  We study the efficiency of genus statistics in differentiating between
different models of structure formation. Simple models which reproduce the
salient features of the structure seeded by topological defects are examined.
We consider accretion onto static point masses, modeling slow-moving cosmic
string loops or other primordial point-like sources. Filamentary structures and
wakes are considered as models of the structures seeded by slow and fast moving
string, respectively. Comparison is made with predictions of genus statistics
for Gaussian fluctuations and with genus curves obtained by the CfA survey. A
generic class of density models with wakes and filaments is found to provide
results comparable or better than Gaussian models for this suite of tests.
