., Andrello, M., Mouillot, D. & Manel, S. Spatial graphs highlight how multi-generational dispersal shapes landscape genetic patterns. Ecography (Cop) https://doi.org/10.1111/ecog.05024 (2020).
Article  Google Scholar 

23
Selmoni, O. et al. Seascape genomics reveals candidate molecular targets of heat stress adaptation in three coral species. BioRxiv. https://doi.org/10.1101/2020.05.12.090050 (2020).
Article  Google Scholar 

24.
Job, S. New Caledonia network of coral reef observation (RORC) – Field campaign report 2017–2018. (French title: Réseau d’observation des récifs coralliens (RORC) de Nouvelle-Calédonie. Campagne 2017–2018. Rapport Pays. Rapport CORTEX. Pour le compte de : Conservatoire d’espaces naturels de Nouvelle-Calédonie – Province des îles Loyauté – Observatoire de l’environnement). (CORTEX, New Caledonia, 2018).

25.
Lefèvre, J., Marchesiello, P., Jourdain, N. C., Menkes, C. & Leroy, A. Weather regimes and orographic circulation around New Caledonia. Mar. Pollut. Bull. 61, 413–431 (2010).
PubMed  Google Scholar 

26.
Marchesiello, P., Lefèvre, J., Vega, A., Couvelard, X. & Menkes, C. Coastal upwelling, circulation and heat balance around New Caledonia’s barrier reef. Mar. Pollut. Bull. 61, 432–448 (2010).
CAS  PubMed  Google Scholar 

27.
Berkelmans, R., Weeks, S. J. & Steinberga, C. R. Upwelling linked to warm summers and bleaching on the Great Barrier Reef. Limnol. Oceanogr. 55, 2634–2644 (2010).
ADS  Google Scholar 

28.
Cravatte, S. et al. Regional circulation around New Caledonia from two decades of observations. J. Mar. Syst. 148, 249–271 (2015).
Google Scholar 

29.
Hénin, C., Guillerm, J. & Chabert, L. Circulation superficielle autour de la Nouvelle-Calédonie. Océanographie Trop. 19, 113–126 (1984).
Google Scholar 

30.
Magris, R. A., Pressey, R. L., Weeks, R. & Ban, N. C. Integrating connectivity and climate change into marine conservation planning. Biol. Cons. 170, 207–221 (2014).
Google Scholar 

31.
Hughes, T. P. et al. Global warming transforms coral reef assemblages. Nature 556, 492–496 (2018).
ADS  CAS  Google Scholar 

32.
Welle, P. D., Small, M. J., Doney, S. C. & Azevedo, I. L. Estimating the effect of multiple environmental stressors on coral bleaching and mortality. PLoS ONE 12, e0175018 (2017).
Article  CAS  PubMed Central  Google Scholar 

33.
Kenkel, C. D., Almanza, A. T. & Matz, M. V. Fine-scale environmental specialization of reef-building corals might be limiting reef recovery in the Florida Keys. Ecology 96, 3197–3212 (2015).
Article  Google Scholar 

34.
Palumbi, S. R. Population genetics, demographic connectivity, and the design of marine reserves. Ecol. Appl. 13, 146–158 (2003).
Article  Google Scholar 

35.
Hock, K. et al. Connectivity and systemic resilience of the Great Barrier Reef. PLoS Biol. 15, (2017).

36.
Robinson, J. P. W., Wilson, S. K. & Graham, N. A. J. Abiotic and biotic controls on coral recovery 16 years after mass bleaching. Coral Reefs 38, 1255–1265 (2019).
ADS  Article  Google Scholar 

37.
Kawecki, T. J. Adaptation to marginal habitats. Annu. Rev. Ecol. Evol. Syst. 39, 321–342 (2008).
Article  Google Scholar 

38.
Treml, E. A. et al. Reproductive output and duration of the pelagic larval stage determine seascape-wide connectivity of marine populations. Integr. Comp. Biol. 52, 525–537 (2012).
Article  Google Scholar 

39.
Storlazzi, C. D., van Ormondt, M., Chen, Y.-L. & Elias, E. P. L. Modeling fine-scale coral larval dispersal and interisland connectivity to help designate mutually-supporting coral reef marine protected areas: insights from Maui Nui, Hawaii. Front. Mar. Sci. 4, 381 (2017).
Article  Google Scholar 

40.
Colberg, F., Brassington, G. B., Sandery, P., Sakov, P. & Aijaz, S. High and medium resolution ocean models for the Great Barrier Reef. Ocean Model. 145, 101507 (2020).
Google Scholar 

41.
Andréfouët, S., Cabioch, G., Flamand, B. & Pelletier, B. A reappraisal of the diversity of geomorphological and genetic processes of New Caledonian coral reefs: A synthesis from optical remote sensing, coring and acoustic multibeam observations. Coral Reefs 28, 691–707 (2009).
ADS  Google Scholar 

42.
Dalleau, M. et al. Use of habitats as surrogates of biodiversity for efficient coral reef conservation planning in Pacific Ocean islands. Conserv. Biol. 24, 541–552 (2010).
PubMed  PubMed Central  Google Scholar 

43.
Loya, Y. et al. Coral bleaching: the winners and the losers. Ecol. Lett. 4, 122–131 (2001).
Google Scholar 

44.
Darling, E. S., Alvarez-Filip, L., Oliver, T. A., McClanahan, T. R. & Côté, I. M. Evaluating life-history strategies of reef corals from species traits. Ecol. Lett. 15, 1378–1386 (2012).
PubMed  PubMed Central  Google Scholar 

45.
Ayre, D. J. & Hughes, T. P. Genotypic diversity and gene flow in brooding and spawning corals along the great barrier reef, Australia. Evolution (NY) 54, 1590–1605 (2000).
CAS  Google Scholar 

46.
Kawecki, T. J. & Ebert, D. Conceptual issues in local adaptation. Ecol. Lett. 7, 1225–1241 (2004).
Google Scholar 

47.
Selmoni, O., Vajana, E., Guillaume, A., Rochat, E. & Joost, S. Sampling strategy optimization to increase statistical power in landscape genomics: A simulation-based approach. Mol. Ecol. Resour. 20, (2020).

48.
EU Copernicus Marine Service. Global Ocean – In-Situ-Near-Real-Time Observations. (2017). Available at: https://marine.copernicus.eu. Accessed: 2nd February 2017

49.
Merchant, C. J. et al. Satellite-based time-series of sea-surface temperature since 1981 for climate applications. Sci. data 6, 223 (2019).
PubMed  PubMed Central  Google Scholar 

50.
UNEP-WCMC, WorldFish-Center, WRI & TNC. Global distribution of warm-water coral reefs, compiled from multiple sources including the Millennium Coral Reef Mapping Project. Version 1.3. (2010). Available at: https://data.unep-wcmc.org/datasets/1. Accessed: 9th May 2017

51.
QGIS development team. QGIS Geographic Information System. Open Source Geospatial Foundation Project. (2009).

52.
Hijmans, R. J. raster: Geographic Data Analysis and Modeling. (2016).

53.
R Core Team. R: A Language and Environment for Statistical Computing. (2016).

54.
Ryan, W. B. F. et al. Global multi-resolution topography synthesis. Geochemistry, Geophys. Geosystems 10, (2009).

55.
van Etten, J. gdistance: Distances and Routes on Geographical Grids. (2018). Available at: https://cran.r-project.org/package=gdistance.

56.
Kilian, A. et al. Diversity arrays technology: A generic genome profiling technology on open platforms. Methods Mol. Biol. 888, 67–89 (2012).
PubMed  Google Scholar 

57.
Zheng, X. et al. A high-performance computing toolset for relatedness and principal component analysis of SNP data. Bioinformatics 28, 3326–3328 (2012).
CAS  PubMed  PubMed Central  Google Scholar 

58.
Frichot, E., Schoville, S. D., Bouchard, G. & François, O. Testing for associations between loci and environmental gradients using latent factor mixed models. Mol. Biol. Evol. 30, 1687–1699 (2013).
CAS  PubMed  PubMed Central  Google Scholar 

59.
Joost, S. et al. A spatial analysis method (SAM) to detect candidate loci for selection: towards a landscape genomics approach to adaptation. Mol. Ecol. 16, 3955–3969 (2007).
CAS  PubMed  PubMed Central  Google Scholar 

60.
Brooks, M. E. et al. glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. R J. 9, 378–400 (2017).
Google Scholar 

61.
Breheny, P. & Burchett, W. Visualization of regression models using visreg. R J. 9, 56–71 (2017).
Google Scholar 

62.
Xuereb, A., Kimber, C. M., Curtis, J. M. R., Bernatchez, L. & Fortin, M. Putatively adaptive genetic variation in the giant California sea cucumber ( Parastichopus californicus ) as revealed by environmental association analysis of restriction-site associated DNA sequencing data. Mol. Ecol. 27, 5035–5048 (2018).
CAS  PubMed  Google Scholar 

63.
Benestan, L. et al. Seascape genomics provides evidence for thermal adaptation and current-mediated population structure in American lobster (Homarus americanus). Mol. Ecol. 25, 5073–5092 (2016).
PubMed  Google Scholar 

64.
Legendre, P. & Gallagher, E. D. Ecologically meaningful transformations for ordination of species data. Oecologia 129, 271–280 (2001).
ADS  PubMed  Google Scholar 

65.
Borcard, D. & Legendre, P. All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecol. Modell. 153, 51–68 (2002).
Google Scholar 

66.
Dixon, P. VEGAN, a package of R functions for community ecology. J. Veg. Sci. 14, 927–930 (2003).
Google Scholar 

67.
Ferrari, S. L. P. & Cribari-Neto, F. Beta regression for modelling rates and proportions. J. Appl. Stat. 31, 799–815 (2004).
MathSciNet  MATH  Google Scholar 

68.
Verbeke, G., Molenberghs, G. & Rizopoulos, D. Random effects models for longitudinal data. In Longitudinal Research with Latent Variables 37–96 (Springer, Berlin, 2010). https://doi.org/10.1007/978-3-642-11760-2_2

69.
Garcia, T. P. & Marder, K. Statistical approaches to longitudinal data analysis in neurodegenerative diseases: Huntington’s disease as a model. Curr. Neurol. Neurosci. Rep. 17, 14 (2017).
PubMed  PubMed Central  Google Scholar 

70.
Bozdogan, H. Model selection and Akaike’s Information Criterion (AIC): the general theory and its analytical extensions. Psychometrika 52, 345–370 (1987).
MathSciNet  MATH  Google Scholar  More

1.
O’Malley, M. P., Lee-Brooks, K. & Medd, H. B. The global economic impact of manta ray watching tourism. PLoS ONE 8(5), e65051. https://doi.org/10.1371/journal.pone.0065051 (2013).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 
2.
Balmford, A. et al. Walk on the wild side: estimating the global magnitude of visits to protected areas. PLoS Biol. 13, e1002074. https://doi.org/10.1371/journal.pbio.1002074 (2015).
CAS  Article  PubMed  PubMed Central  Google Scholar 

3.
Zimmerhackel, J. S. et al. How shark conservation in the Maldives affects demand for dive tourism. Tourism Manage. 69, 263–271 (2018).
Article  Google Scholar 

4.
Burgin, S. & Hardiman, N. Effects of non-consumptive wildlife-orientated tourism on marine species and prospects for their sustainable management. J. Environ. Manage. 151, 210–220 (2015).
Article  PubMed  Google Scholar 

5.
Bruce, B. D. & Bradford, R. W. The effects of shark cage-diving operations on the behaviour and movements of white sharks, Carcharodon carcharias, at the Neptune Islands South Australia. Mar. Biol. 160, 889–907 (2013).
Article  Google Scholar 

6.
Corcoran, M. J. et al. Supplemental feeding for ecotourism reverses diel activity and alters movement patterns and spatial distribution of the Southern stingrays Dasyatis americana. PLoS ONE 8(3), e59235. https://doi.org/10.1371/journal.pone.0059235 (2013).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

7.
Arlettaz, R., Christe, P. & Schaub, M. Food availability as a major driver in the evolution of life-history strategies of sibling species. Ecol. Evol. 7, 4163–4172. https://doi.org/10.1002/ece3.2909 (2017).
Article  PubMed  PubMed Central  Google Scholar 

8.
Huveneers, C. et al. The effects of cage-diving activities on the fine-scale swimming behavior and space use of white sharks. Mar. Biol. 160, 2863–2875 (2013).
Article  Google Scholar 

9.
Semeniuk, C. A. D., Bourgeon, S., Smith, S. L. & Rothley, K. D. Hematological differences between stingrays at tourist and non-visited sites suggest physiological costs of wildlife tourism. Biol. Cons. 142, 1818–1829. https://doi.org/10.1016/j.biocon.2009.03.022 (2009).
Article  Google Scholar 

10.
Maljkovic, A. & Côté, I. M. Effects of tourism-related provisioning on the trophic signatures and movement patterns of an apex predator, the Caribbean reef shark. Biol. Conserv. 144, 859–865. https://doi.org/10.1016/j.biocon.2010.11.019 (2011).
Article  Google Scholar 

11.
Brena, P. F., Mourier, J., Planes, S. & Clua, E. Shark and ray provisioning: functional insights into behavioral, ecological and physiological responses across multiple scales. Mar. Ecol. Prog. Ser. 538, 273–283 (2015).
ADS  CAS  Article  Google Scholar 

12.
Kelly, J. F. Stable isotopes of carbon and nitrogen in the study of avian and mammalian trophic ecology. Can. J. Zool. 78, 1–27. https://doi.org/10.1139/z99-165 (2000).
Article  Google Scholar 

13.
Jeanniard-du-Dot, T., Thomas, A. C., Cherel, Y., Trites, A. W. & Guinet, C. Combining hard-part and DNA analyses of scats with biologging and stable isotopes can reveal different diet compositions and feeding strategies within a fur seal population. Mar. Ecol. Prog. Ser. 584, 1–16 (2017).
ADS  CAS  Article  Google Scholar 

14.
Wetherbee, B.M., Cortés, E. Food consumption and feeding habits In Sharks and Their Relatives I (eds Musick, J.A., Heithaus, M., & Carrier, J.C.) 225–246 (CRC Press, 2004).

