Many traditional models in Finance assume that markets are in equilibrium. However, when we examine data from markets at microscopic time-scales, by sampling data separated by very small time intervals (that is, at high-frequency), we see signs of non-equilibrium dynamics, such as non-Guassian distributions in the changes in the logarithm of the price. The Adaptive Markets Hypothesis (AMH) conjectures that these phenomena result from a non-equilibrium process of adaptation, or natural selection. Although natural selection is usually considered as selection of genes, we can also use it to model a process of cultural evolution in which the participants in the market imitate the most successful behaviours: e.g. forecasting rules, or trading strategies. In many cases mathematical models of evolution, which take the form of coupled systems of differential equations, predict non-equilibrium steady-state behaviour, including not only oscillations but also the possibility of chaos and strange-attractors. Moreover, when we implement cultural evolution in a simulation-model of a financial market (a so-called agent-based model), we are able to reproduce many of the stylized facts of financial time-series, e.g. non-Guassian returns, in support of the AMH. However, thus far, there are very many different models which are able to reproduce the stylized facts, and by their very nature they are only able to account for sufficient conditions, leaving other explanations open. In this talk I will discuss how this issue can be addressed by looking for empirical evidence of evolution directly in high-frequency data itself by systematically fitting different mathematical models of evolution to HF time-series data, and comparing the results with a null model.