Rates of cultural change and patterns of cultural accumulation in stochastic models of social transmission.

Cultural variation in a population is affected by the rate of occurrence of cultural innovations, whether such innovations are preferred or eschewed, how they are transmitted between individuals in the population, and the size of the population. An innovation, such as a modification in an attribute of a handaxe, may be lost or may become a property of all handaxes, which we call "fixation of the innovation." Alternatively, several innovations may attain appreciable frequencies, in which case properties of the frequency distribution-for example, of handaxe measurements-is important. Here we apply the Moran model from the stochastic theory of population genetics to study the evolution of cultural innovations. We obtain the probability that an initially rare innovation becomes fixed, and the expected time this takes. When variation in cultural traits is due to recurrent innovation, copy error, and sampling from generation to generation, we describe properties of this variation, such as the level of heterogeneity expected in the population. For all of these, we determine the effect of the mode of social transmission: conformist, where there is a tendency for each naïve newborn to copy the most popular variant; pro-novelty bias, where the newborn prefers a specific variant if it exists among those it samples; one-to-many transmission, where the variant one individual carries is copied by all newborns while that individual remains alive. We compare our findings with those predicted by prevailing theories for rates of cultural change and the distribution of cultural variation.

[1]  M. Kimura.  The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. , 1969, Genetics.

[2]  B. Hewlett,et al.  Cultural variation in Africa: role of mechanisms of transmission and adaptation. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[3]  E. Rogers,et al.  Diffusion of innovations , 1964, Encyclopedia of Sport Management.

[4]  Carl P. Lipo,et al.  Regular rates of popular culture change reflect random copying , 2007 .

[5]  Robin I. M. Dunbar.  Neocortex size as a constraint on group size in primates , 1992 .

[6]  H. Harpending.  Genes, Mind, and Culture, C.J. Lumsden, E.O. Wilson. Harvard University Press, Cambridge (1980), xii, x428. Price $20.00 , 1982 .

[7]  D. Macdonald,et al.  Subsistence, Sex, and Cultural Transmission in Folsom Culture , 1998 .

[8]  H. Terashima.  Variation and Composition Principles of the Residence Group (Band) of the Mbuti Pygmies -beyond a typical/atypical dichotomy , 1985 .

[9]  S. Shennan.  Demography and Cultural Innovation: a Model and its Implications for the Emergence of Modern Human Culture , 2001, Cambridge Archaeological Journal.

[10]  T. Ohta,et al.  The Average Number of Generations until Fixation of a Mutant Gene in a Finite Population. , 1969, Genetics.

[11]  S. Wright,et al.  Evolution in Mendelian Populations. , 1931, Genetics.

[12]  M. Toro,et al.  Cultural Transmission and Evolution , 2010 .

[13]  Marcus W Feldman,et al.  Inferring population histories using cultural data , 2009, Proceedings of the Royal Society B: Biological Sciences.

[14]  Laurent Lehmann,et al.  On the number of independent cultural traits carried by individuals and populations , 2011, Philosophical Transactions of the Royal Society B: Biological Sciences.

[15]  Barry S. Hewlett,et al.  Cultural Transmission Among Aka Pygmies , 1986 .

[16]  T. Maruyama,et al.  The age of an allele in a finite population. , 1974, Genetical research.

[17]  Stephen J. Lycett,et al.  On questions surrounding the Acheulean ‘tradition’ , 2008 .

[18]  Robert L. Kelly,et al.  The Foraging Spectrum , 2007 .

[19]  Stephen J Shennan,et al.  Random drift and culture change , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  P. Ehrlich,et al.  Natural selection and cultural rates of change , 2008, Proceedings of the National Academy of Sciences.

[21]  N. Pigeot,et al.  Technical and Social Actors. Flintknapping Specialists and Apprentices at Magdalenian Etiolles , 1990 .

[22]  M. Ichikawa.  The residential groups of the Mbuti Pygmies , 1978 .

[23]  J. Felsenstein,et al.  Inbreeding and variance effective numbers in populations with overlapping generations. , 1971, Genetics.

[24]  Magnus Enquist,et al.  One cultural parent makes no culture , 2010, Animal Behaviour.

[25]  M. Feldman,et al.  Sociocultural epistasis and cultural exaptation in footbinding, marriage form, and religious practices in early 20th-century Taiwan , 2009, Proceedings of the National Academy of Sciences.

[26]  J. S. Gale,et al.  Theoretical Population Genetics , 1990, Springer Netherlands.

[27]  Carl P. Lipo,et al.  Cultural Transmission Theory and the Archaeological Record: Providing Context to Understanding Variation and Temporal Changes in Material Culture , 2007 .

[28]  B. Ryan.  The diffusion of hybrid seed corn in two Iowa communities , 1943 .

[29]  J. Henrich.  Demography and Cultural Evolution: How Adaptive Cultural Processes Can Produce Maladaptive Losses—The Tasmanian Case , 2004, American Antiquity.

[30]  P. A. P. Moran,et al.  Random processes in genetics , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.