Pop growth as it is is kinda silly.
From what I can tell all species will grow and decline until their numbers are exactly equal. This leads to the silly situation where as soon as you get a single refugee pop or enter a migration treaty with even a one-planet minor, for a good long while these pops will be literally the only ones that grow on literally all of your planets.
I was playing a bio-asc UNE, so I gave every species the same traits so I wouldn't lose anything by having a total hodge-podge of different species with no consistently growing pops. Around the mid-game I had something like 30 species. There were a few conquests, a few migration treaties, a few uplifts, and then crossbreeds of all. Plus a few migrants going next door to my spiritual friends and then coming back psychic, the gene template of which could then be applied empire-wide. Most of my pops were Psychic, Robust, Very Strong, Intelligent, Communal, and Conservationist. I was doing pretty well.
So luckily it didn't matter so much that on every new world I'd settle after this point, not a single human pop would ever seem to grow. They would literally grow one each of my many species before then growing a second each and so forth. It got the point that my full and crowded capital actually had humans declining so that more xenos could grow. No doubt that over a long enough period of time it would all have become demographically perfectly balanced, with each planet trying to have like three pops of each species.