Jensen's inequality predicts effects of environmental variation.

The fallacy of the average: on the ubiquity, utility and continuing novelty of Jensen's inequality.

Biologists often cope with variation in physiological, environmental and ecological processes by measuring how living systems perform under average conditions. However, performance at average conditions is seldom equal to average performance across a range of conditions. This basic property of nonlinear averaging - known as 'Jensen's inequality' or 'the fallacy of the average' - has important i...

A Univariate Extension of Jensen's Inequality

The result in this paper exp lains some of the qualitative nature of Jensen's inequality. It is shown that the more disperse the distribution of a random variable is, the smaller is the expectation of any concave function of it. This result can be used to show the inadequacy of some current methods of reporting environmental data by using geometric means, and it extends the resu lt of I. Billic...

Jensen's inequality in the calculus of variations

Effects of temporal variation in temperature and density dependence on insect population dynamics

Understanding the effects of environmental variation on insect populations is important in light of predictions about increasing climatic variability. This paper uses the univoltine western corn rootworm (WCR, Diabrotica virgifera virgifera LeConte) as a case study and employs deterministic and stochastic modeling to evaluate how insect population dynamics is shaped by densitydependent survival...

Grüss Type Discrete Inequalities in Inner Product Spaces, Revisited

Some sharp inequalities of Grüss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.