Is it wise to use a Generalized Linear Model (GLM) to investigate trends in abundance over time? Not sure if this would be considered as being a "stupid" question, but I am still very new to statistical analyses. I have population abundance data and I wish to determine whether the trend in abundance (abundance values = counts) over time (time=years) shows an increasing/declining trend. Should (or rather, can) I make use of a GLM to investigate the trend in abundance over time (ie dependent variable = abundance value, independent variable=year (ie time)) ? Or is there perhaps a "better" alternative?
Thanks again :)

You could use Generalized Additive Models (GAM) with a poisson distribution to model this. GAMs are very flexible, allowing you to model both linear and nonlinear effects for predictors. There are lots of good tools, blogs, and books out there. Specifically, look up the mgcv package (by Simon Wood) and the gratia package (by Gavin Simpson). The mgcv package provides an extensive set of tools for building GAM models and the gratia package will allow you to detect significant change points using the finite difference method with the derivatives() function.
The best intro I've found would be Simon Wood's book Generalized Additive Models An Introduction with R.
Some free courses are around the web too here is one and another by Gavin Simpson.
There are a ton of blogs out there too to get you started. Gavin Simpson has a blog where he goes into a lot of details about fitting time series data with GAMs and detecting change points etc here.
Here is a list of additional resources that has been compiled.
Good luck!
