A Probabilistic Model for Population Extinction

model parameters

μ

L

6.

σ

L

1.

threshold

100

run to plot

33

run length n

50

number of runs

200

seed repeatable random numbers

seed value

0

generate new data runs

A fluctuating organismic population can become extinct if its size drops below a certain threshold. This Demonstration simulates hypothetical life histories in which the population's random fluctuations have lognormal distributions, characterized by

μ

L

and

σ

L

, which terminate when the population size falls below this chosen critical number. The program records the extinction times and plots a histogram with a superimposed exponential distribution function having the same mean as the recorded extinction times. It also shows the quantile-quantile (q-q) plot used for testing the exponential distribution as a model.