It sounds as if you want a Poisson or a Negative Binomial Distribution regression model which handles count data - in the former the conditional (after including predictors) residual variance of the counts is equal to the mean; the NBD can accommodate over-dispersion that is the variance is greater then the mean - typically very positively skewed.

THis book has all the details

Joseph M. Hilbe (2011) Negative Binomial Regression 2nd Edition

"The only text devoted entirely to the negative binomial model and its many variations, nearly every model discussed in the literature is addressed. The theoretical and distributional background of each model is discussed, together with examples of their construction, application, interpretation and evaluation. Complete Stata and R codes are provided throughout the text, with additional code (plus SAS), derivations and data provided on the book's website. Written for the practising researcher, the text begins with an examination of risk and rate ratios, and of the estimating algorithms used to model count data. The book then gives an in-depth analysis of Poisson regression and an evaluation of the meaning and nature of overdispersion, followed by a comprehensive analysis of the negative binomial distribution and of its parameterizations into various models for evaluating count data.

• Fully revised to incorporate recent software developments • Every model currently offered in a commercial statistical software package is discussed in detail • Data sets and additional code available on a companion website"

It  treats the Poisson model as a constrained form of the NBD.

Dear kelvyn Jones 

I strongly support your statement.

Hi, have you heard about occupancy modelling as a tool for habitat selection?

https://www.uvm.edu/rsenr/vtcfwru/spreadsheets/occupancy/Occupancy%20Exercises/Exercise3/MacKenzie%20et%20al.%20single-season.pdf

I think that this analysis will be useful to you for estimate habitat selection.