If such a GA uses random reproduction and random mutation, all states always have a positive probability of occurring. A finite GA with random reproduction and mutation is therefore a finite and irreducible Markov chain. This means that the probability that each population occurs rapidly converges to a constant, positive value. The crucial practical implication from the theoretical results of Nix and Vose is that a GA's success as an optimizer depends on having a sufficiently large population of code-strings. If the GA population is not sufficiently large, then the Markov chain that the GA implements is converging to a stationary distribution in which the probabilities of optimal and suboptimal states are not sharply distinguished.
Suboptimal populations can be as likely or even more likely to occur than optimal ones.
Because the Markov chain is irreducible, the GA will necessarily generate an optimal code-string if it is allowed to run for an unlimited number of generations. But if the stationary distribution is not favorable, the run time in terms of generations needed to produce an optimal code-string will be excessive. For all but trivially small state spaces, an unfavorable stationary distribution can easily imply an expected running time in the millions of generations. But if the stationary distribution strongly emphasizes optimal populations, relatively few generations may be needed to find an optimal code-string. In general, the probability of producing an optimum in a fixed number of generations increases with the GA population size.