The competition of two species for a common resource is illustrated using the paradigm of autocatalytic replicators inhabiting a continuous stirred tank reactor (CSTR) environment that is continuously fed with the resource. In most cases presented, one species is robust (appears in reactor feed) while the other is not. The introduction of the second (invading) species into the CSTR via an unsustained disturbance has a strong effect on the steady-state and dynamic behavior of the first, (host) species. New steady states are added to the bifurcation diagram that show that the invading species can coexist in the system with the host species when its growth and death characteristics are similar to those of the latter. The population levels of the host species are greatly reduced in these cases as a result of the considerable decrease in resource concentration at steady state. Open-loop strategies for the elimination of the invading species are developed and discussed. These strategies involve the manipulation of the reactor residence time to destabilize the states of coexistence.