15.
Dehn, L.-A. et al. Feeding ecology of phocid seals and some walrus in the Alaskan and Canadian Arctic as determined by stomach contents and stable isotope analysis. Polar Biol. 30(2), 167–181 (2006).
Article  Google Scholar 

16.
DeNiro, M. J. & Epstein, S. Influence of diet on the distribution of carbon isotopes in animals. Geochim. Cosmochim. Acta 42, 495–506 (1978).
ADS  CAS  Article  Google Scholar 

17.
DeNiro, M. J. & Epstein, S. Influence of diet on the distribution of nitrogen isotopes in animals. Geochim Cosmochim Acta 45, 341–351 (1981).
ADS  CAS  Article  Google Scholar 

18.
Iverson, S. J., Field, C., Bowen, W. D. & Blanchard, W. Quantitative fatty acid signature analysis: a new method of estimating predator diets. Ecol. Monogr. 74, 211–235 (2004).
Article  Google Scholar 

19.
Newsome, S. D., Clementz, M. T. & Koch, P. L. Using stable isotope biogeochemistry to study marine mammal ecology. Mar. Mammal Sci. 26, 509–572 (2010).
CAS  Google Scholar 

20.
Polito, M. J. et al. Integrating stomach content and stable isotope analyses to quantify the diets of Pygoscelid penguins. PLoS ONE 6, e26642. https://doi.org/10.1371/journal.pone.0026642 (2011).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

21.
Couturier, L. I. E. et al. Stable isotope and signature fatty acid analyses suggest reef manta rays feed on demersal zooplankton. PLoS ONE 8(10), e77152. https://doi.org/10.1371/journal.pone.0077152 (2013).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

22.
Käkelä, A. et al. Fatty acid signatures and stable isotopes as dietary indicators in North Sea seabirds. Mar. Ecol. Prog. Ser. 342, 291–301 (2007).
ADS  Article  Google Scholar 

23.
Carlisle, A. B. et al. Using stable isotope analysis to understand the migration and trophic ecology of northeastern Pacific white sharks (Carcharodon carcharias). PLoS ONE 7, e30492. https://doi.org/10.1371/journal.pone.0030492 (2012).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

24.
Watt, C. A. & Ferguson, S. H. Fatty acid and stable isotopes (δ13C and δ15N) reveal temporal changes in narwhal (Monodon monoceros) diet linked to migration patterns. Mar. Mammal Sci. 31, 21–44 (2015).
CAS  Article  Google Scholar 

25.
Minagawa, M. & Wada, E. Stepwise enrichment of 15N along food chains: further evidence and the relation between 15N and animal age. Geochim. Cosmochim. Acta 48, 1135–1140 (1984).
ADS  CAS  Article  Google Scholar 

26.
Vander Zanden, M.J. & Rasmussen, J.B. Variation in delta N-15 and delta C-13 trophic fractionation: implications for aquatic food web studies. Limnol. Oceanogr. 46, 2061-2066 (2001).

27.
Fry, B. Food web structure on Georges Bank from stable C, N, and S isotopic compositions. Limnol. Oceanogr. 33, 1182–1190 (1988).
ADS  CAS  Article  Google Scholar 

28.
Mackenzie, K. M. et al. Locations of marine animals revealed by carbon isotopes. Sci. Rep. 1, 1–6. https://doi.org/10.1038/srep00021 (2011).
CAS  Article  Google Scholar 

29.
DeNiro, M.J. & Epstein, S. You are what you eat (plus a few ‰): the carbon isotope cycle in food chains. Geol. Soc. Amer., Abstr. Programs 8, 834–835 (1976).

30.
Budge, S. M., Iverson, S. J. & Koopman, H. N. Studying trophic ecology in marine ecosystems using fatty acids: a primer on analysis and interpretation. Mar. Mammal Sci. 22(4), 759–801 (2006).
Article  Google Scholar 

31.
Ackman, R.G. Fish lipids in Advances in Fish Science And Technology (ed. Connell, J.J.) 86–103 (Fishing News Books Ltd., 1980).

32.
Tocher, D. R. Metabolism and functions of lipids and fatty acids in teleost fish. Rev. Fish. Sci. 11, 107–184. https://doi.org/10.1080/713610925 (2003).
CAS  Article  Google Scholar 

33.
McMeans, B. C., Arts, M. T. & Fisk, A. T. Similarity between predator and prey fatty acid profiles is tissue dependent in Greenland sharks (Somniosus microcephalus): implications for diet reconstruction. J. Exp. Mar. Biol. Ecol. 429, 55–63. https://doi.org/10.1016/j.jembe.2012.06.017 (2012).
CAS  Article  Google Scholar 

34.
Bigelow, H., & Schroeder, W. Fishes of the Western North Atlantic, Part 2. Sawfishes, Guitarfishes, Skates, Rays and Chimaeroids. 1–588 (Yale University Press, 1953).

35.
Aguiar, A., Valentin, J. & Rosa, R. S. Habitat use by Dasyatis americana in a south-western Atlantic oceanic island. J. Mar. Biol. Assoc. 89, 1147–1152 (2009).
Article  Google Scholar 

36.
Snelson, F. F. Jr. & Williams, S. E. Notes on the occurrence, distribution, and biology of elasmobranch fishes in the Indian River Lagoon system Florida. Estuaries 4, 110–120 (1981).
Article  Google Scholar 

37.
Gilliam, D. S. & Sullivan, K. M. Diet and feeding habits of the Southern stingray Dasyatis americana in the Central Bahamas. Bull. Mar. Sci. 52(3), 1007–1013 (1993).
Google Scholar 

38.
Bowman, R., Stillwell, C., Michaels, W. & Grosslein, M. Food of Northwest Atlantic fishes and two common species of squid. NOAA Technical Memorandum NMFS-NE 155, 1–137 Reprint at https://pdfs.semanticscholar.org/c013/400022949952cc0f261fa71c76195c173e04.pdf (2000).

39.
Vaudo, J. J. et al. Characterization and monitoring of one of the world’s most valuable ecotourism animals, the southern stingray at Stingray City Grand Cayman. Mar. Freshwater Res. 69, 144–154 (2018).
Article  Google Scholar 

40.
Nelson, M. Swim with the rays: a guide to Stingray City, Grand Cayman 37 (Blueline Press, Colorado, 1995).
Google Scholar 

41.
Shackley, M. ‘Stingray city’-managing the impact of underwater tourism in the Cayman Islands. J. Sustain. Tour. 6, 328–338 (1998).
Article  Google Scholar 

42.
Semeniuk, C. A. D., Speers-Roesch, B. & Rothley, K. D. Using fatty-acid profile analysis as an ecologic indicator in the management of tourist impacts on marine wildlife: a case of stingray-feeding in the Caribbean. Environ. Manag. 40, 665–677 (2007).
ADS  Article  Google Scholar 

43.
Semeniuk, C. A. D. & Rothley, K. D. Costs of group-living for a normally solitary forager: effects of provisioning tourism on southern stingrays Dasyatis americana. Mar. Ecol. Prog. Ser. 357, 271–282 (2008).
ADS  Article  Google Scholar 

44.
Abdi, H. The bonferonni and Šidák corrections for multiple comparisons in Encyclopedia of Measurements and Statistics (ed Salkind, N.L.) 1–9 (Sage Publishing, 2007).

45.
Dale, J. J., Wallsgrove, N. J., Popp, B. N. & Holland, K. N. Nursery habitat use and foraging ecology of the brown stingray Dasyatis lata determined from stomach contents, bulk and amino acid stable isotopes. Mar. Ecol. Prog. Ser. 433, 221–236 (2011).
ADS  Article  Google Scholar 

46.
Tilley, A., López-Angarita, J. & Turner, J. R. Diet reconstruction and resource partitioning of a Caribbean marine mesopredator using stable isotope Bayesian modeling. PLoS ONE 8(11), e79560. https://doi.org/10.1371/journal.pone.0079560 (2013).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

47.
Hobson, K. A. & Welch, H. E. Determination of trophic relationships within a high Arctic marine food web using δ13C and δ15N analysis. Mar. Ecol. Prog. Ser. 84, 9–18 (1992).
ADS  CAS  Article  Google Scholar 

48.
Galván, D. E., Jañez, J. & Irigoyen, A. J. Estimating tissue-specific discrimination factors and turnover rates of stable isotopes of nitrogen and carbon in the smallnose fanskate Sympterygia bonapartii (Rajidae). J. Fish. Biol. 89, 1258–1270. https://doi.org/10.1111/jfb.13024 (2016).
CAS  Article  PubMed  Google Scholar 

49.
Ohkouchi, N. et al. Advances in the application of amino acid nitrogen isotopic analysis in ecological and biogeochemical studies. Org. Geochem. 113, 150–174. https://doi.org/10.1016/j.orggeochem.2017.07.009 (2017).
CAS  Article  Google Scholar 

50.
Smith, K. & Herrnkind, W. Predation on early juvenile spiny lobsters Panulirus argus (Latreille): influence of size and shelter. J. Exp. Mar. Biol. Ecol. 157, 3–18 (1992).
Article  Google Scholar 

51.
Randall, J. Food Habits of Reef Fishes of the West Indies. University of Hawaii (1967).

52.
Newsome, D., Lewis, A. & Moncrieff, D. Impacts and risks associated with developing, but unsupervised stingray tourism at Hameline Bay Western Australia. Int. J. Tour. Res. 6, 305–323. https://doi.org/10.1002/jtr.491 (2004).
Article  Google Scholar 

53.
Hobson, K. A., Alisauskas, R. T. & Clark, R. G. Stable-nitrogen isotope enrichment in avian tissues due to fasting and nutritional stress: implications for isotopic analyses of diet. Condor 95, 388–394 (1993).
Article  Google Scholar 

54.
Oelbermann, K. & Sheu, S. Stable isotope enrichment (δ15N and δ13C) in a generalist predator (Pardosa lugubris, Araneae: Lycosidae): effects of prey quality. Oecologia 130, 337–344 (2002).
ADS  Article  PubMed  Google Scholar 

55.
Hertz, E., Trudel, M., Cox, M. K. & Mazumder, A. Effects of fasting and nutritional restriction on the isotopic ratios of nitrogen and carbon: a meta-analysis. Ecol. Evol. 5(21), 4829–4839. https://doi.org/10.1002/ece3.1738 (2015).
Article  PubMed  PubMed Central  Google Scholar 

56.
Doi, H. F., Akamatsu, F. & González, A. L. Starvation effects on nitrogen and carbon stable isotopes of animals: an insight from meta-analysis of fasting experiments. R. Soc. open sci. 4, 170633. https://doi.org/10.1098/rsos.170633 (2017).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

57.
Doucett, R. R., Booth, R. K., Power, G. & McKinley, R. S. Effects of the spawning migration on the nutritional status of anadromous Atlantic salmon (Salmo salar): insights from stable-isotope analysis. Can. J. Fish. Aquat. Sci. 56, 2172–2180 (1999).
Article  Google Scholar 

58.
Cherel, Y., Hobson, K. A., Bailleul, F. & Groscolas, R. Nutrition, physiology, and stable isotopes: new information from fasting and molting penguins. Ecology 86, 2881–2888 (2005).
Article  Google Scholar 

59.
Kempster, B. et al. Do stable isotopes reflect nutritional stress? Results from a laboratory experiment on song sparrows. Oecologia 151, 365–371 (2007).
ADS  Article  PubMed  Google Scholar 

60.
Logan, J. M. & Lutcavage, M. E. Stable isotope dynamics in elasmobranch fishes. Hydrobiologia 644, 231–244 (2010).
CAS  Article  Google Scholar 

61.
Wyatt, A. S. J. et al. Enhancing insights into foraging specialization in the world’s largest fish using a multi-tissue, multi-isotope approach. Ecol. Monogr. 89, e01339. https://doi.org/10.1002/ecm.1339 (2019).
Article  Google Scholar 

62.
Williams, C.T., Buck, C.L., Sears, J. & Kitaysky, A.S. 2007. Effects of nutritional restriction on nitrogen and carbon stable isotopes in growing seabirds. Oecologia 153, 11–18 (2007).

