Abstract
How a maximum principle for evolutionary processes based solely upon mean fitness of behaviors may be misrepresentative and misleading in the analysis of biological systems was shown. Many of the misrepresentations can be corrected by including variance of fitness associated with environmental uncertainty and variability in the structure of the maximum principle. There are many ways of incorporating this variance into a mathematical model. The modified maximum principle was depicted as a discounted function of expected fitness, where the discount is a function of the variance in fitness between behaviors. Such a function under no uncertainty reverts to the simpler mean maxim. Including uncertainty generally results in evolutionary strategies consisting of sets of diverse behaviors whose resulting fitnesses show negative covariance. Under certainty organisms can specialize, showing only single types of behavior. Supporting evidence was gathered from different areas of ecology and evolutionary biology. The model may be consistent with the consequences of uncertainty in sexual processes, herbivory and pollination systems.