Philippa Kaur

Cardoso, Y. P. et al. A continental-wide molecular approach unraveling mtDNA diversity and geographic distribution of the Neotropical genus Hoplias. PLoS ONE 13(8), e0202024. https://doi.org/10.1371/journal.pone.0202024 (2018).CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Bertollo, L. A. C., Born, G. G., Dergam, J. A., Fenocchio, A. S. & Moreira-Filho, O. A biodiversity approach in the Neotropical Erythrinidae fish, Hoplias malabaricus: Karyotypic survey, geographic distribution of karyomorphs and cytotaxonomic considerations. Chrom. Res. 8(7), 603–613 (2000).CAS 
Article 

Google Scholar 
Oyakawa, O. T. Family Erythrinidae (Trahiras). in Check list of the freshwater fishes of South and Central America (Reis, R. E., Kullander, S. O. & Ferraris, C.). Edipucrs 238–240 (Porto Alegre, 2003).Dagosta, F. C. P. & de Pinna, M. C. C. The fishes of the Amazon: distribution and biogeographical patterns, with a comprehensive list of species. Bull. Am. Museum Nat. Hist. 431, 1–163 (2019).
Google Scholar 
Da Rosa, R., Vicari, M. R., Dias, A. L. & Giuliano-Caetano, L. New insights into the biogeographic and Karyotypic Evolution of Hoplias Malabaricus. Zebrafish 11(3), 198–206. https://doi.org/10.1089/zeb.2013.0953 (2014).CAS 
Article 
PubMed 

Google Scholar 
Santos, U. et al. Molecular and karyotypic phylogeography in the neotropical Hoplias malabaricus (Erythrinidae) fish in eastern Brazil. J. Fish Biol. 75(9), 2326–2343. https://doi.org/10.1111/j.1095-8649.2009.02489.x (2009).CAS 
Article 
PubMed 

Google Scholar 
Blanco, D. R., Lui, R. L., Bertollo, L. A. C., Diniz, D. & Filho, O. M. Characterization of invasive fish species in a river transposition region: Evolutionary chromosome studies in the genus Hoplias (Characiformes, Erythrinidae). Rev. Fish Biol. Fish. 20(1), 1–8. https://doi.org/10.1007/s11160-009-9116-3 (2010).Article 

Google Scholar 
Jacobina, U. P. et al. DNA barcode sheds light on systematics and evolution of neotropical freshwater trahiras. Genetica 146, 505. https://doi.org/10.1007/s10709-018-0043-x (2018).CAS 
Article 
PubMed 

Google Scholar 
Marques, D. F., Santos, F. A., da Silva, S. S., Sampaio, I. & Rodrigues, L. R. R. Cytogenetic and DNA barcoding reveals high divergence within the trahira, Hoplias malabaricus (Characiformes: Erythrinidae) from the lower Amazon River. Neotrop. Ichthyol. 11(2), 459–466. https://doi.org/10.1590/S1679-62252013000200015 (2013).Article 

Google Scholar 
Paz, F. P. C., Batista, J. S. & Porto, J. I. R. DNA barcodes of rosy tetras and allied species (Characiformes: Characidae: Hyphessobrycon) from the Brazilian Amazon Basin. PLoS ONE 9(5), e98603. https://doi.org/10.1371/journal.pone.0098603 (2014).ADS 
CAS 
Article 

Google Scholar 
Guimarães, K. L. A., de Sousa, M. P. A., Ribeiro, F. R. V., Porto, J. I. R. & Rodrigues, L. R. R. DNA barcoding of fish fauna from low order streams of Tapajós River basin. PLoS ONE 13(12), e0209430. https://doi.org/10.1371/journal.pone.0209430 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Machado, V. N. et al. One thousand DNA barcodes of piranhas and pacus reveal geographic structure and unrecognized diversity in the Amazon. Sci. Rep. 8, 8387. https://doi.org/10.1038/s41598-018-26550-x (2018).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Hebert, P. D. N., Cywinska, A., Ball, S. L. & Dewaard, J. R. Biological identifications through DNA barcodes. Philos. Trans. R. Soc. B 270(1512), 313–321. https://doi.org/10.1098/rspb.2002.2218 (2003).CAS 
Article 

Google Scholar 
Pugedo, M. L., de Andrade Neto, F. R., Pessali, T. C., Birindelli, J. L. O. & Carvalho, D. C. Integrative taxonomy supports new candidate fish species in a poorly studied neotropical region: the Jequitinhonha River Basin. Genetica 144(3), 1–9. https://doi.org/10.1007/s10709-016-9903-4 (2016).Article 

Google Scholar 
Rosso, J. J. et al. Integrative taxonomy reveals a new species of the Hoplias malabaricus species complex (Teleostei: Erythrinidae). Ichthyol. Explor. Freshw. 1, 1–18. https://doi.org/10.23788/IEF-1076 (2018).Article 

Google Scholar 
Azpelicueta, M. M., Benítez, M., Aichino, D. & Mendez, C. M. D. A new species of the genus Hoplias (Characiformes, Erythrinidae), a tararira from the lower Paraná River, in Missiones, Argentina. Acta Zool. Lilloana 59(1–2), 71–82 (2015).
Google Scholar 
Rosso, J. J. et al. A new species of the Hoplias malabaricus species complex (Characiformes: Erythrinidae) from the La Plata River basin. Cybium 40(3), 199–208 (2016).
Google Scholar 
Cardoso, Y. P. & Montoya-Burgos, J. I. Unexpected diversity in the catfish Pseudancistrus brevispinis reveals dispersal routes in a Neotropical center of endemism: The Guyanas Region. Mol. Ecol. 18(5), 947–964. https://doi.org/10.1111/j.1365-294X.2008.04068.x (2009).CAS 
Article 
PubMed 

Google Scholar 
Hoorn, C., Wesselingh, F. P., Hovikoski, J. & Guerrero, J. The development of the Amazonian mega-wetland (Miocene; Brazil, Colombia, Peru, Bolivia). Amazon. Landsc. Species Evol. https://doi.org/10.1002/9781444306408.ch8 (2010).Article 

Google Scholar 
Albert, J. S. & Reis, R. E. Introduction to neotropical freshwaters. In Historical Biogeography of Neotropical Freshwater Fishes (eds Albert, J. S. & Reis, R. E.) 3–19 (University of California Press, 2011).
Google Scholar 
Leys, M., Keller, I., Räsänen, K., Gattolliat, J.-L. & Robinson, C. T. Distribution and population genetic variation of cryptic species of the Alpine mayfly Baetis alpinus (Ephemeroptera: Baetidae) in the Central Alps. BMC Evol. Biol. https://doi.org/10.1186/s12862-016-0643-y (2016).Article 
PubMed 
PubMed Central 

Google Scholar 
Aljanabi, S. M. & Martinez, I. Universal and rapid salt-extraction of high quality genomic DNA for PCR-based techniques. Nucleic Acids Res. 25(22), 4692–4693 (1997).CAS 
Article 

Google Scholar 
Vitorino, C. A., Oliveira, R. C. C., Margarido, V. P. & Venere, P. C. Genetic diversity of Arapaima gigas (Schinz, 1822) (Osteoglossiformes: Arapaimidae) in the Araguaia-Tocantins basin estimated by ISSR marker. Neotrop. Ichthyol. 13, 557–568. https://doi.org/10.1590/1982-0224-20150037 (2015).Article 

Google Scholar 
Ward, R. D., Zemlak, T. S., Innes, B. H., Last, P. R. & Hebert, P. D. N. DNA barcoding Australia’s fish species. Philos. Trans. R. Soc. B 359, 1847–1857. https://doi.org/10.1098/srtb.2005.1716 (2005).Article 

Google Scholar 
Dunn, I. S. & Blattner, F. R. Sharons 36 to 40: Multienzyme, high capacity, recombination deficient replacement vectors with polylinkers and polystuffers. Nucleic Acids Res. 15, 2677–2698 (1987).CAS 
Article 

Google Scholar 
Thompson, J. D., Higgins, D. G. & Gibson, T. J. CLUSTAL W: Improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res. 22(22), 4673–4680 (1994).CAS 
Article 

Google Scholar 
Castresana, J. Selection of conserved blocks from multiple alignments for their use in phylogenetic analysis. Mol. Biol. Evol. 17, 540–552. https://doi.org/10.1093/oxfordjournals.molbev.a026334 (2000).CAS 
Article 

Google Scholar 
Ratnasingham, S. & Hebert, P. D. N. DNA-Based registry for all animal species: The Barcode Index Number (BIN) system. PLoS ONE 8(7), e66213. https://doi.org/10.1371/journal.pone.0066213 (2013).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Pons, J. et al. Sequence-based species delimitation for the DNA taxonomy of undescribed insects. Syst. Biol. 55(4), 595–609. https://doi.org/10.1080/10635150600852011 (2006).Article 
PubMed 

Google Scholar 
Fujisawa, T. & Barraclough, T. G. Delimiting species using single-locus data and the generalized mixed yule coalescent approach: A revised method and evaluation on simulated data sets. Syst. Biol. 62(5), 707–724. https://doi.org/10.1093/sysbio/syt033 (2013).Article 
PubMed 
PubMed Central 

Google Scholar 
Puillandre, N., Lambert, A., Brouillet, S. & Achaz, G. ABGD, automatic barcode gap discovery for primary species delimitation. Mol. Ecol. 21(8), 1864–1877. https://doi.org/10.1111/j.1365-294X.2011.05239.x (2012).CAS 
Article 
PubMed 

Google Scholar 
Drummond, A. & Rambaut, A. BEAST: Bayesian evolutionary analysis by sampling trees. BMC Evol. Biol. 7, 214. https://doi.org/10.1186/1471-2148-7-214 (2007).CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Posada, D. jModelTest: Phylogenetic model averaging. Mol. Biol. Evol. 25, 1253–1256. https://doi.org/10.1093/molbev/msn083 (2008).CAS 
Article 
PubMed 

Google Scholar 
R Core Team. R: A Language and Environment for Statistical Computing. https://www.R-project.org/ (2017).Ezard, T., Fujisawa, T. & Barraclough, T. splits: Species Limits by Threshold Statistics. R package version 1.0–19/r52. https://R-Forge.R-project.org/projects/splits/ (2017).Paradis, E. & Schliep, K. ape 5.0: An environment for modern phylogenetics and evolutionary analyses in R. Bioinformatics 35, 526–528 (2018).Article 

Google Scholar 
Bermingham, E., McCafferty, S. S. & Martin, A. P. Fish biogeography and molecular clocks: Perspectives from the Panamanian Isthmus. In Molecular Systematics of Fishes (eds Kocher, T. D. & Stepien, C. A.) 113–128 (Academic Press, 1997).Chapter 

Google Scholar 
Thomaz, A. T., Malabarba, L. R., Bonatto, S. L. & Knowles, L. L. Testing the effect of palaeodrainages versus habitat stability on genetic divergence in riverine systems: Study of a Neotropical fish of the Brazilian coastal Atlantic Forest. J. Biogeogr. 42, 2389–2401. https://doi.org/10.1111/jbi.12597 (2015).Article 

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

Google Scholar 
Kumar, S., Stecher, G., Li, M., Knyaz, C. & Tamura, K. MEGA X: Molecular evolutionary genetics analysis across computing platforms. Mol. Biol. Evol. 35, 1547–1549. https://doi.org/10.1093/molbev/msy096 (2018).CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
Guillot, G., Renaud, S., Ledevin, R., Michaux, J. & Claude, J. A unifying model for the analysis of phenotypic, genetic and geograhic data. Syst. Biol. 61(6), 897–911. https://doi.org/10.1093/sysbio/sys038 (2012).Article 
PubMed 

Google Scholar 
Excoffier, L., Laval, G. & Schneider, S. Arlequin: A Software for Population Data Analysis. Version 3.1. http://cmpg.unibe.ch/software/arlequin3 (2007).Wright, S. Evolution and the genetics of populations: Variability within and among natural populations. Univ. Chicago 4, 580 (1978).
Google Scholar 
Rozas, J. et al. DnaSP 6: DNA sequence polymorphism analysis of large datasets. Mol. Biol. Evol. 34, 3299–3302. https://doi.org/10.1093/molbev/msx248 (2017).CAS 
Article 
PubMed 