63.
McMahon, K. W., Thorrold, S. R., Elsdon, T. S. & McCarthy, M. D. Trophic discrimination of nitrogen stable isotopes in amino acids varies with diet quality in a marine fish. Limnol. Oceanogr. 60, 1076–1087 (2015).
ADS  CAS  Article  Google Scholar 

64.
Rajapakse, N., Mendis, E., Byun, H.-G. & Kim, S.-K. Purification and in vitro antioxidative effects of giant squid muscle peptides on free radical-mediated oxidative systems. J. Nutr. Biochem. 16, 562–569 (2005).
CAS  Article  PubMed  Google Scholar 

65.
Hussey, N. E. et al. Expanded trophic complexity among large sharks. Food Webs 4, 1–7 (2015).
Article  Google Scholar 

66.
Bosley, K. L., Witting, D. A., Chambers, R. C. & Wainright, S. C. Estimating turnover rates of carbon and nitrogen in recently metamorphosed winter flounder Pseudopleuronectes americanus with stable isotopes. Mar. Ecol. Prog. Ser. 236, 233–240 (2002).
ADS  Article  Google Scholar 

67.
Fry, B. & Arnold, C. Rapid 13C/12C turnover during growth of brown shrimp (Penaeus aztecus). Oecologia 54, 200–204 (1982).
ADS  Article  PubMed  Google Scholar 

68.
Boecklen, W. J., Yarnes, C. T., Cook, B. A. & James, A. C. On the use of stable isotopes in trophic ecology. Annu. Rev. Ecol. Evol. Syst. 42, 411–440 (2011).
Article  Google Scholar 

69.
Kim, S. L., del Rio, C. M., Casper, D. & Koch, P. L. Isotopic incorporation rates for shark tissues from a long-term captive feeding study. J. Exp. Biol. 215, 2495–2500 (2012).
Article  PubMed  Google Scholar 

70.
Thomas, S. M. & Crowther, T. W. Predicting rates of isotopic turnover across the animal kingdom: a synthesis of existing data. J. Anim. Ecol. 84, 861–870. https://doi.org/10.1111/1365-2656.12326 (2015).
Article  PubMed  Google Scholar 

71.
Hussey, N. E. et al. Stable isotopes and elasmobranchs: tissue types, methods, applications and assumptions. J. Fish Biol. 80(5), 1449–1484. https://doi.org/10.1111/j.1095-8649.2012.03251.x (2012).
CAS  Article  PubMed  PubMed Central  Google Scholar 

72.
MacNeil, M. A., Drouillard, K. G. & Fisk, A. T. Variable uptake and elimination of stable nitrogen isotopes between tissues in fish. Can. J. Fish Aquat. Sci. 63, 345–353. https://doi.org/10.1139/f05-219 (2006).
CAS  Article  Google Scholar 

73.
Caut, S., Jowers, M., Michel, L., Lepoint, G. & Fisk, A. Diet- and tissue-specific incorporation of isotopes in the shark Scyliorhinus stellaris, a North Sea mesopredator. Mar. Ecol. Prog. Ser. 492, 185–198 (2013).
ADS  CAS  Article  Google Scholar 

74.
Miller, T. W., Brodeur, R. D. & Rau, G. H. Carbon stable isotopes reveal relative contribution of shelf-slope production to the northern California Current pelagic community. Limnol. Oceanogr. 53, 1493–1503 (2008).
ADS  CAS  Article  Google Scholar 

75.
Lytle, J. S. & Lytle, T. F. Fatty acid and cholesterol content of sharks and rays. J. Food Compos. Anal. 7, 110–118 (1994).
CAS  Article  Google Scholar 

76.
Jangaard, P. M. & Ackman, R. G. Lipids and component fatty acids of the Newfoundland squid, Illex illecebrosus (Le Sueur). J. Fish. Res. Board Can. 22(1), 131–137. https://doi.org/10.1139/f65-012 (1965).
CAS  Article  Google Scholar 

77.
Kirsch, P. E., Iverson, S. J., Bowen, W. D., Kerr, S. R. & Ackman, R. G. Dietary effects on the fatty acid signature of whole Atlantic cod (Gadus morhua). Can. J. Fish Aquat. Sci. 55, 1378–1386. https://doi.org/10.1139/f98-019 (1998).
CAS  Article  Google Scholar 

78.
Phillips, K. L., Jackson, G. D. & Nichols, P. D. Predation on myctophids by the squid Moroteuthis ingens around Macquarie and Heard Islands: stomach contents and fatty acid analyses. Mar. Ecol. Prog. Ser. 215, 179–189 (2001).
ADS  CAS  Article  Google Scholar 

79.
Premarathna, A. D. et al. Nutritional analysis of some selected fish and crab meats and fatty acid analysis of oil extracted from Portunus pelagicus. IJSRST 4, 197–201 (2015).
Google Scholar 

80.
Javaheri Baboli, J., Velayatzahed, M., Roomiani, L. & Khoramadadi, A. Effects of sex and tissue fatty acid composition in the meat of blue swimming crab (Portunus pelagicus) from the Persian Gulf, Iran. Iran J. Fish. Sci. 15, 818–826 (2016).

81.
Arai, T., Amalina, R. & Bachok, Z. Similarity in the feeding ecology of parrotfish (Scaridae) in coral reef habitats of the Malaysian South China Sea, as revealed by fatty acid signatures. Biochem. Syst. Ecol. 59, 85–90. https://doi.org/10.1016/j.bse.2015.01.011 (2015).
CAS  Article  Google Scholar 

82.
Ayas, D. & Ozogul, Y. The effects of seasonal changes on fat and fatty acid contents of mantis shrimp (Eurogosquilla massavensis). Adv. Food Sci. 34, 164–167 (2012).
CAS  Google Scholar 

83.
Balzano, M., Pacetti, D., Lucci, P., Fiorini, D. & Frega, N. G. Bioactive fatty acids in mantis shrimp, crab and caramote prawn: their content and distribution among the main lipid classes. J. Food Compos. Anal. 59, 88–94 (2017).
CAS  Article  Google Scholar 

84.
Lytle, J. S., Lytle, T. F. & Ogle, J. T. Polyunsaturated fatty acid profiles as a comparative tool in assessing maturation diets of Penaeus vannamei. Aquaculture 89, 287–299 (1990).
CAS  Article  Google Scholar 

85.
Pethybridge, H., Daley, R., Virtue, P. & Nicols, P. Lipid composition and partitioning of deepwater chondrichthyans: inferences of feeding ecology and distribution. Mar. Biol. 157, 1367–1384 (2010).
CAS  Article  Google Scholar 

86.
Pethybridge, P., Daley, R. K. & Nichols, P. D. Diet of demersal sharks and chimeras inferred by fatty acid profiles and stomach content analysis. J. Exp. Mar. Biol. Ecol. 409, 290–299. https://doi.org/10.1016/j.jembe.2011.09.009 (2011).
Article  Google Scholar 

87.
Beckmann, C. L., Mitchell, J. G., Stone, D. A. J. & Huveneers, C. A controlled feeding experiment investigating the effects of a dietary switch on muscle and liver fatty acid profiles in Port Jackson sharks Heterodontus portusjacksoni. J. Exp. Mar. Biol. Ecol. 448, 10–18. https://doi.org/10.1016/j.jembe.2013.06.009 (2013).
CAS  Article  Google Scholar 

88.
Beckmann, C. L., Mitchell, J. G., Stone, D. A. & Huveneers, C. Inter-tissue differences in fatty acid incorporation as a result of dietary oil manipulation in Port Jackson sharks (Heterodontus portusjacksoni). Lipids 49, 577–590 (2014).
CAS  Article  PubMed  Google Scholar 

89.
Gibson, R. A. Australian fish – an excellent source of both arachidonic acid and ω-3 polyunsaturated fatty acids. Lipids 18, 743–752 (1983).
CAS  Article  PubMed  Google Scholar 

90.
Dunstan, G. A., Sinclair, A. J., O’Dea, K. & Naughton, J. M. The lipid content and fatty acid composition of various marine species from southern Australian coastal waters. Comp. Biochem. Physiol. B 91, 165–169. https://doi.org/10.1016/0305-0491(88)90130-7 (1988).
Article  Google Scholar 

91.
Ballantyne, J.S. Jaws: the inside story. The metabolism of elasmobranch fishes. Comp. Biochem. Physiol. B 118, 703–742 (1997).

92.
Wood, C. M., Walsh, P. J., Kajimura, M., McClelland, G. B. & Chew, S. F. The influence of feeding and fasting on plasma metabolites in the dogfish shark (Squalus acanthias). Comp. Biochem. Physiol. A. 155, 435–444 (2010).
Article  CAS  Google Scholar 

93.
Meyer, L., Pethybridge, H., Nichols, P. D., Beckmann, C. & Huveneers, C. Abiotic and biotic drivers of fatty acid tracers in ecology: a global analysis of chondrichthyan profiles. Funct. Ecol. 33, 1–13. https://doi.org/10.1111/1365-2435.13328 (2019).
Article  Google Scholar 

94.
Preston, T. & Owens, N. J. P. Interfacing an automatic elemental analyser with an isotope ratio mass spectrometer: the potential for fully automated total nitrogen and nitrogen-15 analysis. Analyst 108, 971–977 (1983).
ADS  CAS  Article  Google Scholar 

95.
Kim, S. L. & Koch, P. L. Methods to collect, preserve, and prepare elasmobranch tissues for stable isotope analysis. Environ. Biol. Fish. 95, 53–63 (2012).
Article  Google Scholar 

96.
Folch, J., Lees, M. & Sloane-Stanly, G. H. A simple method for the isolation and purification of total lipids from animal tissues. J. Biol. Chem. 226, 497–509 (1957).
CAS  PubMed  Google Scholar  More

1.
Autumn, K. et al. Evidence for van der Waals adhesion in gecko setae. Proc. Natl. Acad. Sci. US 99, 12252–12256 (2002).
ADS  CAS  Article  Google Scholar 
2.
Autumn, K., Niewiarowski, P. H. & Puthoff, J. B. Gecko adhesion as a model system for integrative biology, interdisciplinary science, and bioinspired engineering. Annu. Rev. Ecol. Evol. Syst. 45, 445–470 (2014).
Article  Google Scholar 

3.
Sitti, M. & Fearing, R. S. Synthetic gecko foot-hair micro/nano-structures as dry adhesives. J. Adhes. Sci. Technol. 17, 1055–1073 (2003).
CAS  Article  Google Scholar 

4.
Kim, S. & Sitti, M. Biologically inspired polymer microfibers with spatulate tips as repeatable fibrillar adhesives. Appl. Phys. Lett. 89, 261911 (2006).
ADS  Article  CAS  Google Scholar 

5.
Murphy, M. P., Aksak, B. & Sitti, M. Gecko-inspired directional and controllable adhesion. Small 5, 170–175 (2009).
CAS  Article  PubMed  Google Scholar 

6.
Murphy, M. P., Kim, S. & Sitti, M. Enhanced adhesion by gecko-inspired hierarchical fibrillar adhesives. ACS Appl. Mater. Interfaces 1, 849–855 (2009).
CAS  Article  PubMed  Google Scholar 

7.
Glass, P., Chung, H., Washburn, N. R. & Sitti, M. Enhanced wet adhesion of elastomeric micro-fiber arrays with mushroom tip geometry and a photopolymerized p(DMA-co-MEA) tip coating. Langmuir 26, 17357–17362 (2010).
CAS  Article  PubMed  Google Scholar 

8.
Mengüç, Y., Röhrig, M., Abusomwan, U., Hölscher, H. & Sitti, M. Staying sticky: Contact self-cleaning of gecko-inspired adhesives. J. R. Soc. Interface 11, 20131205 (2014).
Article  PubMed  PubMed Central  Google Scholar 

9.
Song, S. & Sitti, M. Soft grippers using micro-fibrillar adhesives for transfer printing. Adv. Mater. 26, 4901–4906 (2014).
CAS  Article  PubMed  Google Scholar 

10.
Niewiarowski, P. H., Stark, A. Y. & Dhinojwala, A. Sticking to the story: Outstanding challenges in gecko-inspired adhesives. J. Exp. Biol. 219, 912–919 (2016).
Article  PubMed  Google Scholar 

11.
Drotlef, D.-M., Amjadi, M., Yunusa, M. & Sitti, M. Bioinspired composite microfibers for skin adhesion and signal amplification of wearable sensors. Adv. Mater. 29, 1701353 (2017).
Article  CAS  Google Scholar 

12.
Song, S., Drotlef, D.-M., Majidi, C. & Sitti, M. Controllable load sharing for soft adhesive interfaces on three-dimensional surfaces. Proc. Natl. Acad. Sci. 114, E4344–E4353 (2017).
CAS  Article  PubMed  Google Scholar 

13.
Russell, A. P., Stark, A. Y. & Higham, T. E. The integrative biology of gecko adhesion: Historical review, current understanding, and grand challenges. Integr. Comp. Biol. 59, 101–116 (2019).
CAS  Article  PubMed  Google Scholar 

14.
Stark, A. Y. & Mitchell, C. T. Stick or slip: Adhesive performance of geckos and gecko-inspired synthetics in wet environments. Integr. Comp. Biol. 59, 214–226 (2019).
CAS  Article  PubMed  Google Scholar 

15.
Liimatainen, V., Drotlef, D.-M., Son, D. & Sitti, M. Liquid-superrepellent bioinspired fibrillar adhesives. Adv. Mater. 32, 2000497 (2020).
CAS  Article  Google Scholar 

16.
Huber, G. et al. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements. Proc. Natl. Acad. Sci. US 102, 16293–16296 (2005).
ADS  CAS  Article  Google Scholar 

17.
Sun, W., Neuzil, P., Kustandi, T. S., Oh, S. & Samper, V. D. The nature of the gecko lizard adhesive force. Biophys. J. 89, L14–L17 (2005).
CAS  Article  PubMed  PubMed Central  Google Scholar 

18.
Kim, T. W. & Bhushan, B. The adhesion model considering capillarity for gecko attachment system. J. R. Soc. Interface 5, 319–327 (2008).
Article  PubMed  Google Scholar 

19.
Puthoff, J. B., Prowse, M. S., Wilkinson, M. & Autumn, K. Changes in materials properties explain the effects of humidity on gecko adhesion. J. Exp. Biol. 213, 3699–3704 (2010).
Article  PubMed  Google Scholar 

20.
Prowse, M. S., Wilkinson, M., Puthoff, J. B., Mayer, G. & Autumn, K. Effects of humidity on the mechanical properties of gecko setae. Acta Biomater. 7, 733–738 (2011).
Article  PubMed  Google Scholar 

21.
Bauer, A. M. & Good, D. A. Phylogenetic systematics of the day geckos, genus, Rhoptropus (Reptilia: Gekkonidae), of south-western Africa. J. Zool. 238, 635–663 (1996).
Article  Google Scholar 

22.
Pianka, E. R. & Vitt, L. J. Lizards: Windows to the Evolution of Diversity (University of California Press, Berkeley, 2003).
Google Scholar 

