The fitness value of information

Communication and information are central concepts in evolutionary biology. In fact, it is hard to find an area of biology where these concepts are not used. However, quantifying the information transferred in biological interactions has been difficult. How much information is transferred when the first spring rainfall hits a dormant seed, or when a chick begs for food from its parent? One measure that is commonly used in such cases is fitness value: by how much, on average, an individual's fitness would increase if it behaved optimally with the new information, compared to its average Fitness without the information. Another measure, often used to describe neural responses to sensory stimuli, is the mutual information - a measure of reduction in uncertainty, as introduced by Shannon in communication theory. However, mutual information has generally not been considered to be an appropriate measure for describing developmental or behavioral responses at the organismal level, because it is blind to function; it does not distinguish between relevant and irrelevant information. In this paper we show that there is in fact a Surprisingly tight connection between these two measures in the important context of evolution in an uncertain environment. In this case, a useful Measure of fitness benefit is the increase in the long-term growth rate, or the fold increase in number of surviving lineages. We show that in many cases the fitness value of a developmental cue, when measured this way, is exactly equal to the reduction in uncertainty about the environment, as described by the mutual information.