= Closed-population capture-recapture model
{title2=$N=\text{constant}$}
A <closed-population capture-recapture model> assumes the same individuals remain throughout the observations: no births, deaths, immigration, or emigration. Its elementary two-sample version additionally requires retained, correctly recognized marks and a second sample chosen by <simple random sampling> independently of first-sample membership. Mixing and unchanged capture behavior help make this plausible. Equal individual capture <probabilities> alone do not guarantee that every size-$C$ <subset> is equally likely; that stronger sampling assumption gives the <hypergeometric distribution>. See https://www.maths.otago.ac.nz/~rbarker/Thesis/thesis.pdf[Barker, §§1.1.1 and 1.1.3: closure, marks, and catchability assumptions].
Unequal catchability, mark loss, and population change can invalidate this <capture-recapture model>. For example, if especially catchable individuals appear repeatedly, overlap can be inflated and the <Lincoln-Petersen estimator> can underestimate population <cardinality>. Lost marks can decrease recorded overlap and increase the same <ratio estimator>, all else equal. Two samples alone cannot establish that the sampling assumptions hold.
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