23.
Lamb, T. & Bauer, A. M. Footprints in the sand: Independent reduction of subdigital lamellae in the Namib–Kalahari burrowing geckos. Proc. R. Soc. B Biol. Sci. 273, 855–864 (2006).
Article  Google Scholar 

24.
Gamble, T., Greenbaum, E., Jackman, T. R., Russell, A. P. & Bauer, A. M. Repeated origin and loss of adhesive toepads in geckos. PLoS ONE 7, e39429 (2012).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

25.
Collins, C. E., Russell, A. P. & Higham, T. E. Subdigital adhesive pad morphology varies in relation to structural habitat use in the Namib Day Gecko. Funct. Ecol. 29, 66–77 (2015).
Article  Google Scholar 

26.
Autumn, K. & Hansen, W. Ultrahydrophobicity indicates a non-adhesive default state in gecko setae. J. Comp. Physiol. A 192, 1205 (2006).
Article  Google Scholar 

27.
Badge, I., Stark, A. Y., Paoloni, E. L., Niewiarowski, P. H. & Dhinojwala, A. The role of surface chemistry in adhesion and wetting of gecko toe pads. Sci. Rep. 4, 6643 (2014).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

28.
Maderson, P. F. A. Keratinized epidermal derivatives as an aid to climbing in gekkonid lizards. Nature 203, 780–781 (1964).
ADS  Article  Google Scholar 

29.
Ruibal, R. & Ernst, V. The structure of the digital setae of lizards. J. Morphol. 117, 271–293 (1965).
CAS  Article  PubMed  Google Scholar 

30.
Williams, E. E. & Peterson, J. A. Convergent and alternative designs in the digital adhesive pads of scincid lizards. Science 215, 1509–1511 (1982).
ADS  CAS  Article  PubMed  Google Scholar 

31.
Autumn, K. et al. Adhesive force of a single gecko foot-hair. Nature 405, 681–685 (2000).
ADS  CAS  Article  PubMed  Google Scholar 

32.
Autumn, K. & Peattie, A. M. Mechanisms of adhesion in geckos. Integr. Comp. Biol. 42, 1081–1090 (2002).
Article  PubMed  Google Scholar 

33.
Israelachvili, J. N. & Tabor, D. The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm. Proc. R. Soc. Lond. Math. Phys. Sci. 331, 19–38 (1972).
ADS  CAS  Google Scholar 

34.
Niewiarowski, P. H., Lopez, S., Ge, L., Hagan, E. & Dhinojwala, A. Sticky gecko feet: The role of temperature and humidity. PLoS ONE 3, e2192 (2008).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

35.
Hsu, P. Y. et al. Direct evidence of phospholipids in gecko footprints and spatula–substrate contact interface detected using surface-sensitive spectroscopy. J. R. Soc. Interface 9, 657–664 (2012).
CAS  Article  PubMed  Google Scholar 

36.
Jain, D., Stark, A. Y., Niewiarowski, P. H., Miyoshi, T. & Dhinojwala, A. NMR spectroscopy reveals the presence and association of lipids and keratin in adhesive gecko setae. Sci. Rep. 5, 9594 (2015).
ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

37.
Alibardi, L. Immunolocalization of keratin-associated beta-proteins (beta-keratins) in the regenerating lizard epidermis indicates a new process for the differentiation of the epidermis in lepidosaurians. J. Morphol. 273, 1272–1279 (2012).
CAS  Article  PubMed  Google Scholar 

38.
Alibardi, L. Immunolocalization of keratin-associated beta-proteins (beta-keratins) in pad lamellae of geckos suggest that glycine–cysteine-rich proteins contribute to their flexibility and adhesiveness. J. Exp. Zool. Part Ecol. Genet. Physiol. 319, 166–178 (2013).
CAS  Article  Google Scholar 

39.
Peng, Z., Yang, Y. & Chen, S. Coupled effects of the temperature and the relative humidity on gecko adhesion. J. Phys. Appl. Phys. 50, 315402 (2017).
ADS  Article  CAS  Google Scholar 

40.
Huey, R. B. & Kingsolver, J. G. Evolution of thermal sensitivity of ectotherm performance. Trends Ecol. Evol. 4, 131–135 (1989).
CAS  Article  PubMed  Google Scholar 

41.
Huey, R. B., Niewiarowski, P. H., Kaufmann, J. & Herron, J. C. Thermal biology of nocturnal ectotherms: Is sprint performance of geckos maximal at low body temperatures?. Physiol. Zool. 62, 488–504 (1989).
Article  Google Scholar 

42.
Bergmann, P. & Irschick, D. J. Effects of temperature on maximum acceleration, deceleration and power output during vertical running in geckos. J. Exp. Biol. 209, 1404–1412 (2006).
Article  PubMed  Google Scholar 

43.
Losos, J. B. Thermal sensitivity of sprinting and clinging performance in the tokay gecko (Gekko gecko). Asiat. Herpetol. Res. 3, 54–59 (1990).
ADS  Google Scholar 

44.
Bergmann, P. J. & Irschick, D. J. Effects of temperature on maximum clinging ability in a diurnal gecko: Evidence for a passive clinging mechanism?. J. Exp. Zool. A Comp. Exp. Biol. 303A, 785–791 (2005).
Article  Google Scholar 

45.
Pesika, N. S. et al. Gecko adhesion pad: A smart surface?. J. Phys. Condens. Matter 21, 464132 (2009).
Article  CAS  PubMed  Google Scholar 

46.
Grewal, S. H., Piao, S., Cho, I.-J., Jhang, K.-Y. & Yoon, E.-S. Nanotribological and wetting performance of hierarchical patterns. Soft Matter 12, 859–866 (2016).
ADS  CAS  Article  PubMed  Google Scholar 

47.
Stark, A. Y., Klittich, M. R., Sitti, M., Niewiarowski, P. H. & Dhinojwala, A. The effect of temperature and humidity on adhesion of a gecko-inspired adhesive: Implications for the natural system. Sci. Rep. 6, 30936 (2016).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

48.
Cadirov, N., Booth, J. A., Turner, K. L. & Israelachvili, J. N. Influence of humidity on grip and release adhesion mechanisms for gecko-inspired microfibrillar surfaces. ACS Appl. Mater. Interfaces 9, 14497–14505 (2017).
CAS  Article  PubMed  Google Scholar 

49.
Ceseracciu, L., Heredia-Guerrero, J. A., Dante, S., Athanassiou, A. & Bayer, I. S. Robust and biodegradable elastomers based on corn starch and polydimethylsiloxane (PDMS). ACS Appl. Mater. Interfaces 7, 3742–3753 (2015).
CAS  Article  PubMed  Google Scholar 

50.
Stark, A. Y. et al. Surface wettability plays a significant role in gecko adhesion underwater. Proc. Natl. Acad. Sci. US. https://doi.org/10.1073/pnas.1219317110 (2013).
Article  Google Scholar 

51.
Drotlef, D.-M., Dayan, C. B. & Sitti, M. Bio-inspired composite microfibers for strong and reversible adhesion on smooth surfaces. Integr. Comp. Biol. 59, 227–235 (2019).
CAS  Article  PubMed  PubMed Central  Google Scholar 

52.
Tan, D. et al. Humidity-modulated core–shell nanopillars for enhancement of gecko-inspired adhesion. ACS Appl. Nano Mater. 3, 3596–3603 (2020).
CAS  Article  Google Scholar 

53.
Geikowsky, E., Gorumlu, S. & Aksak, B. The effect of flexible joint-like elements on the adhesive performance of nature-inspired bent mushroom-like fibers. Beilstein J. Nanotechnol. 9, 2893–2905 (2018).
CAS  Article  PubMed  PubMed Central  Google Scholar 

54.
Wang, Z. Slanted functional gradient micropillars for optimal bioinspired dry adhesion. ACS Nano 12, 1273–1284 (2018).
CAS  Article  PubMed  Google Scholar 

55.
Moser, R. et al. From playroom to lab: Tough stretchable electronics analyzed with a tabletop tensile tester made from toy-bricks. Adv. Sci. 3, 1500396 (2016).
Article  CAS  Google Scholar 

56.
BS EN ISO 527-2 Plastics-Determination of tensile properties. Br. Stand. BSI (1996).

57.
Kurian, A., Prasad, S. & Dhinojwala, A. Unusual surface aging of poly(dimethylsiloxane) elastomers. Macromolecules 43, 2438–2443 (2010).
ADS  CAS  Article  Google Scholar 

58.
Pinheiro, J., Bates, D., Debroy, S. & Sarkar, D. nlme: Linear and Nonlinear Mixed Effects Models. R Core Team, R package version 3.1-137 (2018).

59.
Lenth, R. emmeans: Estimated Marginal Means, Aka Least-Squares Means. R Core Team, R package version 1.3.4 (2019).

60.
Core Team. R: A Language and Environment for Statistical Computing (Core Team, Vienna, 2019).
Google Scholar  More

1.
Beyer, J. et al. Blue mussels (Mytilus edulis spp.) as sentinel organisms in coastal pollution monitoring: a review. Mar. Env. Res. 130, 338–365 (2017).
ADS  Article  CAS  Google Scholar 
2.
Metzger, M. J., Reinisch, C., Sherry, J. & Goff, S. P. Horizontal transmission of clonal cancer cells causes leukemia in soft-shell clams. Cell 161, 255–263 (2015).
Article  CAS  PubMed  PubMed Central  Google Scholar 

3.
Metzger, M. J. et al. Widespread transmission of independent cancer lineages within multiple bivalve species. Nature 534, 705–709 (2016).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

4.
Rozen, Y. & Belkin, S. Survival of enteric bacteria in seawater. FEMS Microbiol. Rev. 25, 513–529 (2001).
Article  CAS  PubMed  Google Scholar 

5.
Suttle, C. A. The significance of viruses to mortality in aquatic microbial communities. Microbiol. Ecol. 28, 237–243 (1994).
Article  CAS  Google Scholar 

6.
Allam, B. & Raftos, D. Immune responses to infectious diseases in bivalves. J. Invertebr. Pathol. 131, 121–136 (2015).
Article  CAS  PubMed  Google Scholar 

7.
Allam, B. & Espinosa, E. P. Mucosal immunity in mollusks. In Mucosal Health in Aquaculture (eds Beck, B. H. & Peatman, E.) 325–370 (Academic Press, Cambridge, 2015).
Google Scholar 

8.
Lau, Y. T., Sussman, L., Espinosa, E. P., Katalay, S. & Allam, B. Characterization of hemocytes from different body fluids of the eastern oyster Crassostrea virginica. Fish Shellfish Immunol. 71, 372–379 (2017).
Article  CAS  PubMed  Google Scholar 

9.
Lau, Y. T., Gambino, L., Santos, B., Espinosa, E. P. & Allam, B. Transepithelial migration of mucosal hemocytes in Crassostrea virginica and potential role in Perkinsus marinus pathogenesis. J. Invertebr. Pathol. 153, 122–129 (2018).
Article  PubMed  Google Scholar 

10.
Allam, B. & Espinosa, E. P. Bivalve immunity and response to infections: are we looking at the right place?. Fish Shellfish Immunol. 53, 4–12 (2016).
Article  CAS  PubMed  Google Scholar 

11.
Lau, Y. T., Gambino, L., Santos, B., Espinosa, E. P. & Allam, B. Regulation of oyster (Crassostrea virginica) hemocyte motility by the intracellular parasite Perkinsus marinus: a possible mechanism for host infection. Fish Shellfish Immunol. 78, 18–25 (2018).
Article  PubMed  Google Scholar 

12.
Bodkin, J. L. et al. Variation in abundance of Pacific blue mussel (Mytilus trossulus) in the Northern Gulf of Alaska, 2006–2015. Deep Sea Res. Part II(147), 87–97 (2018).
Article  Google Scholar 

13.
Bijlsma, R. & Loeschcke, V. Environmental stress, adaptation and evolution: an overview. J. Evol. Biol. 18, 744–749 (2005).
Article  CAS  PubMed  Google Scholar 

14.
Caza, F., Cledon, M. & St-Pierre, Y. Biomonitoring climate change and pollution in marine ecosystems: a review on Aulacomya ater. J. Mar. Biol. https://doi.org/10.1155/2016/183813 (2016).
Article  Google Scholar 

15.
Farcy, E., Voiseux, C., Lebel, J. M. & Fievet, B. Seasonal changes in mRNA encoding for cell stress markers in the oyster Crassostrea gigas exposed to radioactive discharges in their natural environment. Sci. Total Environ. 374, 328–341 (2007).
ADS  Article  CAS  PubMed  Google Scholar 

16.
Yao, C. L. & Somero, G. N. Thermal stress and cellular signaling processes in hemocytes of native (Mytilus californianus) and invasive (M. galloprovincialis) mussels: cell cycle regulation and DNA repair. Comp. Biochem. Physiol. Part A 165, 159–168 (2013).
Article  CAS  Google Scholar 

17.
Negri, A. et al. Transcriptional response of the mussel Mytilus galloprovincialis (Lam.) following exposure to heat stress and copper. PLoS ONE 8, e66802. https://doi.org/10.1371/journal.pone/0066802 (2013).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

18.
Heare, J. E., White, S. J., Vadopalas, B. & Roberts, S. B. Differential response to stress in Ostrea lurida as measured by gene expression. Peer J. 6, e4261. https://doi.org/10.7717/peerj.4261 (2018).
Article  CAS  PubMed  PubMed Central  Google Scholar 

19.
Caza, F. et al. Comparative analysis of hemocyte properties from Mytilus edulis desolationis and Aulacomya ater in the Kerguelen Islands. Mar. Environ. Res. 110, 174–182 (2015).
Article  CAS  PubMed  PubMed Central  Google Scholar 

20.
Comeau, L. A., Babarro, J. M., Longa, A. & Padin, X. A. Valve-gaping behavior of raft-cultivated mussels in the Ría de Arousa, Spain. Aquac. Rep. 9, 68–73 (2018).
Article  Google Scholar 

