In 1991 the U.S. Fish and Wildlife Service proposed logging restrictions on near

Question

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.1 They divided the female owl population into three categories juvenile (up to one 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 The populations after one year are given by the column matrix The subscript 1 tells us that the matrix gives the population after one year. The column matrices for subsequent years will have subscripts 2, 3, 4, etc. How many sub adult females are there after one year? 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, If the population distribution at any time is given by then the distribution one year later is A Fill in the blanks in the following statements. Each year_juvenile females are born for each 100 adult females. Each year_% of the juvenile females survive to become subadults. Each year_% of the subadults survive to become adults and_% of the adults survive. ^1Lamberson, R. H., R. McKelvey, B. R. Noon, and C. Voss, "A Dynamic Analysis of North* Spotted Owl Viability in a Fragmented Forest Landscape," Conservation Biology. Vol. N

Explanation / Answer

Soution of question 1 ; Here as per given information, the original amount of subadult women as given in the X0 matrix is 200 but its corresponding value in matrix X1 that shows the population of women after one year is 117.

So the total population of subadults women after one year is 117.

This is the answer of questione one.

Again we observe total population of all women under all three categories after 1 year is represented by matrix X1

that is 693+117+2116 =2926

but initially total women were 2950, that means total population of women after one year is decreased. as 2926 is less than 2950

This is the answer of question 2.

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