A two level mutation-selection model of cultural evolution and diversity.

Cultural evolution is a complex process that can happen at several levels. At the level of individuals in a population, each human bears a set of cultural traits that he or she can transmit to its offspring (vertical transmission) or to other members of his or her society (horizontal transmission). The relative frequency of a cultural trait in a population or society can thus increase or decrease with the relative reproductive success of its bearers (individual's level) or the relative success of transmission (called the idea's level). This article presents a mathematical model on the interplay between these two levels. The first aim of this article is to explore when cultural evolution is driven by the idea's level, when it is driven by the individual's level and when it is driven by both. These three possibilities are explored in relation to (a) the amount of interchange of cultural traits between individuals, (b) the selective pressure acting on individuals, (c) the rate of production of new cultural traits, (d) the individual's capacity to remember cultural traits and to the population size. The aim is to explore the conditions in which cultural evolution does not lead to a better adaptation of individuals to the environment. This is to contrast the spread of fitness-enhancing ideas, which make individual bearers better adapted to the environment, to the spread of "selfish" ideas, which spread well simply because they are easy to remember but do not help their individual bearers (and may even hurt them). At the same time this article explores in which conditions the adaptation of individuals is maximal. The second aim is to explore how these factors affect cultural diversity, or the amount of different cultural traits in a population. This study suggests that a larger interchange of cultural traits between populations could lead to cultural evolution not improving the adaptation of individuals to their environment and to a decrease of cultural diversity.