  There are two mechanisms for the generation of an asymmetry between the
strange and anti-strange quark distributions in the nucleon: nonperturbative
contributions originating from nucleons fluctuating into virtual baryon-meson
pairs such as $\Lambda K$ and $\Sigma K$, and perturbative contributions
arising from gluons splitting into strange and anti-strange quark pairs. While
the nonperturbative contributions are dominant in the large-$x$ region, the
perturbative contributions are more significant in the small-$x$ region. We
calculate this asymmetry taking into account both nonperturbative and
perturbative contributions, thus giving a more accurate evaluation of this
asymmetry over the whole domain of $x$. We find that the perturbative
contributions are generally a few times larger in magnitude than the
nonperturbative contributions, which suggests that the best region to detect
this asymmetry experimentally is in the region $0.02 < x < 0.03$. We find that
the asymmetry may have more than one node, which is an effect that should be
taken into account, e.g. for parameterizations of the strange and anti-strange
quark distributions used in global analysis of parton distributions.
