A system and method for storing, shipping, preserving and ripening produce. Packaging of respiring produce, particularly avocados, in sealed tray systems. The tray systems include a lower bowl-shaped tray having an upper lip to which a flexible film is adhered. The flexible film has an aperture covered by a breathable membrane. The film permits passage of water vapor to reduce the chance of mold formation during packaging and shipping. The breathable membrane controls gaseous exchange at different temperatures and has pores that open above the threshold temperature. The breathable membrane alters the O2 and CO2 within the tray above the threshold temperature, thus slowing up the ripening process at elevated temperatures.