Are Firms Like Trees?

Trees are spectacularly successful, and have been for millions of years. They now cover ~30% of Earth’s land. So trees should be pretty well designed to do what they do. Yet the basic design of trees seems odd in many ways. Might this tell us something interesting about design?

A tree’s basic design problem is how to cheaply hold leaves as high as possible to see the sun, and not be blocked by other trees’ leaves. This leaf support system must be robust to the buffeting of winds and animals. Materials should resist being frozen, burned, and eaten by animals and disease. Oh, and the whole thing must keep functioning as it grows from a tiny seed.

Here are three odd features of tree design:

  1. Irregular-Shaped – Humans often design structures to lift large surface areas up high, and even to have them face the sun. But human designs are usually far more regular than trees. Our buildings and solar cell arrays tend to be regular, and usually rectangular. Trees, in contract, are higgledy-piggledy (see pict above). The regularity of most animal bodies shows that trees could have been regular, with each part in its intended place. Why aren’t tree bodies regular?
  2. Self-Blocking – Human-designed solar cells, and sets of windows that serve a similar function, manage to avoid overly blocking each other. Cell/window elements tend to be arranged along a common surface. In trees, in contrast, leaves often block each other from the sun. Yet animal design again shows that evolution could have put leaves along a regular surface – consider the design of skin or wings. Why aren’t tree leaves on a common surface?
  3. Single-Support – Human structures for lifting things high usually have at least three points of support on the ground. (As do most land animals.) This helps them deal with random weight imbalances and sideways forces like winds. Yet each tree usually only connects to the ground via a single trunk. It didn’t have to be this way. Some fig trees set down more roots when older branches sag down to the ground. And just as people trying to stand on a shifting platform might hold each other’s hands for balance, trees could be designed to have some branches interlock with branches from neighboring trees for support. Why is tree support singular?

Now it is noteworthy that large cities also tend to have weaker forms of these features. Cities are less regular than buildings, buildings often block sunlight to neighboring buildings, and while each building has at least three supports, neighboring buildings rarely attach to each other for balance. What distinguishes cities and trees from buildings?

One key difference is that buildings are made all at once on land that is calm and clear, while cities and trees grow slowly in a changing environment, while competing for resources. Since most small trees never live to be big trees, their choices must focus on current survival and local growth. A tree opportunistically adds its growth in whatever direction seems most open to sun at the moment, with less of a long term growth plan. Since this local growth end up committing the future shape of the tree, local opportunism tends toward an irregular structure.

I’m less clear on explanations for self-blocking and single-support. Sending branches sideways to create new supports might seem to distract from rising higher, but if multiple supports allow a higher peak it isn’t clear why this isn’t worth waiting for. Neighboring tree connections might try to grab more support than they offer, or pull one down when they die. But it isn’t clear why tree connections couldn’t be weak and breakable to deal with such issues, or why trees couldn’t connect preferentially with kin.

Firms also must grow from small seeds, and most small firms never make it to be big firms. Perhaps an analogy with trees could help us understand why successful firms seem irregular and varied in structure, why they are often work at cross-purposes internally, and why merging them with weakly related firms is usually a bad idea.

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  • Brian

    No, trees are not weird. You are the weird one for thinking that trees are weird. See this paper, that generates tree plans from scratch, subject to various constraints (height, coverage, mechanical strength, water conservation, etc.)

    http://www.eos.ubc.ca/~mjelline/453website/eosc453/E_prints/newfer06/2004NiklasAREPS.pdf

  • Mark M

    Robin,

    I never thought you’d buy into “intelligent design.” My bad.

  • Vaniver

    This is fascinating. Which tree experts have you asked about this, or are you counting on your readers to have expertise to share?

  • http://hanson.gmu.edu Robin Hanson

    Brain, that paper doesn’t seem to consider the missing variations that puzzle me.

    Mark, I’m only asking that trees be designed as well as animals.

    Vaniver, I don’t know the right tree experts, and searched for a few hours for relevant expert writings.

  • http://www.fractalplanner.com/blog Jim Stone

    Brian Arthur of the Santa Fe Institute would argue that trees and firms (and nearly all of our other creations) share a deep structure — a fractal, branching structure. His “The Nature of Technology” (the book in which he most fully develops this thought) is one of the best books I read last decade.

  • Pingback: Sleep, trees, and firms : David Jinkins Webpage

  • http://www.andreasmoser.wordpress.com Andreas Moser

    I much prefer trees.
    A forest full of them makes me calm and excited at the same time, it’s beautiful, and it’s an especially beautiful place to enjoy a cigar: http://andreasmoser.wordpress.com/2011/10/29/smoking-cigars/

  • http://orderandcreativity.com Daniel S

    Thanks for sharing another interesting problem to ponder!

