  The genus statistics is studied using large $N$-body simulations for several
cosmological models. We consider the effects of nonlinear gravitational
evolution, smoothing the particle data in fully nonlinear regime, and the
redshift-space distortion on the genus curve. Detailed comparison between the
theoretical prediction in weakly nonlinear theory and the appropriate
simulation results shows that the analytic formula describes the behavior of
genus in weakly nonlinear regime fairly accurately. We also find that the
redshift-space distortion on genus statistics is small in linear and weakly
nonlinear regimes. We conclude that if weakly nonlinear theory and direct
numerical simulations are combined, the normalized genus curve $G(\nu)/G(0)$ is
a powerful tool to directly check the random-Gaussian paradigm of the origin of
the large-scale structure in the universe.
