{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:26:19Z","timestamp":1777605979541,"version":"3.51.4"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2011,10,1]],"date-time":"2011-10-01T00:00:00Z","timestamp":1317427200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Theoretical Biology"],"published-print":{"date-parts":[[2011,10]]},"DOI":"10.1016\/j.jtbi.2011.07.022","type":"journal-article","created":{"date-parts":[[2011,8,3]],"date-time":"2011-08-03T03:38:32Z","timestamp":1312342712000},"page":"37-41","source":"Crossref","is-referenced-by-count":34,"special_numbering":"C","title":["Escaping the tragedy of the commons via directed investments"],"prefix":"10.1016","volume":"287","author":[{"given":"Jeromos","family":"Vukov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco C.","family":"Santos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge M.","family":"Pacheco","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jtbi.2011.07.022_bib1","doi-asserted-by":"crossref","first-page":"11149","DOI":"10.1073\/pnas.200327197","article-title":"Classes of small-world networks","volume":"97","author":"Amaral","year":"2000","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2011.07.022_bib2","series-title":"The Evolution of Cooperation Basic Books","author":"Axelrod","year":"1984"},{"key":"10.1016\/j.jtbi.2011.07.022_bib3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"key":"10.1016\/j.jtbi.2011.07.022_bib4","series-title":"Why Cooperate?: The Incentive to Supply Global Public Goods","author":"Barrett","year":"2007"},{"key":"10.1016\/j.jtbi.2011.07.022_bib5","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1073\/pnas.0507229103","article-title":"Punishing and abstaining for public goods","volume":"103","author":"Brandt","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2011.07.022_bib6","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1126\/science.1100735","article-title":"The neural basis of altruistic punishment","volume":"305","author":"de Quervain","year":"2004","journal-title":"Science"},{"key":"10.1016\/j.jtbi.2011.07.022_bib7","series-title":"The Evolution of Social Networks","author":"Doreian","year":"1997"},{"key":"10.1016\/j.jtbi.2011.07.022_bib8","series-title":"Evolution of Networks: From Biological Nets to the Internet and WWW","author":"Dorogotsev","year":"2003"},{"key":"10.1016\/j.jtbi.2011.07.022_bib9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1038\/415137a","article-title":"Altruistic punishment in humans","volume":"415","author":"Fehr","year":"2002","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib10","author":"Gini","year":"1912","journal-title":"Variabilit\u00e0 e mutabilit\u00e0"},{"key":"10.1016\/j.jtbi.2011.07.022_bib11","doi-asserted-by":"crossref","first-page":"108103","DOI":"10.1103\/PhysRevLett.98.108103","article-title":"Dynamical organization of cooperation in complex topologies","volume":"98","author":"G\u00f3mez-Garde\u00f1es","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.jtbi.2011.07.022_bib12","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1126\/science.162.3859.1243","article-title":"The tragedy of the commons","volume":"162","author":"Hardin","year":"1968","journal-title":"Science"},{"key":"10.1016\/j.jtbi.2011.07.022_bib13","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1146\/annurev.soc.24.1.183","article-title":"Social dilemmas: the anatomy of cooperation","volume":"24","author":"Kollock","year":"1998","journal-title":"Ann. Rev. Sociol."},{"key":"10.1016\/j.jtbi.2011.07.022_bib14","series-title":"Evolution and the Theory of Games","author":"Maynard-Smith","year":"1982"},{"key":"10.1016\/j.jtbi.2011.07.022_bib15","series-title":"The Major Transitions in Evolution","author":"Maynard-Smith","year":"1995"},{"key":"10.1016\/j.jtbi.2011.07.022_bib16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM"},{"key":"10.1016\/j.jtbi.2011.07.022_bib17","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1133755","article-title":"Five rules for the evolution of cooperation","volume":"314","author":"Nowak","year":"2006","journal-title":"Science"},{"key":"10.1016\/j.jtbi.2011.07.022_bib18","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1038\/359826a0","article-title":"Evolutionary games and spatial chaos","volume":"359","author":"Nowak","year":"1992","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib19","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1038\/nature04131","article-title":"Evolution of indirect reciprocity","volume":"437","author":"Nowak","year":"2005","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib20","doi-asserted-by":"crossref","first-page":"4877","DOI":"10.1073\/pnas.91.11.4877","article-title":"Spatial games and the maintenance of cooperation","volume":"91","author":"Nowak","year":"1994","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2011.07.022_bib21","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.jtbi.2005.08.008","article-title":"The leading eight: social norms that can maintain cooperation by indirect reciprocity","volume":"239","author":"Ohtsuki","year":"2006","journal-title":"J. Theor. Biol."