We study the steady-state probability distribution p for Markov chains G
describing Genetic Algorithms (GA) and Genetic Programming (GP).  That
means: G p = p.  Based upon a reduction method that associates any such
Markov chain another Markov chain over 2 states only, we derive convergence
properties for p in regard to uniform populations and populations containing
globally optimal candidate solutions.  Strong ergodicity of inhomogeneous
Markov chains as above are discussed.