Nonlinear averaging

A nonlinear average is simply an average taken of a nonlinear function of some variable
quantity. The value of such an average is generally different from the value of the
nonlinear function at the average of the variable quantity. *Jensen’s inequality *is the result
of nonlinear averaging a function that curves in a consistent direction, i.e. is concave up
or concave down. For concave up functions, *Jensen’s inequality *says that the average of
the function is greater than the function of the average, while for concave down functions,
the opposite result is true.

*References*

Chesson, P. 1996. Matters of scale in the dynamics of populations and communities. Pp 353-368
In *Frontiers of Population Ecology* (eds. R.B. Floyd, A.W. Sheppard, and P. J. de Barro)
CSIRO.

Chesson, P. 1998. Making sense of spatial models in ecology. Pp 151-166 in J. Bascompte and R. Sole (eds) “Modelling Spatiotemporal Dynamics in Ecology,” Academic Press.

Chesson, P. 2001. Metapopulations. Pp 161-176 in Encyclopedia of Biodiversity, Vol 4, Simon A. Levin, ed, Academic Press.