Modeling Cultural Evolution on Social Networks using Fractional Diffusion

This abstract presents a first investigation of how to model cultural evolution on social networks using fractional diffusion equations. Social networks are charac- terised by heavy-tailed neighborhood distributions, and this implies that cultural evo- lution on a social network cannot be modeled using the ordinary diffusion equations that have been used successfully to study biological evolution. The abstract presents a number of results that show a) that the fractional diffusion approach works and b) what the qualitative effects of the heavy tails of the neighborhood distribution is on the time it takes for memes to spread on a social network – in particular that more heavy-tailed distributions result in disproportionally faster spread of memes. It ends by discussing a number of shortcomings of the present model and avenues for future research.