Using the Millennium-II Simulation dark matter sub-halo merger histories, we created mock catalogs of Lyman Alpha Emitting (LAE) galaxies at z=3.1 to study the properties of their descendants. Several models were created by selecting the sub-halos to match the number density and typical dark matter mass determined from observations of these galaxies. We used mass-based and age-based selection criteria to study their effects on descendant populations at z~2, 1 and 0. For the models that best represent LAEs at z=3.1, the z=0 descendants have a median dark matter halo mass of 10^12.7 M_Sun, with a wide scatter in masses (50% between 10^11.8 and 10^13.7 M_Sun). Our study differentiated between central and satellite sub-halos and found that ~55% of z=0 descendants are central sub-halos with M_Median~10^12 M_Sun. This confirms that central z=0 descendants of z=3.1 LAEs have halo masses typical of L* type galaxies. The satellite sub-halos reside in group/cluster environments with dark matter masses around 10^14 M_Sun. The median descendant mass is robust to various methods of age determination, but it could vary by a factor of 5 due to current observational uncertainties in the clustering of LAEs used to determine their typical z=3.1 dark matter mass.
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