Abstract

Evolution of a cultural trait has been considered at a theoretical level. Cultural evolution is to be kept distinct from biological evolution, but the discrimination of the two may be difficult in actual cases. In cultural evolution, not only the parents of an individual but also other members of the group, contribute directly to determining the value of a trait in the individual. The cumulative effect of members of the group other than the parents has been called the group effect g. The expected value of the trait of an individual in the next generation has been assumed in the model to be the weighted mean of the individual value (as determined by the trait values in the parent or parents plus a random contribution E the new variation per generation), and the group mean value, the individual and the group contributions being weighted as (1 ‑ g) to g. Effects of age and peers and of generations earlier than parental have also been analyzed. It has been demonstrated that, if g is different from zero and positive, however small, in spite of new variation arising at every generation the variation of the trait within the group will stabilize at a finite level. The stable amount of the variation depends on the mode of transmission, which has been considered here to be either uniparental or biparental, on the value of g, on the size of the group if the progeny size is not constant, and on the amount of new variation produced per generation. Independent groups will differentiate one from the other randomly, at a rate which is a function of the mode of transmission (uni or biparental), the g value, and the size of the group. Ways to study discontinuous traits have been given. If discontinuity arises from imposition of a perceptive threshold on the existing variation, and therefore the variate is not truly discontinuous, its behavior is still predictable by the same rules, and a transformation for study of the frequencies of observations above or below threshold has been given, which permits the prediction of the trend of changes with time. A truly discontinuous character will undergo fixation of one or other character state, as for alleles in random genetic drift, but the rate of fixation will be decreased by group action.