In plants inbreeding may occur naturally in the form of self- pollination. Inbreeding is also deliberately...

  

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In plants inbreeding may occur naturally in the form of self- pollination. Inbreeding is also deliberately practiced as a method to create genetic unifor- mity in populations of interest for genetic or breeding research, for retaining genotypes of inbred cultivars. Suppose the number of plants that are carrying genes AA, Aa, and aa in generation t are called X, Y, and Z, respectively. These variable, X, Y, and Z, changes according the network of nodes that is represented by the following diagram: 1 CC 1/2 Y 1/4 1/4 (a) Explain in words the meaning of connections between nodes and what this diagram repre- sents. (b) Write the matrix equation that related the (t+1)-generation to the t-generation, i.e.. equation of the type 7+1 ATt. 2+1= (c) Solve the eigenvalue problem for the matrix problem of part (a), i.e., find the eigenvalues and the corresponding eigenvectors of matrix A. (d) Based on the results of part (b), write the solution to the eigenvalue problem t [B] (e) Suppose we have the initial condition (IC) 7o = 1 Write the solution to the initial value problem, i.e., 7 subject to IC. (f) Calculate what will happen with the solution found in part (c) in the long run, i.e., find the behavior of solution when t→∞. (g) In the long run, will the population of plants be homozygous or heterozygous? Base you conclusion on the result of calculations performed in part (e). In plants inbreeding may occur naturally in the form of self- pollination. Inbreeding is also deliberately practiced as a method to create genetic unifor- mity in populations of interest for genetic or breeding research, for retaining genotypes of inbred cultivars. Suppose the number of plants that are carrying genes AA, Aa, and aa in generation t are called X, Y, and Z, respectively. These variable, X, Y, and Z, changes according the network of nodes that is represented by the following diagram: 1 CC 1/2 Y 1/4 1/4 (a) Explain in words the meaning of connections between nodes and what this diagram repre- sents. (b) Write the matrix equation that related the (t+1)-generation to the t-generation, i.e.. equation of the type 7+1 ATt. 2+1= (c) Solve the eigenvalue problem for the matrix problem of part (a), i.e., find the eigenvalues and the corresponding eigenvectors of matrix A. (d) Based on the results of part (b), write the solution to the eigenvalue problem t [B] (e) Suppose we have the initial condition (IC) 7o = 1 Write the solution to the initial value problem, i.e., 7 subject to IC. (f) Calculate what will happen with the solution found in part (c) in the long run, i.e., find the behavior of solution when t→∞. (g) In the long run, will the population of plants be homozygous or heterozygous? Base you conclusion on the result of calculations performed in part (e).

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a The diagram represents a transition diagram or a state transition matrix where each node represent... View the full answer