    On the self-blocking issue: Wouldn’t the placement of leaves be a trade-off between catching sun light and absorbing carbon dioxide? If leaves would only be present in the surface that captures sun rays, perhaps there wouldn’t be enough leaves to absorb enough carbon dioxide?

    As for the single-support problem: I believe that the main factor you have left out is that the tree design should ensure the survival of the tree’s genes rather than the tree itself.

    To ensure the future of their off-spring it might be better for a tree to be slightly more fragile so that it falls over when it dies (or when its old enough to have produced a lot of seeds). The benefit for its seed is then off course greater access to sunlight and nutrition (I’m assuming that quite a lot of the seeds will end up close to the tree).

    A single support might be an easier solution than several supports and some more perishable material. Also, the seeds from neighbouring trees of the same kind are possibly family, so ensuring their survival might also be good from the perspective of a tree’s genes.

  • http://facelessbureaucrat.blogspot.com Bill Harshaw

    Bark is a protective structure, with no contribution to tree growth or reproduction. The innards of the trunk is what’s important. In determining one trunk versus three trunks, consider the ratio of the perimeter of the trunk to the area of the cross section. As the size of the trunk grows the area increases faster than does the perimeter. If you have 3 trunks you have a lot more bark and a lot less innards than you do with one trunk

    In talking “trees” you seem to assume deciduous trees, not evergreens.

  • http://samposmolander.fi/ Sampo Smolander

    For 3: When growing in a dense stand, a tree’s (any plant’s) strategy is to outgrow the neighbours in speed/height, so as to be less shadowed by the neighbours. Offering support for the competitors would not be ESS. The objective is not for the forest to grow as tall as possible, but a single tree’s objective is to grow a little taller then the neighbours. Trees growing in an open place don’t put so much effort in growing fast and tall. Also, when a tree is trying to grow tall in the competitive phase, it would be a waste of time and resources to try grow some lateral support, as the hurry is about growing upwards.

    Much of forestry practice is about keeping the stand at a suitable density so that there is enough competition between the trees so that the stems grow tall and straight (but not so dense that the trees are suffocating each other).

  • nelsonal

    Trees make a whole lot less sense because we experience them on human rather than tree time scales. Watch a time lapse video of a younger tree over the course of a season and the tree’s “decisions” and structures make far more sense.

    A tree’s environment makes a huge difference in how the tree’s shape responds (all the trees in my back yard are great for lumber because they have a central trunk that extends way up into the air). Plant those same trees alone, like the cherry in my front yard) and it gets wider much earlier (6 feet in that case). It’s impressive to see the branches that have responded to the clearing created for the house’s footprint (in just 50 years).

    Most trees follow a few simple rules, only a few parts of the tree can grow new branches (shoots) but new shoots can sprout from almost any part of the existing branch structure. Once a shoot is removed from the tree, that shoot will not reform. Shoots move in response to gravitational pulls (away) and toward light. If a shoot’s leaves find light, the branch thickens. There’s usually a general species shape but even that can be tweaked by the environment.

    Trees operate by essentially throwing a huge amount of buds out there and adding resources to the ones that reach sun and survive (and self pruning ones that don’t reach sufficient sun). Orchardists tend to manage this growth (which is why pruning is one of the main things they study and do). Bud growth is not all that different from the traditional competitive market assumptions.

  • John

    Neighboring tree connections might try to grab more support than they offer, or pull one down when they die. But it isn’t clear why tree connections couldn’t be weak and breakable to deal with such issues,

    The tree is working at the margin, without a long term plan tightly optimized for the specific situation. It has no way to evaluate the structural stability of adjacent objects, and no immediate incentive to develop such an evaluation mechanism. In the absence of such an evaluation, cross-bracing directly conflicts with the structural resilience requirements, because every connection to an unknown structure means taking on unknown structural liabilities.

    Most of all, a “weak and breakable” support would not be structurally useful, because it would fail at the very moment when it was needed most! How could that not be clear?

  • Richard Silliker

    “Perhaps an analogy with trees”

    Will not work. How is that?

    Trees are rational paradigms and firms are just paradigms. The difference is a condition known to me as intrinsic. Firms lack that condition.

  • Mario Furtado

    It also has a lot to do with the random distribution of sun at any particular moment and during the day. If you have a regular pattern (or a formative distribution) you’ll run into issues when it’s cloudy. The pattern has to be disjointed to allow the possibility to capture a random distribution of sunlight.

    Look at mem arrays of solar cells. They also have any spot pattern that is disjointed and might look random, but the point is each microstructure is optimized for sunlight at that moment. Trees don’t have this luxury, so instead typically go for the random distribution. This gives them a good chance of collecting sunlight no matter what position the sun is in and what the cloud structure might be at any one moment (barring full obscurity).

