Bacteria navigating a chemical gradient don't steer smoothly toward higher concentrations. They run in straight lines, then tumble — abruptly randomizing their orientation — before running again. If the new direction happens to point up the gradient, they run longer before the next tumble. If it points down, they tumble sooner. This biased random walk achieves net motion up the gradient without ever computing which direction is “up.” The strategy seems crude compared to the smooth turns that larger organisms use. A bacterium with a rudder could steer directly toward the food.
Betancourt, Leighton, Emonet, Machta, and Abbott (arXiv 2602.23324, February 2026) show that the tumble is not crude — it is optimal under the constraint that matters.
The constraint is information. A bacterium swimming in a chemical gradient receives sensory data from its surface receptors, but the data rate is limited by molecular noise, receptor number, and integration time. The organism knows something about the local concentration and its rate of change, but it doesn't know which direction leads uphill. It can sense “better” or “worse” over time, but not “left” or “right” at an instant. The question is: given this information bottleneck, what movement strategy maximizes net displacement up the gradient?
The answer depends on how much directional information is available. When the organism has no directional information — it knows whether things are improving but not which way to turn — smooth steering is useless. Turning gradually in an unknown direction is no better than going straight. The optimal strategy is abrupt reorientation: run straight, and when conditions worsen, randomize your heading completely. This is the tumble. It maximizes the information extracted from each run by converting a temporal signal (conditions improving or worsening) into spatial displacement without requiring spatial information the organism doesn't have.
When modest directional information becomes available — enough to distinguish forward from backward but not enough for precise angular steering — the optimal strategy transitions from tumbles to reversals. The organism runs forward, and when conditions worsen, it reverses direction rather than randomizing. This preserves the information contained in the current heading while exploiting the knowledge that “backward” is at least different from “forward.”
With more directional information, specific turning angles become optimal — not arbitrary values but discrete angles determined by the information rate. The transitions between strategies — tumbles to reversals to discrete turns to smooth steering — occur at specific information thresholds. Each behavioral mode is optimal in its regime. The progression from crude to refined navigation is not a matter of evolutionary sophistication but of sensory capacity.
The framework explains why different organisms use different navigation strategies without invoking different levels of neural complexity. Bacteria tumble because their sensory bandwidth supports tumbles. Larger organisms with richer sensory systems steer smoothly because their information rate supports steering. The strategy matches the sensor, not the anatomy. A bacterium that tried to steer would perform worse than one that tumbles, because steering requires directional information the bacterium doesn't have. The tumble is not a primitive strategy that evolution hasn't improved — it is the best strategy available at that information budget.