# Why does initial population size matter? Is there a critical population size where the relationship between population size and extinction probability changes? What is it? How does this relate to the minimum viable population?

Start with the initial 100 year model in which N(0) is 10, λ=1, and the standard deviation of λ is 0.5. What is the probability of the population surviving for 100 years if current conditions persist?
What value, if any, is there for running your model for 100 years rather than 4 years? What value, if any, is there for running 100 trials rather than 10? Are there any drawbacks to running models for longer time periods or more trials? If so, what are they?
A stochastic model like this should yield the same results as a deterministic model if the variation is very low. Test if this is true by plugging in a very low value for Std λ, 0 or 0.0001. (Excel may not let you use 0). Does the stochastic model behave the same way as the deterministic model at low variation? How do you know?
Explore the effect of varying the standard deviation of λ further. Find the probability of extinction over 100 years and 100 trials for each of the standard deviation in the table below.
Std λ p(extinction)
0 (or 0.0001)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
What value of the standard deviation induces the greatest change in extinction probability and how do you know?
Now reset the 100 year model to N(0)=10, λ=1, std λ=0.25. Vary the N(0) according to the following table.
N(0) p(extinction)
10
100
200
300
400
500
600
700
800
900
1000
Why does initial population size matter? Is there a critical population size where the relationship between population size and extinction probability changes? What is it? How does this relate to the minimum viable population?

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