This paper explores some of the empirical features generated in an agent based computational stock market with market participants adapting and evolving over time. Investors view differing lengths of past information as being relevant to their investment decision making process. The interaction of these memory lengths in determining market prices creates a kind of market ecology in which it is difficult for the more stable, longer horizon agents to take over the market. What occurs is a dynamically changing market in which different types of agents arrive and depart depending on their current relative performance. This paper analyzes several key time series features of such a market. It is calibrated to the variability and growth of dividend payments in the United States. The market generates some features which are remarkably similar to those from actual data. These include magnifying the volatility from the dividend process, inducing persistence in volatility and volume, and generating fat tailed return distributions.