Answers to Exercise 28
Population Viability Analysis
1. Given a mean l = 1 and s = 0.5, our population had a 100% probability of extinction. The
variation, s, was so high that eventually over the 100 year trial the population dipped below
0 at some point in time.
2. There appears to be a risk in running the model for too short a period. For example, given a
mean l = 1 and s = 0.5, our risk of extinction was only 0.2 when the model was run for 4
years. The risk for running the model for extended periods of time is that the conditions in the
model (mean l and s) are specified for the duration of the modeling period. If for some reason
the mean and s change, your model results will not reflect these changes. Note, however, that
you could easily restructure the spreadsheet to draw from a mean l that perhaps changed
deterministically over time.
3. As s decreases to nearly 0, your model becomes a deterministic model. Since l is set to 1, the
population size remains constant over time, with no change. The only way to change this
outcome is to change l in cell C4. With no variance in l, and a fixed l value, the population
will increase geometrically, decrease geometrically, or remain stable over time.
Projection of 10 Population Simulations with
Mean Lambda = 1 and Standard Deviation 0.001
12
Population size
10
8
6
4
2
0
0
1
2
3
4
Year
Answers: Exercise 28
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4. The population changes in size due to the stochasticity incorporated into the model. Our
model results from 100 trials and 100 years show that the probability of extinction increases
as s increases. When s > 0.4, the probability of extinction was 1, indicating that 100% of our
trial simulations went extinct within 100 years.
Probabililty of Extinction for Lambda = 1,
Varying Standard Deviations
Probabillity of extinction
1.2
1
0.8
0.6
0.4
0.2
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Standard deviation of lambda (s )
5. For a fixed parameters, l = 1, s = 0.25, risk of extinction decreases as the initial population
size increases. This relationship is not linear. The extinction probability changes more slowly
when the population size was 500 or greater in our model (your results may be different).
Risk of Extinction for a Population with
Mean Lambda = 1, Standard Deviation = 0.25
Probability of extinction
0.5
0.4
0.3
0.2
0.1
0
100
200
300
400
500
600
700
800
900
1000
Initial population size
Answers: Exercise 28
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