A general expression for the reproductive value of information

Information transfer and utilization is ubiquitous in nature. Animals can increase their reproductive value by changing their behavior in light of new information. Previous work has shown that the reproductive value of information can never be negative given an animal behaves optimally. Statistical decision theory uses Bayes’ theorem as a mathematical tool to model how animals process information gained from their environment. We use this technique with an optimality model to establish a new expression for the value of information when behavior is chosen from a continuous range of possibilities. Our expression highlights that the value of information is proportional to the rate of change of behavior with information. We illustrate our approach using the cooperative behavior between a male and a female raising their common young. We show that the value of knowing about one’s partner can be quantified and establish the value of information to a member of the pair when the continuous trait is how long to spend caring for their young. However, the applications of this expression are wider reaching than parental care decisions and can be used to analyze the behavior of individuals across a variety of species and contexts.