Location: Vienna, Virginia, United States

A graduate of Dartmouth College (2005) and Washington and Lee University School of Law (2010). These are my personal blogs, and the musings expressed on them do not reflect the positions of my employer. They do reflect my readings, thoughts, and aspirations, which I figure is good enough.

Thursday, January 20, 2005

Ecological Settings

I'm bored and procrastinating, so I got to wondering. In the Appendix to The Return of the King, Tolkien says some interesting things about Dwarves that I've always been curious about. If anyone is wondering, my version of the book has the section on dwarves in Appendix A, part III, Durin's Folk, starting on page 438.

Tolkien says that there for ever 2 dwarf males, there is only 1 dwarf woman, max (in other words, a maximum of 1/3 of dwarves are women, and they look a lot like the men). Also, "the number of dwarf men that actually marry is less than 1/3". In other words, with 1 marrying male / 3 males and with 2 males / 3 dwarves which equals 2 marrying males + 2 marrying females / 9 dwarves equals 4 marrying dwarves / 9 dwarves. 4/9 of dwarves are married.

So in other words, if there are 10,000 dwarves in a population, there might be approximately 6700 males and 3300 females. Of those 6700 males, about 2200 of them will marry. So out of 10,000 dwarves, 4400 enter into marriages (which are monogamous). 4500 males and 1100 females never reproduce. This will be an important number later.

This never made too much sense to me. To sustain their population, this would mean that, even discounting increased death rates during times of war (which happened pretty often in Middle Earth - all those Orcs, you know), dwarves have to have a lot of children just because so many of them don't reproduce. Either that, or the death rate for dwarves outside of war is incredibly low (which kind of makes sense).

Of course, I assume that non-marrying dwarves don't reproduce, but considering what Tolkien says about dwarves, monogamy and seriousness of their relationships, I feel fairly safe making this assumption. Also, I assume that Gimli's claim that "there are few dwarf women, probably no more than a third of the whole people" is not an exaggeration.

I wanted to test this out against actual ecological equations, and this is what I found.

First, we need to establish how big a population we're talking about, as well as how long life expectancy for a dwarf is.

We don't have too much of a sample size for dwarf life expectancy, only one table in the Appendix, but this is how it looks in terms of age breakdown (I also assume that Dwarves are not like Numenoreans with declining life-spans as generations progress).

Dain Ironfoot is only 32 when he slays Azog, so dwarves mature pretty quickly for organisms with long lifespans. He was considered young, but we'll assume middle to late adolescence. Dwarf life-spans range from a short of 77 (Kili) to a long of 340 (Dwalin, of all people, by far the oldest), but most that don't die in battle die between the ages of 220 and 260. Balin, who was old in The Hobbit, was ancient by the time he went to Moria and bought it (231). Gimli is 262 when he sails West.

A cohort is defined in ecology as a number of individuals born in a specific time frame, so we'll use the companions from The Hobbit to form a small sample. Of Thorin's generation, the oldest is actually Thorin himself (which doesn't make sense because Balin is written as if he was the oldest member of the party in The Hobbit.) He was born in 2746. The youngest listed (Fili and Kili are a new generation altogether) is Gloin, born in 2783. We'll use the difference, 37 years, as our interval time X. I like this because it means Dain wasn't quite that old when he slew Azog.

But I still need my cohort size. Since Thorin and his people were scattered, I'll use the Iron Hill dwarves, which, after the Battle of Azanulbizar, made up the majority of dwarves and was their largest settlement (I think).

In The Hobbit, Dain only brings 500 dwarves with him, but I'll assume that this wasn't the entire population of dwarven males of fighting age. He had to come quickly you see, and only brought his best men, the veterans of the Orc and Goblin wars.

I'll give him the benefit of the doubt and guess that since the Battle of Abanulzibar or whatever took place 142 years pre-Battle of Five Armies, he brought those veterans and only those veterans. The veterans, if Dain is considered young, are between 142+37 or 179 and however old dwarves get, about 250. There are approximately 2 cohorts represented in this battle (250-179= 71, 71/2=35.5, interval is 37). Using an average, we say that 142/37 rounded to the nearest interger, or 4 intervals have gone by since the Battle. Considering that after the Battle of Azanulbizar "barely half their number, it is said, could still stand or had hope of healing", 500 is actually pretty good number.

Unfortunately, here I have to make some large assumptions. Since I don't have a so-called "normal" mortality figure to determine deaths outside of interspecies war, I have to assign a number. It will be a guess. I also split into two cohorts, a younger, A, and an older, B.

In that first interval for cohort A, birth-37, I'll say that only 1 out of 100 dies. In other words, only 1 dwarf baby/child/adolescent dies. They're hardy and have good midwives. They only die in those last 5 years when they are old enough to go to battle, and not many of them do. Same for Cohort B, although they have an extra interval since their generation is older.

After that, dwarves will die off faster, due to battles with the Orcs and Gobbos. I'll assign a 8% mortality rate. Seems low, but remember, women don't go to war. So for every 1000 dwarves in a cohort, 80 die every 37 years due to raids and stuff (hunting accidents, getting lost while going to the crapper, etc). Cohort A, by the time of The Battle of Azanulbizar, is at .99. Cohort B is at .911, due to the extra interval.

