1. How many subadult females are there after one year?
2. Did the total population of females increase or decrease during the year?
Let A denote the matrix

According to the mathematical model, subsequent population distributions are generated by multiplication on the left by A. That is,
A ˆ™ X0 = X1, A ˆ™ X1 = X2, A ˆ™ X2 = X3, . . . .
If the population distribution at any time is given by

Then the distribution one year later is

3. 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.
4. Calculate the column matrices X2, X3, X4, and X5. With a graphing calculator, you can specify matrix [A] to be the 3 × 3 matrix A and specify [B] to be the initial 3 × 1 population matrix X0. Display [B] in the home screen and then enter the command [A]*Ans. Each press of the ENTER key will generate the next population distribution matrix.
5. Refer to Exercise 4. Is the total female population increasing, decreasing, or neither during the first five years?
6. Explain why calculating [A]^50*[B] gives the column matrix for the population distribution after 50 years.
7. Find the projected population matrix after 50 years; after 100 years; after 150 years. On the basis of this mathematical model, what do you conclude about the prospects for the northern spotted owl?
In this model, the main impediment to the survival of the owl is represented by the number .18 in the second row of matrix A. This number is low for two reasons: (1) The first year of life is precarious for most animals living in the wild. (2) Juvenile owls must eventually leave the nest and establish their own territory. If much of the forest near their original home has been cleared, then they are vulnerable to predators while searching for a new home.
8. Suppose that, through better forest management, the number .18 can be increased to .26. Find the total female population for the first five years under this new assumption. Repeat Exercise 7, and determine whether extinction will be avoided under the new assumption.

Transcribed Image Text:

0 0 .33 .18 0 .71 .94 La