},{"key":"10.1016\/j.jtbi.2011.07.022_bib22","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1038\/nature04605","article-title":"A simple rule for the evolution of cooperation on graphs and social networks","volume":"441","author":"Ohtsuki","year":"2006","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib23","doi-asserted-by":"crossref","first-page":"e1000596","DOI":"10.1371\/journal.pcbi.1000596","article-title":"Population structure induces a symmetry breaking favoring the emergence of cooperation","volume":"5","author":"Pacheco","year":"2009","journal-title":"PLoS Comput. Biol."},{"key":"10.1016\/j.jtbi.2011.07.022_bib24","doi-asserted-by":"crossref","first-page":"098104","DOI":"10.1103\/PhysRevLett.95.098104","article-title":"Scale-free networks provide a unifying framework for the emergence of cooperation","volume":"95","author":"Santos","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.jtbi.2011.07.022_bib25","doi-asserted-by":"crossref","first-page":"3490","DOI":"10.1073\/pnas.0508201103","article-title":"Evolutionary dynamics of social dilemmas in structured heterogeneous populations","volume":"103","author":"Santos","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2011.07.022_bib26","first-page":"454","article-title":"Social diversity promotes the emergence of cooperation in public goods games","author":"Santos","year":"2008","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib27","series-title":"Games of Life: Explorations in Ecology, Evolution and Behaviour","author":"Sigmund","year":"1995"},{"key":"10.1016\/j.jtbi.2011.07.022_bib28","series-title":"The Calculus of Selfishness","author":"Sigmund","year":"2010"},{"key":"10.1016\/j.jtbi.2011.07.022_bib29","doi-asserted-by":"crossref","first-page":"10757","DOI":"10.1073\/pnas.161155698","article-title":"Reward and punishment","volume":"98","author":"Sigmund","year":"2001","journal-title":"Pro. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2011.07.022_bib30","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1038\/nature09203","article-title":"Social learning promotes institutions for governing the commons","volume":"466","author":"Sigmund","year":"2010","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib31","doi-asserted-by":"crossref","first-page":"306\u00f1308","DOI":"10.1143\/PTP.6.306","article-title":"Statistics of kagom\u00c8 lattice","volume":"6","author":"Sy\u00f4zi","year":"1951","journal-title":"Prog. Theor. Phys."},{"key":"10.1016\/j.jtbi.2011.07.022_bib32","doi-asserted-by":"crossref","first-page":"118101","DOI":"10.1103\/PhysRevLett.89.118101","article-title":"Phase transitions and volunteering in spatial public goods games","volume":"89","author":"Szab\u00f3","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.jtbi.2011.07.022_bib33","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.physrep.2007.04.004","article-title":"Evolutionary games on graphs","volume":"446","author":"Szab\u00f3","year":"2007","journal-title":"Phys. Rep."},{"key":"10.1016\/j.jtbi.2011.07.022_bib34","doi-asserted-by":"crossref","first-page":"047107","DOI":"10.1103\/PhysRevE.72.047107","article-title":"Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices","volume":"72","author":"Szab\u00f3","year":"2005","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.jtbi.2011.07.022_bib35","doi-asserted-by":"crossref","first-page":"38003","DOI":"10.1209\/0295-5075\/92\/38003","article-title":"Reward and cooperation in the spatial public goods game","volume":"92","author":"Szolnoki","year":"2010","journal-title":"Europhys. Lett."},{"key":"10.1016\/j.jtbi.2011.07.022_bib36","series-title":"Community, Anarchy and Liberty","author":"Taylor","year":"1982"},{"key":"10.1016\/j.jtbi.2011.07.022_bib37","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1038\/nature05784","article-title":"Evolution of cooperation in a finite homogeneous graph","volume":"447","author":"Taylor","year":"2007","journal-title":"Nature"},{"key":"10.1016\/j.jtbi.2011.07.022_bib38","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1086\/406755","article-title":"The evolution of reciprocal altruism","volume":"46","author":"Trivers","year":"1971","journal-title":"Quat. Rev. Biol."},{"key":"10.1016\/j.jtbi.2011.07.022_bib39","series-title":"Social Evolution","author":"Trivers","year":"1985"},{"key":"10.1016\/j.jtbi.2011.07.022_bib40","doi-asserted-by":"crossref","first-page":"036133","DOI":"10.1103\/PhysRevE.71.036133","article-title":"Evolutionary prisoner's dilemma game on hierarchical lattices","volume":"71","author":"Vukov","year":"2005","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.jtbi.2011.07.022_bib41","series-title":"Small Worlds: The Dynamics of Networks Between Order and Randomness","author":"Watts","year":"1999"},{"key":"10.1016\/j.jtbi.2011.07.022_bib42","doi-asserted-by":"crossref","first-page":"R661","DOI":"10.1016\/j.cub.2007.06.004","article-title":"Evolutionary explanations for cooperation","volume":"17","author":"West","year":"2007","journal-title":"Curr. Biol."}],"container-title":["Journal of Theoretical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519311003729?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519311003729?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:51:41Z","timestamp":1543625501000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0022519311003729"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10]]},"references-count":42,"alternative-id":["S0022519311003729"],"URL":"https:\/\/doi.org\/10.1016\/j.jtbi.2011.07.022","relation":{},"ISSN":["0022-5193"],"issn-type":[{"value":"0022-5193","type":"print"}],"subject":[],"published":{"date-parts":[[2011,10]]}}}