The effects of neutrality on evolutionary search have been considered in a number of interesting studies, the results of which, however, have been contradictory. Some researchers have found neutrality to be beneficial to aid evolution whereas others have argued that the presence of neutrality in the evolutionary process is useless. We believe that this confusion is due to several reasons: many studies have based their conclusions on performance statistics (e.g., on whether or not a system with neutrality could solve a particular problem faster than a system without neutrality) rather than a more in-depth analysis of population dynamics, studies often consider problems, representations and search algorithms that are relatively complex and so results represent the compositions of multiple effects (e.g., bloat or spurious attractors in genetic programming), there is not a single definition of neutrality and different studies have added neutrality to problems in radically different ways. In this paper, we try to shed some light on neutrality by addressing these problems. That is, we use the simplest possible definition of neutrality (a neutral network of constant fitness, identically distributed in the whole search space), we consider one of the simplest possible algorithms (a mutation based, binary genetic algorithm) applied to two simple problems (a unimodal landscape and a deceptive landscape), and analyse both performance figures and, critically, population flows from and to the neutral network and the basins of attraction of the optima.