In recent years there has been a major growth of interest in exploring the analogies between the genetic transmission of information from one generation to the next and the processes of cultural transmission, in an attempt to obtain a greater understanding of how culture change occurs. This article uses computer simulation to explore the implications of a specific model of the relationship between demography and innovation within an evolutionary framework. The consequences of innovation appear far more successful in larger populations than in smaller ones. In conclusion, it is suggested that the model has major implications for the origins of modern human culture in the last 50,000 years, which may be seen not as the result of genetic mutations leading to improved cognitive capacities of individuals, but as a population consequence of the demographic growth and increased contact range which are evident at this time. It is also proposed that the model may be of general relevance for understanding the process of cultural evolution in modern and pre-modern humans.