  In the light of a recently derived evolution equation for genetic algorithms
we consider the schema theorem and the building block hypothesis. We derive a
schema theorem based on the concept of effective fitness showing that schemata
of higher than average effective fitness receive an exponentially increasing
number of trials over time. The equation makes manifest the content of the
building block hypothesis showing how fit schemata are constructed from fit
sub-schemata. However, we show that generically there is no preference for
short, low-order schemata. In the case where schema reconstruction is favored
over schema destruction large schemata tend to be favored. As a corollary of
the evolution equation we prove Geiringer's theorem.
