Help with population dynamics math for a strange case

[PhoenixPhyre]

My halflings have some odd population dynamics, and I'm trying to work out some of the details so I can design "proper" family trees, etc.

1st quirk: gender imbalance. Roughly 60% of all conceptions are female and 40% are male. The reason I stress conceptions there is related to quirk 2
2nd quirk: male fragility. Males are stillborn and/or die in infancy at much higher rates than females. Call it 1/4 survives to maturity.
3rd quirk: female infertility++. Roughly 2/3 females are born kliba, meaning genetically neuter. Not only incapable of giving birth (or even menstruating), but generally genetically and culturally conditioned to be submissive to the matriarchs (the fertile females). Kliba are (generally) larger and stronger than the males or females; males tend to be the smallest and weakest.
4th quirk: quick maturity and low lifespan. Halflings generally mature by age 10-ish and usually don't live past 60.
5th quirk: group births. Twins, triplets, and quadruplets are more common than singles. Triplets are the most common.

Effectively, this is a (mildly) eusocial genetic heritage, reminiscent of a queen bee. Although with less fratricide between queens.

Culturally, the main (relevant) group treats males as somewhere between "valued assets" and "toys", hiding them away from outsiders who might steal them. Male children are traded to other family groups (to avoid inbreeding) at maturity. The matriarchs of a given family share the "husbands" collectively. The kliba do most of the heavy work (and fighting, if needed). The matriarchs rule the roost, with one of them (usually the eldest living one) chosen as Mother Matriarch for the family branch.

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So the question becomes what should the birth rate look like for a growing, but not explosively so, population? I know that for (earth) humans, the relevant number for population stability is ~2.1 births per woman during their lifetime.

My math:
100 halflings
40 are male, 10 of those survive to breed.
60 are female, 20 of those are matriarchs.

That says to me that 20 people have to produce 100 people (for stability). That means that the relevant number (on average) is that each matriarch needs to have ~5 children per lifetime (plus some to account for mortality among matriarchs before reaching maturity--mortality among kliba is relatively irrelevant).

Does that sound about right? What cultural and other quirks might exist among such a population? Pitfalls?

[Yanagi]

I can't do the math, but to calculate stable population growth there's a couple of other factors.

One is how much time gestation takes plus how much post-partum time to recover before another pregnancy...the latter usually being a measure of both physical recovery from birth and how long until a child is weened.

The second is before-maturity mortality rate within the society's physical environment: basically, how often do kids die because of disease, hunger/deficiency, accidents. The stats you've provided are in vaccum, but better or worse living conditions would be another factor to what overall population looks like.

Culturally...you're defiinitely picturing the shape of things, but I'd pose some questions:

How is property held and inherited within this basically clan-like familial structure? It kind of seems to me like with males being what they are, there's no reasons they'd given any kind of legal standing as father/husband/son, particularly if they're being traded and held in common. Indeed, I'd propose that males are scarce enough that they'd literally be an asset such that they wouldn't be given or sold, but rented...particularly since the odds say that within the any given generation there's going to clans that can't afford to keep a bunch of less-useful males or who end up with males that can't do their one fuction.

This is especially the case if your halflings are distributed across multiple living conditions, there are definitely going to be haves and have-nots that handle the triad of matriarchs/kliba/males differently, because there's literally going to be a point where statistically you've don't have the subsistence resources or cash to maintain a households where 14% are cloistered. Like, there might be society ideal of a stable group marriage, but there's the distinct likelihood that lend fertile men would be a part of regional politics and long term control/retention of capital. So the eusocial configuration could on one hand produce

- something like old school group marriage--a group of matriarchs holding "husbands" in common producing children all treats as "offspring" in a kinship chart (eg, each matriarch does not have their own children and their sisters children are their cousins, all matriarch parents are mothers to all chidlren within the group marriage), resulting in parent-generation matriarch wealth being passed to be collective held by the child-generation matriarchs. This would make sense for those in better financial condition and with considerable assets and lots of labor.

- something that looks like concubinage--matriarchs need males but lacking the established assets to simply obtain one through traditional systems--arrangement of a permanent pair- or poly- bond that incorporates social connection with another matriarchal line--instead provide more direct compensation...cash on the barrelhead, kliba labor...to obtain access to a male for reproduction servcies.

- and if males are aestheticized and commodified, there's also going to be single powerful individuals that accrue them as a form of conspicuous consumption and personal indulgence, a show of clout, or as a kind of massive index of sociopolitical alliances that use marriage as a contract.