21.
Weston, S. A. & Parish, C. R. New fluorescent dyes for lymphocyte migration studies: analysis by flow cytometry and fluorescence microscopy. J. Immunol. Meth. 133, 87–97 (1990).
Article  CAS  Google Scholar 

22.
Daley, R. J. & Hobbie, J. E. Direct counts of aquatic bacteria by a modified epifluorescence technique 1. Limnol. Oceanogr. 20, 875–882 (1975).
ADS  Article  Google Scholar 

23.
Ferguson, R. L. & Rublee, P. Contribution of bacteria to standing crop of coastal plankton 1. Limnol. Oceanogr. 21, 141–145 (1976).
ADS  Article  Google Scholar 

24.
Aubry, A., Mougari, F., Reibel, F. & Cambau, E. Mycobacterium marinum. In Tuberculosis and Nontuberculous Mycobacterial Infections (ed. Schlossberg, D.) 735–752 (McGraw-Hill, New York, 2017).
Google Scholar 

25.
Kennedy, G. M., Morisaki, J. H. & Champion, P. A. Conserved mechanisms of Mycobacterium marinum pathogenesis within the environmental amoeba Acanthamoeba castellanii. Appl. Environ. Microbiol. 78, 20249–22052 (2012).
Article  CAS  Google Scholar 

26.
Barker, L. P., George, K. M., Falkow, S. & Small, P. L. Differential trafficking of live and dead Mycobacterium marinum organisms in macrophages. Infect. Immun. 65, 1497–1504 (1997).
Article  CAS  PubMed  PubMed Central  Google Scholar 

27.
Nguyen, L. & Pieters, J. The Trojan horse: survival tactics of pathogenic mycobacteria in macrophages. Trends Cell Biol. 15, 269–276 (2005).
Article  CAS  PubMed  Google Scholar 

28.
Jørgensen, C. B., Larsen, P. S. & Riisgård, H. U. Effects of temperature on the mussel pump. Mar. Ecol. Progr. Ser. 28, 89–97 (1990).
ADS  Article  Google Scholar 

29.
Podolsky, R. D. Temperature and water viscosity: physiological versus mechanical effects on suspension feeding. Science 265, 100–103 (1994).
ADS  Article  CAS  PubMed  Google Scholar 

30.
Riisgård, H. U. & Seerup, D. F. Filtration rates in the soft clam Mya arenaria: effects of temperature and body size. Sarsia 88, 416–428 (2003).
Article  Google Scholar 

31.
Dowd, W. W. & Somero, G. N. Behavior and survival of Mytilus congeners following episodes of elevated body temperature in air and seawater. J. Exp. Biol. 216, 502–514 (2013).
Article  PubMed  Google Scholar 

32.
Cellura, C., Toubiana, M., Parrinello, N. & Roch, P. HSP70 gene expression in Mytilus galloprovincialis hemocytes is triggered by moderate heat shock and Vibrio anguillarum, but not by V. splendidus or Micrococcus lysodeikticus. Dev. Comp. Immunol. 30, 984–997 (2006).
Article  CAS  PubMed  Google Scholar 

33.
Watermann, B. T. et al. Pathology and mass mortality of Pacific oysters, Crassostrea gigas (Thunberg), in 2005 at the East Frisian coast, Germany. J. Fish Dis. 31, 621–630 (2008).
Article  CAS  PubMed  Google Scholar 

34.
Polsenaere, P. et al. Potential environmental drivers of a regional blue mussel mass mortality event (winter of 2014, Breton Sound, France). J. Sea Res. 123, 39–50 (2017).
ADS  Article  Google Scholar 

35.
Vázquez-Luis, M. et al. SOS Pinna nobilis: a mass mortality event in western Mediterranean Sea. Front. Mar. Sci. 4, 220. https://doi.org/10.3389/fmars.2017.00220 (2017).
Article  Google Scholar 

36.
Lattos, A., Giantsis, I. A., Karagiannis, D. & Michaelidis, B. First detection of the invasive Haplosporidian and Mycobacteria parasites hosting the endangered bivalve Pinna nobilis in Thermaikos Gulf, North Greece. Mar. Environ. Res. https://doi.org/10.1016/j.marenvres.2020.104889 (2020).
Article  PubMed  Google Scholar 

37.
Rivetti, I., Fraschetti, S., Lionello, P., Zambianchi, E. & Boero, F. Global warming and mass mortalities of benthic invertebrates in the Mediterranean Sea. PLoS ONE 9, e115655. https://doi.org/10.1371/journal.pone.0115655 (2014).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

38.
Zhang, Y., Li, J., Yu, F., He, X. & Yu, Z. Allograft inflammatory factor-1 stimulates hemocyte immune activation by enhancing phagocytosis and expression of inflammatory cytokines in Crassostrea gigas. Fish Shellfish Immunol. 34, 1071–1077 (2013).
Article  CAS  PubMed  PubMed Central  Google Scholar 

39.
Cellura, C., Toubiana, M., Parrinello, N. & Roch, P. Specific expression of antimicrobial peptide and HSP70 genes in response to heat-shock and several bacterial challenges in mussels. Fish Shellfish Immunol. 22, 340–350 (2007).
Article  CAS  PubMed  PubMed Central  Google Scholar 

40.
Novoa, B. et al. Immune tolerance in Mytilus galloprovincialis haemocytes after repeated contact with Vibrio splendidus. Front. Immunol. 10, 1894. https://doi.org/10.3389/fimmu.2019.01894 (2019).
Article  CAS  PubMed  PubMed Central  Google Scholar 

41.
Palmer, C. V. Immunity and the coral crisis. Commun. Biol. 1, 1–7 (2018).
Article  Google Scholar 

42.
Yonemitsu, M. A. et al. A single clonal lineage of transmissible cancer identified in two marine mussel species in South America and Europe. Elife 8, e47788. https://doi.org/10.7554/eLife.47788 (2019).
Article  CAS  PubMed  PubMed Central  Google Scholar 

43.
Seuront, L., Nicastro, K. R., Zardi, G. I. & Goberville, E. Decreased thermal tolerance under recurrent heat stress conditions explains summer mass mortality of the blue mussel Mytilus edulis. Sci. Rep. 9, 1–4 (2019).
ADS  Article  Google Scholar 

44.
Carroll, P. et al. Sensitive detection of gene expression in mycobacteria under replicating and non-replicating conditions using optimized far-red reporters. PLoS ONE 5, e9823. https://doi.org/10.1371/journal.pone.0009823 (2010).
ADS  Article  CAS  PubMed  PubMed Central  Google Scholar 

45.
Li, Y. F. et al. Elevated seawater temperatures decrease microbial diversity in the gut of Mytilus coruscus. Front. Physiol. 9, 839. https://doi.org/10.3389/fphys.2018.00839 (2018).
Article  PubMed  PubMed Central  Google Scholar  More

1.
Wahl, M. Ecological lever and interface ecology: epibiosis modulates the interactions between host and environment. Biofouling 24, 427–438 (2008).
Article  Google Scholar 
2.
Gutiérrez, J. L., Jones, C. G., Strayer, D. L. & Iribarne, O. O. Mollusks as ecosystem engineers: the role of shell production in aquatic habitats. Oikos 101, 79–90 (2003).
Article  Google Scholar 

3.
Carrapiço, F. How symbiogenic is evolution ?. Theory Biosci. 129, 135–139 (2010).
Article  Google Scholar 

4.
Apprill, A. The role of symbioses in the adaptation and stress responses of marine organisms. Ann. Rev. Mar. Sci. 12, 291–314 (2020).
Article  Google Scholar 

5.
van Ommeren, R. J. & Whitham, T. G. Changes in interactions between juniper and mistletoe mediated by shared avian frugivores : parasitism to potential mutualism. Oecologia 130, 281–288 (2002).
ADS  Article  Google Scholar 

6.
Lee, J. H., Kim, T. W. & Choe, C. J. Commensalism or mutualism: conditional outcomes in a branchiobdellid–crayfish symbiosis. Oecologia 159, 217–224 (2009).
ADS  Article  Google Scholar 

7.
Bronstein, J. L. Conditional outcomes in mutualistic interactions. Trends Ecol. Evol. 9, 214–217 (1994).
CAS  Article  Google Scholar 

8.
Dewitt, P. D., Williams, B. W., Lu, Z., Fard, A. N. & Gelder, S. R. Effects of environmental and host physical characteristics on an aquatic symbiont. Limnologica 43, 151–156 (2013).
Article  Google Scholar 

9.
Wahl, M., Goecke, F., Labes, A., Dobretsov, S. & Weinberger, F. The second skin: ecological role of epibiotic biofilms on marine organisms. Front. Microbiol. 3, 1–21 (2012).
Article  CAS  Google Scholar 

10.
Lacoste, E. & Gaertner-Mazouni, N. Biofouling impact on production and ecosystem functioning: A review for bivalve aquaculture. Rev. Aquac. 7, 187–196 (2015).
Article  Google Scholar 

11.
Sakai, Y. The species of Cladophora from Japan and its vicinity. Sci. Pap. Inst. Algol. Res. Fac. Sci. Hokkaido Univ. 5, 1–104 (1964).
Google Scholar 

12.
Matsuyama, K., Aruga, Y. & Tanaka, J. Ecological and morphological studies of Cladophora conchopheria Sakai (Ulvophyceae, Cladophoraceae). J. Jpn .Bot. 74, 136–141 (1999).
Google Scholar 

13.
Yajima, T. & Yamada, K. Field experiments on the clinging selection by the green alga Cladophora conchopheria Sakai to the shell surfaces of the coronate moon turban Turbo (Lunella) coronatus coreensis (Recluz). Bull. Jpn. Sea Res. Institute, Kanazawa Univ. Nihon-kaiiki kenkyu 33, 87–94 (2002).

14.
Yamada, M., Wada, K. & Ohno, T. Observations on the alga Cladophora conchopheria on shells of the intertidal gastropod Turbo coronatus coreensis. Benthos Res. 58, 1–6 (2003).
ADS  Article  Google Scholar 

15.
Kagawa, O. & Chiba, S. Snails wearing green heatproof suits: the benefits of algae growing on the shells of an intertidal gastropod. J. Zool. 307, 256–263 (2019).
Article  Google Scholar 

16.
Dickinson, J. L. et al. The current state of citizen science as a tool for ecological research and public engagement. Front. Ecol. Environ. 10, 291–297 (2012).
Article  Google Scholar 

17.
Dickinson, J. L., Zuckerberg, B. & Bonter, D. N. Citizen science as an ecological research tool : challenges and benefits. Annu. Rev. Ecol. Evol. Syst. 41, 149–172 (2010).
Article  Google Scholar 

18.
Suzuki-Ohno, Y., Yokoyama, J., Nakashizuka, T. & Kawata, M. Utilization of photographs taken by citizens for estimating bumblebee distributions. Sci. Rep. 7, 1–11 (2017).
CAS  Article  Google Scholar 

19.
Luigi Nimis, P. et al. Mapping invasive plants with citizen science. A case study from Trieste (NE Italy). Plant Biosyst. 153, 700–709 (2019).
Article  Google Scholar 

20.
Sumner, S., Bevan, P., Hart, A. G. & Isaac, N. J. B. Mapping species distributions in 2 weeks using citizen science. Insect Conserv. Divers. 12, 382–388 (2019).
Article  Google Scholar 

21.
Sequeira, A. M. M., Roetman, P. E. J., Daniels, C. B., Baker, A. K. & Bradshaw, C. J. A. Distribution models for koalas in South Australia using citizen science-collected data. Ecol. Evol. 4, 2103–2114 (2014).
Article  Google Scholar 

22.
Giovos, I. et al. Citizen-science for monitoring marine invasions and stimulating public engagement: a case project from the eastern Mediterranean. Biol. Invasions 21, 3707–3721 (2019).
Article  Google Scholar 

23.
Morii, Y. & Nakano, T. Citizen science reveals the present range and a potential native predator of the invasive slug Limax maximus Linnæus, 1758 in Hokkaido Japan. Bioinvasions Rec. 6, 1–5 (2017).
Article  Google Scholar 

24.
Silvertown, J. A new dawn for citizen science. Trends Ecol. Evol. 24, 467–471 (1888).
Article  Google Scholar 

25.
Kerstes, N. A. G., Breeschoten, T., Kalkman, V. J. & Schilthuizen, M. Snail shell colour evolution in urban heat islands detected via citizen science. Commun. Biol. 2, 1–11 (2019).
Article  Google Scholar 

26.
Rotman, D. et al. Dynamic changes in motivation in collaborative citizen-science projects. In CSCW ’12 Proc. ACM 2012 Conf. Comput. Support. Coop. Work 217–226 (2012). https://doi.org/10.1145/2145204.2145238

27.
Newman, G. et al. The future of citizen science: emerging technologies and shifting paradigms. Front. Ecol. Environ. 10, 298–304 (2012).
Article  Google Scholar 

28.
Brossard, D., Lewenstein, B. & Bonney, R. Scientific knowledge and attitude change: the impact of a citizen science project. Int. J. Sci. Educ. 27, 1099–1121 (2005).
Article  Google Scholar 

29.
Schluter, D. The Ecology of Adaptive Radiation (Oxford University Press, Oxford, 2000).
Google Scholar 

30.
Williams, S., Apte, D., Ozawa, T., Kaligis, F. & Nakano, T. Speciation and dispersal along continental coastlines and Island arcs in the Indo-West Pacific turbinid gastropod genus Lunella. Evolution (N. Y). 65, 1752–1771 (2011).
Google Scholar 

31.
Yukihira, H., Noda, M., Hashimoto, H. & Gushima, K. On the distribution and foraging of the moon Coronate Turban, Lunella coronatacoreensis (Récluz, 1853). J. Fac. Appl. Biol. Sci. Hiroshima Univ. 34, 113–124 (1995).
Google Scholar 

