Phase transitions induced by resource limitations in biological information processing

While the information processing of organisms is optimized through evolution, it exhibits significant variability among different species. One potential source of this diversity is the limitation of resources available for information processing. However, we lack a theoretical framework for investigating biological information processing under resource limitations. To address this issue, we propose a novel optimal estimation theory that accounts for the resource limitations inherent in biological systems. This theory explicitly formulates the memory that organisms can store and operate and optimizes it using optimal control theory. This approach reveals optimal estimation strategies under various resource limitations, such as memory capacity, intrinsic noise, and energy cost. We apply this theory to a minimal model of biological information processing and investigate the dependence of optimal estimation strategies on resource limitations. As a result, we find that resource limitations induce discontinuous and non-monotonic phase transitions between memory-less and memory-based estimation strategies. This result suggests that resource limitations may contribute to the rich diversity observed in biological information processing.