. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.

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The relationship of total basal area to soil and topographic factors was studied in 47 undisturbed, mature, compositionally stable (climax) stands. Forward stepwise multiple linear regression was used to develop two predictive models. Effective soil depth, percentage stone, aspect, and slope position were predictor variables in model I. Soil profile available water capacity, slope position, and aspect were predictor variables in model II. Model I is the more practical and easily applied model in stands where soil depth can be rapidly determined; model II requires additional soil measurements but can be used to assess the more direct biological relationship between soil water and basal area.Models I and II accounted for 91 and 93% of the variation in stand basal area, respectively, and were validated with data from seven additional mature stands. Subsequently the models were used to predict potential (maximum) basal area in eight stands where it had been reduced by disturbance; the models also were used to evaluate the effect of farming on the productivity of fields abandoned in the 1930s. Presettlement basal area was estimated to have been between 18 and 26 m 2 /ha but soil loss due to erosion has reduced the potential basal area to 8-21 m 2 /ha should hardwood stands redevelop.For comparison with a standard site evaluation technique, 27 undisturbed Quercus alba stands were used to develop another multiple linear regression model to predict site index from site factors. Soil profile available water holding capacity, slope position, and aspect were predictor variables in model III, which accounted for 73% of the variation in site index, a substantial reduction in predictive value from model II, which predicts potential stand basal area using the same three variables. Simple regression indicated a strong positive linear relationship between stand basal area and site index (r = 0.85, P < .01).The strong relationship of stand basal area to soil and topographic factors and to standard site index measurements indicates that models to predict potential basal area may be used to evaluate site productivity in the Illinois Shawnee Hills.