  We present extended simulations of the distribution of galaxy clusters in
different dark matter models, using an optimized version of the Zel'dovich
approximation. Six different dark matter models are studied: Standard CDM, Open
CDM, Tilted CDM, Cold + Hot DM, low-density CDM with cosmological constant, and
low Hubble constant ($h=0.3$) CDM. We compare simulations with an Abell/ACO
redshift sample. We find that the models that best reproduce the clustering of
the real data sets are the Cold + Hot DM model and the CDM model with a
cosmological constant. The probability density function of all models and data
is always well approximated by a lognormal distribution. We also find that the
linear biasing parameter for the simulated clusters is nearly constant over a
large range of scales, but its value depends on the model. We also note that
the abundances of clusters predicted by the Press-Schechter theory provide
strong constraints on these models: only the Cold + Hot DM model and the low-H
CDM model appear to produce the correct number-density of clusters. Taking this
constraint together with the cluster clustering statistics leads one to
conclude that the best of our models is the Cold + Hot DM scenario.