Another important thing is the precise parameters of what "conditioning" means in the case of the kliba. Lacking reproductive capacity removes them from generational inheritance...but the labor is what keeps the society operational, so they actually have power and leverage within their generation even if it isn't formally codified. Therefore exactly how much they can be controlled, and how that control functions, is going to dictate the shape of the society. If the conditioning is within the clan-system and strong, then there will be less politics or a need to build accommodating structures to keep the kliba. If it's within the clan-system and weak, then there's more likely to be ranks and titles and traditions that keep the kliba engaged. If this conditioning is more amorphous and can...wander to side with other clan matriarchs...the more likely there's going to be at least some kliba that are given political power over other kliba...basically to be enforcers of the status quo through both cultural pressure and, theoretically, legal structures that create formal punishment for violations of social norms.

Another part of this is...what is the social relations between kliba and the rest of society, because on one hand they are both born and raised to be servile, but they are also kin. By the numbers in any birth cohort there's going to be matriarchs and kliba that are siblings--so what is the ideal picture of that sibling-sibling relationship, how close do the reality get to that ideal, and what kinds of emotions and tensions are generated by the interweave of family and conditioned obedience? All variations of this eusocial species are going to have to have etiquette for how this dynamic should work, and probably have a larger body of cultural documents--ranging from prescriptive ethical writing describing what should be to art romanticizing certain social dynamics by creating tropes and iconic figures. And it's not that there's necessarily one answer...there could be more harsh societies where being kliba is closer to chattelage, and subordination is the only virtue; and societies in which their contributions are held very high and the kinship relations emphasize filia over submissiveness.

[Adamantrue]

So the question becomes what should the birth rate look like for a growing, but not explosively so, population? I know that for (earth) humans, the relevant number for population stability is ~2.1 births per woman during their lifetime.

My math:
100 halflings
40 are male, 10 of those survive to breed.
60 are female, 20 of those are matriarchs.

That says to me that 20 people have to produce 100 people (for stability). That means that the relevant number (on average) is that each matriarch needs to have ~5 children per lifetime (plus some to account for mortality among matriarchs before reaching maturity--mortality among kliba is relatively irrelevant).

Does that sound about right? What cultural and other quirks might exist among such a population? Pitfalls?

Just eyeballing it, not breaking out a spreadsheet:

Out of 100, 10 would be mature males, 20 would be matriarchs. The male population is largely irrelevant for the population growth, since they don't rear children.

Assuming triplets are the statistical average (you said most common), matriarchs would usually have 2 "litters" in their lifetimes, for an average of 6 kids per female. That would get you to 120 in a generation, 12 of which would become mature males and 24.

Run that iteratively for a few generations, it basically doubles you population every 4th generation, so by your 12th generation your village is 10x bigger (in about 150 years, more or less).

This doesn't take into account matriarchal death before maturity. With such a small population, even losing 1 or 2 per hundred skews the numbers in surprising ways. So would the "average" of triplets being closer to 2.6 or 2.7, rather than 3.

Again, eyeballing it.

[Quizatzhaderac]

Eusocial mammals exist, the naked mole ratWhere most females never go through puberty and most males just never get to participate in sex.

The population wouldn't be stable throughout history, and would need to be able to recover from plagues/ wars/ famines/ et cetra so they'd need to be able to, on occasion, have much more than replacement levels of children. Something like 4 litters per matriarch.

In normal times 2 liters would be the norm with one or three not being uncommon.

Being sapient they will exercise some control over their birth rates. This is something all cultures do and was probably done by Neanderthals and other almost humans.

The one in 4 males surviving raises questions. Biologically, there would be no reason males to be more fragile than kliba since they have the body plan in their genes; so there would need to be special dangers. One such possibility would be if they were like roosters where the males basically kill each other on sight. Another would be that most males aren't "good enough" due to weakness or insubordination and are castrated/ killed, or exiled.

These explanations are pretty horrible, but pretty much anything where you lose 3/4 of a population will be.

If you want your society to not be terrible, I'd recommend that male puberty only happens occasionally with the following genders:
Matriarchs, studs (fertile males), genetically female kliba, genetically male kliba, girls (juvenile females that could become either matriarchs or kliba), and boys.

[PhoenixPhyre]

Eusocial mammals exist, the naked mole ratWhere most females never go through puberty and most males just never get to participate in sex.

The population wouldn't be stable throughout history, and would need to be able to recover from plagues/ wars/ famines/ et cetra so they'd need to be able to, on occasion, have much more than replacement levels of children. Something like 4 litters per matriarch.

