To estimate the number of leaves in a forest, count the number of leaves on a typical branch, multiply by the number of branches in a tree, and multiply by the number of trees in the forest. |
But what's a typical branch? Surely a small branch has fewer leaves than a large branch. For that matter, what's a typical tree? |
West, Enquist, and Brown took a different approach. |
In a Costa Rican rain forest, they found a power law relation between the diameter of a branch, and the number of branches with that diameter. |
Additionally, they found a power law relation between the number of trees in a forest and the trunk diameter. |
In both power laws, the exponent is the same. |
Branch is to tree as tree is to forest. |
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