Google Scholar 
Bandelt, H. J., Forster, P. & Röhl, A. Median-joining networks for inferring intraspecific phylogenies. Mol. Biol. Evol. 16(1), 37–48 (1999).CAS 
Article 

Google Scholar 
Leigh, J. W. & Bryant, D. POPART: Full-feature software for haplotype network construction. Methods Ecol. Evol. 6, 1110–1116. https://doi.org/10.1111/2041-210X.12410 (2015).Article 

Google Scholar 
Tajima, F. Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics 123, 585–595 (1989).CAS 
Article 

Google Scholar 
Fu, Y. X. Statistical tests of neutrality of mutations against population growth, hitchhiking and background selection. Genetics 147, 915–925 (1997).CAS 
Article 

Google Scholar 
Austin, M. P. Continuum concept, ordination methods, and niche theory. Annu. Rev. Ecol. Syst. 16(1), 39–61. https://doi.org/10.1146/annurev.es.16.110185.000351 (1985).MathSciNet 
Article 

Google Scholar 
Graham, A., Atkinson, P. & Danson, F. Spatial analysis for epidemiology. Acta Trop. 91(3), 219–225. https://doi.org/10.1016/j.actatropica.2004.05.001 (2004).CAS 
Article 
PubMed 

Google Scholar 
Phillips, S. J., Anderson, R. P. & Schapire, R. E. Maximum entropy modeling of species geographic distributions. Ecol. Model. 190(3–4), 231–259. https://doi.org/10.1016/j.ecolmodel.2005.03.026 (2006).Article 

Google Scholar 
Guimarães, K. L. A., Rosso, J. J., Souza, M. F. B., de Astarloa, J. M. D. & Rodrigues, L. R. R. Integrative taxonomy reveals disjunct distribution and first record of Hoplias misionera (Characiformes: Erythrinidae) in the Amazon River basin: Morphological, DNA barcoding and cytogenetic considerations. Neotrop. Ichthyol. 19(2), e200110. https://doi.org/10.1590/1982-0224-2020-0110 (2021).Article 

Google Scholar 
Queiroz, L. J. et al. Evolutionary units delimitation and continental multilocus phylogeny of the hyperdiverse catfish genus Hypostomus. Mol. Phylogenet. Evol. 145, 106711. https://doi.org/10.1016/j.ympev.2019.106711 (2020).Article 

Google Scholar 
Phillips, J. D., Gillis, D. J. & Hanner, R. H. Incomplete estimates of genetic diversity within species: Implications for DNA barcoding. Ecol. Evol. https://doi.org/10.1002/ece3.4757 (2019).Article 
PubMed 
PubMed Central 

Google Scholar 
Blaxter, M. L. The promise of a DNA taxonomy. Philos. Trans. R. Soc. B. 359(1444), 669–679. https://doi.org/10.1098/rstb.2003.1447 (2004).CAS 
Article 

Google Scholar 
Nwani, C. D. et al. DNA barcoding discriminates freshwater fishes from southeastern Nigeria and provides river system-level phylogeographic resolution within some species. Mitochondrial DNA 22(1), 43–51. https://doi.org/10.3109/19401736.2010.536537 (2011).CAS 
Article 
PubMed 

Google Scholar 
Aguirre, W. E., Shervette, V. R., Navarrete, R., Calle, P. & Agorastos, S. Morphological and genetic divergence of Hoplias microlepis (Characiformes: Erythrinidae) in rivers and artificial impoundments of Western Ecuador. Copeia 2013(2), 312–323. https://doi.org/10.1643/ci-12-083 (2013).Article 

Google Scholar 
Pires, W. M. M., Barros, M. C. & Fraga, E. C. DNA Barcoding unveils cryptic lineages of Hoplias malabaricus from Northeastern Brazil. Braz. J. Biol. 81(4), 917–927. https://doi.org/10.1590/1519-6984.231598 (2020).Article 

Google Scholar 
Souza, F. H. S. et al. interspecific genetic differences and historical demography in South American Arowanas (Osteoglossiformes, Osteoglossidae, Osteoglossum). Genes 10(9), 693. https://doi.org/10.3390/genes10090693 (2019).CAS 
Article 
PubMed Central 

Google Scholar 
Torati, L. S. et al. Genetic diversity and structure in Arapaima gigas populations from Amazon and Araguaia-Tocantins river basins. BMC Genet. https://doi.org/10.1186/s12863-018-0711-y (2019).Article 
PubMed 
PubMed Central 

Google Scholar 
Lovejoy, N. R. & Araujo, M. L. G. Molecular systematics, biogeography and population structure of Neotropical freshwater needlefishes of the genus Potamorrhaphis. Mol. Ecol. 9(3), 259–268. https://doi.org/10.1046/j.1365-294x.2000.00845.x (2000).CAS 
Article 
PubMed 

Google Scholar 
Mabesoone, J. M. Sedimentary Basins of Northeast Brazil (Federal University of Pernambuco, 1994).
Google Scholar 
Haffer, J. & Prance, G. T. Impulsos climáticos da evolução na Amazônia durante o Cenozóico: Sobre a teoria dos Refúgios da diferenciação biótica. Estudos Avançados USP 46, 175–208. https://doi.org/10.1590/S0103-40142002000300014 (2002).Article 

Google Scholar 
Riker, S. R. L., Lima, F. J. C., Motta, M. B. Evidências de glaciação Pleistocênica na Amazônia Brasileira. Anais do 14° Simpósio de Geologia da Amazônia, Sociedade Brasileira de Geologia 15–18 (2015).Albert, J. S., Val, P. & Hoorn, C. The changing course of the Amazon River in the Neogene: Center stage for Neotropical diversification. Neotrop. Ichthyol. 16(3), e180033. https://doi.org/10.1590/1982-0224-20180033 (2018).Article 

Google Scholar 
Lundberg, J. G. et al. The stage for Neotropical fish diversification: a history of tropical South American rivers. (eds. Malabarba, L. R., Reis, R. E., Vari, R. P., Lucena, Z. M., Lucena, C. A. S. Phylogeny and classification of Neotropical fishes). Edipucrs 13–48 (1998).Hubert, N. & Renno, J. F. Historical biogeography of South American freshwater fishes. J. Biogeogr. 33(8), 1414–1436. https://doi.org/10.1111/j.1365-2699.2006.01518.x (2006).Article 

Google Scholar 
Farias, I. P. & Hrbek, T. Patterns of diversification in the discus fishes (Symphysodon spp. Cichlidae) of the Amazon basin. Mol. Phylogenet. Evol. 49, 32–43. https://doi.org/10.1016/j.ympev.2008.05.033 (2008).CAS 
Article 
PubMed 

Google Scholar 
Tagliacollo, V. A., Bernt, M. J., Craig, J. M., Oliveira, C. & Albert, J. S. Model-based total evidence phylogeny of Neotropical electric knifefishes (Teleostei, Gymnoti-formes). Mol. Phylogenet. Evol. 95, 20–33. https://doi.org/10.1016/j.ympev.2015.11.007 (2015).Article 
PubMed 

Google Scholar 
Hutchinson, G. E. Concluding remarks. Cold Spring Harbor Symposium. Quant. Biol. 22, 415–427 (1957).Article 

Google Scholar 
Wiens, J. J. & Graham, C. H. Niche conservatism: Inte-grating evolution, ecology, and conservation biology. Annu. Rev. Ecol. Evol. Syst. 36, 519–539 (2005).Article 

Google Scholar 
McNyset, K. M. Ecological niche conservatism in North American freshwater fishes. Biol. J. Lin. Soc. 96, 282–295 (2009).Article 

Google Scholar 
Silva, W. C., Marceniuk, A. P., Sales, J. B. L. & Araripe, J. Early pleistocene lineages of Bagre bagre (Linnaeus, 1766) (Siluriformes: Ariidae), from the Atlantic coast of South America, with insights into the demography and biogeography of the species. Neotrop. Ichthyol. https://doi.org/10.1590/1982-0224-20150184 (2016).Article 

Google Scholar 
Lemopoulos, A. & Covain, R. Biogeography of the freshwater fishes of the Guianas using a partitioned parsimony analysis of endemicity with reappraisal of ecoregional boundaries. Cladistics 35(2019), 106–124. https://doi.org/10.1111/cla.12341 (2018).Article 
PubMed 

Google Scholar 
Hoorn, C. Marine incursions and the influence of Andean tectonics on the Miocene depositional history of northwestern Amazonia: Results of a palynostratigraphic study. Palaeogeogr. Palaeoclimatol. Palaeoecol. 105, 267–309. https://doi.org/10.1016/0031-0182(93)90087-Y (1993).Article 

Google Scholar 
Hoorn, C., Guerreiro, J. & Sarmiento, G. Andean tectonics as a cause for changing drainage patterns in Miocene Northern South America. Geology 23(3), 237–240. https://doi.org/10.1130/0091-7613(1995)023%3c0237:ATAACF%3e2.3.CO;2 (1995).ADS 
Article 

Google Scholar 
Ribeiro, A. C. Tectonic history and the biogeography of the freshwater fishes from the coastal drainages of eastern Brazil: An example of faunal evolution associated with a divergent continental margin. Neotrop. Ichthyol. 4(2), 225–246. https://doi.org/10.1590/S1679-62252006000200009 (2006).Article 

Google Scholar 
Lovejoy, N. R., Albert, J. S. & Crampton, W. G. R. Miocene marine incursions and marine/freshwater transitions: Evidence from Neotropical fishes. J. S. Am. Earth Sci. 21(1–2), 5–13. https://doi.org/10.1016/j.jsames.2005.07.009 (2006).Article 

Google Scholar  More

.readcube-buybox { display: none !important;}

Swarms of ‘crazy ants’ that invade houses, cause electrical short circuits and overrun birds’ nests might have met their match: a naturally occurring parasite1.

