Poisson or Gamma distribution for density or encounter rate data? [duplicate]

I am unsure whether turning count data into density still makes Poisson as the appropriate distribution for modelling.

If a given response data are, for example, counts of animals, then such data are best modelled using a Poisson (or quasi-Poisson) distribution.

If the response data are continuous (but bound by zero), then the gamma distribution is likely appropriate.

But what happens when data from counts are turned into density (number of animals per unit area) or encounter rate (number of animals per unit of effort)? Is Poisson distribution still appropriate? Or would one need to use a gamma (or some other) distribution?

I assume it should still be Poisson (or quasi-Poisson, in case of overdispersion).