this packing using fractal geometry. If you imagine the environment’s resources as a fractal, rather than a stick, small species will see that fractal at a higher magnification than large ones. Small species will see, and exploit, all the twists, turns, and branches in resource space invisible to larger species. Large animals perceive the world at a coarser scale and need more space—from feeding ground, to waterhole, to breeding ground, to roost—to get life’s jobs done.

On Monte Pellegrino, Hutchinson noticed that the two bug species in the pool were of different sizes. If body size determines how much ecological space a species occupies, differences in body size seem an obvious way to occupy different niches and thus avoid competition. Different-sized organisms need different amounts of space and food, they can get and use different types of food, and they can tolerate different environments. Hutchinson sought a rule to explain size differences in coexisting species. In groups of animal species exploiting the same resource, he noticed, each species is often about twice the weight, or 1.3 (the cube root of 2) times the length, of its nearest neighbor. Hutchinson thought that the critical size difference was between the body parts used to obtain food. If you line up the Galapagos finches studied by Darwin in order of their size, each species has a bill about 1.3 times longer than the next smallest finch. Insects go through several different larval stages before adulthood, and each stage is roughly 1.3 times longer than the next. The idea caught on, and many more examples of what became known as Hutchinson ratios were spotted. In 1977 the ecologists Henry Horn and Robert May noted that in consorts of viols and recorders each instrument, as one moves from treble to tenor or tenor to bass, is about 1.3 times longer than its neighbor. They seem to divide up musical space so that each has a separate job and does not compete with the other group members. And in some sets of iron skillets sold together, they pointed out, each is 1.3 times wider than the next. No one would buy a set of five identical frying pans, but like animals the coexisting skillets have been selected to specialize in handling food items of different sizes. Horn and May suggested that Hutchinson’s ratios might apply generally to sets of complementary tools.

Jared Diamond, a friend and colleague of MacArthur, offered another example of how competition between species might control

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