## 2. The calculation

The initial batch of marked animals has a chance to mix with unmarked animals when they are released, and have the same chance of being recaptured during the second sampling as the unmarked animals. The second sampling yields marked and unmarked animals. The marked animals are assumed to be a random selection from the population, so that we can calculate a proportion, P_{r}, of the original marked animals that have been recaptured.

P_{r} = |
M_{2} |

M_{1} |

where M_{1} and M_{2} are the numbers of marked animals captured on the first and second samplings respectively. P_{r} is, in effect, an estimate of the probability that an animal will be recaptured.

If the marked animals released back into the habitat had mixed randomly with the rest of the population, then the total number captured on the second sampling should represent the same proportion of the total population as P_{r}. So:

P_{r} = |
M_{2} |
= | (U_{2}+M_{2}) |

M_{1} |
Pop_{total} |

where U_{2} is the number of unmarked animals captured in the second sampling, so that the total number of animals captured in the second sampling is (U_{2} + M_{2}).

It is easy to rearrange the equation to give the estimated total population, N:

N = | (U_{2}+M_{2}) |
= M_{1} |
(U_{2}+M_{2}) |

P_{r} |
M_{2} |