You are studying a population of a rare shark to assess its long-term prospects
ID: 172431 • Letter: Y
Question
You are studying a population of a rare shark to assess its long-term prospects for survival. Assume that you can determine the age and gender of each shark.
You perform a mark-recapture study to estimate the number of individuals of each age. You capture sharks, determine their age and sex, and mark them. You return 3 months later, capture sharks again, note age and sex and whether they had been marked on your first visit. You obtain the following data:
Shark Age
# Marked and
# Captured
# Marked
Estimated Total
(years)
Released
(2nd visit)
(2nd visit)
Nx
(1st visit)
0
97
59
11
1
66
54
15
2
36
51
13
3
32
38
13
4
42
52
32
5
37
35
27
6
37
30
21
7
20
17
14
8
9
6
4
9
0
0
0
Based on these results, estimate the number of individuals (Nx) in the population for each age (complete the last column of the table). Show your work for the first two rows.
2. Assuming that your mark-recapture estimates are accurate, and that the population age structure is stable, use your estimates of Nx to complete the following life table for your sharks. Show your work for the first two rows.
Shark Age
(years)
Nx
lx
dx
qx
0
1
2
3
4
5
6
7
8
9
3. Assuming the values for lx in your life table are correct, what type of survivorship curve does this population have? Make a graph of lx vs age to answer this question (remember to graph it on log scale). Explain what this tells us about the life history of these sharks in 2-3 complete sentences. Give an example of another species with a similar survivorship curve (justify your answer).
4. In a captive population of 108 goldfish, you determine that they can give birth to 11 baby goldfish per month under ideal conditions. On average, 7 die per month. Based on these numbers, and given unlimited space and resources, how many goldfish would be in your captive population in 6 months? 2 years (24 months)? Show all your work.
5. A population of a species exhibits logistic growth. If the carrying capacity of their habitat is 427 individuals and r = 0.17 (individuals per month), what is the maximum population growth rate for the population? Show all your work.
Shark Age
# Marked and
# Captured
# Marked
Estimated Total
(years)
Released
(2nd visit)
(2nd visit)
Nx
(1st visit)
0
97
59
11
1
66
54
15
2
36
51
13
3
32
38
13
4
42
52
32
5
37
35
27
6
37
30
21
7
20
17
14
8
9
6
4
9
0
0
0
Explanation / Answer
Capture-recapture is a method which is widely used to estimate the population size. By capturing a small random sample of the population and then marking them and releasing them back into their environment will make them to disperse in the general population.
Again you will try to capture a sample of the population (recaptured) and will try to estimate the ratio of marked to recaptured individuals in the second sample, and this will be used to estimate the general population size.
Nx= Total individuals marked in first sample x size of second sample/ Number recaptured individuals in second sample
Shark Age(years)
# Marked and Released (1st visit)
# Captured(2nd visit)
# Marked(2nd visit)
Estimated Total Nx
0
97
59
11
97x 59/11=520.3
1
66
54
15
66x 54/15=237.6
2
36
51
13
36x 51= 13=141.2
Shark Age (Years)
Estimated Total Nx
Ix (Nx/520.3)
dx
qx (dx/Ix)
0
520.3
520.3/520.3=1.000
1-0.457=0.543
0.457/1=0.457
1
237.6
237.6/520.3=0.457
0.543-0.457=0.086
0.086/0.457=0.188
2
141.2
141.2/520.3=0.271
0.457-0.271=0.186
0.186/0.271=0.686
Shark Age(years)
# Marked and Released (1st visit)
# Captured(2nd visit)
# Marked(2nd visit)
Estimated Total Nx
0
97
59
11
97x 59/11=520.3
1
66
54
15
66x 54/15=237.6
2
36
51
13
36x 51= 13=141.2
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