Derive an expression for the distribution of the three possible genotypes in the population after n generations
Learning Goal: I’m working on a linear algebra report and need an explanation and answer to help me learn.Study the genetic problems which is one application of Linear Algebra(keywords for searching:
genetics linear algebra or you can find this problem in the book of Howard Anton, page 663).
• Display the mathematical background of this problem, do not copy from the book or
Internet, just show your understanding. Problems. In autosomal inheritance, offspring inherit one gene of the pair belonging toeach parent in order to get a pair. For the following, assume that either of a parent’sgenes is equally likely to be inherited.I) A farmer has a large population of plants consisting of some distribution of allthree possible genotypes: AA, Aa, aa. First show that the following table correctlydescribes the probabilities of the possible genotypes of the offspring for all possiblecombinations of the genotypes of the parents.
II) The farmer undertakes a breeding program in which each plant in the populationis always fertilized with a plant of genotype AA.(a) Derive an expression for the distribution of the three possible genotypes in thepopulation after one generation in terms of the fractions present in the initialpopulation.(b) Derive an expression for the distribution of the three possible genotypes in thepopulation after n generations in terms of the fractions present after n − 1.