| Abstract: | We test the success of Principal Components, Factor and Regression Analysis at recovering environmental signals using numerical experiments in which we control species environmental responses, the environmental conditions and the sampling scheme used for calibration. We use two general conditions, one in which sampling of a continental margin for benthic foraminiferal assemblages is done in a standard grid and the driving environmental variables are correlated to one another, and the other where sampling is done so that the environmental variables are uncorrelated. The first condition mimics many studies in the literature. We find that where the controlling environmental variables are correlated, Principal Components/Factor Analysis yield factors that reflect the common variance (correlation) of those variables. Since this common variance is largely a product of the sampling scheme, the factors extracted do not reliably present true species ecologic behavior. This behavior cannot be accurately diagnosed and faulty interpretations may lead to substantial error when using factor coefficients to reconstruct conditions in the past. When the sampling scheme is constructed so that the controlling environmental variables for the calibration data set are uncorrelated the factor patterns will reflect these variables more accurately. Species responses can be more successfully interpreted from the Principal Components/Factor Analysis structure matrices. Additionally, regression analysis can successfully extract the independent environmental signals from the biotic data set. However, matrix closure is a confounding effect in all our numerical results as it distorts species' abundances and spatial distribution in the calibration data set. Our results show clearly that a knowledge of the controlling environmental variables, and the correlations among these variables over a study area, is essential for the successful application of multivariate techniques for paleoenvironmental reconstruction. |