32.
Xing, Y. & Wada, K. Temporal and spatial patterns of the alga Cladophora conchopheria on the shell of the intertidal gastropod Turbo coronatus coreensis. Publ. SETO Mar. Biol. Lab. 39, 103–111 (2001).
Article  Google Scholar 

33.
Brown, B. L., Creed, R. P., Skelton, J., Rollins, M. A. & Farrell, K. J. The fine line between mutualism and parasitism : complex effects in a cleaning symbiosis demonstrated by multiple field experiments. Oecologia 170, 199–207 (2012).
ADS  Article  Google Scholar 

34.
Baeza, J. A. & Stotz, W. Host-use and selection of differently colored sea anemones by the symbiotic crab Allopetrolisthes spinifrons. J. Exp. Mar. Biol. Ecol. 284, 25–39 (2003).
Article  Google Scholar 

35.
Takada, Y. Influence of shade and number of boulder layers on mobile organisms on a warm temperate boulder shore. Mar. Ecol. Prog. Ser. 189, 171–179 (1999).
ADS  Article  Google Scholar 

36.
Stachowicz, J. J. Mutualism, facilitation, and the structure of ecological communities. Bioscience 51, 235–246 (2001).
Article  Google Scholar 

37.
Wahl, M. Increased drag reduces growth of snails: comparison of flume and in situ experiments. Mar. Ecol. Prog. Ser. 151, 291–293 (1997).
ADS  Article  Google Scholar 

38.
Wahl, M. Fouled snails in flow: potential of epibionts on Littorina littorea to increase drag and reduce snail growth rates. Mar. Ecol. Prog. Ser. 138, 157–168 (1996).
ADS  Article  Google Scholar 

39.
Miller, L. P., Denny, M. W., Station, H. M. & Grove, P. Importance of behavior and morphological traits for controlling body temperature in Littorinid snails. Biol. Bull. 220, 209–223 (2011).
Article  Google Scholar 

40.
Chan, D. H. L. & Chan, B. K. K. Effect of epibiosis on the fitness of the sandy shore snail Batillaria zonalis in Hong Kong. Mar. Biol. 146, 695–705 (2005). https://doi.org/10.1007/s00227-004-1468-6.
Article  Google Scholar 

41.
Buschbaum, C. & Reise, K. Effects of barnacle epibionts on the periwinkle Littorina littorea (L.). Helgol. Mar. Res. 53, 56–61 (1999).
ADS  Article  Google Scholar 

42.
Mouritsen, K. N. & Bay, G. M. Fouling of gastropods: a role for parasites?. Hydrobiologia 418, 243–246 (2000).
Article  Google Scholar 

43.
Gerhart, D. J., Rittschof, D. & Mayo, S. W. Chemical ecology and the search for marine antifoulants – Studies of a predator-prey symbiosis. J. Chem. Ecol. 14, 1905–1917 (1988).
CAS  Article  Google Scholar 

44.
Solomon Ogunola, O. & Ahmed Onada, O. Anti-biofouling defence mechanism of basibionts (a chemical Warfare)—a critical review. J. Environ. Anal. Toxicol. 6, 380 (2016).
Article  Google Scholar 

45.
McGowan, K. L. & Iyengar, E. V. The difference between a rock and a biological hard place: epibionts in the rocky intertidal. Mar. Biol. 164, 1–15 (2017).
Article  Google Scholar 

46.
Wahl, M. & Mark, O. The predominantly facultative nature of epibiosis: experimental and observational evidence. Mar. Ecol. Prog. Ser. 187, 59–66 (1999).
ADS  Article  Google Scholar 

47.
Harvey, P. H. & Pagel, M. D. The comparative method in evolutionary biology. Trends Ecol. Evol. 239, 239 (1991).
Google Scholar 

48.
Braverman, H., Leibovitz, L. & Lewbart, G. A. Green algal infection of American horseshoe crab (Limulus polyphemus) exoskeletal structures. J. Invertebr. Pathol. 111, 90–93 (2012).
Article  Google Scholar 

49.
Laudien, J. & Wahl, M. Indirect effects of epibiosis on host mortality: seastar predation on differently fouled mussels. Mar. Ecol. 20, 35–47 (1999).
ADS  Article  Google Scholar 

50.
Lyu, J., Auker, L. A., Priyadarshi, A. & Parshad, R. D. The effects of invasive epibionts on crab-mussel communities: a theoretical approach to understand mussel population decline. J. Biol. Syst. 28, 1–40 (2020).
MathSciNet  MATH  Article  Google Scholar 

51.
Abe, N. Food and feeding habit of ( preliminary report some carnivorous gastropods. Benthos Res. 19, 39–47 (1980).
Article  Google Scholar 

52.
Shigemiya, Y. Does the handedness of the pebble crab Eriphia smithii influence its attack success on two dextral snail species? J. Zool. 260, 259–265 (2003).
Article  Google Scholar 

53.
Fujii, A. Predation on young topshell Batillus cornutus by carnivorous marine animals. SUISANZOUSHOKU 39, 123–128 (1991).
Google Scholar 

54.
Kohn, A. J. & Leviten, P. J. Effect of habitat complexity on population density and species richness in tropical intertidal predatory gastropod assemblages. Oecologia 25, 199–210 (1976).
ADS  Article  Google Scholar 

55.
Menge, B. A. & Sutherland, J. P. Community regulation: Variation in disturbance, competition, and predation in relation to environmental stress and recruitment. Am. Nat. 130, 730–757 (1987).
Article  Google Scholar 

56.
Marsh, C. P. Impact of avian predators on high intertidal limpet populations. J. Exp. Mar. Biol. Ecol. 104, 185–201 (1986).
Article  Google Scholar 

57.
Kiyosu, Y. Birds of Japan. (koudansya, 1978).

58.
Nakamura, T. & Nakamura, M. Bird’s life in Japan with color pictures: birds of marsh, shore and ocean. (Hoikusya, 1995).

59.
Underwood, A. J. & Zoology, P. J. Effects of interactions between algae and grazing gastropods on the structure of a low-shore intertidal algal community. Oecologia 48, 221–233 (1981).
ADS  CAS  Article  Google Scholar 

60.
Wada, Y., Iwasaki, K., Ida, T. Y. & Yusa, Y. Roles of the seasonal dynamics of ecosystem components in fluctuating indirect interactions on a rocky shore. Ecology 98, 1093–1103 (2017).
Article  Google Scholar 

61.
Wang, X. Y. & Sakai, Y. Life history of Cladophora opaca and Cl. conchopheria (Chlorophyta). Jpn. J. Phycol. 34, 209 (1986).
Google Scholar 

62.
Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).
CAS  Article  Google Scholar 

63.
Burrows, M. T. Influences of wave fetch, tidal flow and ocean colour on subtidal rocky communities. Mar. Ecol. Prog. Ser. 445, 193–207 (2012).
ADS  Article  Google Scholar 

64.
Kahma, K. K. A study of the growth of the wave spectrum with fetch. J. Phys. Oceanogr. 11, 1503–1515 (1981).
ADS  Article  Google Scholar 

65.
Burrows, M. T., Harvey, R. & Robb, L. Wave exposure indices from digital coastlines and the prediction of rocky shore community structure. Mar. Ecol. Prog. Ser. 353, 1–12 (2008).
ADS  Article  Google Scholar 

66.
Yamazaki, D., Hirano, T., Uchida, S., Miura, O. & Chiba, S. Relationship between contrasting morphotypes and the phylogeny of the marine gastropod genus Tegula (Vetigastropoda: Tegulidae) in East Asia. J. Molluscan Stud. 85, 92–102 (2019).
Article  Google Scholar 

67.
Seers, B. fetchR: Calculate Wind Fetch. (2018). Available at: https://cran.r-project.org/package=fetchR.

68.
R Core Team. R: A Language and Environment for Statistical Computing. (2018). Available at: https://www.r-project.org/.

69.
Infrastructure Transport Ministry Tourismof Land. National Land Numerical Information’s download site. (2020). Available at: https://nlftp.mlit.go.jp/ksj/index.html.

70.
Agency Japan Meteorological. Japan Meteorological Agency website. (2020). Available at: https://www.jma.go.jp/jma/kishou/know/yougo_hp/toki.html.

71.
Douma, J. C. & Weedon, J. T. Analysing continuous proportions in ecology and evolution : a practical introduction to beta and Dirichlet regression. Methods Ecol. Evol. 10, 1412–1430 (2019).
Article  Google Scholar 

72.
Chapperon, C., Studerus, K. & Clavier, J. Mitigating thermal effect of behaviour and microhabitat on the intertidal snail Littorina saxatilis (Olivi) over summer. J. Therm. Biol. 67, 40–48 (2017).
Article  Google Scholar 

73.
Keddy, P. A. Quntifying within-lake gradients of wave enagy: interrelationships of wave energy, substrate particle size and shoreline plants in axe lake, ontario. Aquat. Bot. 14, 41–58 (1982).
Article  Google Scholar 

74.
Gilks, W. R. & Roberts, G. O. Strategies for improving MCMC. Markov Chain Monte Carlo Pract. 6, 89–114 (1996).
MATH  Google Scholar 

75.
Gelman, A. & Shirley, K. Inference from simulations and monitoring convergence. Handb. Markov Chain Monte Carlo 6, 163–174 (2011).
MathSciNet  MATH  Google Scholar 

76.
Kruschke, J. K. Bayesian estimation supersedes the t test. J Exp Psychol 142, 573–603 (2013).
Article  Google Scholar  More

Overview of the model
This model simulates the population and evolutionary dynamics of different pathogen strains, as they interact with different crop resistant cultivars planted in a single field over successive years. We assume one cultivar is planted each year and we consider a field divided into a finite number m of spatial units (representing limited spaces for infections, or potential lesion sites), in which the spatial aspect is implied rather than explicitly represented. For each year during the cropping season, a number of pathogen spores are released from the infested crop residues, it then lands on the crop plants leading to infections (Fig. 1). These infections are apportioned between the different pathogen strains depending on their previous abundance and interactions with the crop cultivar. At the end of the year, during the non-cropping season, these strains are assumed to sexually recombine in the crop residue. The number of spores released and the number of infections are considered as random variables. We denote these both quantities with an uppercase letter (for example N) in general sense, while their particular realisation or draw in the simulation will be noted with a lowercase letter (for example n). The model was developed using the R Language and Environment for Statistical Computing49.
Figure 3

Case 1, model predictions of total infection by each pathogen genotype (proportion of total locations infected, left), and the corresponding frequencies of each virulent allele (right) changing over time under different rotation strategies (From top to bottom: (S1) no rotation; (S2) rotation every year; (S3) rotation every 5 years; and (S4) rotation every year with stacked resistance genes). The parameters are at baseline values: the initial frequency of each virulent allele equals (5%), the fitness modifier is set at 0.9, the modifier of increase rate for non-virulent strains equals 0.05, and the initial amount of inoculum represents (10 %) of available locations.

Full size image

Figure 4

Case 2, model predictions of total infection by each pathogen genotype (proportion of total locations infected, left), and the corresponding frequencies of each virulent allele (right) changing over time under different rotation strategies (from top to bottom: (S1) no rotation; (S2) rotation every year; (S3) rotation every 5 years; and (S4) rotation every year with stacked resistance genes). The initial frequency of each virulent allele equals (50%), and other parameters are at baseline values: the fitness modifier is set at 0.9, the modifier of increase rate for non-virulent strains equals 0.05, and the initial amount of inoculum represents (10 %) of available locations.

Full size image

We applied the general model described above to a specific situation with four genes of interaction where there are four different resistance genes that may or may not be deployed within each crop cultivar, and four virulence genes that may or may not be present within each pathogen strain. We assume that the presence of each virulence gene reduces the fitness of a strain independently. Specifically, for each strain i, we define the fitness of that strain (delta _i = delta ^{n_{vir,i}}), where (n_{vir,i}) is the number of virulence alleles present in strain i, and (delta) is a fixed model parameter with potential values between zero and one (Table 1).
Table 1 Baseline model parameter values used for our analysis, with alternative values shown in parentheses.
Full size table

We first set the model parameter values to define a baseline situation where there is a relatively small fitness penalty for virulence alleles (i.e. (delta) is very close to 1, where the value 1 means no penalty); the pathogen has a relatively low ability to reproduce if it does not carry effective virulence genes (i.e. low value for (epsilon), in this baseline situation equal to 0.05); the initial virulence allele frequency (Init.freq) is relatively low, reflecting a low historical selection pressure and lastly the initial quantity of pathogen (Init.path) is also low at (10 %) of carrying capacity (Table 1). We then considered and compared four different strategies for rotating resistant crop cultivars:
S1.
No rotation, the same cultivar with only one gene of resistance is employed every year;

S2.
A cultivar with a single gene of resistance is employed each year, and the gene of resistance in the cultivar is changed every year, giving a 4-year rotation;

S3.
A cultivar with a single gene of resistance is employed each year, and the gene of resistance in the cultivar is changed every 5 years, giving a 20-year rotation; and

S4.
A cultivar with two genes of resistance (i.e. pyramided resistance) is employed each year, and the genes of resistance in the cultivar are changed every year, giving a 2-year rotation

We then investigated how different parameterisations of the model would interact with the selected rotation strategies. We develop four cases in addition to the baseline case described above:
Case 1.
Baseline scenario (Table 1).

Case 2.
Baseline scenario, except for Init.freq which was increased from 0.05 to 0.5.

Case 3.
Baseline scenario, except for Init.freq which was increased from 0.05 to 0.5 and (delta) which was decreased from 0.9 to 0.7.

Case 4.
Baseline scenario, except for Init.freq which was increased from 0.05 to 0.5, (delta) which was decreased from 0.9 to 0.7 and (epsilon) which was increased from 0.05 to 0.5.

