Optimizing reproduction in a randomly varying environment when a correlation may exist between the conditions at the time a choice has to be made and the subsequent outcome.

Abstract A model is constructed of organisms which optimize their reproduction in a randomly varying environment, and can also receive some information about their environment. The model is of organisms which complete their reproduction and life cycle within a discrete time interval and produce seeds in yields which are random variables depending on environmental conditions. Maximal long-term growth rate of the organism is achieved when for each environmental event or signal, which may be correlated with eventual yield, there is an optimal fraction of seeds which germinate. These optimal responses depend on the probabilities of yields, on the conditional probabilities between the external signals and the yields, which are a measure of the degree of correlation between the external signals and the yields, and on the viability of seeds which do not germinate. It has been shown in this model that optimized long-term growth rate is increased by increased correlation between external signals and yields, which is equivalent to the amount of relevant information about the environment which is processed by the organism. The quantity of external information to be processed may be minimized without decreasing growth by lumping together those external signals for which the optimized responses are identical.