Editing Mark and recapture (section)

=== Derivation ===

It is assumed<ref name=Krebs1999>{{cite book |title=Ecological Methodology |author=Charles J. Krebs |edition=2nd |date=1999 |publisher=Benjamin/Cummings |url=https://books.google.com/books?id=1GwVAQAAIAAJ |isbn=9780321021731 }}</ref> that all individuals have the same probability of being captured in the second sample, regardless of whether they were previously captured in the first sample (with only two samples, this assumption cannot be tested directly).

This implies that, in the second sample, the proportion of marked individuals that are caught (<math>k/K</math>) should equal the proportion of the total population that is marked (<math>n/N</math>). For example, if half of the marked individuals were recaptured, it would be assumed that half of the total population was included in the second sample.

In symbols,
:<math>\frac{k}{K} = \frac{n}{N}.</math>
A rearrangement of this gives
:<math>\hat{N}=\frac{nK}{k}, </math>
the formula used for the Lincoln–Petersen method.<ref name=Krebs1999 />