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Unformatted text preview: Linear Algebra in Genetics Carter Butaud Michael Yamamoto June 4, 2008 1 1 Problems: In autosomal inheritance, offspring inherit one gene of the pair belonging to each parent in order to get a pair. For the following, assume that either of a parents genes is equally likely to be inherited. 1. A farmer has a large population of plants consisting of some distribution of all three possible genotypes: AA, Aa, aa. First show that the following table correctly describes the probabilities of the possible genotypes of the offspring for all possible combinations of the genotypes of the parents. AA,AA AA,Aa AA,aa Aa,Aa Aa,aa aa,aa Genotype AA 1 .5 .25 of Aa .5 1 .5 .5 Offspring aa .25 .5 1 Let a , b , c denote the portion of the initial population with genotype AA, Aa, aa, respectively. Solution: One can use Punnett squares for each of the six cases to see all possible outcomes. The following are the completed Punnett squares: A A A AA AA A AA AA A a A AA Aa A AA Aa a a A Aa Aa A Aa Aa A a A AA Aa a Aa Aa a a A Aa Aa a aa aa a a a aa aa a aa aa By looking at the first Punnett square, one can determine the possible outcomes of an AA,AA pairing. As expected, all four boxes are also filled in with AA as those are the only possible outcomes and there is therefore a probability of 1 that the child with have a genotype of AA....
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