Although it is recognised that the performance of evolutionary systems such as genetic algorithms (GAs) is affected by the parameters that are employed to implement them, there is hardly any work known to us that has shed much light on the interdependencies and interactions between these parameters. Most studies on the effects of these parameters on the performance of GA-based systems have focused on a parameter at a time without considering the effect of other parameters on that parameter and vice versa. Consequently there is hardly any theory about the interactions and interdependencies of these parameters. This paper contributes towards correcting the situation mentioned above by examining empirically the relationship between two parameters of genetic algorithms (GAs): population size and replacement methods in the performance of GA-based systems. Results are presented that appear to show a link between replacement strategy and an appropriate population size when applying genetic algorithms to a particular problem. It is suggested that, in the domain of application considered in this paper one can infer that the more individuals that are replaced during reproduction the larger the population size that is needed for all optimum performance of GA-based systems. It is suggested that directing our efforts towards establishing the interdependencies and interactions between parameters of evolutionary systems will enhance the advancement of this new technology.