The Dwarves' numbers, although they sometimes flourished, often faced periods of decline, especially in periods of war. The slow increase of their population was due to the rarity of Dwarf-women, who made up only about a third of the total population. Dwarves seldom wedded before the age of ninety or more, and rarely had so many as four children. They took only one husband or wife in their lifetime, and were jealous, as in all matters of their rights. The number of Dwarf-men that married was actually less than half, for not all the Dwarf-women took husbands; some desired none, some wanted one they could not have and would have no other. Many Dwarf-men did not desire marriage because they were absorbed in their work.
"Dis" (Fili and Kili's mother) as imagined by Ancalinar - but I suspect she was (even-) less feminine than this, since Tolkien said dwarf-women were indistinguishable from the men.
From Tolkien Gateway, summarizing the available 'canonical' information from the Appendices of Lord of the Rings and History of Middle Earth Volume 12.
JRR Tolkien clearly wanted his dwarves to be dedicated to their craft; and not interested in sexual relationships; but he went too far in this and inadvertently made dwarves biologically non-viable.
He describes the 'slow increase' in their numbers; but from the information given dwarf numbers could not increase at all over the long term, but would inevitably decline - since dwarf fertility was far below the minimum rate needed to replace those who died.
The fact that dwarf women were only about 1/3 of the population means that each woman would need to replace herself, and two men - plus a margin to account for death before the age of fertility. So minimum replacement fertility would be three-point-something.
But we are also told that not-all the dwarf-women took husbands (and it is implied they did not reproduce at all) meaning that women were effectively less than 1/3 of the dwarves.
Therefore each dwarf women who did reproduce would need to have considerably more than three-point-something children. For instance perhaps only 1/4 of the dwarves were women who reproduced - meaning that the minimum replacement level would need to be four-point-something children per dwarf women.
However, we are told that dwarf-women only rarely had as many as four children; and the tone of the passage suggests that four children was an upper limit and the usual number was considerably less.
Putting this all together; this means that the dwarves fertility was less than the minimum required to replace those who died.
There could be a modest increase before the first generation of dwarves began to die out. Their 'average' life expectancy was given as 250 years. However, this number did not take account of premature deaths; and it is described in Tolkien's writings that large numbers of dwarves were slain in battle, through all the ages of the world.
And Tolkien also says that dwarves married later than 90 years old - so only a couple of new generations could be fitted-in before even the first dwarf generation began to die out (even if only a small proportion of these founders were slain prematurely).
Pretty obviously this was a mistake of Tolkien's - and he would have wanted to revise it had the problem been pointed-out.
The simplest solution would be to state that those dwarf women who did have children had enormous families.
Alternatively, we can imagine a tragic scenario where a large first generation of dwarves was created - but after a couple of hundred years, the race began inexorably to go extinct...
This is interesting. I had not noticed that before. It looks like Tolkien had his idea about the dwarves but did not think about how the numbers he chose would work out.
The idea of a large initial generation for the dwarves that then started to die off is interesting. Something like that could work with all dwarves already made by Aule and then they come forth as needed. And then once all the dwarves have been born, their time on Middle Earth would have been completed and they would gradually dwindle in numbers.
Even though this is not what Tolkien envisioned for the dwarves, it may be that it was how he viewed the elves. It seems like there were a set number of elves, relatively small in relation to the other peoples of Middle Earth and once all of them were born, that was it. The generations of the elves unfolded in parallel to their mission on Middle Earth and ended at the same time their mission was complete. We see this in the fact that by the Third Age almost no elf-children were born. Also, in that at least one elf was reincarnated.
@NLR - Having studied demography a bit, and looking around at the world; it is clearly not an intuitively obvious matter that species will go extinct if they have less than replacement offspring.
You mention that the elves too were very slow reproducers, the Numenorean-descended Men similarly - and then there were the Ents who had reverted to a non-sexual mode of reproduction.
But 'lower' Men and Hobbits were both abundant reproducers, with bigger families and quick population growth in suitable conditions (especially Sam!).
It seems likely that (in a broad brush, non-mathematical way) Tolkien saw this differential reproduction as a partial explanation of why the magical/ legendary species have disappeared (or all but gone - some elves remain in a 'faded' - perhaps immaterial, perhaps shrunken fashion) and why Men (and some Hobbits!) are still around.
Having reviewed the various sections in Appendix A and the History of the Ring, I have my own suggestion. But first, I'd like to point out this section, which seems to buttress your own suggestion:
Volume XI pg 205 (The Later Quenta Silmarillion): "It is said, also, that their womenkind are few, and that save their kings and chieftains few Dwarves ever wed; wherefore their race multiplied slowly, and now is dwindling."
However, my suggestion is that the mathematical puzzle is best solved by postulating that Dwarvish women have a very high childbed, though almost no infant, mortality. Perhaps as high as 35%.
