Finding proto-clusters to trace galaxy evolution: I. The finder and its performance

We develop a method to identify proto-clusters based on dark matter halos represented by galaxy groups selected from surveys of galaxies at high redshift. We test the performance of this method on halos in N-body simulations, and find it can correctly identify more than 85% of the true proto-clusters with $\gtrsim$ 95% purity and with mass estimates typical within 0.25 dex from their true values. We show how the information provided by the proto-clusters can be used to link galaxies in present-day clusters of galaxies with their high redshift progenitors. Our tests show that the proto-clusters identified by our method can recover reliably the progenitor stellar mass distribution of galaxies, thereby providing an avenue to investigate the formation and evolution of present-day galaxy clusters and their member galaxies.