Access options

Access through your institution

Change institution

Buy or subscribe

/* style specs start */
style{display:none!important}.LiveAreaSection-193358632 *{align-content:stretch;align-items:stretch;align-self:auto;animation-delay:0s;animation-direction:normal;animation-duration:0s;animation-fill-mode:none;animation-iteration-count:1;animation-name:none;animation-play-state:running;animation-timing-function:ease;azimuth:center;backface-visibility:visible;background-attachment:scroll;background-blend-mode:normal;background-clip:borderBox;background-color:transparent;background-image:none;background-origin:paddingBox;background-position:0 0;background-repeat:repeat;background-size:auto auto;block-size:auto;border-block-end-color:currentcolor;border-block-end-style:none;border-block-end-width:medium;border-block-start-color:currentcolor;border-block-start-style:none;border-block-start-width:medium;border-bottom-color:currentcolor;border-bottom-left-radius:0;border-bottom-right-radius:0;border-bottom-style:none;border-bottom-width:medium;border-collapse:separate;border-image-outset:0s;border-image-repeat:stretch;border-image-slice:100%;border-image-source:none;border-image-width:1;border-inline-end-color:currentcolor;border-inline-end-style:none;border-inline-end-width:medium;border-inline-start-color:currentcolor;border-inline-start-style:none;border-inline-start-width:medium;border-left-color:currentcolor;border-left-style:none;border-left-width:medium;border-right-color:currentcolor;border-right-style:none;border-right-width:medium;border-spacing:0;border-top-color:currentcolor;border-top-left-radius:0;border-top-right-radius:0;border-top-style:none;border-top-width:medium;bottom:auto;box-decoration-break:slice;box-shadow:none;box-sizing:border-box;break-after:auto;break-before:auto;break-inside:auto;caption-side:top;caret-color:auto;clear:none;clip:auto;clip-path:none;color:initial;column-count:auto;column-fill:balance;column-gap:normal;column-rule-color:currentcolor;column-rule-style:none;column-rule-width:medium;column-span:none;column-width:auto;content:normal;counter-increment:none;counter-reset:none;cursor:auto;display:inline;empty-cells:show;filter:none;flex-basis:auto;flex-direction:row;flex-grow:0;flex-shrink:1;flex-wrap:nowrap;float:none;font-family:initial;font-feature-settings:normal;font-kerning:auto;font-language-override:normal;font-size:medium;font-size-adjust:none;font-stretch:normal;font-style:normal;font-synthesis:weight style;font-variant:normal;font-variant-alternates:normal;font-variant-caps:normal;font-variant-east-asian:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-position:normal;font-weight:400;grid-auto-columns:auto;grid-auto-flow:row;grid-auto-rows:auto;grid-column-end:auto;grid-column-gap:0;grid-column-start:auto;grid-row-end:auto;grid-row-gap:0;grid-row-start:auto;grid-template-areas:none;grid-template-columns:none;grid-template-rows:none;height:auto;hyphens:manual;image-orientation:0deg;image-rendering:auto;image-resolution:1dppx;ime-mode:auto;inline-size:auto;isolation:auto;justify-content:flexStart;left:auto;letter-spacing:normal;line-break:auto;line-height:normal;list-style-image:none;list-style-position:outside;list-style-type:disc;margin-block-end:0;margin-block-start:0;margin-bottom:0;margin-inline-end:0;margin-inline-start:0;margin-left:0;margin-right:0;margin-top:0;mask-clip:borderBox;mask-composite:add;mask-image:none;mask-mode:matchSource;mask-origin:borderBox;mask-position:0% 0%;mask-repeat:repeat;mask-size:auto;mask-type:luminance;max-height:none;max-width:none;min-block-size:0;min-height:0;min-inline-size:0;min-width:0;mix-blend-mode:normal;object-fit:fill;object-position:50% 50%;offset-block-end:auto;offset-block-start:auto;offset-inline-end:auto;offset-inline-start:auto;opacity:1;order:0;orphans:2;outline-color:initial;outline-offset:0;outline-style:none;outline-width:medium;overflow:visible;overflow-wrap:normal;overflow-x:visible;overflow-y:visible;padding-block-end:0;padding-block-start:0;padding-bottom:0;padding-inline-end:0;padding-inline-start:0;padding-left:0;padding-right:0;padding-top:0;page-break-after:auto;page-break-before:auto;page-break-inside:auto;perspective:none;perspective-origin:50% 50%;pointer-events:auto;position:static;quotes:initial;resize:none;right:auto;ruby-align:spaceAround;ruby-merge:separate;ruby-position:over;scroll-behavior:auto;scroll-snap-coordinate:none;scroll-snap-destination:0 0;scroll-snap-points-x:none;scroll-snap-points-y:none;scroll-snap-type:none;shape-image-threshold:0;shape-margin:0;shape-outside:none;tab-size:8;table-layout:auto;text-align:initial;text-align-last:auto;text-combine-upright:none;text-decoration-color:currentcolor;text-decoration-line:none;text-decoration-style:solid;text-emphasis-color:currentcolor;text-emphasis-position:over right;text-emphasis-style:none;text-indent:0;text-justify:auto;text-orientation:mixed;text-overflow:clip;text-rendering:auto;text-shadow:none;text-transform:none;text-underline-position:auto;top:auto;touch-action:auto;transform:none;transform-box:borderBox;transform-origin:50% 50% 0;transform-style:flat;transition-delay:0s;transition-duration:0s;transition-property:all;transition-timing-function:ease;vertical-align:baseline;visibility:visible;white-space:normal;widows:2;width:auto;will-change:auto;word-break:normal;word-spacing:normal;word-wrap:normal;writing-mode:horizontalTb;z-index:auto;-webkit-appearance:none;-moz-appearance:none;-ms-appearance:none;appearance:none;margin:0}.LiveAreaSection-193358632{width:100%}.LiveAreaSection-193358632 .login-option-buybox{display:block;width:100%;font-size:17px;line-height:30px;color:#222;padding-top:30px;font-family:Harding,Palatino,serif}.LiveAreaSection-193358632 .additional-access-options{display:block;font-weight:700;font-size:17px;line-height:30px;color:#222;font-family:Harding,Palatino,serif}.LiveAreaSection-193358632 .additional-login >li:not(:first-child)::before{transform:translateY(-50%);content:”;height:1rem;position:absolute;top:50%;left:0;border-left:2px solid #999}.LiveAreaSection-193358632 .additional-login >li:not(:first-child){padding-left:10px}.LiveAreaSection-193358632 .additional-login >li{display:inline-block;position:relative;vertical-align:middle;padding-right:10px}.BuyBoxSection-683559780{display:flex;flex-wrap:wrap;flex:1;flex-direction:row-reverse;margin:-30px -15px 0}.BuyBoxSection-683559780 .box-inner{width:100%;height:100%}.BuyBoxSection-683559780 .readcube-buybox{background-color:#f3f3f3;flex-shrink:1;flex-grow:1;flex-basis:255px;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .subscribe-buybox{background-color:#f3f3f3;flex-shrink:1;flex-grow:4;flex-basis:300px;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .subscribe-buybox-nature-plus{background-color:#f3f3f3;flex-shrink:1;flex-grow:4;flex-basis:100%;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .title-readcube{display:block;margin:0;margin-right:20%;margin-left:20%;font-size:24px;line-height:32px;color:#222;padding-top:30px;text-align:center;font-family:Harding,Palatino,serif}.BuyBoxSection-683559780 .title-buybox{display:block;margin:0;margin-right:29%;margin-left:29%;font-size:24px;line-height:32px;color:#222;padding-top:30px;text-align:center;font-family:Harding,Palatino,serif}.BuyBoxSection-683559780 .title-asia-buybox{display:block;margin:0;margin-right:5%;margin-left:5%;font-size:24px;line-height:32px;color:#222;padding-top:30px;text-align:center;font-family:Harding,Palatino,serif}.BuyBoxSection-683559780 .asia-link{color:#069;cursor:pointer;text-decoration:none;font-size:1.05em;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:1.05em6}.BuyBoxSection-683559780 .access-readcube{display:block;margin:0;margin-right:10%;margin-left:10%;font-size:14px;color:#222;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .access-asia-buybox{display:block;margin:0;margin-right:5%;margin-left:5%;font-size:14px;color:#222;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .access-buybox{display:block;margin:0;margin-right:30%;margin-left:30%;font-size:14px;color:#222;opacity:.8px;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .usps-buybox{display:block;margin:0;margin-right:30%;margin-left:30%;font-size:14px;color:#222;opacity:.8px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .price-buybox{display:block;font-size:30px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;padding-top:30px;text-align:center}.BuyBoxSection-683559780 .price-from{font-size:14px;padding-right:10px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .issue-buybox{display:block;font-size:13px;text-align:center;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:19px}.BuyBoxSection-683559780 .no-price-buybox{display:block;font-size:13px;line-height:18px;text-align:center;padding-right:10%;padding-left:10%;padding-bottom:20px;padding-top:30px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif}.BuyBoxSection-683559780 .vat-buybox{display:block;margin-top:5px;margin-right:20%;margin-left:20%;font-size:11px;color:#222;padding-top:10px;padding-bottom:15px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:17px}.BuyBoxSection-683559780 .button-container{display:flex;padding-right:20px;padding-left:20px;justify-content:center}.BuyBoxSection-683559780 .button-container >*{flex:1px}.BuyBoxSection-683559780 .button-container >a:hover,.Button-505204839:hover,.Button-1078489254:hover,.Button-2808614501:hover{text-decoration:none}.BuyBoxSection-683559780 .readcube-button{background:#fff;margin-top:30px}.BuyBoxSection-683559780 .button-asia{background:#069;border:1px solid #069;border-radius:0;cursor:pointer;display:block;padding:9px;outline:0;text-align:center;text-decoration:none;min-width:80px;margin-top:75px}.BuyBoxSection-683559780 .button-label-asia,.ButtonLabel-3869432492,.ButtonLabel-3296148077,.ButtonLabel-1566022830{display:block;color:#fff;font-size:17px;line-height:20px;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;text-align:center;text-decoration:none;cursor:pointer}.Button-505204839,.Button-1078489254,.Button-2808614501{background:#069;border:1px solid #069;border-radius:0;cursor:pointer;display:block;padding:9px;outline:0;text-align:center;text-decoration:none;min-width:80px;max-width:320px;margin-top:10px}.Button-505204839 .readcube-label,.Button-1078489254 .readcube-label,.Button-2808614501 .readcube-label{color:#069}
/* style specs end */Subscribe to Nature+Get immediate online access to the entire Nature family of 50+ journals$29.99monthlySubscribeSubscribe to JournalGet full journal access for 1 year$199.00only $3.90 per issueSubscribeAll prices are NET prices. VAT will be added later in the checkout.Tax calculation will be finalised during checkout.Buy articleGet time limited or full article access on ReadCube.$32.00BuyAll prices are NET prices.

Additional access options:

Log in

Learn about institutional subscriptions

doi: https://doi.org/10.1038/d41586-022-00888-9

ReferencesLeBrun, E. G., Jones, M., Plowes, R. M. & Gilbert, L. E. Proc. Natl Acad. Sci. USA 119, e2114558119 (2022).PubMed 
Article 

Google Scholar 
Download references

Subjects

Ecology

Latest on:

Ecology

Dozens of unidentified bat species likely live in Asia — and could host new viruses
News 29 MAR 22

The marine biologist whose photography pastime became a profession
Career Column 25 MAR 22

Subaqueous foraging among carnivorous dinosaurs
Article 23 MAR 22

Jobs

Research Associate / Postdoc (m/f/x)

Technische Universität Dresden (TU Dresden)
01069 Dresden, Germany

wiss. Mitarbeiter/in (m/w/d)

Technische Universität Dresden (TU Dresden)
01069 Dresden, Germany

Postdoctoral Researchers in AI for Medical Data Science

University of Luxembourg
Luxembourg, Luxembourg

Postdoc – Ultra-high vacuum lithography of high-performance superconducting qubits

Jülich Research Centre (FZJ)
Jülich, Germany More

If you are a scientist hoping to photograph and share your own research:
•    Don’t underestimate the power of modern media and social-media platforms. Content is changing the world and people’s lives, and it can easily change your life. Stay at the forefront of media technology, or at least be aware of developments. It’s a never-ending race, but it’s easy to get into.
•    If you plan to share your work with others, imagine what will be of interest to them. If you can excitingly describe your work to a 5-year-old, you won’t have any trouble getting anyone interested. Beautiful pictures help, but the story always comes first.

