#1 Modeling the female pinniped population ' This problem is based on the presentation by Eli Holmes of the National Marine Fisheries Service. In his presentation he describes how Leslie matrices are used in species conservation and, more importantly, how to estimate the values that go into a Leslie matrix, such as the fecundity rates and the survivorship rates. The assumptions about the pin niped population are as follows: Reproduction starts at age 4 On average 60% of the mature adult females have a pup every year; the sex ratio of pups is 50:50 Juveniles have a survival rate of 80%; the other age groups have a survival rate of 90%. Mature adults remain in the 4+ age group a] Explain why the element L15 is 0.3. b) Explain the meaning of the entry L55. 100 800 c) Assume the initial population is given as X(0) = 500 . Go to the and enter the Leslie matrix 300 200 given above as matrix A and the initial population as matrix B. Use appropriate powers of the matrix (compute the power and then ask that the answer be used as matrix A] to compute the female pinniped population in years 1, 5, and 20. Clearly write down which formula you used to compute each ofthese, using L for the Leslie matrix of the pinniped population. Round your answers to the nearest integer. Formula: X01) = H1) = d) Use the to compute the eigenvalues and eigenvectors for the matrix L. Write down the eigenvalue and a specific eigenvector for this eigenvalue. [Since this is a 5 X 5 matrix, you will see 5 eigenvalues. You are interested in the largest one, which is listed at the top.] Eigenvalue: Eigenvector: e] What does the eigenvalue tell you about the long-term behavior of the population? 1') What is the long-term proportion of the individuals in each age group? That is, what is the percentage of pups, 1-year-olds, etc? Round your percentages to one decimal place. #2 Explain in your own words the geometric meaning of the eigenvector. #3 What does the largest eigenvalue of the Leslie matrix for age-structured populations mean in the context of the application