Polyamory, specifically polyandry, would be an interesting solution to the oddball population of the Shire.
The Shire is excellent farming country, with consistently good weather, and only one tough winter in living memory; hobbits like to produce large families; they’re resistant to disease, rarely violent, and encounter few dangers. It is usual for hobbits to produce many children, so that (for example) Bilbo and Frodo are unusual in both being only children, with no siblings, and not having children of their own. All of this should point to a population that increases every generation if not doubling outright. Young people (and their ideologies!) should rapidly outnumber the old with an ever-increasing effect and impact on society. However, the Shire has a surprisingly stable history; it never seems to increase or decrease greatly in population, and the bell curve of age seems… demographically balanced? There certainly isn’t a conflict from rising young bloods challenging the middle-aged reactionaries; there’s no unemployment; there are no housing crises or waves of emigration, or even a tendency for young people leaving home to marry. Meanwhile, not only does the Shire not suffer from internal pressures, but it remains obscure and hardly noticed in global politics.
What makes sense here is that adult hobbits form a loose group. Four parents in a polycule, between them all, may produce four children. All four parents claim to have four children. An outsider would assume this meant the adults had eight children.
Hobbits therefore are not especially fertile or fecund. They simply have large families. Much of their interest in genealogy is due to the complex relationships of blood-kin, hearth-kin, love-kin and pledge-kin, who must all be carefully tracked and measured - not just because you need to make sure that you don’t climb into bed with an un-permitted degree of blood-kin, but to track family alliances and carefully quantify the precise level of thoughtfulness to put into the proper present to gift your father’s lover’s lover (too much implies a degree of intimacy that might upset the polycule.)
Thus, while a hobbit matron may tell a startled dwarf that she has seven sons, she might only have borne five of them herself, and have one hearth-son by her wife, and a pledge-son of her first husband’s. There are between three and four fathers involved at various stages of production, from conception to pledge-duty, but there is debate about the precise number of fathers, as one child was festival-conceived and therefore provisionally pledged to the Brandybucks until more distinctive paternal traits should materialise. It’s expected that four of the sons will be uninterested in women, and their contribution to family life will be in raising hearth-children and pledge-duty. However, this level of detail is normally negotiated later in conversation, as a mutual overture of friendship. So she’s just clear and simple: yes, certainly, she has seven sons. Yes, they’re all hers. Yes, that’s fairly normal - yes, hobbits like big families. How big? That’s really hard to say! Well, about thirteen hobbits live in her house… er, she has forty-three nieces and nephews. Yes! She has nine siblings, that’s correct, but some of them are still babies themselves..
In this way, a bewildered dwarf might assume that hobbits are absurdly fertile, producing an average of seven children per couple, at an absurd pace.
When in fact, with about half of hobbits never bearing biological children, the population of hobbits is pretty much always the same.
Tl:dr, hobbit population works perfectly well, both internally and in the perceptions of outsiders, if the majority of the Shire is gay, they’re all polyamorous, and they all firmly claim to be parents of high numbers of children. Of course Frodo fathered Sam’s kids - he named them! They were pledge-kin but not hearth-kin, as Frodo needed a lot of quiet and stability in the home.
No outsider ever parses hobbit genealogy well enough to understand this except for Gandalf, who never explains anything either.
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