Using selection functions to describe changes in environmental variables

The selection function (which shows how the frequency of sampling units with the value X = x at one point in time must change in order to produce the distribution that occurs at a later point in time) is proposed for describing the changes over time in an environmentally important variable X. It is shown that the theory of selection functions as used in the study of natural selection and resource selection by animals requires some modifications in this new application and that a selection function is a useful tool in long-term monitoring studies because all changes in a distribution can be examined (rather than just changes in single parameters such as the mean), and because graphical presentations of the selection function are easy for non-statisticians to understand. Estimation of the selection function is discussed using a method appropriate for normal distributions and bootstrapping is suggested as a method for assessing the precision of estimates and for testing for significant differences between samples taken at different times. Methods are illustrated using data on water chemical variables from a study of the effects of acid precipitation in Norway.