Ayres Abstracts
| Ruel, J. J., and M.P. Ayres. 1999. Jensen's inequality predicts direct effects of environmental variation. Trends in Ecology and Evolution 14:361-366. Full text in pdf. |
| Environmental variance can exert important effects on patterns and processes in nature that are independent of average conditions. Appropriately, there are an increasing number of ecological studies that explicitly explore environmental variance. Jensen's Inequality is a mathematical proof that is seldom mentioned in the ecological literature but which provides a powerful tool for predicting the direct effects of environmental variance on biological systems. For example, consideration of the inequality suggests that 1) variance in irradiance tends to depress net photosynthesis, 2) variance in temperature tends to elevate metabolic rates in poikilotherms, and 3) variance in dietary nitrogen tends to depress the growth and survival of herbivores while variance in secondary metabolite concentrations tends to elevate the performance of herbivores. These qualitative predictions can be derived from the form of the relevant response functions (accelerating vs. decelerating). Knowledge of the frequency distribution (especially the variance) of the driving variables allows quantitative estimates of effects due to Jensen's Inequality. Jensen's Inequality has relevance in any field of biology that includes non-linear processes. |
| Jensen's Inequality; nonlinear functions; variance; photosynthesis; temperature; respiration; herbivory; plant defense; secondary metabolites; nutrition |