The Federation by the 24th century is indeed a very large union. I was wondering though, if there was any indication of which species formed the largest portion of the Federation's population by the 24th century (I don't mean to ask if there's a species that occupies greater than 50% of the Federation, but rather which member of the Federation (in terms of species) has the greatest population). I'm not asking for exact numbers either, as that would be particularly difficult I imagine, but rather if there is any reference to the species with the greatest population in any Trek materials.
Geoffrey Mandel's "Star Trek : Star Charts" (which isn't generally considered truly canon but was at least 'advised on' by Senior Trek Designer Michael Okuda) indicates that the homeworld population of Andoria was 38.2 Billion, representing some 3.2% of the total population of the Federation of just under 1 trillion.
Per this excellent answer we can reasonably assert that the Human population (including Earth and its associated colonies) was anything between 12 and 20 Billion in the same time period, representing some 2% of the total population of the United Federation of Planets.
Purely as a matter of interest, the Borg planet of Arehaz (AKA Borg Prime) had a combined population of over 50 Trillion in the same time period