•    You will stand out much more if you have a niche and unique story. It could be your rare field of science or a special angle that you use to tell the story of your work. Being different is awesome.
•    Set the bar very high. You can find dozens of examples of truly high-quality content on the Internet. And you can almost always find resources that can help you to learn how to create work of the same calibre. With practice, your skills will inevitably rise — but at any given time, it’s important to know the level you should aim for.
•    Find people who are cooler than you. Don’t hesitate to ask them for advice or to shadow them. Have them share their experiences, stand behind them and observe their work if they’ll let you. Few things are more useful than real work experience, both your own and that of others.
•    Take on a project. This could be a an illustrated workbook for colleagues or students, a guide book, a lecture for schoolchildren with compelling visuals, a course for students or a documentary on your topic.
•    If you work in a team, you can raise the bar even higher. Use each other’s strengths, share experiences, make plans, apply for grants and take on challenging science-communication projects together. This multiplies the fun and the results. More

ModelsConsider an IPD game with misperception such as implementation errors and observation errors22,23,31. Due to the misperception, the parameter in the real game changes from (omega _1=[T_1,R_1,P_1,S_1]) to (omega _2=[T_2,R_2,P_2,S_2]), and only player X notices the change. Thus, player Y’s cognition of the parameter is (omega _1), while player X’s cognition of the parameter is (omega _2). In each round, player X chooses a strategy from its strategy set (Omega _X={{mathbf {p}}=[p_{cc},p_{cd},p_{dc},p_{dd}]^T|p_{xy} in [0,1],xyin {cc,cd,dc,dd}}), e.g., (p_{xy}) is player X’s probability for cooperating with given previous outcome (xyin {cc,cd,dc,dd}). Similar to (Omega _X), player Y’s strategy set is (Omega _Y={{mathbf {q}}=[q_{cc},q_{dc},q_{cd},q_{dd}]^T|q_{xy} in [0,1],xyin {cc,dc,cd,dd}}). According to Press and Dyson7, this game can be characterized by a Markov chain with a state transition matrix (M=[M_{jk}]_{4times 4}) (see “Notations” for details). Denote ({mathbf {v}}=[v_{cc},v_{cd},v_{dc},v_{dd}]^T) as a probability vector such that ({mathbf {v}}^T M={mathbf {v}}^T) and (v_{cc}+v_{cd}+v_{dc}+v_{dd}=1). Let ({mathbf {S}}^{omega _i}_{X}=[R_i,S_i,T_i,P_i]^T), and ({mathbf {S}}^{omega _i}_{Y}=[R_i,T_i,S_i,P_i]^T,) (iin {1,2}). The expected utility functions of players are as follows:$$begin{aligned} begin{aligned} u_X^{omega _i}({mathbf {p}},{mathbf {q}})={mathbf {v}} cdot {mathbf {S}}^{omega _i}_{X}, u_Y^{omega _i}({mathbf {p}},{mathbf {q}})={mathbf {v}} cdot {mathbf {S}}^{omega _i}_{Y},iin {1,2}. end{aligned} end{aligned}$$Denote (G_1 = {{mathbf {P}}, {varvec{Omega }}, {mathbf {u}}, omega _1}), and (G_2={{mathbf {P}},{varvec{Omega }},{mathbf {u}},omega _2}), where ({mathbf {P}}={X,Y}), ({varvec{Omega }}=Omega _Xtimes Omega _Y), and ({mathbf {u}}={u_X^{omega _i},u_Y^{omega _i}}, iin {1,2}). Thus, the actual utilities of players are obtained through (G_2), and in the view of player Y, they are playing game (G_1). In the view of player X, they are playing game (G_2) but player X knows that player Y’s cognition is (G_1). (G_1) and (G_2) are shown in Table 2.Table 2 Utility matrices in IPD games with misperception.Full size tableLet ({mathbf {p}}_0=[1,1,0,0]^T). For (iin {1,2}), ({mathbf {p}}=alpha {mathbf {S}}^{omega _i}_{X} +beta {mathbf {S}}^{omega _i}_Y +gamma {mathbf {1}}+{mathbf {p}}_0), where (alpha ,beta ,gamma in {mathbb {R}}), is called a ZD strategy7 of player X in (G_i) since the strategy makes the two players’ expected utilities subjected to a linear relation:$$begin{aligned} alpha u_X^{omega _i}({mathbf {p}},{mathbf {q}})+beta u_Y^{omega _i}({mathbf {p}},{mathbf {q}})+gamma =0, end{aligned}$$for any player Y’s strategy ({mathbf {q}}). All available ZD strategies for player X in G can be expressed as (Xi (omega _i)={{mathbf {p}}in Omega _X|{mathbf {p}}=alpha {mathbf {S}}^{omega _i}_{X} +beta {mathbf {S}}^{omega _i}_Y +gamma {mathbf {1}}+{mathbf {p}}_0,alpha ,beta ,gamma in {mathbb {R}} }.) Also, the three special ZD strategies are denoted as:

(1)

equalizer strategy7,12: ({mathbf {p}}=beta {mathbf {S}}^{omega _i}_{Y}+gamma {mathbf {1}}+{mathbf {p}}_0);

(2)

extortion strategy7,13: ({mathbf {p}}=phi [({mathbf {S}}^{omega _i}_X-P_i{mathbf {1}})-chi ({mathbf {S}}^{omega _i}_Y-P_i{mathbf {1}})]+{mathbf {p}}_0,chi geqslant 1);

(3)

generous strategy14,15: ({mathbf {p}}=phi [({mathbf {S}}^{omega _i}_X-R_i{mathbf {1}})-chi ({mathbf {S}}^{omega _i}_Y-R_i{mathbf {1}})] +{mathbf {p}}_0,chi geqslant 1).

Based on the past experience, player Y knows that player X prefers ZD strategies, which has been widely considered in many IPD games7,9. To avoid that player Y notices the change, which may result in potential decrease of player X’s utility21 or collapse of the model28, player X keeps choosing ZD strategies according to (G_1), such that the strategy sequence matches player Y’s anticipation. To sum up, in our formulation,

the real game is (G_2);

player Y thinks that they are playing game (G_1), and player X thinks that they are playing game (G_2);

player X knows that player Y’s cognition is (G_1);

player Y believes that player X chooses ZD strategies;

player X tends to choose a ZD strategy according to (G_1) to avoid player Y’s suspicion of misperception.

In fact, player X can benefit from the misperception through the ZD strategy. For example, player X can adopt a generous strategy in (G_1) to not only promote player Y’s cooperation behavior, but also make player X’s utility higher than that of player Y, if the generous strategy is an extortion strategy in (G_2). A beneficial strategy for player X is able to maintain a linear relationship between players’ utilities or improve the supremum or the infimum of its utility in its own cognition. In the following, we aim to analyze player X’s implementation of a ZD strategy in IPD with misperception, and proofs are given in the Supplementary Information.Invariance of ZD strategyPlayer X’s ZD strategies may be kept in IPD games with misperception from implementation errors or observation errors. In particular, player X keeps choosing a ZD strategy ({mathbf {p}}) in (G_1) to avoid player Y’s suspicion about possible misperception. In the view of player X, it can also enforce players’ expected utilities subjected to a linear relationship if ({mathbf {p}}) is also a ZD strategy in (G_2). The following theorem provides a necessary and sufficient condition for the invariance of the linear relationship between players’ utilities.Theorem 1
Any ZD strategy ({mathbf {p}}) of player X in (G_1) is also a ZD strategy in (G_2) if and only if$$begin{aligned} frac{R_1-P_1}{2R_1-S_1-T_1}=frac{R_2-P_2}{2R_2-S_2-T_2}. end{aligned}$$
(1)

If (1) holds, player X can ignore the misperception and choose an arbitrary ZD strategy based on its opponent’s anticipation since it also leads to a linear relationship between players’ utilities, as shown in Fig. 1; otherwise, player X can not unscrupulously choose ZD strategies based on player Y’s cognition. There is a player X’s ZD strategy in player Y’s cognition which is not the ZD strategy in player X’s cognition. Further, because of the symmetry of (omega _1) and (omega _2), player X’s any available ZD strategy ({mathbf {p}}) in (G_2) is also a ZD strategy in (G_1) if and only if (1) holds. It indicates that (Xi (omega _1)=Xi (omega _2)) and player X can choose any ZD strategy based on its own cognition, which does not cause suspicion of the opponent since it is also consistent with player Y’s anticipation. Additionally, the slopes of linear relations between players’ utilities may be different, as also shown in Fig. 1, and player X can benefit from the misperception by choosing a ZD strategy to improve the corresponding slope.In fact, (1) covers the following two cases:

(1)

(2P_i=T_i+S_i), (iin {1,2}), is a sufficient condition of (1). Thus, when (2P_i=T_i+S_i), (iin {1,2}), player X’s any ZD strategy ({mathbf {p}}) in (G_1) is also a ZD strategy in (G_2). Actually, (2P_i=T_i+S_i), (iin {1,2}), means that the sum of players’ utilities when players mutual defect is equal to that when only one player chooses defective strategies.

(2)

(R_i+P_i=T_i+S_i), (iin {1,2}), is another sufficient condition of (1). Thus, when (R_i+P_i=T_i+S_i), (iin {1,2}), player X’s any ZD strategy ({mathbf {p}}) in (G_1) is also a ZD strategy in (G_2). Actually, (R_i+P_i=T_i+S_i), (iin {1,2}), means that the game has a balanced structure in utilities32. At this point, the relationship between cooperation rate and efficiency is monotonous, i.e., the higher the cooperation rate of both sides, the greater the efficiency (the sum of players’ utilities).

Furthermore, for the three special ZD strategies, player X can also maintain a linear relationship between players’ utilities in the IPD game with misperception.Figure 1Player X can also enforce a linear relationship between players’ utilities in its own cognition. Let (omega _1=[T,R_1,P_1,S]=[5,3,1,0]) and (omega _2=[T,R_2,P_2,S]=[5,frac{23}{7},frac{1}{7},0]), which satisfy (1). Consider that player X chooses two different ZD strategies in (a) and (b), respectively, and the red lines describe the relationships between players’ utilities in (G_1). We randomly generate 100 player Y’s strategies, and blue circles are ((u^{omega _2}_X,u^{omega _2}_Y)), correspondingly. Notice that blue circles are indeed on a cyan line in both (a) and (b).Full size imageEqualizer strategyBy choosing equalizer strategies according to player Y’s cognition, player X can unilaterally set player Y’s utilities, as shown in the following corollary.
Corollary 1
Player X’s any equalizer strategy ({mathbf {p}}) in (G_1) is also an equalizer strategy in (G_2) if and only if$$begin{aligned} frac{R_1-P_1}{R_2-P_2}=frac{R_1-T_1}{R_2-T_2}=frac{R_1-S_1}{R_2-S_2}. end{aligned}$$
(2)

(2) is also a sufficient condition of (1). If (2) holds, player X can unilaterally set player Y’s utility by choosing any equalizer strategy in (G_1) even though they have different cognitions; otherwise, player X can not unscrupulously choose an equalizer strategy based on player Y’s cognition since it may not be an equalizer strategy in player X’s cognition.Extortion strategyBy choosing extortion strategies according to player Y’s cognition, player X can get an extortionate share, as shown in the following corollary.
Corollary 2
For player X’s extortion strategy ({mathbf {p}}) with extortion factor (chi >1) in (G_1), ({mathbf {p}}) is also an extortion strategy in (G_2) if (1) and the following inequality hold:$$begin{aligned} begin{aligned} (S_1-P_1)(R_2-P_2)-(R_1-P_1)(T_2-P_2)-chi ((T_1-P_1)(R_2-P_2)-(R_1-P_1)(T_2-P_2))1) in (G_1), ({mathbf {p}}) is also a generous strategy in (G_2) if (1) and the following inequality hold:$$begin{aligned} begin{aligned}(S_1-R_1)(R_2-P_2)-(R_1-P_1)(T_2-R_2)-chi ((T_1-R_1)(R_2-P_2)-(R_1-P_1)(T_2-R_2))b^1_i, iin {1,2}, end{aligned} end{aligned}$$
(5)
where (a^1_i) and (b^1_i,iin {1,2}) are parameters shown in “Notations”.
Actually, when player Y chooses the always cooperate (ALLC) strategy35, i.e., ({mathbf {q}}=[1,1,1,1]^T), player X gets the supremum of the expected utility in (G_1) and player X’s utility is improved in the IPD game with misperception.Figure 4Player X can use either equalizer strategies and extortion strategies to raise the supremum of its expected utility or generous strategies to raise the infimum of its expected utility. (a) and (b) consider that (omega _1=[T,R_1,P,S]) and (omega _2=[T,R_2,P,S]), where (R_1ne R_2); (c) considers that (omega _1=[T,R,P_1,S]) and (omega _2=[T,R,P_2,S]), where (P_1ne P_2). The red lines in (a), (b), and (c) describe utilities’ relationships when player X chooses an equalizer strategy, an extortion strategy, and a generous strategy in (G_1), respectively; The yellow area contains all possible relationships between players’ utilities in (G_2) if player X does not change its strategy. In (a) and (b), r is the supremum of player X’s utility in (G_1), and (r’) is lower than the supremum of player X’s utility in (G_2); In (c), l is the infimum of player X’s utility in (G_1), and (l’) is lower than the infimum of player X’s utility in (G_2).Full size imageExtortion strategyBy choosing extortion strategies according to player Y’s cognition, player X can also improve the supremum of its expected utility.
Corollary 5
For player X’s extortion strategy ({mathbf {p}}) with extortion factor (chi >1) in (G_1), the supremum of player X’s expected utility in (G_2) is larger than that in (G_1) if$$begin{aligned} begin{aligned}a^2_ichi ^2+b^2_ichi +c^2_i1), the infimum of player X’s expected utility in (G_2) is larger than that in (G_1) if$$begin{aligned} begin{aligned}a^3_ichi ^2+b^3_ichi +c^3_i More

