N-mixture models are used in situations where you think that your ability to detect the animals you are monitoring is not perfect. In those case, if you conduct a survey you end up with an index of the population instead of the “true” population count. To correct for this bias people will try to use a sampling scheme, usually repeated visits at the same sites, to tease apart the detection process from the true underlying abundance population process and will analyse the data with a hierarchical model where both the detection process and the abundance process are estimated. The basic N-mixture model combines a binomial distribution (detection) and a Poisson distribution (Abundance) to tease apart the two process.

There is a lot of information on N-mixture models in the literature. Article and the books written by Andrew Royle and Mark Kéry are a good starting point.

Thanks Christian. I will look these reference to get more ideas of N-mixture models and I will contact you if I have any questions. I hope you are happy with this. Best, Vy