White light emitting diodes (LEDs) based on III-nitride InGaN/GaN quantum wells currently offer the highest overall efficiency for solid state lighting applications. Although current phosphor-converted white LEDs have high electricity-to-light conversion efficiencies, it has been recently pointed out that the full potential of solid state lighting could be exploited only by color mixing approaches without employing phosphor-based wavelength conversion. Such an approach requires direct emitting LEDs of different colors, including, in particular, the green-yellow range of the visible spectrum. This range, however, suffers from a systematic drop in efficiency, known as the "green gap," whose physical origin has not been understood completely so far. In this work, we show by atomistic simulations that a consistent part of the green gap in c-plane InGaN/GaN-based light emitting diodes may be attributed to a decrease in the radiative recombination coefficient with increasing indium content due to random fluctuations of the indium concentration naturally present in any InGaN alloy.