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In Search of the Optimal Scumsucking Bottomfeeder

Brian Hayes

Five years ago a column in this series titled "How to Avoid Yourself" described the geometry of paths traced out by a random walker who refuses to set foot in the same place twice. Soon after the article appeared, I received a letter from Mark A. Wilson of the College of Wooster, who pointed out that some of my computer-generated paths were anticipated by millions of years in the fossil record of early life. He referred me to the Treatise on Invertebrate Paleontology, an immense multivolume work sponsored by the Geological Society of America. Specifically, I was directed to Part W, Miscellanea, and within that part to Supplement 1, Trace Fossils and Problematica, written by the late Walter Häntzschel. As promised, I found there photographs and drawings of rock surfaces bearing intricate zigzag and spiral patterns that look very much indeed like certain computer-generated self-avoiding walks. Most of these "trace fossils" are interpreted as trails left behind by worms foraging in the muddy sediments of the seafloor. Can computer programs that generate similar geometric figures reveal anything about the creatures that made the fossil trails?

Wilson and I were not the first to ask this question. As a matter of fact, trace fossils were the inspiration for one of the earliest computer simulations of animal behavior, published in 1969 by David M. Raup of the University of Rochester and Adolf Seilacher of the University of Tübingen. Their ingenious model reproduced some of the more distinctive features of the fossilized trails, such as the prevalence of zigzag and spiral motifs. And the principle of the self-avoiding walk was a key element of the simulations: No worm was allowed to waste effort grazing in territory that had already been traversed.

In the decades since then, convoluted worm trails have remained a favorite subject for computer simulations. Here I shall review four more models designed specifically to explain the same trace fossils. The point of departure for all the simulations is a supposition about why the animals created trails of this general type. The driving force is taken to be a need to optimize foraging efficiency, so that every bit of territory is grazed once but only once. Given this underlying imperative, the question becomes how the animals created the patterns, or in other words what algorithms they employed to guide their movement. Because the primitive organisms had limited sensory and cognitive capabilities, the algorithms must have been fairly simple. And the computer simulations confirm that a few simple rules are enough to generate most of the observed patterns. Thus it appears that the how question has a plausible answer. But certain doubts remain about the why question. Is foraging efficiency really what motivated these mysterious animals?

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