Hi again, @jessegrabowski!
Thank you VERY much for your suggestions and gist; they go nicely with my goal. I originally proposed a GP to include the nonlinear relationship between variables and time, but your proposed model makes a lot of sense.
I made a mistake in explaining the problem, though, saying it is a longitudinal design when it is not (my bad). To clarify, for every species-isotope-year, there are n randomly sampled individuals (n varies per species/year, and the individuals most likely are not the same in any case). On the other hand, the environmental data are thousands of satellite measurements (basically maps of each variable).
Anyway, I could extract the annual mean values for every variable and then work with your gist as is; however, I think I’m missing your point?
P.S. I’m marking your answer as a solution.