Several single-species GLMMs -> A multi-species GLMM (random effects syntax?) I'm looking to describe annual relative abundance for several species over several years by analyzing point count data. I'm using a Poisson GLMM in glmmTMB for each species, it looks like this:
m[[i]] <- glmmTMB(count ~ year_numeric + (1|year_factor) + (1|site), 
                  family = "poisson", data = data[[i]])

As an aside: This has a linear trend for year, plus year random effects, which is conceptually similar to the Sauer & Link models from the Breeding Bird Survey (though they use a Poisson log-linear regression, and it's Bayesian).
Instead of having a separate GLMM for each species, though, I'd like to have one single GLMM for all species (a multi-species model). I know I could do part of this by using year_numeric*species, but: what would be the syntax for the random effects?
Thanks!

You can also consider running a Joint Species Distribution Model (JSDM), which is basically a multivariate GLMM. You can include temporal autocorrelation structures in the model implemented in Hierarchical Model of Speceis Communities (HMSC) and Generalized Linear Latent Variable Models (GLLVM)