In normal times 2 liters would be the norm with one or three not being uncommon.

Being sapient they will exercise some control over their birth rates. This is something all cultures do and was probably done by Neanderthals and other almost humans.

The one in 4 males surviving raises questions. Biologically, there would be no reason males to be more fragile than kliba since they have the body plan in their genes; so there would need to be special dangers. One such possibility would be if they were like roosters where the males basically kill each other on sight. Another would be that most males aren't "good enough" due to weakness or insubordination and are castrated/ killed, or exiled.

These explanations are pretty horrible, but pretty much anything where you lose 3/4 of a population will be.

If you want your society to not be terrible, I'd recommend that male puberty only happens occasionally with the following genders:
Matriarchs, studs (fertile males), genetically female kliba, genetically male kliba, girls (juvenile females that could become either matriarchs or kliba), and boys.

My thinking is as follows--

* The halfling race is both small (so genetically bottlenecked intrinsically) and not traditionally "evolved". They came into being due to (basically) magical fallout. They also hit an external bottleneck (catastrophe that killed ~70% of everyone) ~ 250 years ago. So their genetics are rather bizarre.
* There's a "fragile X" problem--basically those with male genetics tend to be simply stillborn/miscarried more frequently than not, and if they are born, they are often weak and die in childhood. Females with this fragile X problem end up looking like female eunuchs, females except without functional reproductive anatomy who go through an altered "puberty" (gaining physical size but not sexual maturity). So physiologically kliba are females...except without functional ovaries or other sexual characteristics.

As for the litter rate--my idea for their society is "we have reserves/human wave" style zerg-rushes when threatened. They tend to overproduce in times of societal stress (or in general), but don't consider kliba lives all that meaningful. Nor are they super individualistic (although that's changing)--the default is to think of the family first, then worry about the individual. Coupled with their (genetic) resistance to fear (they just don't experience it quite the same way), and you have a rather messed up culture.

Which is somewhat of the intentional point--all my cultures have some form of screwy-ness built in. High elves of one culture are intentionally selectively breeding for magical power (causing all sorts of dislocations). Many dwarves are so traditional that doing something new is literally considered suicide; they're also pair bonded at an extreme level--almost always born as twins, 1 male, 1 female, and aren't considered adults until they're married, and divorce/adultery/widowhood are basically the same thing, and frequently result in the suicide of the other partner (either directly or through extreme risk-seeking behavior). The dwarven word for "widow/divorcee" is the same as the word for "broken." Each of the human cultures has quirks and oddities--the human-dominant cultures are among the only really religiously-zealot-driven cultures. Etc.

[sktarq]

One thing you could have is that male puberty is very hormonally stressful and results in a crash in the immune system for several years causing many to die from various otherwise sub-fatal infections.

The also is the question of when in development a kliba and matriarch split? When can someone tell who was born?
i would figure that to be "conditioned" it would have to be quite early but by altering it you could actually shift certain idea of how close to each other the kliba and matriarch's are...especially socially.

Another trait you may wish to drive is the idea that kliba are generally non-aggressive to their own species. If they have some basically neurological link between the part of their brain that says "another halfling" and an inhibited aggression level it would explain a lot of their general subservience (as the agression level would cover both social and physical issues) which could even be reflected by an attack penalty.

Also the idea of "fragile X" need a bit of work as any who have such will obviously not breed. So every halfling will have parents who don't have this problem....so either the X has some form of replication issue (especially zygote split perhaps) or they need to exactly carry one dominant and one recessive version of a trait with double dominant or double recessive causing issues...possible on two separate genes (which would give a 75 kliba rate...and with males only ever getting one copy of one of these genes will always have issues (causing their high death rate)....that way both recesive and dominant genes get passed down.

Also all this assumes a no outside death rate. Which doesn't translate well to most "middle ages" era setups. Infant mortality was high and that would include a lot of "surviving" males and matriarch to be. Many women who had 7 or even a dozen children may have only had 2 or 3 adult children who bred themselves (just hitting replacement) during times of stress especially.

So even if with a bit of clerical magic we say that infant mortality (0-5) is 50% then you'd need them to have 4 "litters" each averaging triplets.

Also it kinda depends on the feel and result you want and work backwards.

[PhoenixPhyre]

One thing you could have is that male puberty is very hormonally stressful and results in a crash in the immune system for several years causing many to die from various otherwise sub-fatal infections.

The also is the question of when in development a kliba and matriarch split? When can someone tell who was born?
i would figure that to be "conditioned" it would have to be quite early but by altering it you could actually shift certain idea of how close to each other the kliba and matriarch's are...especially socially.

