  We present theoretical results for the expected fraction of Lyman Break
Galaxies (LBGs) to be detected as strong Lyman alpha emitters (LAEs) in the
redshift range 5 < z < 7. We base our analysis on the 2-billion particle SPH
simulation MareNostrum High-z Universe. We approximate galaxies as static dusty
slabs with an additional clumpy dust distribution affecting stellar populations
younger than 25 Myr. The model for the Lyman alpha escape fraction is based on
the results of our Monte-Carlo radiative transfer code (CLARA) for a slab
configuration. We also fix the transmission of Lyman alpha photons through the
intergalactic medium to a constant value of 50% at all redshifts. From the
results of this model we calculate xLya, the fraction of Lyman Break Galaxies
with Lyman alpha equivalent width (EW) larger than 50 Angstrom. We find a
remarkable agreement with observational data at 4.5 < z < 6. For bright (-22 <
MUV < -20.5) and faint (-20.5 < MUV < -18.5) galaxies our model predicts xLya =
0.02 \pm 0.01 and xLya = 0.47 \pm 0.01 while observers report xLya = 0.08 \pm
0.02 and xLya = 0.47 \pm 0.16, respectively. Additional evolution of the
extinction model at redshift z \sim 7, that decreases the intensity of
transmitted Lyman alpha radiation by a factor of f_T = 0.4 as to match the LAE
luminosity function at z \sim 6.5, naturally provides a good match for the
recently reported xLya fractions at z > 6.3. Exploring different toy models for
the Lyman alpha escape fraction, we show that a decreasing Lyman alpha escape
fraction with increasing UV galaxy luminosity is a key element in our model to
explain the of larger xLya fractions for fainter LBGs.