Tsering, D. Transport development in Tibet since the democratic reform in 1959. J. Tibetan Stud. 76–85 (2019).Yan, X. et al. Relationships between heavy metal concentrations in roadside topsoil and distance to road edge based on field observations in the Qinghai-Tibet Plateau, China. Int. J. Environ. Res. Public Health. 10(3), 762–765 (2013).CAS 
PubMed 
PubMed Central 

Google Scholar 
Berling-Wolff, S. & Jianguo, W. U. Modeling urban landscape dynamics: A case study in Phoenix, USA. J. Urban Ecosyst. 7(3), 215–240 (2004).
Google Scholar 
Jianzhou, G., Yansui, L. & Beicheng, X. Spatial heterogeneity of urban land-cover landscape in Guangzhou from 1990 to 2005. J. Geogr. Sci. 19(2), 213–224 (2009).
Google Scholar 
Pan, L., Zhang, H. & Liu, A. Analysis of threshold of road networks effecting landscape fragmentation in Chongqing. J. Ecol. Sci. 34(5), 45–51 (2015).CAS 

Google Scholar 
Paukert, C. P., Pitts, K. L., Whittier, J. B. & Oldenc, J. D. Development and assessment of a landscape-scale ecological threat index for the Lower Colorado River Basin. J. Ecol. Indic. 11(2), 304–310 (2011).
Google Scholar 
Li, H., Yu, Q., Li, N., Wang, J. & Yang, Y. Study on landscape dynamics and driving mechanisms of the Shudu Lake catchment wetlands in Northwest Yunnan. J. West China Forest. Sci. 42(3), 34–39 (2013).Yunqing, H., Jinxi, W. & Hong, J. The dynamics of land cover change pattern and landscape fragmentation in Jiuzhaigou Nature Reserve, China. J. Proc. SPIE Int. Soc. Opt. Eng. 7498, 74983P (2009).Hu, L. et al. Landscape pattern in Nanwenghe nature reserve and its driving forces. J. Protect. Forest Sci. Technol. 0(7), 18–21 (2015).Li, X. et al. Land use/cover and landscape pattern changes in Manas River Basin based on remote sensing. J. Int. J. Agric. Biol. Eng. 13(5), 141–152 (2020).Andrejs, R. & Merkurjevs, J. Software tool implementing the fuzzy AHP method in ecological risk assessment. J. Inform. Technol. Manag. Sci. 20(1), 34–39 (2017).Peng, J., Dang, W., Liu, Y., Zong, M. & Hu, X. Research progress and prospect of landscape ecological risk assessment. J. Acta Geogr. Sin. 70(04), 664–677 (2015).
Google Scholar 
Xu, Y., Fu, B. & Lü, H. Research on landscape pattern and ecological processes based on landscape models. J. Acta Ecol. Sin. 30(1), 212–220 (2010).
Google Scholar 
Forman, R. Road ecology: A solution for the giant embracing us. J. Landsc. Ecol. 13(4), 3–5 (1998).
Google Scholar 
Minxi, W., Shiliang, L., Baoshan, C. & Min, Y. Impacts of hydroelectric project construction on nature reserve and assessment. J. Acta Ecol. Sin. 28(4), 1663–1671 (2008).
Google Scholar 
Yang, K., Deng, X., Xue-Ling, L. I. & Wen, P. Impacts of hydroelectric cascade exploitation on river ecosystem and landscape: A review. J. Acta Ecol. Sin. 22(5), 1359–1367 (2011).
Google Scholar 
Chen, L. D., Wang, J. P., Jiang, C. L. & Zhang, H. P. Quantitative study on effect of linear project construction on landscape pattern along pipeline. J. Sci. Geogr. Sin. 30(2), 161–167 (2010).
Google Scholar 
Qianqian, H., Luomeng, C. & Shanlin, W. Impact of expressway on land use and landscape pattern: A case study of Putan Guai to Chenghao section of Inner Mongolia Provincial Highway 103. J. Environ. Protect. Sci. 35(05), 58–61 (2009).
Google Scholar 
Huang, Y., Li, Y. & Ying, H. Responses of Chongqing-Yi Expressway to land use change and landscape pattern. J. Nat. Resourc. 30(09), 1449–1460 (2015).
Google Scholar 
Keken, Z., Sebkova, M. & Skalos, J. Analyzing land cover change—The impact of the motorway construction and their operation on landscape structure. J. Geogr. Inform. Syst. 6(5), 559–571 (2014).Mengna, H. & Ting, M. Assessing the impacts of China’s road network on landscape fragmentation and protected areas. J. Geo-inform. Sci. 21(8), 1183–1195 (2019).
Google Scholar 
Mothorpe, C., Hanson, A. & Schnier, K. The impact of interstate highways on land use conversion. J. Ann. Reg. Sci. 51(3), 833–870 (2013).
Google Scholar 
Wu, C.-F., Lin, Y.-P., Chiang, L.-C. & Huang, T. Assessing highway’s impacts on landscape patterns and ecosystem services: a case study in Puli Township, Taiwan. J. Landsc. Urban Plan. 128, 60–71 (2014).
Google Scholar 
Jia, L., Lei, T. & Yan, S. H. Environmental impact analysis and control measures in tunnel construction. J. Appl. Mech. Mater. 90–93, 3250–3253 (2011).ADS 

Google Scholar 
Wang, M. Analysis of high-speed railway construction on ecological environment impact and environmental protection contribution. J. Railway Constr. Technol. https://doi.org/10.3969/j.issn.1009-4539.2015.04.019 (2015).Article 

Google Scholar 
He, Y. & Xiong, C. Environmental impact of waste slurry in pile foundation construction of high-speed railway bridges and its countermeasures. J. Adv. Mater. Res. 383–390, 3690–3694 (2011).
Google Scholar 
Jing, C. et al. Influence of cross-sea bridge project on water quality and ecological environment of nearby sea and its tracking, monitoring and verification. J. Ocean Dev. Manag. 37(10), 96–100 (2020).
Google Scholar 
Jianhua, X., Mingquan, W., Shijian, Z. & Zheng, N. Remote sensing monitoring of ecological and economic impacts of major Railway construction along the Belt and Road. J. Sci. Technol. Eng. 20(11), 9 (2020).
Google Scholar 
Fang, L. On ecological environment impact assessment of metal mine construction project. J. Nonferrous Metals (Min. Sect.). 64(03), 58–60 (2012).
Google Scholar 
Bian, B., Lin, C. & Wu, H. S. Contamination and risk assessment of metals in road-deposited sediments in a medium-sized city of China. J. Ecotoxicol. Environ. Saf. 112, 87–95 (2015).CAS 

Google Scholar 
Limin, Y., Yanhai, Z., Rongzu, Q. & Xisheng, H. The influence of regional road construction on landscape ecology on both sides: A case study of Jiangle County, Fujian Province. J. Sichuan Agric. Univ. 33(2), 159–165 (2015).
Google Scholar 
Liang, Z. & Nianlai, C. Analysis on the impact of Jinwu Expressway on ecological environment based on comprehensive index evaluation method. J. Environ. Sustain. Dev. 44(3), 137–139 (2019).
Google Scholar 
Ting, W. & Zongmin, W. Study on eco-environmental impact assessment system of highway construction. J. Resourc. Econom. Environ. Protect. 3, 129–132. (2015).
Google Scholar 
Igondova, E., Pavlickova, K. & Majzlan, O. The ecological impact assessment of a proposed road development (the Slovak approach). J. Environ. Impact Assessm. Rev. 59, 43–54 (2016).
Google Scholar 
Chen, L., Fu, B. & Zhao, W. Source-sink landscape theory and its ecological significance. J. Front. Biol. China 3(2), 131–136 (2008).
Google Scholar 
Wu, J. et al. Spatial differentiation of landscape ecological risk in opencast mining area. J. Acta Ecol. Sin. 33(12), 3816–3824 (2013).
Google Scholar 
Wang, J., Cui, B., Liu, J., Yao, H. & Juan, H. The effect of land use and its change on ecological risk in the Lancang River watershed of Yunnan Province at the landscape scale. J. Acta Sci. Circumstan. 2, 269–277 (2008).CAS 
Article 

Google Scholar 
Xie, H. Regional eco-risk analysis based on landscape structure and spatial statistics. J. Acta Ecol. Sin. 28(10), 5020–5026 (2008).
Google Scholar 
Jinggang, L. I., Chunyang, H. E. & Xiaobing, L. I. Landscape ecological risk assessment of natural/semi-natural landscapes in fast urbanization regions——A case study in Beijing, China. J. Nat. Resourc. 23(1), 33–47 (2008).
Google Scholar 
Jie, W., Wanqi, B. & Guoxing, T. Temporal and spatial characteristics of landscape ecological risk in Qinghai-Tibet Plateau. J. Resour. Sci. 42(9), 1739–1749 (2020).
Google Scholar 
Xuegong, X., Huiping, L., Zaiyi, F. & Rencang, B. Ecological risk assessment of wetland area in Yellow River Delta. J. Acta Sci. Nat. Univ. Pekinensis. 01, 111–120 (2001).
Google Scholar 
Malekmohammadi, B. & Blouchi, L. Ecological risk assessment of wetland ecosystems using multi criteria decision making and geographic information system. J. Ecol. Indic. 41, 133–144 (2014).
Google Scholar 
Campos, P., Paz, T., Lenz, L., Qiu, Y. & Paz, I. Multi-criteria decision method for sustainable watercourse management in urban areas. J. Sustain. 12(16), 6493–6514 (2020).
Google Scholar 
Peng, L. et al. Research on ecological risk assessment in land use model of Shengjin Lake in Anhui province, China. J. Environ. Geochem. Health. 41(6), 2665–2679 (2019).CAS 

Google Scholar 
Zhang, D., Yang, S., Wang, Z., Yang, C. & Chen, Y. Assessment of ecological environment impact in highway construction activities with improved group AHP-FCE approach in China. J. Environ. Monit. Assess. 192(7), 451–469 (2020).
Google Scholar 
Luan, B. et al. Evaluating green stormwater infrastructure strategies efficiencies in a rapidly urbanizing catchment using SWMM-based topsis. J. Clean. Prod. 223, 680–691 (2019).
Google Scholar 
Ramya, S. & Devadas, V. Integration of GIS, AHP and TOPSIS in evaluating suitable locations for industrial development: A case of Tehri Garhwal district, Uttarakhand, India. J. Clean. Prod. 238, 117872 (2019).Koc, K., Ekmekciolu, M. & Zger, M. An integrated framework for the comprehensive evaluation of low impact development strategies. J. Environ. Manag. 294, 113023 (2021).Xiumei, T., Yu, L., Yanmin, R., Yuchun, P. & Xingyao, H. Study on change of land use and ecosystem service value along expressway. J. China Agric. Univ. 21(2), 132–139 (2016).
Google Scholar 
Fei, Z., Shanjiang, Y. & Dongfang, W. Ecological risk assessment due to land use/cover changes (LUCC) in Jinghe County, Xinjiang, China from 1990 to 2014 based on landscape patterns and spatial statistics. J. Environ. Earth. Sci. 77(13), 491 (2018).
Google Scholar 
Rangel-Buitrago, N., Neal, W. J. & de Jonge, V. N. Risk assessment as tool for coastal erosion management. J. Ocean Coast. Manag. 186, 105099 (2020).
Google Scholar 
Mo, W., Wang, Y., Zhang, Y. & Zhuang, D. Impacts of road network expansion on landscape ecological risk in a megacity, China: A case study of Beijing. J. Sci. Total Environ. 574, 1000–1011 (2017).ADS 
CAS 

