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Further matrices — Question 274

Original QCE Vault practice · 7 marks

Q274 · Practice questionTechnology-activeComplex familiar7 marks

QUESTION 274 (7 marks)

A breeding program models females in three one-year age classes. The table gives births per female during a step, the proportion surviving into the next age class, and initial counts. Offspring enter the youngest class; no females survive beyond the oldest class. Fractional expected counts are permitted.
Question 127 stimulus; see the question for exact data and required construction.
a)
Write the Leslie matrix and the initial population column vector in youngest-to-oldest order.
[2 marks]
b)
Determine the earliest integer year step at which the total female count falls below 150. Show the neighbouring totals.
[3 marks]
c)
Give one limitation of the prediction and explain its possible effect.
[2 marks]
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