Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies

Organisms adapt to volatile environments by integrating sensory information with internal memory, yet their information processing is constrained by resource limitations. Such limitations can fundamentally alter optimal estimation strategies in biological systems. For example, recent experiments suggest that organisms exhibit phase transitions between memoryless and memory-based estimation strategies depending on energy availability and sensory reliability. However, a theoretical understanding of how resource limitations induce these transitions is still missing. This Letter presents an analytical characterization of the resource-induced phase transitions in optimal estimation strategies. Our results identify the conditions under which resource limitations alter estimation strategies and analytically reveal the mechanism underlying the emergence of discontinuous, nonmonotonic, and scaling behaviors. These results provide a theoretical foundation for understanding how limited resources shape information processing in biological systems.