Google Scholar 
Getis, A. & Ord, J. K. The analysis of spatial association by use of distance statistics. J. Springer Berlin Heidelberg. 24(3), 189–206 (2010).
Google Scholar 
Yingxue, Z., Wenbo, M., Yong, W. & Dafang, Z. Impact of land use change on landscape pattern around expressways in Beijing. J. Geo-Inform. Sci. 19(001), 28–38 (2017).
Google Scholar 
Gang, Z., HuiJun, G. & Guang, Z. Changes of wetland landscape pattern in arid inland area of Northwest China: A case study of inner flow area in Junggar, Xinjiang. J. Arid Land Resourc. Environ. 28(8), 77–82 (2014).
Google Scholar 
Haihang, W., Qianhui, Z., Jiayao, Z. & Chunguo, Z. Analysis on dynamic change of landscape pattern of land use in Zhushan County. J. Forest Resourc. Manag. 6, 76–83 (2018).
Google Scholar 
Shiliang, L., Zhifeng, Y., Baoshan, C. & Shu, G. Impact of road on landscape and ecological risk assessment: A case study of Lancang River Basin. J. Chin. J. Ecol. 8, 897–901 (2005).
Google Scholar 
Yuan, Y. et al. Flood-landscape ecological risk assessment under the background of urbanization. J. Water. 11(7), 1418 (2019).Xie, H., Wang, P. & Huang, H. Ecological risk assessment of land use change in the Poyang lake Eco-economic zone, China. J. Int. J. Environ. Res. Public Health. 10(1), 328–346 (2013).
Google Scholar 
Fengjiao, X. & Xiao, L. Ecological risk pattern in coastal areas of Jiangsu Province based on land use change. J. Acta Ecol. Sin. 38(20), 7312–7325 (2018).
Google Scholar 
Mann, D., Anees, M. M., Rankavat, S. & Joshi, P. K. Spatio-temporal variations in landscape ecological risk related to road network in the Central Himalaya. J. Hum. Ecol. Risk Assess. https://doi.org/10.1080/10807039.2019.1710693 (2020).Article 

Google Scholar 
Oliveira, B. R. D., Costa, E. L. D., Carvalho-Ribeiro, S. M. & Maia-Barbosa, P. M. Land use dynamics and future scenarios of the Rio Doce State Park buffer zone, Minas Gerais, Brazil. J. Environ. Monit. Assessm. 192(1), 39.1–39.12 (2020).
Google Scholar 
Li, Y., Sun, Y. & Li, J. Heterogeneous effects of climate change and human activities on annual landscape change in coastal cities of mainland China. J. Ecol. Indic. https://doi.org/10.1016/j.ecolind.2021.107561 (2021).Dadashpoor, H., Azizi, P. & Moghadasi, M. Land use change, urbanization, and change in landscape pattern in a metropolitan area. J. Sci. Total Environ. 655(10), 707–709 (2019).ADS 
CAS 

Google Scholar  More

Spatial and temporal distribution of ecological vulnerabilityBased on the SPCA model, the temporal and spatial distribution of ecological vulnerability in Shennongjia is obtained, as shown in Fig. 3. From 1996 to 2018, the area of micro vulnerability areas continued to increase and occupied a dominant position. Moreover, their distribution pattern tended to be gradually integrated, indicating that the structure and function of the ecosystem in most areas of Shennongjia were relatively complete, and in a healthy and stable state. However, the ecological environment of the severely vulnerable areas in the northeast, south and southwest of Shennongjia is in a trend of continuous deterioration, and the risk of extreme vulnerability is gradually emerging. From the spatial distribution of ecological vulnerability in 2018, it can be seen that the extremely vulnerable areas have increased significantly, and exhibit a dense and continuous distribution trend in some areas, accompanied by the development of rapid urbanization and highway traffic construction. There are also high-risk ecological vulnerable zones and the extremely vulnerability areas.Figure 3Spatial and temporal distribution of ecological vulnerability in Shennongjia. Spatial and temporal distribution of ecological vulnerability for (a) 1996, (b) 2007, (c) 2018 in Shennongjia, China.Full size imageIt can be seen from the area proportion of different levels of vulnerable areas (Fig. 4) that the area proportion of micro and extremely vulnerable areas increased significantly. Specifically, the area proportion of micro vulnerable areas increased from 59.98% in 1996 to 71.02% in 2018, while the area proportion of extremely vulnerable areas increased from 1.23% in 1996 to 7.32% in 2018. This shows that the ecological vulnerability of Shennongjia exhibits a significant two-level differentiation trend.Figure 4Proportion of the area of vulnerable districts at all levels in Shennongjia.Full size imageDynamic change of ecological vulnerabilityDuring the study period, the areas with a positive fitting slope account for more than 90% of the total area of the study area, which indicates that the overall vulnerability of Shennongjia presents a downward trend. According to the natural discontinuity point method, the dynamic change results of ecological vulnerability in Shennongjia are divided into five levels (Fig. 5), in order to discern the spatial angle more intuitively and clearly. It can be seen that the ecological vulnerability of most regions exhibits a decreasing trend, while the ecological vulnerability of certain regions increases.Figure 5Dynamic changes of ecological vulnerability in Shennongjia. Changes in the ecological vulnerability of Shennongjia in different periods: (a) 1996–2007, (b) 2007–2018, (c) 1996–2018.Full size imageFrom 1996 to 2007, whether the spatial distribution trend of ecological vulnerability increased or decreased is not obvious. However, from 2007 to 2018, the areas with significantly increased ecological vulnerability were concentrated in Yangri and Songbai in the northeast and near the Hongping airport in Shennongjia in the midwest. During this same time period, in the areas around the main urban areas and along the roads that were seriously disturbed by human activities, ecological vulnerability also exhibited a decreasing trend.Change trend of comprehensive ecological vulnerability indexAnnual change of the comprehensive ecological vulnerability indexThe results of the comprehensive ecological vulnerability index of 1996, 2007, and 2018 are 2.77, 2.71, and 2.51, respectively. From the annual change of the ecological vulnerability index in Shennongjia (Fig. 6), it can be seen that the ecological vulnerability of Shennongjia showed a downward trend from 1996 to 2018, and the stability and health of the ecosystem were improved overall.Figure 6Annual change of the comprehensive ecological vulnerability index. CEVI, comprehensive ecological vulnerability index.Full size imageAmong them, the decline of ecological vulnerability is relatively small from 1996 to 2007, which may be ascribed to the preliminary implementation of restrictive policies, such as banning logging and returning farmland to forest, which reduced ecological exposure factors, such as illegal logging and deforestation. From 2007 to 2018, the comprehensive index of ecological vulnerability in Shennongjia decreased significantly, which is mainly due to the designation of national nature reserves and the implementation of various ecological protection projects36. While reducing the exposed ecological disturbance, it simultaneously markedly improved the adaptability of the ecosystem, and further reduced the overall ecological vulnerability of the region.Changes of the comprehensive ecological vulnerability Index in different townsAccording to the comprehensive index of ecological vulnerability of eight towns in the Shennongjia (Table 5, Fig. 7), the ecological vulnerability difference of each town is obvious. In 2018, the comprehensive index of ecological vulnerability of each town is lower than that in 1996 and 2007. The results show that the average value of CEVI is, from high to low, Yangri, Xiaguping, Songbai, Xinhua, Jiuhu, Hongping, Muyu, and Songluo. The maximum value of the CEVI appeared in Yangri in 1996, and the minimum value occurred in Songluo in 2018.Table 5 Comprehensive ecological vulnerability index of towns.Full size tableFigure 7Radar chart of the comprehensive ecological vulnerability index of towns.Full size imageDriving factors of spatial and temporal evolution of ecological vulnerabilityThe formation and evolution of ecological vulnerability in Shennongjia constitutes a dynamic process, which is the result of interactions of human and natural factors. Based on the principle of SPCA of ecological vulnerability, the transformed principal components are extracted, and the rotated factor load matrix is obtained to reflect the different effects of various factors on the evaluation results. Each principal component possesses a different ability to explain the original index factors, but it has similar rules in the first four principal components (Table 6). The cumulative contribution rate of the first four principal components in the three groups of data reached more than 80%, which can reflect the information of most factors, and thus it has good representativeness.Table 6 Principal component loading and score.Full size tableAmong the first principal component and the third principal component, the contribution of land-use type index (C9) is higher; in the second principal component, the contribution of population density (C1) is higher; among the fourth principal components, the contribution of vegetation coverage (C13) is higher. Moreover, the contribution of other factors in different years and main components is dissimilar.The influence of land-use type on ecological vulnerabilityWhether due to natural or human factors, the original properties of the ecosystem are altered by changing the surface cover. Therefore, land-use type is an important factor affecting regional ecological vulnerability. The difference of surface cover leads to the difference of ecological community, and then produces varied ecological environmental benefits. Forest land is the most important land-use type in the study area, and the ecological vulnerability of the distribution area is mainly micro degree and light. However, consider the important ecological value of the forest ecosystem, attention should be given to its vulnerability. The ecological vulnerability of the construction land is mainly severe and extreme, which is largely due to the expansion of construction land, which destroys the original ecological structure and ecological community. Furthermore, a large number of manmade patches replace natural patches in the construction land, and biodiversity decreases, leading to the decline of the stability of ecological structures and the increase of vulnerability.The influence of population density on ecological vulnerabilityPopulation density is one of the most direct exposure factors in the vulnerability of ecological environments. Population density is generally higher than that in high area, and it is also a region with a developed economy and high urbanization. In these areas, human activities are frequent, which usually impart a negative disturbance to the natural environment, including the rapid expansion of cultivated land and construction land area, as well as high discharge of production and domestic wastewater waste, which has caused great pressure on the ecological environment, leading to a significant increase in ecological vulnerability.The influence of vegetation cover on ecological vulnerabilityFrom 1996 to 2018, the vegetation coverage of the Shennongjia exhibited an overall upward trend, which is of positive significance to the reduction of the vulnerability of the ecosystem. Vegetation, as the main body of the land ecosystem, maintains the balance of ecological environment through interactions with climate, landform, and soil37. Extant literature shows that the change of vegetation coverage is an major factor of regional ecological environment change, and has a clear indication function for the change of regional ecological environment38. The spatial distribution trend of ecological vulnerability in the Shennongjia is markedly similar to that of vegetation coverage. The ecological vulnerability of regions with higher vegetation coverage is lower, exhibiting a significant negative correlation. In the Shennongjia, the change of vegetation coverage is also obviously influenced by human factors.Contribution of landscape pattern index to ecological vulnerabilityThe spatial distribution of each index in Shennongjia have been obtained from previous studies47. From the unary linear regression analysis, in the years of 1996, 2007 and 2018, the NP, LPI, AI, DIVISION and SHDI are all significantly correlated with the ecological vulnerability index (Fig. 8).Figure 8Scatter plot of linear regression of landscape pattern index and ecological vulnerability index. EVI, ecological vulnerability index.Full size imageIn the case of different independent variable combinations in 1996, 2007 and 2018, the multiple regression relationship between the independent variable and the dependent variable of each group is significantly correlated, and the multiple linear regression equation of the full model is obtained as follows:$$1996{:};;{text{ Y}} = 6.443 + 0.014{text{X}}_{1} + 0.006{text{X}}_{2} – 0.038{text{X}}_{3} – 0.066{text{X}}_{4} + 0.058{text{X}}_{5}$$$$2007{:};;{text{ Y}} = 4.497 + 0.016{text{X}}_{1} + 0.007{text{X}}_{2} + 0.793{text{X}}_{3} – 0.047{text{X}}_{4} – 0.305{text{X}}_{5}$$$$2018{:};;{text{ Y}} = – 1.980 + 0.037{text{X}}_{1} + 0.006{text{X}}_{2} + 0.703{text{X}}_{3} + 0.019{text{X}}_{4} – 0.123{text{X}}_{5}$$The contribution rate of landscape pattern index to ecological vulnerability in different years of 1996, 2007, and 2018 is shown in Table 7. The contribution of AI and NP to ecological vulnerability in 1996 was high; the contribution of NP and AI to ecological vulnerability was higher in 2007; and the NP in 2018 had the highest contribution to ecological vulnerability, reaching 95.77%.Table 7 Contribution of the landscape pattern index to the ecological vulnerability index.Full size tableBased on the analysis results from 1996 to 2018, the contribution of NP and AI to ecological vulnerability is relatively high. The main reason for this is that the forest coverage rate of Shennongjia is as high as 91%. Specifically, with the forest as the landscape matrix, the NP is small and the connectivity between patches is high, showing a trend of aggregation. The degree of landscape fragmentation is relatively low and decreases annually, and ecological vulnerability decreases with the decrease of the degree of landscape fragmentation, Therefore, the impact of NP and AI on ecological vulnerability is highly significant.The AI and ecological vulnerability index always exhibit a significant negative correlation in the study period. In the 1996 research results, the contribution of AI to ecological vulnerability is the most obvious. Combined with the spatial distribution of ecological vulnerability, it can be seen that most of the severe and extremely vulnerable areas are distributed in areas with low AI. Most of them are the distribution areas of artificial patches, such as rural living areas, airports, tourism centers, etc., which are obviously disturbed by human activities, resulting in low connectivity among various landscape types, which greatly reduces the aggregation degree of landscape and increases regional vulnerability.There is also a significant positive correlation between the NP and the ecological vulnerability index. This is especially the case in 2018, when the contribution of the NP to ecological vulnerability is as high as 95.77%, which is mainly attributable to the urbanization construction of Songbai town in Shennongjia. Combined with the land-use structure map, it can be seen that the number of construction land patches in the northeast region increased sharply. In this process, the renewal of patches aggravates the degree of landscape fragmentation and plays a key role in the aggravation of regional vulnerability risk.Although the impact of LPI, SHDI and DIVISION on ecological vulnerability always exists, the contribution is not very significant. Among them, SHDI contributed 10.38% in 2007, which was more sensitive to the unbalanced distribution of each patch type. In areas with high SHDI, landscape heterogeneity is high, the ecological pattern is unstable, and ecological vulnerability increases. More

