  A theory of evolution for the Universe requires both a mutation mechanism and
a selection mechanism. We propose that both can be encountered in the
stochastic approach to quantum cosmology. In Brans--Dicke chaotic inflation,
the quantum fluctuations of Planck mass behave as mutations, such that new
inflationary domains may contain values of Planck mass that differ slightly
from their parent's. The selection mechanism establishes that the value of
Planck mass should be such as to increase the proper volume of the inflationary
domain, which will then generate more offsprings. For generic chaotic
potentials we find runaway probability distributions that move towards large
values of both inflaton and dilaton fields. Therefore, this mechanism predicts
that the effective Planck scale should be much larger than any given scale in
the problem.