The Battle of Azanulbizar kills 50% of all dwarves present. But since it's only males, it's not really 50% of the cohort, but 2/3 of 50% or 33.33%. The older ones that survive I'm not concerned with, since they're no longer alive anyway by the Battle of the Five Armies. I'm only concerned with cohort A and B. After the Battle of Azanulbizar and that interval, Cohort A is down to .990 - (.333 of .990) - (.08 (of the .990 times .333)), which is .607. Cohort B is left with .911 - (.333 of .911) -.08 yadda yadda, which is .559

Cohort A has 4 more intervals (members are between 185 and 222) before the Battle of Five Armies. That last interval I'll up the mortality rate since dwarves seems to die in there, sometimes. At a rate of .08 per 37 years and .15 that last interval, by the time this generation marches off to the Battle of Five Armies, they have .402 of their original number left.

Cohort B has 4 more intervals, and I'm upping the mortality since those members are between 222 and 259. 2 intervals of .08, 1 interval of .15 and 1 interval of .24 (dwarves seem to drop dead all at once) result in a final fraction of .306. Actually seems pretty good considering half of them got wiped out in an interval.

If we have 500 dwarves left after 4 intervals (plus the initial one and the Battle interval), we can do some calculations to determine how many there were in the beginning.

if the 500 dwarves divide evenly between cohorts, there will be about 286 from A and 214 from B. 286 represents the number of living males, and to that we add one third, the number of females. We do this for 214 as well and get the existing number of dwarves from those cohorts. This is 381 and 285. 381 is .402 of the original, so there were once 948 dwarves in that cohort. Cohort B had 932.

I can provide figures if anyone wants, but I'm using the Cohort A size of 948 dwarves, 381 of which are still alive. That means 633 males and 315 females per cohort originally. Up to 210, but not that many, of the females became mothers.

We can get an age specific birth rate that is necesary to sustain a net replacement rate of 1 (no gain, no loss). Since Lx (remaining individuals/original) is .402, for replacement rate to be 1, Mx, births / people left, must be 2.488. This basically means the another cohort must have been made, or 948 babies. 948 babies for a maximum of 210 dwarf wives equals about 4.5 per wife, minimum.

This means that married dwarf women had to bear an average of 4.5 children during their lives, 1.5 of which were female and 3 of which were male. That's a lot of dwarf babies, although it is true that they live three times as long. This number is skewed because of the high rate of death in the cataclysmic Battle of Azanulbizar, I think, but then again, my other mortality numbers might be low.

This also means that if the fighting age for a dwarf was between 32 and 260, or about 6 cohorts, only 3800 dwarves were present for the Battle of Azanulbizar. Although those are dwarves that end up in the Iron Hills, so actually it might make sense. I think it very appropriate to give this age range, since dwarves in Tolkien are pretty much fighting non-stop, whether it be with Orcs or Goblins or Elves or Dragons.

I have too much time on my hands. Or should I say, I'm not spending enough time on writing my thesis.

Also, in conlcusion, the less said about dwarf sex, the better.


Anonymous Anonymous said...

Holy shit... That was amazing. Not the sort of amazing that would change my life, mind you, but more like the sort of amazing that leaves me wondering what possessed you to do that.

I will admit, however, that it's sort of impressive, if in a geeky way...

7:16 PM  
Blogger Satchmo said...

Oh, it's very geeky.

And no, I don't know what possessed me to do this. I just felt like it. That and I didn't want to write my thesis.

Something something very little sleep last night studying for a physiology test. There's that too.

9:44 PM  
Blogger Satchmo said...

A couple more things for anyone that cares

This figure and calculation (which might be wrong) does not factor in the concept of gay marriage, which might change our numbers again. I assumed all marriages heterosexual, so if anyone has a problem with this, tough. I can factor in gay and lesbian dwarves at another time, but not now.

Also, 3800 dwarves max came from the Iron Hills. Since they "came fresh to the field" and turned the tide, the number makes sense. Might even have been too big.

11:52 AM  
Blogger William Li said...

4.5 children would not be unusual for the type of "old world" family structure that is suggested by Tolkein's middle earth, nor would a high mortality rate. What would be unusual is for so many pregancies to result in surivial of both the mother and/or offspring.

Several things to thing about:

1) Why do so few dwarf men marry?
The dwarfs are warlike people and the men are constantly getting themselves killed before reaching a good marrying age

2) You are assuming too many women will never reproduce. I think that's probably wrong. What does the appendix say about Dwarf widows remarrying?

3) Thorin Oakenshield had a brother and sister (mentioned). There are also several other sets of brothers in "The Hobbit"

A popular internet site for this topic is

Although I prefer my copy of "The Tolkein Companion"

by the way, my wife had the baby. You can check my blog.

1:46 AM  
Blogger Satchmo said...

Thanks for the comments and congratulations on the newborn!!

You wrote:
1) Why do so few dwarf men marry?
The dwarfs are warlike people and the men are constantly getting themselves killed before reaching a good marrying age

2) You are assuming too many women will never reproduce. I think that's probably wrong. What does the appendix say about Dwarf widows remarrying?

Actually, Tolkien does kind of address these. The mortality rate of male dwarves could have to do with it, but he also says that dwarves are monogamous to the point that if they have one person in mind, they will never settle for another dwarf. He writes this to explain why the marriage rate for women is so low. If they can't marry the one they want, they won't marry at all.

This led me to figure that not only do dwarves not have children outside of marriage, but that they don't remarry. It is true that this does not preclude having children outside of marriage, but I just kind of figured being that stubborn about mates would cut down on the illegitimate children. But for all I know, they might have had rampant sexual relations, defined marriage differently, and not cared a whole lot about how procreation figured into it. Since they seem to value the nuclear family though, I would tend towards the more conservative picture of dwarven society.

Thanks for the site, btw, I'll definitely check it out!!

1:58 AM  

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