1) At birth the male/female ratio is 50/50 as one would expect. However, by the age of 100, 75% of Dwarf females have passed away from childbirth complications in the decade following marriage. In a stable population, this means that only 1/3rd of the total population is female, as Gimli reports. (This can be calculated from the Dwarf life expectancy of 250.)
2) In this model, 35% of women would have only 1 child, 22% 2 children, 40% 3 children, and 2% either no children or 4 or more, allowing for (barely) replacement fertility. Slow growth or dwindling would be the norm for a Dwarf population.
3) Gimli is evidently mistaken about less than 1/3rd of male Dwarves ever marrying. However, the total male Dwarf single population is very large. 35% of the male Dwarf population is below the age of 90, and therefore unmarried. But due to the presence of widowers or late marrying males, only 1/5th of the male Dwarf population would be married at a given time. (Though, contra-Gimli, most male Dwarves would in fact marry at some point.) Given the fast number of single males and the normal Dwarvish reticence on family subjects, Gimli's impression of less than 1/3rd of Dwarves marrying seems understandable.
What could be the cause of this childbed mortality? I suspect that it may not be childbed mortality at all. Given the biological sturdiness that seems to be required of female Dwarves, it would seem that the nutritional requirements for bringing a Dwarf child to term must be extremely high, and presumably commonly lead to severe nutritional deficit, and therefore the postulated mortality.
The sheer tragic nature of this suggestion might also explain a number of aspects of Dwarvish culture.
I remember making similar calculations a while ago when we were discussing the potential Dwarven populations of Erebor and the Iron Hills, and coming to more or less the same conclusions, though I don't think I shared them at the time. My own belief is that all his other statements on Dwarven reproduction, including the assertion that their populations were capable of increasing during times of peace (albeit slowly) should probably be taken at face value, and that he simply hadn't got round to doing his calculations properly (or if he had, to correlating results with his other statements and making the necessary corrections).
At the very least, four children must have been commonplace for reproductive Dwarven women, with five or more also occurring (frequency of larger families depending on how many had three or fewer or remained unwed), for their population to actually increase under any circumstances, given all the other information we have and that you quoted. This distribution at least enables populations to be replenished, albeit slowly, following drastic events such as major wars, while still allowing for the Dwarven race's apparently very slow demographic decay over a larger timeframe. (The latter can be presumed due to their sensitivity to wars, population movement and other disruptive circumstances frequently restricting birthrates to below replacement level for long periods, combined with their chronic social preference for reproducing at below their biological potential.)
I don't see much solid evidence for the alternative theory, which would seem to require Dwarves once having had very large populations (which would likely make them the most numerous non-evil race in the Elder days); whereas most indications are that their numbers were always quite modest compared to those of contemporary Men and (in earlier times) Elves.
The dwarves should have been having litters if their reproductive rates were that low. Sci Fi and Fantasy authors don't tend to think about biology that much when constructing their fake races, since they're more interested in creating drama than depicting realism. Star Trek Voyager had the Ocampa, a race of space elves who only lived to be 9 years old and their women only gave birth to one child in their entire lifetime. It doesn't take a math expert to see why this race wouldn't be viable beyond a few generations.
@Joel - An ingenious idea, but overall so many women dying in childbirth seems to make things even worse for the prospect of population growth. A knock-on problem would be child care - since this scheme would create so many mother-orphans.
(In traditional human societies baby mother-orphans often/ usually die (of starvation in the first place, chronic neglect in the longer term - the clannishness of dwarves seems to suggest that kids would need to be raised by a relative to be well cared for; and in a society where there is so little motivation to have children, and so many 'career women'; it may be hard to arrange for so many orphans to be brought-up.)
I don't see much solid evidence for the alternative theory, which would seem to require Dwarves once having had very large populations (which would likely make them the most numerous non-evil race in the Elder days)"
No - if Tolkien made that choice, he would need to make some changes to the stories of the Eldar days. The idea of 'big litters' seems the best.
There is a delightful (imagined) account of a dwarf family in Moria in my favourite Tolkien fan-fiction "The Question of Pengolod" in this chapter - https://ansereg.com/mpqp10.html
"Crawling at your feet,” said the Gnat (Alice drew her feet back in some alarm), “you may observe a Bread-and-butter-fly. Its wings are thin slices of bread-and-butter, its body is a crust, and its head is a lump of sugar.”
“And what does it live on?”
“Weak tea with cream in it.”
A new difficulty came into ALice’s head. “Supposing it couldn’t find any?” she suggested.
“Then it would die, of course.”
“But that must happen very often,” Alice remarked thoughtfully.
“It always happens,” said the Gnat.
After this, Alice was silent for a minute or two, pondering.
whitney has left a comment:
I'm reading these books right now. I have just started the two towers. I haven't read them since I was a child but it's really great to read books about nobility and virtue springing up as evil overtakes the land. Everything so debased now. It's good to remember that it wasn't always and I don't mean the world of the books I mean the world that read the books and can be inspired by them
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