Chapter 2, Problem 3P

Population Dynamics

In 1991, the U.S. Fish and Wildlife Service proposed logging restrictions on nearly 12  million acres of Pacific Northwest forest to help save the endangered northern spotted owl. This decision caused considerable controversy between the logging industry and environmentalists.

Mathematical ecologists created a mathematical model to analyze the population dynamics of the spotted owl. They divided the female owl population into three categories: juvenile (up to 1 year old), subadult (1 to 2 years old), and adult (over 2 years old). Suppose that in a certain region there are currently 2950 female spotted owls made up of 650 juveniles, 200 subadults, and 2100 adults. The ecologists used matrices to project the changes in the population from year to year. The original numbers can be displayed in the column matrix

$X_0=\left[\begin{array}{c}650\\ 200\\ 2100\end{array}\right]$.

The populations after one year are given by the column matrix

$X_1=\left[\begin{array}{c}693\\ 117\\ 2116\end{array}\right]$.

The subscript 1 tells us that the matrix gives the population after one year. The names of the matrices for subsequent years will have subscripts 2, 3, 4, etc.

Fill in the blanks in the following statements.

(a) Each year, _____juvenile females are born for each 100 adult females.

(b) Each year, _____% of the juvenile females survive to become subadults.

(c) Each year, _____% of the subadults survive to become adults and _____ % of the adults survive.