With all the recent discussions on Dwarves following up The Hobbit: An Unexpected Journey there is one question that keeps popping up:
“How can Dwarves keep up their population with their low number of women?”

This essay will take a closer look at this question and other demographic issues concerning Tolkien’s Dwarves.

Let’s start with a quote from the Appendices in The Lord of the Rings:

“Dís was the daughter of Thráin II. She is the only dwarf-woman named in these histories. It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people. They seldom walk abroad except at great need. They are in voice and appearance, and in garb if they must go on a journey, so like to the dwarf-men that the eyes and ears of other peoples cannot tell them apart. This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves ‘grow out of stone’.
It is because of the fewness of women among them that the kind of the Dwarves increases slowly, and is in peril when they have no secure dwellings. For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.”

So the much quoted “one third of the Dwarves are female” is not an exact number, but it is only estimated by ONE individual (Gimli) of the Dwarf race. For easier calculations though we will work with this exact number, assuming that one third, or 33.3% of all Dwarves are female.

A dwarf girl and a dwarf woman. http://www.wetanz.com/daniel-falconer/

What about sex ratio in the real world? Humans roughly conceive 50% male and 50% female babies (with a slight favour to males which we’ll neglect for easier assumptions). There are animals with much different sex ratios than this rather simple model. Just think of bees or ants where most individuals are female. Some animals need certain ecologic parameters to give birth to a certain sex. And the extreme example of course are parthenogenetic animals, such as certain crustaceans or stick insects of which males are completely unknown to science. Without getting too much into detail those species reproduce by “cloning” the mothering animal, making males completely unnecessary.

Whichever example one wants to take from the real world though, if the sex ratio leaves the classic 50/50 mark it always goes in the direction to favour female offspring. The reason is simple: females are more “valuable” to reproduction since they produce egg cells (which are a lot richer in resources than sperm cells) and also because they usually invest a lot more time and effort in raising their offspring (pregnancy, nursing, etc…) than males. Seahorse fathers are the laudable exception to this of course.
In real world species in theory it only takes one male individual to inseminate several females, which makes males a lot less valuable as well.
So the fact that Dwarven sex ratio distinctly favours males is odd. It does definitely help during warfare, but there is no biologic reason whatsoever to get to this awkward proportion. The only plausible explanations here could be that Y sperm cells are more common than X sperm cells (assuming Dwarves have the same XY-system as humans) that female Dwarves might be more sickly, female embryos die a lot more often during pregnancy and so on.

Of course all these assumptions would be a horrible initial situation for any species, and in the real world evolution would have definitely gone into a different direction.

So with this unfavourable point of departure, what would it take to keep a population at the same level? For humans (1:1 ratio) every woman statistically has to give birth to two children. There are women that can’t conceive, die early or simply choose not to have children, so in reality for women that DO give birth this number has to be slightly higher since the statistic also includes women that never have a child. Luckily there seems to be a lot of women getting three, four, five…. children because our number is constantly increasing.

For Dwarves however (1:2 ratio) every female statistically needs to give birth to three children to keep up the population. But in the case of Dwarves what are the conditions we have to consider in this statistic?

Lego dwarf family. http://www.flickr.com/photos/mooseteg/

Maybe we should first check how many Dwarves Tolkien actually ever gave a name throughout all of his works. Luckily there is a neat list of all his Dwarves on Wikipedia:
http://en.wikipedia.org/wiki/List_of_Middle-earth_Dwarves
The list gives 53 names, and we know both from the above quote and this list that Dís is the only female Dwarf ever mentioned. This gives us a horrible 1:52 ratio, which is a lot worse than the 1:2 we started with! However we do know that Tolkien didn’t mention names of a whole lot of female characters for all his peoples, so we can safely go back to keep our 1:2 ratio.

As for this list, a totally useless number to know: one fourth of all male Dwarves EVER mentioned in Tolkien’s works are going on the Quest of Erebor!

But not only is just one third of the whole population capable of giving birth, no, not even everybody of this third chooses to do so! And what is even worse: if they marry (= choose a mate for reproduction, as they don’t bring forth children otherwise) and their husband dies early, they won’t choose another Dwarf man to wed and therefore let precious reproduction resources slip by.

