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Ecology - Case Study Example

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Calculate the average relative rate of population change, [N(t+1) – N(t)]/N(t), and its standard deviation from the population data for the southern resident population of the killer whale, British Columbia, Canada.
3. Estimate the average time until extinction for a…
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1. Calculate the average relative rate of population change, [N(t N(t N(t), and its standard deviation from the population data for the southern resident population of the killer whale, British Columbia, Canada.
Bolded Values to be calculated by the student
Year
Reproductive
females
Births
Fecundity
Total
deaths
Total
population
Growth
rate
1974
19
2
0.105
2
73
 
1975
19
1
0.053
1
73
0.0000
1976
20
8
0.400
0
73
0.0000
1977
21
2
0.095
1
81
0.1096
1978
18
3
0.167
2
82
0.0124
1979
17
3
0.176
1
83
0.0122
1980
16
1
0.063
3
85
0.0241
1981
16
1
0.063
4
83
-0.0235
1982
16
0
0.000
2
80
-0.0362
1983
19
3
0.158
5
78
-0.0250
1984
21
5
0.238
3
76
-0.0256
1985
23
7
0.304
2
78
0.0263
1986
25
4
0.160
1
83
0.0641
1987
24
1
0.042
1
86
0.0362
1988
23
3
0.130
2
86
0.0000
1989
28
2
0.071
3
87
0.0116
1990
28
7
0.250
1
86
-0.0115
1991
27
3
0.111
2
92
0.0698
1992
26
6
0.231
1
93
0.0109
1993
27
2
0.074
4
98
0.0537
1994
26
6
0.231
4
96
-0.0204
1995
25
5
0.200
4
98
0.0208
1996
23
0
0.000
6
99
0.0102
1997
25
2
0.080
4
93
-0.0606
1998
26
2
0.077
7
91
-0.0215
1999
27
3
0.125
5
86
-0.0550
2000
24
3
0.130
7
84
-0.0233
2001
23
 
 
 
80
-0.0476
Sum
632
85
3.734
2.88889
  2383
 0.112
Average
22.5714
3.14814
0.138
78
85.107
0.004
Std dev
0.040
2. Did the population increase or decrease over this period? Was the average exponential growth rate positive or negative?
The population increased slightly, at an average rate of 0.4% per year. The average exponential growth rate was positive.
3. Estimate the average time until extinction for a population of killer whales. Assume that for the killer whale population the average growth rate (r) is zero. Based on the population size in 2001, what is your estimate for the average time to extinction?
The equation for time to extinction with r = 0 is; T (N) = 2/S2 ln (1+s2N) + 1.The observed value of S is 0.04, and the value of N is 80 individuals. The expected time of extinction is approximately 1400years.
4. How does T(N) change with the size of the initial population and with the variance in the rate of change in population size?
As the population increases, the chances of extinction becomes smaller. Increase in variation makes extinction more likely i.e. as variation increases, the time to extinction decreases.
5. Fill in the expected times to extinction for the range of population sizes (N) and standard deviations of population growth rate (S) in Table DA7-1:
Initial population size
S
10
100
1000
10000
0.05
20.75401
179.5148
1003.2104
2607.477
0.1
20.062036
219.7225
480.5791
924.024
0.2
17.82361
81.4719
186.6786
300.698
0.5
11.022104
27.06478
45.20362
63.596
6. What would T(N) be for the killer whale population at its largest and smallest sizes? If a population grows just by chance, does this mean that its prospects for long-term survival improve? Assume that the sample standard deviation of r in the spreadsheet accurately estimates the underlying value of S.
The killer whale population ranged between 73 individual (lowest) and 99 individuals (highest).If we assume the same value of S as 0.04, the respective values of T (N) would be;
T (73) is approximately 139 years.
T (99) is approximately 184 years.
If a population grows, even by chance, its expected survival time increases, since it is further from N = 0.
7. If this were always the case, why should we be worried about small populations? Under what conditions might you expect a population not to increase when reduced to low population size? This certainly has been the case for many endangered species that have gone extinct or now teeter on the edge. Do some populations simply not “have what it takes” to maintain healthy levels?
If this was always the case, we should be worried of small population since their rate of extinction is high. Small population takes few years to become extinct than large population.
Condition that can lead to population not to increase when reduced in size include;
Low Fecundity ratio ÷ this is the ability to produce abundant healthy offspring. If the fecundity ratio is low, it means that few young born will survive, Hence reducing the growth rate
Few reproducing females ÷ if a population contains few reproducing females, the growth rate will be low, and eventually the population will be approaching extinction.
Few fertile males ÷if a population contain only a few fertile males, the rate of growth will be low since only a few females will be fertilized. This will lead to few births than deaths, hence the population will approach extinct values. Read More
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