{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:28:02Z","timestamp":1760243282325,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2014,7,29]],"date-time":"2014-07-29T00:00:00Z","timestamp":1406592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We consider a simple mathematical approach to the rise and fall of societies based on population growth and its effects on the environment, both beneficial and detrimental. We find that in any simple model of population dynamics with environmental coupling, stable cultures are impossible. Populations inevitably grow or decline exponentially. Further, if the parameters defining a civilisation are allowed to evolve towards an evolutionarily stable state, the only possible solutions are those where each culture ultimately declines. However, computer simulation with multiple competing cultures show that while each eventually collapses, some are always extant and the system is robust. In this broad class of models, individual death is a requirement for system survival.<\/jats:p>","DOI":"10.3390\/computation2030083","type":"journal-article","created":{"date-parts":[[2014,7,29]],"date-time":"2014-07-29T10:58:58Z","timestamp":1406631538000},"page":"83-101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Cultural Collapse and System Survival Due to Environmental Modification"],"prefix":"10.3390","volume":"2","author":[{"given":"Graeme","family":"Ackland","sequence":"first","affiliation":[{"name":"School of Physics, the University of Edinburgh, Edinburgh, EH9 3JZ, UK"}]},{"given":"Adrien","family":"Henry","sequence":"additional","affiliation":[{"name":"School of Physics, the University of Edinburgh, Edinburgh, EH9 3JZ, UK"},{"name":"UMR de G\u00e9n\u00e9tique V\u00e9g\u00e9tale du Moulon, INRA\/CNRS\/Univ Paris-Sud\/AgroParisTech,Ferme du Moulon, Gif sur Yvette, France"}]},{"given":"Alexander","family":"Williams","sequence":"additional","affiliation":[{"name":"School of Physics, the University of Edinburgh, Edinburgh, EH9 3JZ, UK"}]},{"given":"Morrel","family":"Cohen","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Rutgers, the State University of New Jersey, 136Frelinghuysen Road, Piscataway, NJ 08854-8019, USA"}]}],"member":"1968","published-online":{"date-parts":[[2014,7,29]]},"reference":[{"key":"ref_1","unstructured":"De Condorcet, J.A.N., and de Condorcet, M.J.A.N.C. (1795). Esquisse d\u2019un Tableau Historique des Progress de L\u2019esprit Humain, Masson et Fils. (In French)."},{"key":"ref_2","unstructured":"Malthus, T. (1798). An Essay on the Principle of Population, John Murray."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1126\/science.132.3436.1291","article-title":"Duckworth Doomsday: Friday, 13 November, A.D. 2026. At this date human population will approach infinity if it grows as it has grown in the last two millennia","volume":"132","author":"Mora","year":"1960","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1126\/science.7618100","article-title":"Population growth and earth\u2019s human carrying capacity","volume":"269","author":"Cohen","year":"1995","journal-title":"Science"},{"key":"ref_5","unstructured":"Renfrew, C. (1973). The Explanation of Culture Change: Models in Prehistory, University of Pittsburgh Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4161","DOI":"10.1073\/pnas.1301246110","article-title":"Fifty years to prove Malthus right","volume":"110","author":"Kaack","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1038\/325031a0","article-title":"Mitochondrial DNA and human evolution","volume":"325","author":"Cann","year":"1987","journal-title":"Nature"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1126\/science.262.5130.27","article-title":"Pleistocene Population Explosions","volume":"262","author":"Gibbons","year":"1993","journal-title":"Science"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1006\/jhev.1998.0219","article-title":"Late Pleistocene human population bottlenecks, volcanic winter, and differentiation of modern humans","volume":"34","author":"Ambrose","year":"1998","journal-title":"J. Hum. Evol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/j.1469-1809.1937.tb02153.x","article-title":"The wave of advance of advantageous genes","volume":"7","author":"Fisher","year":"1937","journal-title":"Ann. Eugen."},{"key":"ref_11","first-page":"1","article-title":"A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem","volume":"1","author":"Kolmogorov","year":"1937","journal-title":"Bull. Mosc. Univ. Math. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"674","DOI":"10.2307\/2799190","article-title":"Measuring the Rate of Spread of Early Farming in Europe","volume":"6","author":"Ammerman","year":"1971","journal-title":"Man"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ammerman, A.J., and Cavalli-Sforza, L.L. (1984). The Neolithic Transition and the Genetics of Populations in Europe, Princeton University Press.","DOI":"10.1515\/9781400853113"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1103\/PhysRevLett.82.867","article-title":"Time-delayed theory of the Neolithic transition in Europe","volume":"82","author":"Fort","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1088\/0034-4885\/65\/6\/201","article-title":"Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment","volume":"65","author":"Fort","year":"2002","journal-title":"Rep. Prog. