What kind of tree is Treebeard?

J.R.R. Tolkien spends so much time talking about trees, telling us details of their species and their growth, that it’s curious there’s one omission. What kind of tree is Treebeard?

A few seemed more or less related to Treebeard, and reminded them of beech-trees or oaks. But there were other kinds. Some recalled the chestnut: brown-skinned Ents with large splayfingered hands, and short thick legs. Some recalled the ash: tall straight grey Ents with many-fingered hands and long legs; some the fir (the tallest Ents), and others the birch, the rowan, and the linden. [LR 3.04.142]

We get a hint here that Treebeard sort-of looks like an oak (400 species) or a beech (13 species), but it’s never explicitly stated and that doesn’t narrow it down much. Can we use external information to figure out what Tolkien might have been thinking? Of course we can!

Since Treebeard can get most of the Ents of Fangorn to a moot with one morning’s work, he must be a central figure in the Ent community. If we had a graph of relationships between trees, then we could look for centrally-positioned tree species. Treebeard is probably one of those.

The European Commission has funded research into forest types and the species that make them up, all available on line.¹ With a lot of transcription² and a little bit of matrix algebra, we can turn their tree species matrix into a species adjacency matrix, and thence into a graph.³ All matrix algebra and graph metrics were computed with the R statistical software, version 4.2.2.

I have omitted the species that only live by themselves, most conspicuously the junipers. (See the Canary Island pine, all off by its lonesome? Some species are even more isolated than that.) The introduced species are also removed,⁴ because Treebeard is nothing if not native to his forest. There are 112 species in the graph, after we remove the singletons. There are 92 types/subtypes of forest.

The European Forest Matrix converted to a graph. Hardwoods are in orange and softwoods in blue. Click to embiggen.

Even blown up to full size, that graph is too tightly connected to analyze with just eyeballs, so we need mathematical measures of centrality. I used four:

• Degree just counts how many species can live next to the tree of interest, because they exist in the same kinds of forest. The Ent with the most friends has the highest degree.
• Page Rank is how the Google search engine works. If your species is around other species that are themselves around lots of species, your centrality is higher. If organizing an Entmoot involves recruiting highly-connected Ents to help you out, the tree with the highest page rank would be a good one to do it.
• Closeness is a measure of how many steps through the graph (friend-of-a-friend) a species needs to get to every other species. This would be useful for organizing an Entmoot by yourself.
• Betweenness (that’s really the word) looks at the shortest paths through the graph connecting each pair of species. The species that’s on the most of those paths is the most between — this is the tree that would know all the news in the forest.

We don’t know how Treebeard did it; it might have been any of them, so I looked at these measures to find species that are near the top on all of them. Here are the candidates.

Ash: The European ash tree has the highest degree centrality. 65 other species connected to it. That’s because the range map on Wikipedia says it grows basically anywhere with water. Definite possibility! Except the text says that other Ents look like ashes, and they’re not Treebeard. Also, Gandalf’s staff was made of ash, so I doubt an ash-ent would think he’s such a good friend. So the ash is out.

Black elder: Besides elderberries being tasty, the Black elder has the highest page rank. Unfortunately, it looks more like a bush than a tree. I’m sad that this one didn’t work out because Celeborn addressing an elder as “Eldest” would have been a great joke.

Field maple: This tree isn’t number one on any metric, but it’s #3 or #4 on all of them so it’s a contender. It loses out because it doesn’t have any textual support. It doesn’t look anything like an oak or a beech. (No beech ranks above #8 on any metric.)

Pedunculate oak: This is the good old English oak. It’s a very long-lived tree, and very tall. The Wikipedia article says there are more ancient oaks in England than any other country in Europe. It also cites old myths saying oaks were the “thunderstorm trees”, with which Saruman might agree.  Merry said “The Forest had felt as tense as if a thunderstorm was brewing inside it”. [LR 3.09.059] Though it’s not higher than #3 on any metric, this is almost certainly the species Tolkien was thinking of.  But… the graph suggests a dark-horse candidate.

Turkey oaks in New York’s Central Park

Turkey oak: It’s got a funny name (OK, maybe not as funny as “pedunculate”), but it’s #1 on the betweenness metric. Turkey oaks have an interesting history. Wikipedia says, “The species’ range extended to northern Europe and the British Isles before the previous ice age, about 120,000 years ago.” I can’t help remembering Elrond saying the Old Forest once stretched all the way from the Shire to Dunland, but had shrunk since.  Almost like Treebeard could have walked among Turkey oaks from Wellinghall to England, but now there’s just empty lands between them.

So I liked Turkey oaks, but on top of that, searching for Turkey oaks on line took me to the website for Central Park. They have Turkey oaks there, and look at them! The one on the left is absolutely an Ent, caught in mid-pandiculation.

Credit where credit is due

About a quarter of the way through this exercise, I realized I was tracing the steps of Kieran Healy of Duke University, whose essay on how British intelligence might have caught Paul Revere if only they’d known some math is one of the funniest things ever written about graph analysis.  Note for his most-obscure joke: “eigenvector centrality” is the same as what I called “page rank” here.

1. Pividori, M., et al. “European Forest Types: tree species matrix.” San-Miguel-Ayanz, J., de Rigo, D., Caudullo, G., Houston Durrant, T., Mauri, A.(Eds.), European Atlas of Forest Tree Species. Publ. Off. EU, Luxembourg, pp. e01f162 (2016).
2. The online version of the matrix is unreadable by any programming art I possess, so I did it by hand. This is the stage where any errors will be.
3. To be precise, I converted their matrix to 0 if a tree is not in that kind of forest, and 1 if it is. Then I multiplied the matrix by its transpose to make a square matrix of species vs. species.
4. Ailanthus altissima, this means you!