modeling count data with replacement



I have a population of mammals and i'm trying to estimate the population size at a bunch of different sites. However, the population is small so every time I sample there is a chance that i'm going to resample an individual that i've already seen.

I'm wondering if there is a way to predict the number of mammals that I find in an observation (e.g., using a poisson model) separately from the probability of that one of them being sampled has already been seen. Somehting like a poisson model accounting for replacement. Any ideas?
Can you mark the individuals? If so then capture-mark-recapture seems an obvious solution.
There are techniques that allow abundance estimates from just count data e.g for when using spotlight counts - what technique are you using?