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"031913","DOI":"10.1103\/PhysRevE.70.031913","article-title":"Multidelayed random walks: Theory and application to the neolithic transition in Europe 32 yr generation","volume":"70","author":"Fort","year":"2004","journal-title":"Phys. Rev. E Stat. Nonlin. Soft Matter Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1017\/S0959774300000019","article-title":"At the Edge of Knowability: Towards a Prehistory of Languages","volume":"10","author":"Renfrew","year":"2000","journal-title":"Camb. Archaeol. J."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Abdullaev, F., Bishop, A.R., and Pnevmatikos, S. (1992). Nonlinearity with Disorder, Springer-Verlag.","DOI":"10.1007\/978-3-642-84774-5"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8714","DOI":"10.1073\/pnas.0702469104","article-title":"Cultural hitchhiking on the wave of advance of beneficial technologies","volume":"104","author":"Ackland","year":"2007","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cohen, M.H., and Ackland, G.J. (2012). Boundaries between Ancient Cultures: Origins and persistence. Adv. Complex Syst., 15.","DOI":"10.1142\/S0219525911003220"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1353\/hub.2002.0003","article-title":"Colonization Models and Initial Genetic Diversity in the Americas","volume":"74","author":"Fix","year":"2002","journal-title":"Hum. Biol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.jas.2005.09.017","article-title":"The role of waterways in the spread of the Neolithic","volume":"33","author":"Davison","year":"2006","journal-title":"J. Arch. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.tpb.2005.09.001","article-title":"Transport on fractal river networks: Application to migration fronts","volume":"69","author":"Campos","year":"2006","journal-title":"Theor. Popul. Biol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"026107","DOI":"10.1103\/PhysRevE.78.026107","article-title":"Stochastic model for population migration and the growth of human settlements during the Neolithic transition","volume":"78","author":"Fedotov","year":"2008","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_25","unstructured":"Butzer, K.W. (1976). Early Hydraulic Civilization in Egypt, University of Chicago Press."},{"key":"ref_26","first-page":"572","article-title":"Relocation of civilization centers in ancient China: Environmental factors","volume":"27","author":"Duan","year":"1998","journal-title":"Ambio"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","article-title":"The logic of animal conflict","volume":"246","author":"Price","year":"1973","journal-title":"Nature"},{"key":"ref_28","unstructured":"Rathbone, D. (2006). Poverty in the Roman World, Cambridge University Press. Chapter 6."},{"key":"ref_29","unstructured":"McEvedy, C., and Jones, R. (1978). Atlas of World Population History, Puffin."},{"key":"ref_30","unstructured":"Diamond, J. (2005). Collapse, Penguin."},{"key":"ref_31","unstructured":"Tainter, J. (1990). The Collapse of Complex Societies, Cambridge University Press."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1111\/0020-8833.00053","article-title":"Expansion and Contraction Patterns of Large Polities","volume":"41","author":"Taagepera","year":"1997","journal-title":"Int. Stud. Q."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"218102","DOI":"10.1103\/PhysRevLett.94.218102","article-title":"Predator-prey cycles from resonant amplification of demographic stochasticity","volume":"94","author":"McKane","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"48003","DOI":"10.1209\/0295-5075\/79\/48003","article-title":"Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers","volume":"79","author":"Mitchell","year":"2007","journal-title":"Europhys. Lett."},{"key":"ref_35","first-page":"161","article-title":"Emergent patterns in space and time from daisyworld: A simple evolving coupled biosphere-climate model","volume":"368","author":"Ackland","year":"2010","journal-title":"Philos. Trans. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1086\/200169","article-title":"Neolithic diffusion rates","volume":"2","author":"Edmonson","year":"1961","journal-title":"Curr. Anthropol."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/2\/3\/83\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:14:09Z","timestamp":1760217249000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/2\/3\/83"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,29]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,9]]}},"alternative-id":["computation2030083"],"URL":"https:\/\/doi.org\/10.3390\/computation2030083","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2014,7,29]]}}}