    If you limit the overall distribution of sunlight to a small window and regular pattern all plants will grow towards that particular spot and develop a canopy to capture the available light.

    Mario.

    • Noumenon

      Thanks, this cleared up a lot of the issue with leaves that seem to be blocking other leaves.

  • S

    Why aren’t tree leaves on a common surface?

    Palm trees tend to have larger leaves, fewer of them, and all at the top of the tree.

  • http://timtyler.org/ Tim Tyler

    I think I can explain why trees are somewhat asymmetrical. Tree growth is adaptive – it takes place where light is good. There’s selection on growing branch tips. The result is an adaptive fit to the tree’s environment – which rarely results in a particularly symmetrical form.

  • http://timtyler.org/ Tim Tyler

    Hmm – Robin already wrote on that in the post. Aerial roots do exist (banyan, mangrove. I’m not 100% sure why they aren’t more common – but probably predation is involved. Plenty of plants do physically hold each other up – e.g. bamboo supports its nearby relatives.

  • Jody

    The confusion comes from assuming either a firm or a tree are indivisible units rather than collections of independent actors with some mutually beneficial goals.

  • http://www.johnicholas.com Johnicholas

    Though Dr. Hanson answered “I only want them to be as well designed as animals”, I still think “Evolution is dumb” is the best answer to these questions. Evolution ties itself into knots, committing a species to certain technologies, and has difficulties untying those knots.

  • Dennis

    The design and arrangement of tree leaves is quite well understood. The leaves at the top of the tree are generally orientated at a greater angle – they absorb some light whilst avoiding direct exposure to the harshest midday light. The light that passes through is absorbed by the ‘shaded’ leaves below. The structure of the canopy changes from top to bottom in line with this phenomena – thinner,flatter, larger leaves with less chlorophyll per unit area right at the base. Interestingly these shade adapted leaves at the base are often right at the margin in terms of energy production/cost.
    The total light absorption through the complete crown is often very high (spp dependent of course), and can be described with the Beer-Lambert law.

    Now this is weird – some studies suggest that trees can ‘see’ their neighbours by responding to shifts in the incoming spectra when a neighbouring tree begins to grow and intercept light. Some trees seem to respond to this by focusing more growth in such a manner as to out-compete these interlopers.

  • http://kim.oyhus.no Kim Øyhus

    CO2 is the most limited resource for trees,
    so they maximize their ability to get this by touching a lot of air,
    hence the tree shapes.

    If energy was a limiting resource, trees would be black, or purple, since most of the energy in light is in the green colours.

  • Ari

    Insightful and interesting post. I was writing a longer reply when I realized you just said what I was going to say in your seventh paragraph. Especially regarding cities and trend towards local maximum.

    3. I haven’t done strength mechanics but skyscrapers rarely have more than single branch. Skyscrapers don’t lean to each other for support though either.

    Also related article regarding bird flight and mechanical flight. Interesting.

  • Damon Willis

    1. Trees aren’t irregularly shaped, they follow very regular growth and branching rules, but they are not symmetrical. Symmetry is hard. It takes effort coordinating growth at a distance over time. Symmetry is not in itself good design, it is only good design if it benefits the organism. It is useful for coordinating movement. Organisms that don’t move, don’t bother with it.
    2.Self blocking may cost the tree some sunlight, but it produces shade, which makes it hard for any competing plant to sprout up from below it and usurp the tree’s spot in the sun.
    3. Multiple supports are mostly useful for stiffness, not strength. Trees don’t gain anything by trying to hold their top levels steady. Buildings that sway too much have a difficult time getting tenants on upper stories, trees don’t have that problem.

  • Santiago

    The constructal principle can explain the configuration of systems pretty well in terms of the physics of flows and the realization that systems that survive in time will tend to evolve towards a configuration that minimizes the resistance to the flow (the constructal principle).
    This paper would explain the overall configuration of trees which addresses points 1 and 3.
    http://www.constructal.org/en/art/JTB_Trees.pdf.
    As for self blocking consider first the movement of the sun during the day and throughout the year. Then the shape that maximizes surface area would be a sphere subject to mechanical constraints of the material. But if you also consider that leaves that block each other don’t block each other out completely because of light diffracting and movement from the wind, then having what seems to be a self blocking structure may actually increase the effective surface area of leaves. This falls in line with a casual observation (from memory not many leaves on trees now), most leaves that block each other are far enough away that they can receive diffracted light while most leaves that are close to each other aren’t self blocking and are roughly on the same plane.

  • subba

    this will be the consequence if there is no right managment!