The question
Name: ______________________ Date: ____________ Logistic growth and carrying capacity in a seal colony (4 points)
Graph
Gray seals on an island group after hunting stopped
Hunting of gray seals on a group of islands stopped in 1960. Researchers counted the seals every 5 years from aerial photographs of the breeding beaches. Researchers estimate that r_max for this population is 0.12 per year.
Data table
| Year | Seals counted |
|---|---|
| 1960 | 1200 |
| 1965 | 2000 |
| 1970 | 3100 |
| 1975 | 4500 |
| 1980 | 6000 |
| 1985 | 7300 |
| 1990 | 8300 |
| 1995 | 9000 |
| 2000 | 9400 |
| 2005 | 9700 |
| 2010 | 9800 |
| 2015 | 9900 |
| 2020 | 9850 |
(a) Describe the pattern of population growth from 1960 to 2020, and identify the approximate carrying capacity. [1 point]
(b) Calculate the average rate of population growth between 1975 and 1980, in seals per year. [1 point]
(c) Use dN/dt = r_max N (K − N)/K, with r_max = 0.12 per year and K = 10,000, to calculate the growth rate when N = 9,000. Then explain why it is lower than the growth rate between 1975 and 1980, even though the population was larger. [1 point]
(d) In 2020, a new fishery begins catching large numbers of the fish the seals eat. Predict the effect on the seal population over the next decade, and justify your prediction. [1 point]