imagine a species of creature that each year either dies or gives birth to asingleoffspring. That offspring itself will either give birth or die in the following year, and so on. We could represent this with the following transition matrix:

infantsadultsdead

infants00.20.8

adults3.30.550.45

dead001

This is not properly a Markov matrix, because the middle row does not add to 1. Instead, the matrix says the following: 20% of infants survive to adulthood. Adults have a 45% annual mortality rate. Adults who survive have a litter of 6 infants (3.3 = 0.55 6). The techniques of the lecture can still be applied to a matrix such as this. Because the questions are most easily done by multiplying the transition matrix by an initial vector many times, you may want to do them on a spreadsheet. In Excel, the command to multiply two matrices is MMULT()

a) Show for at least 10 years, how an initial population of 2 adults grows. (How do you make the 1x3 initial vector? It reflects infants, adults and deaths; that should give you the clue)

b) Show that if adult survival drops to 45% (for example, from overharvesting), the population dies out. (Which value in the initial vector so you change to reflect the new death rate?)