Shannon information and biological fitness

When studying information, biologists and behavioral scientists often eschew Shannon entropy. Instead, they commonly use a decision-theoretic measure of the value of information, on the grounds that Shannon's measure draws no distinction between useful and useless information. Here we show that these two measures are intimately related in the context of biological evolution. We present a simple model of evolution in an uncertain environment, and calculate the increase in Darwinian fitness that is made possible by information about the environmental state. This fitness increase - the fitness value of information - is a composite of both the Shannon entropy and the decision-theoretic measure of information value. Furthermore, the Shannon entropy of the environment, which seemingly fails to take anything about Darwinian fitness into account, nonetheless imposes an upper bound on the fitness value of information.