Many biologists now recognize that environmental variance can exert important effects on patterns and processes in nature that are independent of average conditions. Jensen's inequality is a mathematical proof that is seldom mentioned in the ecological literature but which provides a powerful tool for predicting some direct effects of environmental variance in biological systems. Qualitative predictions can be derived from the form of the relevant response functions (accelerating versus decelerating). Knowledge of the frequency distribution (especially the variance) of the driving variables allows quantitative estimates of the effects. Jensen's inequality has relevance in every field of biology that includes nonlinear processes.