However you may remember what I said earlier: to keep the population stable (I am not even talking about increasing yet!) every dwarf woman needs to give birth to three children. Now we know not all of them marry and some of them may lose the possibility to reproduce after the early death of their husband. We even have an almost exact number of the marriages in the above quote: Two thirds of all Dwarves are male, less than one third of those marry. Now some simple math: 2/3 * 1/3 = 2/9 = 22.2%. Each of those has a wife, so only (less than!!!) 2/9 = 22.2% of all Dwarves ever get the chance to even give birth!

This means our number of children per woman goes up enormously! To actually increase the Dwarven population in Middle-earth we have to assume every married Dwarf woman statistically has to give birth to at least five children (22.2% being slightly more than a fifth). Do they?

Dwarf family tree from the Lord of the Rings appendices

Unfortunately we don’t know too much about Dwarf families. We know of a couple of brother pairs (Oin – Gloin, Balin – Dwalin, etc.), but the only families we can safely say we know “as a whole” are Dís’ sons Fili and Kili, and Dís’ two siblings Frerin and Thorin. Of course, we do know Bofur and Bombur are brothers for example, but we don’t know whether there are more siblings. So the two families we know (almost) for sure as a whole bore two and three children. That is definitely not enough for our estimation!

The sad thing is that we really don’t know too much about family size. Brothers are never mentioned more than as a pair but then we never know about the rest of their families.

In fact the above quote even mentions that Dwarves’ numbers increase only slowly and even more so if they lost their homeland. Unfortunately though in Middle-earth history Dwarves have lost almost all their realms which would also explain why their numbers dwindle and why they so desperately try to get Erebor, Moria and even Gundabad back!

So is there anything left we could cling to? What about the longevity of Dwarves? Shouldn’t that help them with their reproduction somehow? Well, it would, if they decided to marry another partner should the first one die. It also would if they decided to marry a little bit earlier than they do.
Let’s look at this. Dwarves are considered battle-ready at the age of 30, but they rarely ever marry before they are 80! Just imagine how much could happen in those 50 years in between. I am going to use an unusual comparison here to make this clear: Galápagos tortoises are possibly the longest-lived animals in our recent world with ages above 150 years being not uncommon. Of course when having so much time at hand one’s whole development is really slow, so Galápagos tortoises don’t reach sexual maturity until roughly 30 years. Now while a 100 year old Galápagos tortoise is almost as indestructible as a 150 year old battle hardened Dwarf, both are very vulnerable when young! The tortoise might be eaten before it even had a chance to grow big enough and reach adulthood and the Dwarf, well… we all know how much they love battle. And a young yet untrained Dwarf is more likely to fall in battle, which is also before he had a chance to reproduce. Examples? Frerin died at the age of 48, Fili was aged 82, and Kili 77, all of them before they had a chance to marry. Dain was only 32 when he slew Azog (well, in the book at least…) and was lucky he survived the battle of Azanulbizar to be able to marry afterwards. But it shows that he also risked his life at an exceptionally young age.

To get back to those Galápagos tortoises: They actually live under the same dangerous conditions as Dwarves in Middle-earth when we think about their possibility of reproduction. And we all know that those tortoises are on the brink of extinction themselves.

So, the longevity WOULD help the Dwarves to bring forth more offspring but they simply don’t take that advantage.

And now we get back to our initial question:

How can Dwarves keep up their population with their low number of women?

Well, with the given numbers they simply can’t! In fact considering all we know for sure, they are less likely to survive than the Giant Panda is in our world!

So is there no hope for Dwarves?

Dwarf families fleeing Erebor.

Yet there might be. Interesting enough Tolkien only gives us a sex ratio for Dwarf populations. Never at any point does he say what proportion of Dwarven population is of royal lineage. However all the numbers concerning family sizes we only know of the royal line of Durin’s Folk! So there really is only one way for Dwarves to survive their own extinction: The other six houses of Dwarves and/or the commoners must have much higher reproduction rates as those royal Longbeards. And this is actually a rather elegant solution, since Tolkien never really provides us with information about any other Dwarves, and this might well be true.

Royal Dwarves seem to be rare, but this was true of any royal families in our world as well. And just as it was in our case in historic monarchies it would be up to the common people among Dwarves to keep them from going extinct!