The Large Area Lyman Alpha survey has found \approx 150 Lyman- \alpha emitters at z=4.5 .
While stellar models predict a maximum Lyman- \alpha equivalent width ( EW ) of 240 Å 60 % of the Lyman- \alpha emitters have EWs exceeding this value .
We attempt to model the observed EW distribution by combining stellar population models with an extrapolation of Lyman break galaxy luminosity function at z=4 , incorporating observational selection effects and Malmquist bias .
To reproduce the high EWs seen in the sample we need to postulate a stellar initial mass function ( IMF ) with extreme slope \alpha = 0.5 ( instead of 2.35 ) ; zero metallicity stars ; or narrow-lined active galactic nuclei .
The models also reveal that only 7.5-15 % of galaxies need show Lyman- \alpha emission to explain the observed number counts .
This raises the possibility that either star-formation in high redshift galaxies is episodic or the Lyman- \alpha galaxies we are seeing are the youngest 7.5-15 % and that Lyman- \alpha is strongly quenched by dust at about 10 ^ { 7 } years of age .