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How did Mendel explain this result?

We don't know exactly how Mendel figured it out, but he probably tried several ideas until he found the one that made sense. You can do it too. Suppose that each plant has TWO trait controllers (Mendel did not know about genes, or we would say two genes). He realized that something in the plant controlled for pea color and that there must be two controllers in the peas of each plant. In any plant, if either one of the two genes is for green, the peas will be green, because green is a dominant trait in peas. So how could you get a 3 to 1 ratio of green peas to yellow peas? You assume that both parents have one gene for green and another for yellow. The combination possibilities predict a 3:1 ratio. Setting up a  little table like the one below shows how easy it is to see all the possible combinations.

  G y
G GG  (green) Gy  (green)
y yG  (green) yy  (yellow)

Remember, anytime one of the two genes is for green, the peas will be green because green is dominant over yellow. The only way peas can be yellow is if BOTH genes control for yellow.

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