Why are the lowest and highest protein types so rare in the F2?
The plant with the highest protein would have the genotype AABBDDEEFFGGHH. The F1 was Aa so when selfed, ¼ of the progeny should be AA. The same logic holds for every gene pair and thus the expected frequency of AABBDDEEFFGGHH from selfing the AaBbDdEeFfGGHh F1 would be ¼ X ¼ X ¼ X¼ X ¼ X 1X ¼ = 1/4096. The same would be true of the lowest possible protein genotype (aabbddeeffGGhh). If we do not plant a large number of F2s, it is unlikely that our extreme phenotypes would be observed since there is only one chance out of 4096 of it being produced.