Thanks for the great response @Ax3man! This is a very helpful way to think of it (and to explain it to reviewers :)
My understanding is that this is not a general result, but I’d be keen to hear why this would be the case. It would make sense when the phylogenetic heritability (Pagel’s lambda) is close to 1, since in that case the
(1 | species)term will capture much less of the variance than the(1| gr(phylo), cov = A)term, and removing it will not matter that much. But if lambda is closer to 0 then I don’t expect this to be generally true.
I think you hit on it right there. Often I am working with relatively deep nodes of quite divergent taxa, rather than a pedigree within a single species or 2, and I’ve rarely, if ever, had a heritability/lambda value close to 0. It’s almost always over 0.5. So maybe that’s why the population-level estimates don’t differ. I will say that the pop-level estimates differ depending on whether the phylogeny is included or not. Using the phylogeny and the intraspecific variation, or just the phylogeny, the population-level estimates (not the group-level) are the same, but running a model just the intraspecific variation and not the phylogeny will result in different estimates, which makes sense to me, especially with high heritability scores.
I’ve also noticed that, the closer the heritability (Pagel’s lambda) score is to 1, the more trouble the model has parsing between the intraspecific variation sd(Species) and the sd(Phylo) values. Often the trace plots bounce between 2 similar values for each, like there are 2 values and the model doesn’t know which one each parameter should be. I read somewhere that mcmcGlmm uses an algorithm that’s better at determining the differences between these two parameters, but brms often seems mixed up when using both (but again, this problem never really affects pop-level estimates, and is typically kept in check with fairly regularizing priors).