``````

In [3]:

from numpy.random import normal
from scipy.stats import norm

``````

We have the following constants for the two lizard species.

``````

In [10]:

sexual_mean, sexual_standard_deviation = 1.1, 0.15
asexual_mean, asexual_standard_deviation = 1.2, 0.3

``````

One way to figure out the expected extinction time is to figure out the expected number of generations until the mean population growth rate dips below \$0\$. We'll call it "Probability of Death", or pod, for short.

``````

In [25]:

pod_sexual = norm.cdf(0, loc=sexual_mean, scale=sexual_standard_deviation)
pod_asexual = norm.cdf(0, loc=asexual_mean, scale=asexual_standard_deviation)

print("The probability that the sexual lizards die off in a given generation is {}".format(pod_sexual))
print("The probability that the asexual lizards die off in a given generation is {}".format(pod_asexual))

``````
``````

The probability that the sexual lizards die off in a given generation is 1.1224881271355393e-13
The probability that the asexual lizards die off in a given generation is 3.167124183311986e-05

``````

Now that we know the probability of both populations dying out in a given generation, we can easily compute their expected number of generations, which is the mean of a geometric random variable whose probability of "failure" is the variable pod.

``````

In [26]:

expected_generations_sexual = int(1/pod_sexual)
expected_generations_asexual = int(1/pod_asexual)
print("The sexual lizards are expected to survive {} generations".format(expected_generations_sexual))
print("The asexual lizards are expected to survive {} generations".format(expected_generations_asexual))

``````
``````

The sexual lizards are expected to survive 8908780198431 generations
The asexual lizards are expected to survive 31574 generations

``````

A random population growth/decrease will just increase the standard deviation in both the cases. And as the standard deviation goes up, the probability of death in a given generation goes up, which means the expected number of generations will go down. That makes sense, because in a nutshell, it's the variability in their mean growth rate that is killing the population, i.e. once the mean growth rate goes below \$0\$, they are dead. It makes sense that adding more randomness will kill them faster.