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We present simulations of the cluster distribution in several dark mattermodels, using an optimized version of the truncated Zel'dovich approximation(TZA). We compare them with N-body cluster simulations and find that the TZAprovides a very accurate description of the cluster distribution as long asfluctuations on the cluster mass scale are in the mildly non-linear regime. Thesimulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) withn=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant(h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with\Omega_0=0.2. We compare the simulations with a redshift sample of Abell/ACOclusters, using the integral of the 2-point correlation function and theprobability density function. We find that the best models at reproducing thedata are CHDM and LCDM. All the other models are ruled out. The reducedskewness S_3 is fairly constant with S_3=1.9, independent of the DM model andconsistent with observational data. The abundances of clusters predicted usingthe Press--Schechter theory provide strong constraints: only the CHDM, LOWH andLCDM models appear to produce the correct number-density of clusters.Comment: 14 pages + 10 figures (Fig. 5 on request to borgani@vaxpg.pg.infn.it)  uuencoded gzipped tarred postscript file, accepted for publication in MNRA

The cluster distribution as a test of dark matter models - I. Clustering properties