Weighted Averaging, Logistic Regression and the Gaussian Response Model

• Published in: Vegetatio Vol. 65; no. 1; pp. 3 - 11
• Main Authors: Braak, Cajo J. F. ter, Looman, Caspar W. N.
• Format: Journal Article
• Language: English
• Published: Dordrecht DR W. Junk Publishers 1986; Kluwer
• Subjects: Animal and plant ecology; Animal, plant and microbial ecology; Biological and medical sciences; Confidence interval; Datasets; Estimation bias; Fundamental and applied biological sciences. Psychology; General aspects; Logistic regression; Species; Standard deviation; Standard error; Statistical discrepancies; Truncation; Wageningen University; Weighted averages; Environmental factor; Gauss method; Gradient method; Ecosystem; Statistical model; Vegetation
• ISSN: 0042-3106; 1573-5052
• DOI: 10.1007/bf00032121

The indicator value and ecological amplitude of a species with respect to a quantitative environmental variable can be estimated from data on species occurrence and environment. A simple weighted averaging (WA) method for estimating these parameters is compared by simulation with the more elaborate method of Gaussian logistic regression (GLR), a form of the generalized linear model which fits a Gaussian-like species response curve to presence-absence data. The indicator value and the ecological amplitude are expressed by two parameters of this curve, termed the optimum and the tolerance, respectively. When a species is rare and has a narrow ecological amplitude -- or when the distribution of quadrats along the environmental variable is reasonably even over the species' range, and the number of quadrats is small -- then WA is shown to approach GLR in efficiency. Otherwise WA may give misleading results. GLR is therefore preferred as a practical method for summarizing species' distributions along environmental gradients. Formulas are given to calculate species optima and tolerances (with their standard errors), and a confidence interval for the optimum from the GLR output of standard statistical packages.