The pilot reported the airplane, which was equipped with long range fuel tanks, had full fuel tanks prior to the flight. After 3.8 hours of flight time, the engine began to surge then lost power. An off airport forced landing was made during which time the airplane nosed over. When the airplane was righted, it was discovered that the right fuel cap was missing, although the chain and spring clip were still in place. The pilot reported that the purpose of the flight was to act as a safety aircraft for Operation Migration. She stated that most of the flying involves making right hand turns which results in a higher fuel quantity in the right tank than in the left. The right fuel quantity indicator was indicating 3/8 to 1/2 tank of fuel and the left fuel tank was lower when the engine lost power. The pilot and pilot-rated passenger viewed the top of the wings twice after the airplane was fueled. Once to install the canopy cover and again to remove the canopy cover. The fuel cap was not checked for security nor was the fuel level visually checked after the airplane was fueled five days prior to the accident.