The distribution of the number of individuals across \(M\) different sites in any given year is given a \(Poisson(λ)\) distribution (see \citealt*{Royle2003} for details). The reporting rate of the species of interest at site \(i\) (number of detections at site \(i\)/total number of visits to site \(i\)) is modelled as a binomial process that is conditional on the (unobserved) number of individuals on this site. The likelihood of the number of detections at site \(i\) is: