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H. Whitehead, P.J. Richerson / Evolution and Human Behavior 30 (2009) 261–273269low-frequency environmental change may reduce meanfitness and lead to population decline.The model does not include a prominent element of bothhistorical collapses in human societies, and our currentpredicament: the influence of humans and our cultures onenvironmental change. These can exacerbate the modelscenario in two related modes. First, cultural behavior can,and often does, stabilize environmental variation throughniche construction (Laland, Odling-Smee, & Feldman,2000). Humans do this in many ways including the storageand transport of food and other resources. This artificialenvironmental stabilization, while it works, reduces theadvantages of individual learning and makes it more likelythat social learning, and cultural conformism, will becomevery common or fixed in the population. The command andcontrol institutions necessary to make complex nicheconstructions work may restrict the capacity for innovationto a small elite who are overwhelmed by red noise events.Even the most sophisticated niche constructions are bound tobe challenged by red environmental events, and when theyfail, the environment may change very rapidly indeedbecause of human influence (Diamond, 2005), a situationpotentially disastrous for a population of largely conformistsocial learners. Currently, successful methods of stabilizingthe local environments of individual humans throughheating, air-conditioning, transport and other systemswhich use fossil fuels are simultaneously destabilizing theglobal environment. Climatologists warn that anthropogenicclimate change will inevitably lead to surprises (NationalResearch Council, 2002).Richerson and Boyd (2005) suggest that the capacity forcomplex social learning and culture arose in humans duringthe highly variable Pleistocene climate. Such an environment,with high variation over many time scales, may haveparticularly favored a contingent individual/social learningstrategy. However, during the more recent Holocene, climatehas been much less variable (Ditlevsen et al., 1996),potentially providing an environment favoring pure sociallearning strategies which could invade, become verycommon or fixed, and lead to societal collapse. The varianceof the Holocene climate, while much smaller than that of thelate Pleistocene, is dominated by abrupt low-frequencyevents (Mayewski et al., 2004); the spectrum remains redeven if the intensity of variation was decreased across thespectrum. Some evidence suggests that the Holocene mighthave had this effect. Human encephalization (brain sizerelative to body size) declined slightly in the Holocenerelative to the Late Pleistocene (Ruff, Trinkhaus, & Holliday,1997), while the size of the cerebellum relative to thecerebral hemispheres increased (Weaver, 2006). Weaver(2006) suggests that the functional significance of thischange has to do with better processing of rule-based culturalinformation. Guthrie's (2005) analysis of Upper Paleolithicart suggests that the people who lived under highlyfluctuating climates were highly naturalistic. Supernaturalthemes were scarce in their art compared to that of Holocenehunter-gatherers. Rappaport (1979: p. 100) argued thatreligion functions “to drape nature in supernatural veils… toprovide her with some protection against human folly andexcess.” That is, supernatural beliefs may protect culturaladaptations from skeptical empirical examination. AsRappaport suggested, this may be highly adaptive to protecta complex fine-tuned cultural adaptation from excessivetinkering by inevitably error prone individual learning andcollective innovation. But when the inevitable challengecomes, supernatural veils may defeat attempts to learn,innovate and borrow solutions to the new problem. Somecombination of genetic and cultural changes might well havedecreased individual learning relative to social learning inthe Holocene, leading to a risk of collapse in the face of rarered noise events.While the population sizes considered during the modelruns (500, 1500 and 5000 breeding individuals) are withinthe ranges of some of the archetypal collapsed societies (theGreenland Norse for example), they are much smaller thanothers (such as the Maya) and minuscule in comparison withtoday's interconnected global human community. Hardwarelimitations mean that individual-based models of thisphenomenon cannot be run with populations of more thansome thousand individuals. Can we reasonably extrapolatethe results of such model runs upwards to scales of millions(the Maya) or billions (the current human population)? Theresults of the model runs indicate that increased populationsize reduces the likelihood of fixation of social learning andthus extirpation (Table 1). Additionally, with very largepopulation size, mutant or innovative (in the case ofculturally determined learning strategies) individuals whomight realign behavior in more environmentally appropriateways are more likely to arise, although their impact onpopulation behavior will be correspondingly smaller. Thus,extrapolation to much larger population sizes is moot,although the case of the Maya collapse (Webster, 2002)seems to fit many aspects of the model. We speculate thatlarge populations will mitigate the chances of extirpation andthe severity of collapses short of extirpation. Largepopulations, all else equal, will tend to have at least a fewinnovators who can introduce new adaptations. Henrich(2004) modeled the equilibrium toolkit complexity of asociety as a function of population size. His modelessentially depends upon uncommon reinvention of complexartifacts whose complexity is degraded in everyday transmissionevents. The same reinvention process should furnishadaptive novelties in a changing environment.The time scales of the collapses in the model, about 2600time units or 65 generations from fixation (Table 1), arereassuringly long in historical terms. However, as notedabove, if the inheritance of learning strategy is throughconformist culture or if culture affects environmentalchange, the speed of the process may greatly increase. Insuch cases, collapse could occur much more quickly thansuggested by the results in Table 1. Turchin's (2003) reviewof the rise and collapse of agrarian states suggests that typical