Another trait you may wish to drive is the idea that kliba are generally non-aggressive to their own species. If they have some basically neurological link between the part of their brain that says "another halfling" and an inhibited aggression level it would explain a lot of their general subservience (as the agression level would cover both social and physical issues) which could even be reflected by an attack penalty.

Also the idea of "fragile X" need a bit of work as any who have such will obviously not breed. So every halfling will have parents who don't have this problem....so either the X has some form of replication issue (especially zygote split perhaps) or they need to exactly carry one dominant and one recessive version of a trait with double dominant or double recessive causing issues...possible on two separate genes (which would give a 75 kliba rate...and with males only ever getting one copy of one of these genes will always have issues (causing their high death rate)....that way both recesive and dominant genes get passed down.

Also all this assumes a no outside death rate. Which doesn't translate well to most "middle ages" era setups. Infant mortality was high and that would include a lot of "surviving" males and matriarch to be. Many women who had 7 or even a dozen children may have only had 2 or 3 adult children who bred themselves (just hitting replacement) during times of stress especially.

So even if with a bit of clerical magic we say that infant mortality (0-5) is 50% then you'd need them to have 4 "litters" each averaging triplets.

Also it kinda depends on the feel and result you want and work backwards.

Yeah. Although, there isn't really mendelian genetics in this setting. It's all based on souls, anima compatibility, etc. So the "fragile X" idea isn't exactly right, but there's something similar.

As for outside death rate, it's relatively low...right now. The area the halflings are in is prosperous, at peace, and mostly free of monsters and plagues and such. But I do think that 3-4 sets of triplets for an average matriarch sounds about right.

As for the kliba, I like that idea. Kliba tend toward the nurturing role...to other halflings. They stabilize society by not competing and by accepting that they're the ones that will get jettisoned if there's resource crunches. As to when the effect is noticeable--it's locked in by puberty at the latest. As if they started down that path, but puberty failed. But my (vague) idea was that most of the "conditioning" is innate, not learned. Kliba struggle to resist the demands of matriarchs.

Another thought is that maybe baby halflings are of indeterminate gender for several years. They're born, but then go through (maybe?) an extended developmental period analogous to puberty.
Before this, they're all physiologically similar (at least at the level they can tell, you could probably tell by looking at the soul).

At around ages 5-7, they start changing. Those who are destined to be kliba grow bigger, those destined to be males or matriarchs start developing sexual characteristics. And, as you suggest, this process is especially hard on the males, who tend to die (if they haven't already). This lets the stillbirth rate drop quite a lot, and it's more about helping them survive the Change.

By age 10, they're mature and "stable".

[Grek]

Just looking at replacement rates, the average adult male halfling needs to have ~12 children and every adult matriarch halfling needs to have about 6 in order to maintain a stable-to-slightly-growing population that is at least minimally resistant to wars, famines, accidents and diseases. But if we further accept both of these as true:

* The halfling race is both small (so genetically bottlenecked intrinsically) and not traditionally "evolved".

5th quirk: group births. Twins, triplets, and quadruplets are more common than singles. Triplets are the most common.

Then we have to rather sharply increase those numbers, as we're not just concerned with the raw number of children produced in each generation, but also in the numble of unique mother-father pairings in each generation, as to prevent half-sibling or quarter-sibling inbreeding from becoming a massive public health issue. Realistically, you're looking at something more like two dozen children per father and a dozen per mother, which in turn requires that there be a high mortality rate to maintain the desired "growing, but not explosively so" population.

[Bohandas]

So basically they're bees

[PhoenixPhyre]

So basically they're bees

That is the primary point of inspiration, yes. Having a biological basis for a caste-based matriarchy, combined with swarm behavior.

[Balyano]

One explanation for the biology of these halflings could be a lack of normal meiosis in the halfling species resulting in diploid matriarchs, haploid males with no fathers, and triploid kilba.
A matriarchs eggs sit around as diploid eggs.
Sometimes those diploid eggs undergo meiosis into normal haploid eggs.
Unfertilized haploid eggs become males. Being haploid any detrimental mutations would weaken or kill them, thus 75% death rate. Weak mutations weeded out.
Fertilized haploid eggs become fertile females.
Fertilized DIPLOID Eggs become triploid sterile kilba with an extra dose of a lot of genes.
Thus in halflings biological sex is due to gene dosing.
If halflings have 23 chromosomes then
Males n=23
Females 2n=46
Kilba 3n=69