Case 5.
Baseline scenario, except for (epsilon) which was increased from 0.05 to 0.5.

Genetics
Cultivar and pathogen strain are both defined through their genotype being restricted to a specific set of interaction genes (loci) related to resistance (for the cultivar) or virulence (for the pathogen). Each gene has two versions (alleles): virulence or avirulence allele for the pathogen and resistance or susceptibility for the cultivar. Virulence and resistance are represented with a 1 and avirulence and susceptibility are represented with a 0 (Fig. 2). If we call ({mathcal {I}}) the set of strains and if (nu) genes of interaction are involved, then the total number of strains will be (left| {mathcal {I}}right| = 2^{nu }). During the infection process, after pathogen spores land on the cultivar, an interaction factor (beta (i,c)) defines the relative rate at which strain i can reproduce within a field of cultivar c, for each strain and cultivar combination (Fig. 2). We consider that a strain overcomes the cultivar genotype when the strain has a virulence allele for every resistance allele of the cultivar (Fig. 2), in which case (beta (i,c)=1), indicating maximum reproduction rate. Otherwise, if the strain does not have a virulence allele for every resistance allele of the cultivar, (beta (i,c)= epsilon), where (epsilon) is a model parameter with constant value (0 le epsilon < 1), indicating a less-than-maximum reproduction rate. As such, (epsilon) is the model parameter modifying the growth and reproduction of pathogen strains not carrying multiple virulence alleles (e.g. 0100) and/or an avirulent pathogen strain (e.g. 0000) (Fig. 2). Accordingly, lower (closer to 0) (epsilon) values represent reduced ability to grow and reproduce in pathogen strains with increasing number of avirulence alleles. Moreover, any strain i with one or more virulence genes is also assumed to suffer a fitness penalty (delta _i) depending on the number of genes involved. Together these interaction factors make a cultivar-strain interaction matrix (B = (beta (i,c))). This code and method for modelling resistance and virulence interactions (without fitness penalty) is similar to those in previous studies48,50. Figure 5 Case 3, model predictions of total infection by each pathogen genotype (proportion of total locations infected, left), and the corresponding frequencies of each virulent allele (right) changing over time under different rotation strategies (from top to bottom: (S1) no rotation; (S2) rotation every year; (S3) rotation every 5 years; and (S4) rotation every year with stacked resistance genes). The fitness modifier is set at 0.7, the initial frequency of each virulent allele equals (50%), and other parameters are at baseline values: the modifier of increase rate for non-virulent strains equals 0.05, and the initial amount of inoculum represents (10 %) of available locations. Full size image Figure 6 Case 4, model predictions of total infection by each pathogen genotype (proportion of total locations infected, left), and the corresponding frequencies of each virulent allele (right) changing over time under different rotation strategies (from top to bottom: (S1) no rotation; (S2) rotation every year; (S3) rotation every 5 years; and (S4) rotation every year with stacked resistance genes). The fitness modifier is set at 0.7, the initial frequency of each virulent allele equals (50%), the modifier of increase rate for non-virulent strains equals 0.5, and other parameters are at baseline values: the initial amount of inoculum represents (10 %) of available locations. Full size image Initial genetic structure of pathogen population At the start of each case, we define the initial proportion of each pathogen genotype using the equation: $$begin{aligned} strains.init = Init.freq^{nr}left( 1-Init.freqright) ^{4-nr} end{aligned}$$ (1) where strains.init is the initial proportion of each pathogen genotype; Init.freq is the frequency of the virulent genes as set by each case and nr is the number of virulent genes present in a given pathogen genotype. We then used a random Poisson distribution generator (rpois function from the stats package in R) to obtain the initial number of spores for each pathogen genotype, where the mean of the Poisson distribution is the proportion of a given pathogen genotype multiplied by the pre-determined pathogen load (Init.path, Table 1). Model dynamics The annual dynamics (Fig. 1) can be divided into two main phases: the phase of parasitic activity, representing events occurring through the cropping season, and the phase of dormancy, representing events occurring between the cropping seasons. During the phase of parasitic activity, the pathogen produces spores which are spread both through the air (sexual ascospores) and via water splash (asexual conidia). These spores may then infect leaves and stems of the cultivar, resulting in new lesions of different strains. During the phase of dormancy, the pathogen remains within the infected crop residue and sexual recombination occurs. These processes are modelled with four steps, three for the parasitic phase and one for the dormancy phase. Figure 7 Case 5, model predictions of total infection by each pathogen genotype (proportion of total locations infected, left), and the corresponding frequencies of each virulent allele (right) changing over time under different rotation strategies (from top to bottom: (S1) no rotation; (S2) rotation every year; (S3) rotation every 5 years; and (S4) rotation every year with stacked resistance genes). The modifier of increase rate for non-virulent strains equals 0.5 and other parameters are at baseline values: the initial frequency of each virulent allele equals (5%), the fitness modifier is set at 0.9, and the initial amount of inoculum represents (10 %) of available locations. Full size image Total amount of spores released First, the model generates the amount of pathogen spores of each strain that is released, using the equation: $$begin{aligned} lambda _{{ released},i}(t) = alpha . n_{{ recombined},i}(t-1) end{aligned}$$ (2) where (lambda _{{ released},i}(t)) represents the expected dispersed propagule (spore) pressure in the field due to strain (i in {mathcal {I}}) during the year t, the parameter (alpha) represents the normal rate of growth for the pathogen from 1 year to the next, and (n_{{ recombined},i}(t-1)) represents the number of spatial units or locations infected by the strain i at the end of the previous year and after genetic recombination. The actual quantity of pathogen strain i released in the current year, (n_{{ released},i}(t)) is then simulated as a Poisson random variable: $$begin{aligned} N_{{ released},i}(t) hookrightarrow {mathcal {P}}(alpha . n_{{ recombined},i}(t-1)) end{aligned}$$ (3) The infective pressure (lambda _{{ infected},i}(t)) is then calculated as: $$begin{aligned} lambda _{{ infected},i}(t) = beta (i,c(t)) . delta _i . n_{{ released},i}(t) end{aligned}$$ (4) where (beta (i,c(t))) is the interaction factor between the strain i and the cultivar c(t) i.e. the cultivar grown in year t, and (delta _i) is the fitness penalty for the particular strain i. Total number of infections Second, the model calculates the total number of infected sites, following a binomial distribution: $$begin{aligned} N_{ infected}(t) hookrightarrow {mathcal {B}}left( m, 1 - prod _{i = 1}^{2^{nu }} (1- rho _i(t))^{n_{{ released},i}(t)}right) end{aligned}$$ (5) where (rho _i(t)) is the probability that a particular given location (among the m possible locations in the field) during year t, will have a given spore from strain i fall down on it and cause a lesion, and thus (displaystyle 1 - prod nolimits _{i = 1}^{2^{nu }} (1- rho _i(t))^{n_{{ released},i}(t)}) represents the probability that at least one of the (displaystyle n_{ released}(t) = sum nolimits _{i = 1}^{2^{nu }} n_{{ released},i}(t)) spores produces a lesion. This equation can be justified in more detail as follows: $$begin{aligned}&P({At; least; one; of; the; n_{ released}(t); spores; produces; a; lesion}) \&quad = 1 - P({ No; released; spores; produces; a; lesion}) \&quad = 1 - prod _{i = 1}^{2^{nu }} P({ A; single; released; spore; of ; strain ; i ; doesn't; produce; a; lesion})^{n_{{ released},i}(t)} \&quad = 1 - prod _{i = 1}^{2^{nu }} (1 - P({A; single; released; spore; of ; strain ; i ; produces; a; lesion}))^{n_{{ released},i}(t)} end{aligned}$$ We assume that a spore will fall on any of the m specific locations with the same probability independently of its infection capabilities. The number of locations m is assumed to be the same for all years whatever the cultivar grown and thus, this probability is independent of the time dimension. Next, we assume that the probability that a spore will induce an infection depends on the interaction factor between the crop cultivar genotype and the pathogen strain (beta (i,c(t))) together with the fitness penalty for that strain (delta _i) . These assumptions mean that: $$begin{aligned} rho _i(t) = P({a; spore; fall; down; on; a; given; location; during ; year; t; and; causes; a; lesion}) \ = P({a; spore; falls; on; a; given; place; where; c(t); is; grown })times \ P({ the; spore; causes; a; lesion} mid { the; spore; falls; on; a; place; where; c(t); is; grown}) \ = frac{1}{m} . beta (i,c(t)) . delta _i end{aligned}$$ Number of infections for each strain Third, the number of infections of each strain is derived from the total number of infections depending on genetic interactions between each strain and crop cultivar being employed that year. Specifically, the total number of infections (N_{ infected}(t) = n_{ infected}(t)) is distributed among the different strains using the multinomial distribution: $$begin{aligned} left( N_{{ infected},1}(t), ldots , N_{{ infected},2^{nu }}(t)right) hookrightarrow {mathcal {M}}left( frac{lambda _{{ infected},1}(t)}{lambda _{ infected}(t)},ldots , frac{lambda _{{ infected},2^{nu }}(t)}{lambda _{{ infected}}(t)}, n_{ infected}(t)right) end{aligned}$$ (6) where (displaystyle lambda _{{ infected}} (t) = sum nolimits _{i = 1}^{2^{nu }} lambda _{{ infected},i}(t)). The number of infected sites due to strain i, without no loss of generalities, follows then the binomial distribution (displaystyle {mathcal {B}}left( n_{ infected}(t),frac{lambda _{{ infected},i}(t)}{lambda _{{ infected}}(t)}right)). Genetic recombination The fourth step involves simulating the process of sexual recombination, where new quantities of each strain are generated based on the previous quantities of each strain. At the end of the year t, we calculate the frequencies (f_j(t)) of each virulent version of each gene from the different genotypes of strains in the crop stubble. We let the genotype of any new spore be represented by a random vector (displaystyle G_i(t) = left( G_{i,1}(t), ldots ,G_{i,nu }(t)right)), where each (G_{i,j}(t)) is a Bernoulli random variable (displaystyle {mathcal {B}}(1,f_j(t))). This vector representation of genotype follows the coding illustrated in (Fig. 2). Assuming that strains recombine independently gene by gene, the probability that (G_i(t)) will be a particular genotype (displaystyle g_i(t) = left( g_{i,1}(t), ldots ,g_{i,nu }(t)right)) is given by: $$begin{aligned} p_i(t) = Pleft( G_i(t) = g_i(t)right) &= prod _{j=1}^{nu } P(G_{i,j}(t) = g_{i,j}(t)) nonumber \ &= prod _{j=1}^{nu } f_j(t)^{g_{i,j}(t)} left( 1 - f_j(t)right) ^{left( 1 - g_{i,j}(t)right) } end{aligned}$$ We can also confirm that across all possible genotypes these probabilities sum to one: $$begin{aligned} sum _{i=1}^{2^{nu }} Pleft( G_i(t) = g_i(t)right) = sum _{i=1}^{2^{nu }} prod _{j=1}^{nu } f_j(t)^{g_{i,j}(t)} left( 1 - f_j(t)right) ^{left( 1 - g_{i,j}(t)right) } = 1 end{aligned}$$ (7) If we shorten the notation for (P(G_i(t) = g_i(t))) to be (p_i(t)) then we can define the recombined version of infected numbers of units of each strain with the following multinomial distribution: $$begin{aligned} left( N_{{ recombined},1}(t), ldots , N_{{ recombined},2^{nu }}(t)right) hookrightarrow {mathcal {M}}left( p_1(t),ldots , p_{2^{nu }}(t), n_{ infected}(t)right) end{aligned}$$ (8) Poisson, binomial and multinomial distribution In plant pathology, it is often relevant to model infections by a random variable. Let’s imagine a released spore flying in the air, we can say that this spore will land on a specific leaf and infect it with a given probability p, then it won’t with probability (1 - p) because these are the only two possible events. We can define Y a random variable to model the situation. If we say the event ({Y = 1}) represents the success of the event (landing and infection) and ({Y = 0}) represents the failure, with this definition we say that Y follows a Bernoulli distribution. The values attributed to the variable depending on the events allow the following generalisation: If we consider n spores, each of them realizing an infection on a specific plant area they fell on with the same probability p, then we can associate to each spore a Bernoulli distribution (Y_i) where (i in {1,ldots ,n }). If we are interested in the total number of infections occurring on this leaf, assuming the fact that they will happen independently of each other, we can model this situation by the variable (displaystyle S = sum nolimits _{i = 1}^n{Y_i}), called binomial variable. We can also denote briefly (S hookrightarrow {mathcal {B}}(n,p)), where n represents the number of events and p the probability of success of each event. Moreover, the Bernoulli variable Y is related to binomial distribution in the way that we can write (Y hookrightarrow {mathcal {B}}(1,p))51,52. Usually it is more likely to model such events by a Poisson law rather than binomial law53,54. When the number of events is so big that we can approximate it by infinity, and when the probability of success of each event is very small, close to zero, it is possible to link both Poisson and binomial distribution through their respective expectations. So if (lim nolimits _{begin{array}{c} n nearrow +infty \ p searrow 0 end{array}} n*p = lambda ,) then if we define (X hookrightarrow {mathcal {P}}(lambda )), we have (S xrightarrow {text {distribution}} X). Returning to our example, that means that if we have a ‘close to infinity’ number of spores that could fall onto a given plant and infect it with a very small probability p for each of them and still acting independently, we can model the total number of infections by both S or X. Even if there are millions and millions of spores released, this amount is still small compared to infinity, so using X is still a modelling approximation. The use of binomial or Poisson laws depends on the complexity of the situation. For example, if the modeller wants to simulate a model where he anticipates 15 infections, they can use (X hookrightarrow {mathcal {P}}(15)) or (S hookrightarrow {mathcal {B}}(10000,0.0015)) or (S hookrightarrow {mathcal {B}}(1000000,0.000015)). We consider now a situation where the plant is attacked by a big number of spores, but with different genotypes modifying their ability to infect, some strains being more efficient than others. To model this situation, we can use a vector of variables, each component representing the number of successes due to a specific genotype. We can choose a vector of binomial number or Poisson number. If we consider the case of a threshold in terms of available space to be infected (a maximum number of infections for the plant), such that spores of different strains are competing for those places, we suggest using a vector of random numbers that follows a multinomial law. This distribution derives from the binomial law, although each component is a specified binomial distribution defined from the parameters of the multinomial distribution. But, it is still possible to interpret some of these components via a conditional Poisson distribution. From binomial to multinomial distribution The binomial distribution is a particular case of the multinomial distribution. We consider S a binomial distribution of parameters (n, p) counting the number of success of n independent events where the basic probability of success is p. Let U the random variable be defined by (n-S) the number of failures. In the case where S represents the number of infections, U represents the number of uninfected places. The probability to get k infections is given by: $$begin{aligned} P(S = k) = {n atopwithdelims ()k} p^k (1-p)^{n-k} = {n atopwithdelims ()n-k} p^k (1-p)^{n-k} = P(U = n-k) end{aligned}$$ (9) As a result, the probability of having k success is the same that having (n-k) failures. Then the Eq. (9) shows that U follows a binomial distribution with parameters ((n, 1-p)). We can also say that the couple (S, U) follows a multinomial distribution of parameter ((p, 1-p, n)), that we can denote ((S,U) hookrightarrow {mathcal {M}}(p, 1-p, n)). In a more general way, the analogue of the binomial distribution is the multinomial distribution, where each trial results in exactly one of some fixed finite number k possible successes, with probabilities (p_1), ..., (p_k) (so that (p_ige 0) for i = 1, ..., k and (sum nolimits _{i=1}^k p_i = 1)), and there are n independent trials. Then if the random variables (X_i) indicate the number of times outcome number i is observed over the n trials, the vector (X = (X_1, ldots , X_k)) follows a multinomial distribution with parameters n and p, where (p = (p_1, ldots , p_k)), that we can also write ({mathcal {M}}left( p_1,ldots ,p_n, N = kright))55. From Poisson to multinomial distribution We consider here a total number of successes (meaning in our example a number of spores that fall on a place and infect it) X being the sum of the infections due to (omega) different strains (X_i) ((1le i le omega)). If we consider that each (X_i) follows a Poisson law of parameter (lambda _i) and that they are all independent, then X follows a Poisson law of parameter (displaystyle lambda = sum nolimits _{i=1}^{omega } lambda _i). The distribution of each (X_i) conditionally to (X = n) is a binomial distribution ({mathcal {B}}(n,frac{lambda _i}{lambda })). We can prove it for all variable (X_j), with (j in {1,ldots ,omega }): $$begin{aligned} Pleft( X_j = k left| right. sum _{i=1}^{omega } X_i = n right) &= frac{P left( X_j = k,displaystyle sum nolimits _{begin{array}{c} i = 1 \ ine j end{array}}^{omega } X_i = n-k right) }{P left( displaystyle sum nolimits _{i = 1}^{omega } X_i = n right) } \ &= frac{Pleft( X_j = k right) Pleft( displaystyle sum nolimits _{begin{array}{c} i = 1 \ i ne j end{array}}^{omega } X_i = n-k right) }{P left( displaystyle sum nolimits _{i = 1}^{omega } X_i = n right) } end{aligned}$$ that we obtain using the Bayes formula for conditioning and the use of independence between the (X_i)’s. Then we replace the probabilities by their Poisson values: $$begin{aligned} Pleft( X_j = k left| right. sum _{i = 1}^{omega } X_i = n right) &= frac{e^{-lambda _j}{lambda _j}^k}{k!} frac{e^{- displaystyle sum nolimits _{begin{array}{c} i = 1 \ ine j end{array}}^{omega } lambda _i}{left( displaystyle sum nolimits _{begin{array}{c} i = 1 \ ine j end{array}}^{omega } lambda _i right) }^{n-k}}{(n-k)!} frac{n!}{e^{-displaystyle sum nolimits _{i = 1}^{omega } lambda _i}{left( displaystyle sum nolimits _{i = 1}^n lambda _i right) }^{omega }} \ &= {n atopwithdelims ()k} frac{{lambda _j}^k {left( displaystyle sum nolimits _{begin{array}{c} i = 1 \ ine j end{array}}^{omega } lambda _i right) }^{n-k}}{{left( displaystyle sum nolimits _{i = 1}^{omega } lambda _i right) }^n} = {n atopwithdelims ()k}{left( frac{lambda _j}{displaystyle sum nolimits _{i = 1}^{omega } lambda _i}right) }^k {left( frac{displaystyle sum nolimits _{begin{array}{c} i = 1 \ ine j end{array}}^{omega } lambda _i}{displaystyle sum nolimits _{i = 1}^{omega } lambda _i}right) }^{n-k} end{aligned}$$ Generalizing this result to the random vector of the (displaystyle (X_i)_{1 le ile omega }) for (omega) strains, the distribution of this vector conditionally to the total number X is a multinomial distribution ({mathcal {M}}left( frac{lambda _1}{lambda },ldots ,frac{lambda _n}{lambda }, X = nright))55. Properties of the model Let (X_1),..., (X_{2^{nu }}) independent random variables such that (X_j hookrightarrow {mathcal {P}}(lambda _{{ infected},j}(t))) for all (j in {1,ldots ,2^{nu }}), we have the following results: A. When (m rightarrow infty), (displaystyle N_{ infected}(t) hookrightarrow {mathcal {P}}(sum nolimits _{j=1}^{2^{nu }} lambda _{{ infected},j}(t))), B. For all (j in {1,ldots ,2^{nu }}), (displaystyle N_{ infected, j}(t) xrightarrow {text {distribution}} X_j left| right. sum nolimits _{i = 1}^{2^{nu }} X_i = n), C. With A and B when (m rightarrow infty), it is equivalent to either simulate (N_{ infected}(t)) then the conditional multinomial vector (displaystyle left( N_{{ infected},1}(t), ldots , N_{{ infected},2^{nu }}(t)right)) conditionally to the realisation (n_{ infected}(t)), or to simulate directly the previously defined variables (X_1),..., (X_{2^{nu }}). The number of infected sites due to strain j, without any loss of generalities, follows the binomial distribution (displaystyle {mathcal {B}}left( n_{ infected}(t),frac{lambda _{{ infected},j}(t)}{lambda _{{ infected}}(t)}right)). It is important to notice that it is the same law as a Poisson variable with parameter (lambda _{{ infected},j}(t)) conditionally to the realisation (n_{ infected}(t)) of a Poisson variable with parameter (lambda _{{ infected}}(t)). Referring to formula (10), we can see that when the number of sites available for infection goes towards infinity, meaning that (N_{{ infected}}(t)) behaves like a Poisson law of parameter (sum nolimits _{i = 1}^{2^{nu }} lambda _{{ infected},i}(t)), then the variables (displaystyle left( N_{{ infected},i}(t)right) _{1 le i le 2^{nu }}) behave like independent Poisson law of respective rates (displaystyle left( lambda _{{ infected},i}(t)right) _{1 le i le 2^{nu }}). Proof of the properties of the model A. With the help of the reminder, we just have to prove this result: $$begin{aligned} lim _{m rightarrow infty } Eleft( N_{ infected}(t)right) = sum _{i=1}^{2^{nu }} lambda _{{ infected},i}(t), end{aligned}$$ (10) which could be obtained with the mean value theorem56. It means that if the total number of places available for infections was unlimited, these infections could be regarded as being Poisson distributed, with infection pressure as defined previously. We consider the notation of (5), and to simplify the formula we will note: (rho _i = frac{1}{m} . beta _i) and because the result (10) does not depend on time we reduce the notation such that (10) is equivalent to: $$begin{aligned} lim _{m rightarrow infty } Eleft( N_{ infected}right) = sum _{i=1}^{2^{nu }} lambda _{{ infected}, i}, end{aligned}$$ (11) and then we want to prove that: $$begin{aligned} lim _{m rightarrow infty } m . left( 1 - prod _{i=1}^{2^{nu }} left( 1- frac{beta _i}{m}right) ^{n_{{ released},i}}right) = sum _{i=1}^{2^{nu }} lambda _{{ infected}, i} end{aligned}$$ (12) Replacing m by (frac{1}{x}), with (xne 0), the latest equation equals: $$begin{aligned} lim _{x rightarrow 0} frac{1}{x}. left( 1 - prod _{i=1}^{2^{nu }} (1- xbeta _i)^{n_{{ released},i}}right) = sum _{i=1}^{2^{nu }} lambda _{{ infected}, i} end{aligned}$$ (13) We define (displaystyle f_{beta , n_{released}}(x) = prod _{i=1}^{2^{nu }} f_{i,({beta , n_{released}})}(x) = prod _{i=1}^{2^{nu }} (1 - xbeta _i)^{n_{{ released},i}}). Taking into account the fact that $$begin{aligned} f_{beta , n_{released}}'(x) = left( prod _{i=1}^{2^{nu }} f_{i,({beta , n_{released}})}(x)right) ' = sum _{i=1}^{2^{nu }} left[ f_{i,({beta , n_{released}})}'(x) prod _{begin{array}{c} i=1 \ jne i end{array}}^{2^{nu }}f_{j,({beta , n_{released}})}(x)right] , end{aligned}$$ (14) we apply the mean value theorem (56) to the derivable function (f_{beta , n_{released}}), we got the following result: $$begin{aligned} lim _{x rightarrow 0} frac{left( 1 - f_{beta , n_{released}}(x)right) }{x} &= - lim _{x rightarrow 0} frac{left( f_{beta , n_{released}}(0) - f_{beta , n_{released}}(x)right) }{0 - x} nonumber \ &= -left( f_{beta , n_{released}}'(0)right) = sum _{i=1}^{2^{nu }} beta _i n_{released, i} end{aligned}$$ (15) that finishes the proof of point A. B. The result is immediate knowing the upper reminder concerning the Poisson–Multinomial laws relationship. We just have to take the value of (omega = 2^{nu }). C. When m is close to infinity, (N_{ infected}(t)) follows a Poisson distribution whose parameter (expectation) is a sum of parameters. A property of Poisson distribution is that the law of a sum equals in distribution the sum of independent Poisson variables with the respective terms. So that we can rewrite B: For all (j in {1,ldots ,2^{nu }}), (displaystyle N_{ infected, j}(t) xrightarrow {text {distribution}} X_j left| right. N_{ infected}(t) = n). More

