3. A swan population can be subdivided into young swans (Y) and mature swans (M). We...

 

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3. A swan population can be subdivided into young swans (Y) and mature swans (M). We can then set up a discrete-time model of these populations as follows: Y+1 [0.57 1.5] Y [Mt+1] = 0.25 0.88 M (a) Explain the biological meaning of each of the four numbers in the matrix of this model. (b) It turns out that the eigenvectors of this matrix are approximately as follows: (You can check this using Sage if you wish.) 1.9] -0.6 with eigenvalue 0.09, and [1.9] with eigenvalue 1.36. What will happen to the swan population in the long run? (Again, be specific. Which eigenvalue is dominant in this case, and what does this mean about the long-term behavior?) 3. A swan population can be subdivided into young swans (Y) and mature swans (M). We can then set up a discrete-time model of these populations as follows: Y+1 [0.57 1.5] Y [Mt+1] = 0.25 0.88 M (a) Explain the biological meaning of each of the four numbers in the matrix of this model. (b) It turns out that the eigenvectors of this matrix are approximately as follows: (You can check this using Sage if you wish.) 1.9] -0.6 with eigenvalue 0.09, and [1.9] with eigenvalue 1.36. What will happen to the swan population in the long run? (Again, be specific. Which eigenvalue is dominant in this case, and what does this mean about the long-term behavior?)