We study the properties of Lyman- \alpha emitters ( LAEs ) and Lyman-break galaxies ( LBGs ) at z = 3 - 6 using cosmological SPH simulations . We investigate two simple scenarios for explaining the observed Ly \alpha and rest-frame UV luminosity functions ( LFs ) of LAEs : ( i ) the “ escape fraction ” scenario , in which the effective escape fraction ( including the IGM attenuation ) of Ly \alpha photons is f _ { Ly \alpha } \approx 0.1 ( 0.15 ) at z = 3 ( 6 ) , and ( ii ) the “ stochastic ” scenario , in which the fraction of LAEs that are turned on at z = 3 ( 6 ) is { C _ { stoc } } \approx 0.07 ( 0.2 ) after correcting for the IGM attenuation . Our comparisons with a number of different observations suggest that the stochastic scenario is preferred over the escape fraction scenario . We find that the mean values of stellar mass , metallicity and black hole mass hosted by LAEs are all smaller in the stochastic scenario than in the escape fraction scenario . In our simulations , the galaxy stellar mass function evolves rapidly , as expected in hierarchical structure formation . However , its evolution is largely compensated by a beginning decline in the specific star formation rate , resulting in little evolution of the rest-frame UV LF from z = 6 to 3 . The rest-frame UV LF of both LAEs and LBGs at z = 3 & 6 can be described well by the stochastic scenario provided the extinction is moderate , E ( B - V ) \approx 0.15 , for both populations , although our simulation might be overpredicting the number of bright LBGs at z = 6 . We also discuss the correlation function and bias of LAEs . The Ly \alpha LFs at z = 6 in a field-of-view of 0.2 \deg ^ { 2 } show a significantly larger scatter owing to cosmic variance relative to that in a 1 \deg ^ { 2 } field , and the scatter seen in the current observational estimates of the Ly \alpha LF can be accounted for by cosmic variance .