1.
Day, K. et al. Endanger. Species Res. 40, 171–182 (2019).
Google Scholar 
2.
Fernandes, K. et al. Restor. Ecol. 26, 1098–1107 (2018).
Google Scholar 

3.
van der Heyde, M. et al. Mol. Ecol. Resour. 20, 732–745 (2020).
Google Scholar 

4.
Thomsen, P. F. & Willerslev, E. Biol. Conserv. 183, 4–18 (2015).
Google Scholar 

5.
Giguet-Covex, C. et al. Nat. Commun. 5, 3211 (2014).
PubMed  Google Scholar 

6.
Willerslev, E. et al. Science 300, 791–795 (2003).
CAS  PubMed  Google Scholar 

7.
Willerslev, E. et al. Nature 506, 47–51 (2014).
CAS  PubMed  Google Scholar 

8.
Slon, V. et al. Science 356, 605–608 (2017).
CAS  PubMed  Google Scholar 

9.
Claw, K. G. et al. Nat. Commun. 9, 2957 (2018).
PubMed  PubMed Central  Google Scholar 

10.
Garrison, N. A. et al. Annu. Rev. Genomics Hum. Genet. 20, 495–517 (2019).
CAS  PubMed  Google Scholar 

11.
Kowal, E. in Biomapping Indigenous Peoples: Towards an Understanding of the Issues (eds Berthier-Folgar, S. et al.) 329–347 (Rodopi, 2012).

12.
Adams, K., Faulkhead, S., Standfield, R. & Atkinson, P. Women Birth 31, 81–88 (2018).
PubMed  Google Scholar 

13.
National Health and Medical Research Council (NHMRC), Australian Research Council (ARC) & Australian Vice-Chancellors’ Committee (AVCC) National Statement on Ethical Conduct in Human Research (2007) – Updated 2015 (National Health and Medical Research Council, 2015).

14.
Pawu-Kurlpurlunu, W. J., Holmes, M. & Box, L. A. Ngurra-kurlu: A Way of Working with Warlpiri People DKCRC Report 41 (Desert Knowledge CRC, 2008); https://go.nature.com/3jl4TR4

15.
Rose, D. B. Dingo Makes Us Human: Life and Land in an Australian Aboriginal Culture (Cambridge Univ. Press, 1992).

16.
Stanner, W. E. H. in White Man Got No Dreaming: Essays 1938-1973 198–248 (Australian National Univ. Press, 1979).

17.
Lewis, C. M. Jr, Obregón-Tito, A., Tito, R. Y., Foster, M. W. & Spicer, P. G. Trends Microbiol. 20, 1–4 (2012).
CAS  PubMed  Google Scholar 

18.
Ma, Y., Chen, H., Lan, C. & Ren, J. Protein Cell 9, 404–415 (2018).
PubMed  PubMed Central  Google Scholar 

19.
Kistler, L., Ware, R., Smith, O., Collins, M. & Allaby, R. G. Nucleic Acids Res. 45, 6310–6320 (2017).
CAS  PubMed  PubMed Central  Google Scholar 

20.
Andersen, K. et al. Mol. Ecol. 21, 1966–1979 (2012).
CAS  PubMed  Google Scholar 

21.
Haile, J. et al. Mol. Biol. Evol. 24, 982–989 (2007).
CAS  PubMed  Google Scholar  More