.., The Wright-Fisher model is a Markov chain model for genetic drift, de- scribed as follows....

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.., The Wright-Fisher model is a Markov chain model for genetic drift, de- scribed as follows. Consider a population of a species over time. Assume that over time, the population consists of generations 0, 1, 2, 3, . . ., with no overlap between generations. Assume each generation has the same number N individuals. We focus on a particular gene in this population. Every individual has two copies of this gene, and therefore every gener- ation has 2N copies of the gene. Every copy of the gene can be one of two variants (alleles), A or B. We want to keep track of the frequencies of A and B through each generation. Let X be the number of copies of allele A in generation t. We set transition probabilities as follows: P(Xt+1 = j | X = i) = j (2) (1-2) (2N)! j!(2N-j)! 2N 2N 2N-j This can be interpreted as follows: When a new generation is created, each of its 2N genes is drawn independently and uniformly at random from the set of 2N genes of the previous generation. (a) What are the absorbing states of this Markov chain? In real-world terms, what do these absorbing states mean? (b) Let N=50. If generation 0 has i = 10 copies of allele A, find the probability that eventually all copies of the gene in the population will be allele A. .., The Wright-Fisher model is a Markov chain model for genetic drift, de- scribed as follows. Consider a population of a species over time. Assume that over time, the population consists of generations 0, 1, 2, 3, . . ., with no overlap between generations. Assume each generation has the same number N individuals. We focus on a particular gene in this population. Every individual has two copies of this gene, and therefore every gener- ation has 2N copies of the gene. Every copy of the gene can be one of two variants (alleles), A or B. We want to keep track of the frequencies of A and B through each generation. Let X be the number of copies of allele A in generation t. We set transition probabilities as follows: P(Xt+1 = j | X = i) = j (2) (1-2) (2N)! j!(2N-j)! 2N 2N 2N-j This can be interpreted as follows: When a new generation is created, each of its 2N genes is drawn independently and uniformly at random from the set of 2N genes of the previous generation. (a) What are the absorbing states of this Markov chain? In real-world terms, what do these absorbing states mean? (b) Let N=50. If generation 0 has i = 10 copies of allele A, find the probability that eventually all copies of the gene in the population will be allele A.