A population contains two alleles, X and Y, with 98% of the population initially having allele...

 

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A population contains two alleles, X and Y, with 98% of the population initially having allele X and 2% allele Y. The mutation rate from X to Y is 4% per generation, and the mutation rate from Y to X is 2% per generation. (a) Write down a linear system that describes how allele frequencies change from one generation to the next. (b) Write your linear system as a matrix equation in the form +1 = A. (c) What is the approximate distribution of allele frequencies in the third generation? (d) By finding the eigenvalues of A, show that the alleles will eventually stabilise, with neither reaching fixation. (e) Find the eigenvector associated with the dominant eigenvalue of A. (f) What does (e) tell you about the long-term distribution of alleles? A population contains two alleles, X and Y, with 98% of the population initially having allele X and 2% allele Y. The mutation rate from X to Y is 4% per generation, and the mutation rate from Y to X is 2% per generation. (a) Write down a linear system that describes how allele frequencies change from one generation to the next. (b) Write your linear system as a matrix equation in the form +1 = A. (c) What is the approximate distribution of allele frequencies in the third generation? (d) By finding the eigenvalues of A, show that the alleles will eventually stabilise, with neither reaching fixation. (e) Find the eigenvector associated with the dominant eigenvalue of A. (f) What does (e) tell you about the long-term distribution of alleles?