Weighted Averaging of Species Indicator Values: Its Efficiency in Environmental Calibration

A common bioassay problem in applied ecology is to estimate values of an cnvironmental variable from species incidence or abundance data. An example is the problem of reconstructing past changes in acidity (pH) in lakes from diatom assemblages found in successive strata of the bottom sediment. The method of weighted averaging is based on indicator values, the indicator value of a species being, intuitively, the value of the environmental variable most preferred by that species. Indicator values of all species present in a site are averaged to give an estimate of the value of the environmental variable at the site. The average is weighted by species abundances, if known, with absent species having zero weight. Using field data, several authors have compiled lists of indicator values of species for various environmental variables for use in weighted averaging, e.g. pH indicator values of diatom species. In this paper the properties of the method of weighted averaging are studied, starting from the idea that indicator values are parameters of response curves that describe the expected abundance of each species in relation to the environmental variable. In practice the response curves must be estimated by regression methods. but here they are assumed to be known in advance. Conditions are derived under which the weighted average is a consistent and efficient estimator for the value of an environmental variable at a site. Because weighted averaging is central to the ordination technique known as reciprocal averaging or correspondence analysis, the conditions also define models that are implicitly invoked when reciprocal averaging is used in ecological ordination studies,