The Biology of What Is Not There
Is it only natural selection that guides the shapes seen in nature?
Following the Rules
In our search to account for the occupancy of shape space, we have much to gain by paying closer attention to the rules and mechanisms that generate form. Simultaneous progress in computational methods and developmental biology repeatedly leads to the same conclusion: Simple rules can give rise to enormously complex forms. A graphic example, first described by British physicist and mathematician Stephen Wolfram, is shown in the second figure. In this computer simulation, a simple set of generating rules (such as “branch out into 3 [or 2 or 4], increase the branching angle by 15 degrees, repeat”) gives rise to an array of leaflike forms. These forms are striking in their variety. Note, too, that every shape is discrete and does not appear to blend with an adjacent shape: The generating rules themselves populate shape space in characteristic ways, overstuffing certain parts of it while leaving others nearly deserted. By attending to the construction of biological forms, we can begin to appreciate just how much pattern and structure can arise before natural selection even has a hand in the process.
Provocative as they are, however, these relatively simple simulations need to be interpreted with caution: They are not meant to simulate the actual biological mechanisms of leaf development. We have yet to elucidate fully the actual dynamics that determine leaf shape. Similarly, we need to remember that the developmental process—the biological counterpart of the computer program that created these leaf shapes—itself evolves. Indeed, the evolution of developmental programs has resulted in the opening up of regions of shape space that might previously have been inaccessible. For instance, take the Cambrian explosion some 600 million years ago. Changes in the rules of construction, coupled with changes in the geochemistry of the oceans, suddenly allowed certain groups of marine organisms to make hard shells. Whole new dimensions of shape space abruptly opened, and the diversity of organisms on this planet was forever changed.
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