# Gregor Mendel - Laws Of Inheritance

### offspring factors dominant factor

To explain the numerical relationships he obtained, Mendel developed the Law of Segregation. He proposed that during the process of egg and sperm formation, the two factors separate, or segregate, so that each egg or sperm contain only one factor. For a parent containing one of each type of factor, this means that half the sperm (or eggs) will contain the dominant factor, and half the recessive factor. During fertilization, these randomly pair up, so that some offspring will have two dominants, some two recessives, and some one of each. Simple algebra shows that the ratio of offspring in such a cross will be 3:1, just as Mendel found.

To show how this works, let 0.5D be the proportion of dominant factors and 0.5r be the proportion of recessive factors. Multiplying (0.5D + 0.5r) times itself gives the offspring ratios, 0.25D^{2} + 0.5Dr + 0.25r^{2}. In this expression, 0.25D^{2} indicates that one-quarter of the offspring will have both dominant factors, 0.5Dr means half will have one of each type, and 0.25r^{2}means one-quarter will have both recessive factors. Since both the D^{2} and Dr organisms will show the dominant trait, the ratio of dominant to recessive traits in the offspring will be 0.75:0.25, or 3:1.

Mendel went on to study crosses between peas with multiple sets of traits, such as round seeds plus tall plants crossed with wrinkled seeds plus short plants. He found that the factors for each trait acted independently, so that the offspring of these crosses showed all possible combinations of traits. From the results of these experiments, he formulated his second principle, known as the Law of Independent Assortment, which states that the members of factor pairs assort (segregate) independently of each other during sperm and egg formation, and combine again randomly.

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