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COMPUTING SCIENCE

In Search of the Optimal Scumsucking Bottomfeeder

Brian Hayes

Phobotaxis, Thigmotaxis, Strophotaxis

When Raup and Seilacher wrote their fossil-trail simulation in the 1960s, the output of the program was a path drawn by an x-y plotter, a mechanical contraption that today is in itself something of a fossil. In other respects, however, the model takes a thoroughly modern, algorithmic approach to understanding animal behavior. Following earlier work by Rudolf Richter, they assumed the worm obeys three basic impulses. Phobotaxis forbids the worm to cross its own trail (or any other trail, for that matter). Thigmotaxis, in contrast, urges the worm to stay close to an existing trail. Finally strophotaxis is a proclivity for making U-turns from time to time. Raup and Seilacher added a fourth action: Go straight if none of the other rules apply.

Figure 2. Three basic patterns of behaviorClick to Enlarge Image

In the program, the worm examines the territory immediately ahead and to each side, looking for evidence of previous passages, then acts accordingly. If it senses a trail, it turns either toward it or away from it, depending on the balance of phobotactic and thigmotactic forces; if the way ahead is clear, the worm can either go straight or make a U-turn. Program parameters determine the propensity to choose each of these alternatives, as well as other variables such as the length of a straight run or the minimum turning radius. By tuning the parameters, Raup and Seilacher were able to reproduce some features of fossil tracks with impressive fidelity. The plotter's pen traced out spirals and meanders as well as curves that begin as a spiral and later switch to meandering (a transition frequently observed in real fossils).

But perhaps the program's ability to match the fossil patterns is not so surprising, since it was designed explicitly for that purpose. Present-day tastes favor a less direct approach. The rules of phobotaxis and thigmotaxis—which together cause the worm to adhere to its own path without crossing it—seem natural enough, but strophotaxis—the penchant for making U-turns—is something one would like to see emerge from simpler rules rather than being a built-in axiom.

Consider a worm burrowing parallel to a straight segment of trail. What happens when the segment abruptly ends? A spiral-drawing program handles this situation gracefully: The worm just continues applying the thigmotactic rule, turning around the end of the segment. The zigzag algorithm is not so simple. One idea is to interpret the end of the guide segment as a signal to make a hairpin turn in the opposite direction. This works well in the mathematically uniform world of computer simulations but might be unreliable for real worms on an irregular seafloor. Another strategy is to let the worm generate the pattern without reference to external cues, alternating left and right U-turns and connecting them by straight segments of equal length. But such an algorithm seems to require more cognitive capacity than we want to attribute to a Paleozoic worm. The trail-maker must remember when to turn left and right and must measure the straight segments.

Seilacher proposed an ingenious alternative: The worm's body length might serve as a natural unit of measure. The worm would start a new U-turn whenever it sensed its tail uncoiling from the last one, and this same signal would also indicate the direction to turn. It's a clever notion and seems like just the kind of thing that natural selection would come up with. But natural selection has come up with something else as well. Certain fossil trails have a recursive, multiscale structure: Large meanders are composed of smaller meanders of similar shape. It's hard to see how Seilacher's mechanism could account for these paths.








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