There is a way though to estimate and monitor a changing population. Suppose from a population of a species of total size
\[N\]
, \[n\]
animals are tagged. The fraction of animals that are tagged is \[\frac{n}{N}\]
.The tagged animals are freed, and a second sample of size
\[m\]
is then taken. \[x\]
of these animals are wearing the tag. Assuming the proportion of animals wearing the tag is the same as the proportion of animals that were tagged, \[\frac{n}{N}=\frac{x}{m}\]
. Rearranging this gives \[N=\frac{nm}{x}\]
.200 wild pandas are tagged and released, and a year later, a sample of 300 is taken, of which 50 are wearing a tag. The population estimate is then
\[N=\frac{200 \times 300}{50}=1200\]
.This estimate assumes that there have not been any births or deaths since the animals were tagged, and the tagged and untagged animals are properly mixed.