  For $M$ $\omega$-categorical and stable, we investigate the growth rate of
$M$, i.e. the number of orbits of $Aut(M)$ on $n$-sets, or equivalently the
number of $n$-substructures of $M$ after performing quantifier elimination. We
show that monadic stability corresponds to a gap in the spectrum of growth
rates, from slower than exponential to faster than exponential. This allows us
to give a nearly complete description of the spectrum of slower than
exponential growth rates (without the assumption of stability), confirming some
longstanding conjectures of Cameron and Macpherson and proving the existence of
gaps not previously recognized.
