This paper is related to Holland's result on implicit parallelism. Rou
ghly speaking, Holland showed a lower bound of the order of n3/c1 squa
re-root l to the number of schemata usefully processed by the genetic
algorithm in a population of n = c1 . 2l binary strings, with c1 a sma
ll integer. We analyze the case of a population of n = 2betal binary s
trings where beta is a positive parameter (Holland's result is related
to the case beta = 1). In the main result, we state a lower bound on
the expected number of processed schemata for all beta > 0; moreover,
we prove that this bound is tight up to a constant for all beta greate
r-than-or-equal-to 1 and, in this case, we strengthen in probability t
he previous result.