I'm trying to calculate various functional diversity measures (Fric, Feve and Fdiv) for bird communities by using count data which is collected annually. My ultimate aim is to compare functional diversity of the communities from different years and relate functional diversity to a single environmental predictor variable. My question is should I use structural equation models (SEM) in this case? Keep in mind I only have a single and continuous environmental variable. Does the answer change when I use two environmental variables?
This seems to be your situation. With SEM, you can create a latent variable from the FD measures, and use one or more environmental variables to predict the latent variable. You can also use time to predict the first latent variable to compare the different years. I think the standard name for such models is Multiple Indicator Multiple Causes model (MIMIC).
As a side note, it is useful to know that you can handle this situation within multilevel regression but you'll have to assume that the latent variable has the same relationship (factor loading) with all its FD indicators (unless you use Bayesian software).
You can proceed with this analysis in the SEM framework. Depending on how skewed the count data are, you probably want to use an estimation and inferential technique that is robust to non normality. Nothing changes if you have multiple environmental variables.
The complication comes from the annual data you have. Hence, certain records come from the same bird communities. This may result in a consequential violation of statistical independence. You should be able to construct a multilevel SEM model accounting for the bird communities. This will involve creating a latent variable for the means of FD variables by bird community.