Comparison of T
ag calculated from publicly available data and actual measurement dataThe calculated Tag (m2/kg-FM) in each year is summarized for each species in Supplemental Table 1:

The geometric means (GMs) of Tag values calculated using the collected samples ranged from 8.1 × 10−6 to 2.5 × 10−2 m2/kg-FM; the minimum was for western bracken fern in 2019 and the maximum was for koshiabura in 2018 at Kawamata, Fukushima.

The GMs of Tag values calculated using the publicly available data ranged from 1.6 × 10−5 to 1.2 × 10−2 m2/kg-FM and thus were similar to the actual measurement data. The minimum GM was for udo in 2019 and the maximum was for koshiabura in 2019. The geometric standard deviation (GSD) range was 1.5–4.5.

Annual GMs of Tag values calculated from publicly available data and actual measurement data are compared in Fig. 1. The values for individual years are represented by different points. The Tag values were distributed close to the 1:1 line, which suggested that Tag values calculated from the publicly available data generally agreed with those calculated from actual measurements. Hence, an obvious overestimation of Tag from the publicly available data described above was not observed in the present data. We confirmed that Tag calculated from the publicly available food monitoring data and the total deposition data from the airborne survey are reliable surrogates for actual measurement samples. We discuss Tag calculated from the publicly available data hereafter.Figure 1Comparison of annual geometric means of the aggregated transfer factor (Tag) calculated from publicly available data and actual measurement data. Circles, diamonds, and triangles indicate deciduous perennial spermatophytes, deciduous tree spermatophytes, and deciduous perennial pteridophytes, respectively. Values for individual years are represented by different points. Error bars indicate the geometric standard deviation in cases where more than three samples were available.Full size imageRelationship between soil deposition and radioactivity in edible wild plants from publicly available dataWe confirmed the relationship between deposition and concentration of 137Cs for the publicly available data for butterbur scape, fatsia sprout, and western bracken fern in a year (Fig. 2), as a representative deciduous perennial and tree spermatophyte, and deciduous perennial pteridophyte, respectively, in the year of the maximum number of detections. Butterbur scape, fatsia sprout, and western bracken fern showed positive significant, nonsignificant, and weak negative significant correlations, respectively (Spearman’s rank correlation, butterbur scape, p = 0.001, rs = 0.45; fatsia sprout, p = 0.85, rs = − 0.03; western bracken fern, p = 0.03, rs = − 0.21). Among 29 subdata with more than 20 detections for each species in a year, in addition to the data shown in Fig. 2, 13 showed statistically significant positive correlations (Butterbur scape in 2014 and 2016; bamboo shoot in 2012, and 2014 − 2019; fatsia sprout in 2013 and 2016; koshiabura in 2013; and ostrich fern in 2012), and western bracken fern in 2017 showed a significant negative correlation. These weak correlations may be affected by uncertainty in the deposition data. We used a representative deposition value for each municipality and the original deposition data grid was of low resolution (see the “Methods” section Radiocesium deposition data from airborne survey). Especially for the cases lacking a clear positive correlation, the degree of radiocesium absorption by edible wild plants was largely different even in the same deposition. Radiocesium uptake by plants in an environment is also affected by other factors (e.g., soil characteristics25,26). The edible wild plants targeted in the present study were not cultivated but were collected in a variety of environments, such as forests with high organic matter content in the soil and paddy field margins with poorly drained soil high in clay content, although we cannot precisely confirm the growth environment of each species included in the present study.Figure 2Correlation between deposition and concentration of 137Cs in three edible wild plants. Circles, diamonds, and triangles indicate butterbur scape, fatsia sprout, and western bracken fern, respectively. The three species are representative deciduous perennial and tree spermatophyte, and deciduous perennial pteridophyte, respectively, in the year of the maximum number of detections.Full size imageTemporal change in T
ag
The time-dependence of Tag for each species in the period 2012–2019 is shown in Fig. 3. The Tag values of deciduous perennial spermatophytes and pteridophytes showed a decreasing trend with time. Given that the bioavailability of 137Cs in the soil in the plant root zone decreased with time, as observed in previous studies27,28, we also observed a decrease in Tag. The Tag of deciduous trees did not show a decreasing trend with time.Figure 3Temporal change in the aggregated transfer factor (Tag) in the period 2012–2019. Circles, diamonds, and triangles indicate deciduous perennial spermatophytes, deciduous tree spermatophytes (including bamboo shoot), and deciduous perennial pteridophytes, respectively. Single exponential fitted lines are shown. Solid lines indicate statistically significant parameters (see Table 2).Full size imageAfter the Chernobyl nuclear accident, radiocesium concentrations in deciduous tree leaves decreased with time owing to the effect of direct deposition at an early stage and the following root uptake effect29, and the Tag of tree leaves decreased accordingly. In previous studies conducted in orchards after the Chernobyl and Fukushima accidents, radiocesium concentrations in deciduous tree leaves showed a decreasing trend30,31. The lack of a declining trend for woody edible wild plants Tag in the present study may be due to a smaller effect of direct deposition at the early stage resulting from interception by tall tree canopies in the vicinity. The height of trees with edible wild plants is usually at eye level. The samples collected soon after the accident were possibly affected by direct deposition, whereas in the latter study period, many of the data were from trees grown after the accident. If the effect of direct deposition was large, a declining trend in Tag might have been observed as observed in orchards. Thus, the absence of a declining trend in Tag indicates that the effect of direct deposition was relatively small.As an additional possibility for the absence of a declining trend in tree Tag, the continuous supply of bioavailable radiocesium from the organic layer on the forest floor may affect the temporal change in Tag. Compared with the managed conditions in orchards of previous studies30,31, an organic layer develops on the soil surface in a forest and, therefore, reabsorption of radiocesium from the organic layer via the roots may be more active. Imamura et al.17 also observed a similar trend to that in the present study, namely that radiocesium concentrations in leaves of the canopies of the deciduous tree konara oak (Quercus serrata) did not show a temporal change from 2011 to 2015 in two Fukushima forests. These authors’ results included the effect of direct deposition on the tree bodies at an early stage of the accident, although the emergence of leaves was after the deposition. Nevertheless, a clear decreasing trend in the radiocesium concentration was not observed, which implies that a deciduous tree actively absorbs radiocesium via the roots in Fukushima forests, and a sufficient amount of radiocesium is absorbed to conceal a decline at an early stage owing to the effect of direct deposition.Single exponential fitted lines for each species are shown in Fig. 3. The estimated parameters and the Teff (year) calculated with Eq. (2) in “Methods” section are presented in Table 2. The Teff for Tag values that showed a decreasing trend was approximately 2 years, except for bamboo shoot. Tagami and Uchida10 reported that the Teff of the slow loss component for three edible wild plants of deciduous perennial spermatophytes was 970–3830 days. The 137Cs decline in pteridophytes, and deciduous shrub and herbaceous species on the floor of European forests was reported to be 1.2–8 years for Teff excluding the rapid loss component after the Chernobyl nuclear accident32. The present results are thus within the range of previous studies.Table 2 Estimated parameters and standard errors for correlations of Tag (m2/kg-FM) in the period 2012–2019 with time (day) calculated using Eq. (3) and effective half-lives [Teff, (year)] calculated using Eq. (2) for 11 parts of 10 edible wild plant species. A0 is estimated initial Tag, and λ (/day) is the 137Cs loss rate in edible parts of the plants.Full size tableFor bamboo shoot, applying a single exponential function, a relatively long Teff of 8.3 years was estimated. The Tag decreased between 2012 and 2014, and thereafter no notable change was observed. This observation may reflect the effect of rapid and a slow loss components. Indeed, we applied a two-component exponential function for bamboo shoot, and observed Teff of 0.7 years and − 7.8 years for the rapid and slow loss components, respectively. For edible wild tree species, statistically significant single exponential fitted lines were not observed, which reflected the absence of change in Tag with time, as discussed above in this section.The Tag varied for all species, varying by 1–3 orders of magnitude within a year that included more than two detections (Fig. 3, Supplemental Table 1). As demonstrated in previous studies5, the present study also showed substantial variation in Tag values, which may be for several reasons. Recently, Tagami et al.12 calculated Tag using the radiocesium concentration in edible wild plants measured by local municipalities from higher-resolution publicly available data (accurate to district level) for giant butterbur, bamboo shoot, fatsia sprout, and koshiabura. The municipalities in these authors’ study are located within the present study area. These authors’ results differed in being one or two orders of magnitude smaller than the present results. The lower resolution of the present deposition data may be one of the causes of the greater Tag variation. The other source of variation is the site dependency of radiocesium absorption by edible wild plants from the soil as described above. Clarification of factors that contribute to the variation in Tag other than 137Cs deposition, and its trends consistent with species, is necessary, which will decrease uncertainty and lead to more accurate estimation of Tag of 137Cs with wild plants.Summary of T
ag for estimation of long-term ingestion dose to the publicTo estimate long-term potential ingestion dose to the public, Tag with small temporal variability excluding high values at the early stage after the accident is required. However, for the edible wild plant species in the present study, no Tag information in an equilibrium condition from before the Fukushima accident is available. Therefore, average values of Tag for the period after the decrease in Tag has weakened and a certain number of samples is available would be appropriate. The Teff for Tag showing a decreasing trend was approximately 2 years except for bamboo shoot, which has not shown any temporal variation since 2014. The Tag for the other species, udo, uwabamisou, momijigasa, fatsia sprout, koshiabura and Japanese royal fern, has not shown temporal variation throughout 2012–2019 (see the “Results and discussion” section Temporal change in Tag). Therefore, Tag values since 2014 are applicable for estimation of long-term potential ingestion dose to the public. The GMs and GSDs of the Tag values for 2014–2019 for each species are shown in Table 3 listed in order of decreasing GM.Table 3 Aggregated transfer factor (m2/kg-FM) calculated from publicly available data for 2014–2019 for 11 parts of 10 edible wild plant species.Full size tableSignificant differences in Tag were observed among the species (one-way ANOVA with Tukey’s post hoc test, p  More

