Combining cosmological smoothed particle hydrodynamics (SPH) simulations with a previously developed Lyα production/transmission model and the Early Reionization Model (ERM; reionization ends at redshift z∼ 7), we obtain Lyα and UV luminosity functions (LFs) for lyman alpha emitters (LAEs) at 5.7 ≤z≤ 7.6. Matching model results to observations at z∼ 5.7 requires escape fractions of Lyα, fα= 0.3, and UV (non-ionizing) continuum photons, fc= 0.22, corresponding to a colour excess, E(B−V) = 0.15. We find that (i) fc increases towards higher redshifts, due the decreasing mean dust content of galaxies, (ii) the evolution of fα/fc hints at the dust content of the interstellar medium becoming progressively inhomogeneous/clumped with decreasing redshift. Using the model assumptions, clustering of sources has little effect on the Lyα LF for a cosmic hydrogen neutral fraction χH i≤ 10−4, a value attained at z≤ 6.6 in the ERM. However, during the initial reionization phases (z≳ 7), the clustering photoionization boost becomes important. We quantify the physical properties of observed LAEs and their redshift evolution, for which we give handy analytical fitting functions. Halo (stellar) masses are in the range 10.0 < log Mh < 11.8 (8.1 < log M* < 10.4) with Mh∝M0.64*. The star formation rates are , mass-weighted mean ages are t* > 20 Myr at all redshifts, while the mean stellar metallicity increases from Z= 0.12 Z⊙ at z∼ 7.6 to Z= 0.22 Z⊙ at z∼ 5.7; both t* and Z positively correlate with stellar mass. The brightest LAEs are all characterized by large and intermediate ages (≈200 Myr), while objects in the faint end of the Lyα LF show large age and star formation rate spreads. With no more free parameters, the spectral energy distributions of three LAE at z∼ 5.7 observed by Lai et al. (2007) are well reproduced by an intermediate age (182–220 Myr) stellar population and the above E(B−V) value. The model uncertainties, mostly related to the simplified treatment of dust and to the possible effects related to gas outflow/infall, are discussed along with their impact on the results.