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Question: question 1 20 marks a consider a leslie model of...

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Question 1 20 marks (a) Consider a Leslie model of a population with three age groups, 0-1 month, 1-2 months, and 2-3 months respectively. Assume that the fecundity rates of the first, second and the third age group are 2, 15, and 8 respectively. The survival rate from the first to the second age group is 45%, the survival rate from the second to the third age group is 70%. (i) Write out the Leslie matrix L for this model (i) Find L2 and hence determine the population vector in two months if the current population consists of 100 individuals in the first age group, 600 individuals in the second age group, and 500 individuals in the third group (b) Assume the Leslie matrix 1 10 0.6 0 (i) What are survival rates for the first and the second age groups? (i) Find the eigenvalues and eigenvectors of the Leslie matrix M. Which eigenvalue is dominating? Does the population become extinct, stay steady or grow?

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