Hierarchical Value of Information in Microbial Predator-Prey Interactions

Information is fundamental to biological survival, but the amount of information and its biological value are not equivalent. Shannon information quantifies uncertainty reduction, whereas Volkenstein's value of information measures how information changes the probability of a biologically relevant outcome. Although originally developed for molecular biology contexts, the latter concept has rarely been applied to environmental sensing and ecological interactions. Here we develop a value-of-information framework for microbial predator-prey interactions based on hydrodynamic sensing, in which prey detect fluid disturbances generated by approaching predators. Using a mechanistic model that incorporates sensory thresholds, memory, false alarms, biological benefits and costs, and predator encounter probability, we characterize mutual information from three hierarchical measures of biological value: encounter-conditional value, ecological value, and lifetime fitness value. The framework reveals how small amounts of sensory information can produce disproportionately large survival benefits during predator encounters, generating encounter-level value amplification in which biological value exceeds Shannon information. However, although global sensitivity analysis shows that such amplification is common, it is not universal and becomes progressively diluted at broader ecological and lifetime scales by encounter rarity, background noise, and sensory costs. Across most parameter combinations, the encounter-conditional value exceeded the ecological value, which in turn exceeded the lifetime fitness value. These results demonstrate that environmental sensing should be evaluated not only by how accurately it represents the external world, but by how strongly it changes biologically relevant outcomes. More broadly, the framework extends Volkenstein's concept of information value to ecological interactions and provides a quantitative framework for predicting when environmental information enhances survival and fitness, thereby providing a platform for explaining the evolution, maintenance, diversification, and loss of sensory systems.