Quicke, D. L. Parasitic Wasps (Chapman & Hall Ltd., 1997).
Google Scholar 
Godfray, H. C. J. Parasitoids: Behavioral and Evolutionary Ecology (Princeton University Press, 1994).
Google Scholar 
Mayhew, P. J. & van Alphen, J. J. M. Gregarious development in alysiine parasitoids evolved through a reduction in larval aggression. Anim. Behav. 58 , 131–141 (1999).Mayhew, P. J. & Hardy, I. C. W. Nonsiblicidal behavior and the evolution of clutch size in bethylid wasps. Am. Nat. 151, 409–424 (1998).ADS 
CAS 
PubMed 

Google Scholar 
Schmidt, J. M. & Smith, J. J. B. Correlations between body angles and substrate curvature in the parasitoid wasp Trichogramma minutum: A possible mechanism of host radius measurement. J. Exp. Biol. 125, 271–285 (1986).
Google Scholar 
Boivin, G. & Baaren, J. The role of larval aggression and mobility in the transition between solitary and gregarious development in parasitoid wasps. Ecol. Lett. 3, 469–474 (2000).
Google Scholar 
Rosenheim, J. A., Wilhoit, L. R. & Armer, C. A. Influence of intraguild predation among generalist insect predators on the suppression of an herbivore population. Oecologia 96, 439–449 (1993).ADS 
PubMed 

Google Scholar 
Mayhew, P. J. The evolution of gregariousness in parasitoid wasps. Proc. R. Soc. Lond. B Biol. 265, 383–389 (1998).
Google Scholar 
Harvey, P. H. & Partridge, L. Murderous mandibles and black holes in hymenopteran wasps. Nature 326, 128–129 (1987).ADS 

Google Scholar 
Pexton, J. J. & Mayhew, P. J. Competitive interactions between parasitoid larvae and the evolution of gregarious development. Oecologia 141, 179–190 (2004).ADS 
PubMed 

Google Scholar 
Pexton, J. J. & Mayhew, P. J. Immobility: The key to family harmony? Trends Ecol. Evol. 16, 7–9 (2001).CAS 
PubMed 

Google Scholar 
Godfray, H. C. J. The evolution of clutch size in parasitic wasps. Am. Nat. 129, 221–233 (1987).
Google Scholar 
Laing, J. E. & Corrigan, J. E. Intrinsic competition between the gregarious parasite, Cotesia glomeratus and the solitary parasite Cotesia rubecula (Hymenoptera: Braconidae) for their host Artogeia rapae (Lepidoptera: Pieridae). Entomophaga 32, 493–501 (1987).
Google Scholar 
Pexton, J. J. & Mayhew, P. J. Clutch size adjustment, information use and the evolution of gregarious development in parasitoid wasps. Behav. Ecol. Soc. 58, 99–110 (2005).
Google Scholar 
Reitz, S. R. & Adler, P. H. Fecundity and oviposition of Eucelatoria bryani, a gregarious parasitoid of Helicoverpa zea and Heliothis virescens. Entomol. Exp. Appl. 75, 175–181 (1995).
Google Scholar 
Wei, K., Tang, Y. L., Wang, X. Y., Cao, L. M. & Yang, Z. Q. The developmental strategies and related profitability of an idiobiont ectoparasitoid Sclerodermus pupariae vary with host size. Ecol. Entomol. 39, 101–108 (2014).
Google Scholar 
van Alphen, J. J. M. & Visser, M. E. Superparasitism as an adaptive strategy for insect parasitoids. Ann. Rev. Entomol. 35, 59–79 (1990).
Google Scholar 
Mayhew, P. J. & Glaizot, O. Integrating theory of clutch size and body size evolution for parasitoids. Oikos 92, 372–376 (2001).
Google Scholar 
Samková, A., Hadrava, J., Skuhrovec, J. & Janšta, P. Reproductive strategy as a major factor determining female body size and fertility of a gregarious parasitoid. J. Appl. Entomol. 143, 441–450 (2019).
Google Scholar 
Hardy, I. C. W., Griffiths, N. T. & Godfray, H. C. J. Clutch size in a parasitoid wasp: A manipulation experiment. J. Anim. Ecol. 61, 121–129 (1992).
Google Scholar 
Visser, M. E. The importance of being large: The relationship between size and fitness in females of the parasitoid Aphaereta minuta (Hymenoptera: Braconidae). J. Anim. Ecol. 63, 963–978 (1994).
Google Scholar 
Sagarra, L. A., Vincent, C. & Stewart, R. K. Body size as an indicator of parasitoid quality in male and female Anagyrus kamali (Hymenoptera: Encyrtidae). Bull. Entomol. Res. 91, 363–367 (2001).CAS 
PubMed 

Google Scholar 
Bezemer, T. M. & Mills, N. J. Clutch size decisions of a gregarious parasitoid under laboratory and field conditions. Anim. Behav. 66, 1119–1128 (2003).
Google Scholar 
Takagi, M. The reproductive strategy of the gregarious parasitoid, Pteromalus puparum (Hymenoptera: Pteromalidae). Oecologia 68, 1–6 (1985).ADS 
PubMed 

Google Scholar 
Jervis, M. A., Ferns, P. N. & Heimpel, G. E. Body size and the timing of egg production in parasitoid wasps: A comparative analysis. Funct. Ecol. 17, 375–383 (2003).
Google Scholar 
Waage, J. K. & Lane, J. A. The reproductive strategy of a parasitic wasp: II. Sex allocation and local mate competition in Trichogramma evanescens. J. Anim. Ecol. 53, 417–426 (1984).
Google Scholar 
Waage, J. K. & Ming, N. S. The reproductive strategy of a parasitic wasp: I. Optimal progeny and sex allocation in Trichogramma evanescens. J. Anim. Ecol. 53, 401–415 (1984).
Google Scholar 
Rabinovich, J. E., Jorda, M. T. & Bernstein, C. Local mate competition and precise sex ratios in Telenomus fariai (Hymenoptera: Scelionidae), a parasitoid of triatomine eggs. Behav. Ecol. Sociobiol. 48, 308–315 (2000).
Google Scholar 
Goubault, M., Mack, A. F. & Hardy, I. C. W. Encountering competitors reduces clutch size and increases offspring size in a parasitoid with female–female fighting. Proc. R. Soc. B Biol. 274, 2571–2577 (2007).
Google Scholar 
Duval, J. F., Brodeur, J., Doyon, J. & Boivin, G. Impact of superparasitism time intervals on progeny survival and fitness of an egg parasitoid. Ecol. Entomol. 43, 310–317 (2018).
Google Scholar 
Mesterton-Gibbons, M. & Hardy, I. C. W. The influence of contests on optimal clutch size: A game–theoretic model. Proc. R. Soc. Lond. B Biol. 271, 971–978 (2004).
Google Scholar 
Koppik, M., Thiel, A. & Hoffmeister, T. S. Adaptive decision making or differential mortality: What causes offspring emergence in a gregarious parasitoid? Entomol. Exp. Appl. 150, 208–216 (2014).
Google Scholar 
Heimpel, G. E. Host–parasitoid population dynamics. In Parasitoid population biology (eds Hochberg, M. E. & Ives, A. R.) 27–40 (Princeton, 2000).
Google Scholar 
Zaviezo, T. & Mills, M. Factors influencing the evolution of clutch size in a gregarious insect parasitoid. J. Anim. Ecol. 69, 1047–1057 (2000).
Google Scholar 
Kazmer, D. J. & Luck, R. F. Field tests of the size-fitness hypothesis in the egg parasitoid Trichogramma pretiosum. Ecology 76, 412–425 (1995).
Google Scholar 
Segoli, M. & Rosenheim, J. A. The effect of body size on oviposition success of a minute parasitoid in nature. Ecol. Entomol. 40, 483–485 (2015).
Google Scholar 
Gao, S. K., Wei, K., Tang, Z. L., Wang, X. Y. & Yang, Z. Q. Effect of parasitoid density on the timing of parasitism and development duration of progeny in Sclerodermus pupariae (Hymenoptera: Bethylidae). Biol. Control 97, 57–62 (2016).
Google Scholar 
Anderson, R. C. & Paschke, J. D. The biology and ecology of Anaphes flavipes (Hymenoptera: Mymaridae), an exotic egg parasite of the cereal leaf beetle. Ann. Entomol. Soc. Am. 61, 1–5 (1968).
Google Scholar 
Hoffman, G. D. & Rao, S. Oviposition site selection on oats: The effect of plant architecture, plant and leaf age, tissue toughness, and hardness on cereal leaf beetle, Oulema melanopus. Entomol. Exp. Appl. 141, 232–244 (2011).
Google Scholar 
Samková, A., Hadrava, J., Skuhrovec, J. & Janšta, P. Host population density and presence of predators as key factors influencing the number of gregarious parasitoid Anaphes flavipes offspring. Sci. Rep. UK 9, 1–7 (2019).ADS 

Google Scholar 
Hardy, I. C. W. Sex ratio and mating structure in the parasitoid Hymenoptera. Oikos 69, 3–20 (1994).
Google Scholar 
Godfray, H. C. J. Models for clutch size and sex ratio with sibling interaction. Theor. Popul. Biol. 30, 215–231 (1986).MATH 

Google Scholar 
Hardy, I. C. W. Non-binomial sex allocation and brood sex ratio variances in the parasitoid Hymenoptera. Oikos 65, 143–158 (1992).
Google Scholar 
Petersen, G. & Hardy, I. C. W. The importance of being larger: Parasitoid intruder–owner contests and their implications for clutch size. Anim. Behav. 51, 1363–1373 (1996).
Google Scholar 
Klomp, H. & Teerink, B. J. The significance of oviposition rates in the egg parasite, Trichogramma embryophagum Htg. Arch. Neerl. Zool. 17, 350–375 (1967).
Google Scholar 
May, R. M., Hassell, M. P., Anderson, R. M. & Tonkyn, D. W. Density dependence in host–parasitoid models. J. Anim. Ecol. 50, 855–865 (1981).MathSciNet 

Google Scholar 
Hoddle, M. S., Van Driesche, R. G., Elkinton, J. S. & Sanderson, J. P. Discovery and utilization of Bemisia argentifolii patches by Eretmocerus eremicus and Encarsia formosa (Beltsville strain) in greenhouses. Entomol. Exp. Appl. 87, 15–28 (1998).
Google Scholar 
Samková, A., Raška, J., Hadrava, J. & Skuhrovec, J. Scarcity of hosts for gregarious parasitoids indicates an increase of individual offspring fertility by reducing their own fertility. bioRxiv https://doi.org/10.1101/2021.03.05.434037 (2021).Article 

Google Scholar 
van Dijken, M. J. & Waage, J. K. Self and conspecific superparasitism by the egg parasitoid Trichogramma evanescens. Entomol. Exp. Appl. 43, 183–192 (1987).
Google Scholar 
van de Vijver, E. et al. Inter-and intrafield distribution of cereal leaf beetle species (Coleoptera: Chrysomelidae) in Belgian winter wheat. Environ. Entomol. 48, 276–283 (2019).PubMed 

Google Scholar 
Samková, A., Hadrava, J., Skuhrovec, J. & Janšta, P. Host specificity of the parasitic wasp Anaphes flavipes (Hymenoptera: Mymaridae) and a new defence in its hosts (Coleoptera: Chrysomelidae: Oulema spp.). Insects 11, 175 (2020).PubMed Central 

Google Scholar 
Bezděk, J. & Baselga, A. Revision of western Palaearctic species of the Oulema melanopus group, with description of two new species from Europe (Coleoptera: Chrysomelidae: Criocerinae). Acta Entomol. Mus. Nat. Pragae 55, 273–304 (2015).
Google Scholar 
Anderson, R. C. & Paschke, J. D. Additional observations on the biology of Anaphes flavipes (Hymenoptera: Mymaridae), with special reference to the effects of temperature and superparasitism on development. Ann. Entomol. Soc. Am. 62, 1316–1321 (1969).
Google Scholar 
R Core Team. A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (R Core Team, 2020).
Google Scholar 
Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effects models using lme4. J. Stat. Softw. 67, 1–48 (2015). https://CRAN.R-project.org/package=lme4. More