||In an adaptive population that models financial markets, we consider how the dynamics depends on the agents' initial preferences of strategies as well as different payoff functions. When the diversity of the initial preferences of the strategies decreases, more agents tend to adapt their strategies together. In systems with linear payoffs, this change in the environment results in dynamical transitions from vanishing to non-vanishing step sizes. For low signal dimensions, we find a cascade of dynamical transitions for the different signals and this cascade will gradually disappear as signal dimensions increases. We also find that different profile of the initial preferences distribution of strategies determines different dynamics of the adaptation and a discontinuous profile results in a more erratic temporal behavior. The last but not the least we find is that different ways of updating signals are irrelevant to the macroscopic behavior of the system, although their microscopic dynamics are different. All above results are supported by the good agreement between simulations and theory. Finally, I introduced a modified model to address some unrealistic features of the standard MG model, such as forcing the agents to bid at every time step, neglecting wealth constraints, leaving out the price definition, neglecting the consideration of wealth in choosing the strategies, and not allowing for evolution. The new model is equipped with the definition of the price and wealth, and allows agents to hold stocks besides buying or selling. Thus it is more powerful in reflecting the behavior of real markets.