Cultural complexity and evolution in fluctuating environments.

The effect of environmental change on the rate of innovation and level of cultural complexity in a population is a theoretically understudied piece of an important puzzle at the heart of cultural evolution. Many mathematical models of cultural complexity have focused on the role of demographic factors such as population size or density. However, statistical studies often point to environmental variability as an important factor determining complexity in many cases. The aim of this study is to explore the interaction between environmental fluctuations and the rate of cultural innovation within a population and to examine the relationship between rates of innovation and the probability of maintaining a complex cultural repertoire in a changing environment. Two models are presented that draw on previous models used to examine rates of genetic mutation. The models show that, as in a genetic system, the stable rate of cultural innovation in a population decreases with environmental stability and increases in unstable environments. This effect is similar but quantitatively different for different modes of cultural transmission (success bias, conformity bias and random oblique learning). The model shows that innovation can increase diversity but that this relationship depends critically on learning mode and learning parameters.This article is part of the theme issue 'Bridging cultural gaps: interdisciplinary studies in human cultural evolution'.