Statolith Size Polydispersity as Natural Experiment — Larger Statoliths Carry More Fisher Information Per Unit Mass

Plants can sense gravity — that's how roots grow down and shoots grow up. They do this using tiny, dense starch granules called statoliths that settle under gravity inside specialized cells, a bit like a built-in snow globe that always shows which way is 'down.' What's puzzling is that these granules come in a range of sizes, even within the same plant. Why the variation? Is it noise in the system, or does it serve a purpose? This hypothesis borrows a powerful idea from statistics called the Cramér-Rao bound — essentially a mathematical law that sets a fundamental limit on how precisely any sensor can estimate a signal, no matter how clever you are. The hypothesis proposes that when you apply this framework to statoliths, you get a striking prediction: the information a statolith carries about gravitational direction scales with the *sixth power* of its radius. That's an enormous advantage for larger granules — double the radius and you get 64 times more useful signal. This would mean that size variation in statoliths isn't just biological messiness; it could be a tunable feature, with the population of granule sizes acting like an array of sensors with very different sensitivities. The real cleverness here is treating a cell full of differently-sized granules as a 'heterogeneous sensor array' — a concept from engineering applied to biology. If the math holds, it would give researchers a precise, testable framework for why statoliths are the size they are, and whether plants with bigger statoliths are genuinely better at detecting subtle tilts.

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