The evolutionary algorithm stochastic process is well-known to be

Markovian. These have been under investigation in much of the

theoretical evolutionary computing research. When mutation rate is

positive, the Markov chain modeling an evolutionary algorithm is

irreducible and, therefore, has a unique stationary distribution,

yet, rather little is known about the stationary distribution. On the other

hand, knowing the stationary distribution may provide

some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population

genetics to assess what's called a ``genetic load" (see the

introduction for more details). In this talk I will show how the quotient

construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of

the state space. In fact, some of the bounds obtained in the current

work are expressed in terms of the parameters involved in all the

three main stages of an evolutionary algorithm: namely selection,

recombination and mutation. I will also discuss the newest developments which may allow for further improvements of the bounds