NATURAL VARIABILITY AND THE ESTIMATION OF EMPIRICAL RELATIONSHIPS - AREASSESSMENT OF REGRESSION METHODS

Ecologists often rely on empirically defined statistical relationships to infer how variables might be related. However, the usual method of estimating such relationships (ordinary least-squares (OLS)) is gener ally inappropriate because of the substantial natural variability of m ost ecological variables. Natural error variability in the regressor v ariable can artificially create a significant empirical trend where no underlying or structural relationship exists, or fail to reveal a tru e structural relationship. In multivariate relationships, natural vari ability in one variable can induce statistical significance in colline ar variables even if they bear no structural relationship. We propose a simple new method, based on instrumental variables, to detect and qu antify natural error variability in the regressor variables and to est imate the parameters of the structural relationship. We apply this met hod to two examples: (1) we show that the structural relationship betw een adenosine triphosphate concentration (total planktonic biomass) an d chlorophyll concentration (autotrophic biomass) does not vary latitu dinally in the Southern Ocean despite a significant increase in the OL S slope relating the two at more southerly stations and (2) we demonst rate that the significance of nitrogen in nutrient-chlorophyll relatio nships in lakes probably reflects natural variability in phosphorus co ncentration, and not the fertilizing effect of nitrogen.