Quantitative paleo-estimation: hypothetical experiments with extrapolationand the no-analog problem

We experiment with artificial data to test the response of five numerical t echniques in extrapolating paleo-environments for no-analog conditions. No- analog conditions are those beyond the technique calibration (modern) data set and will be encountered in applications to the geologic past, though th ey may not be easy to recognize. In the ideal, a numerical technique will c orrectly extrapolate to no-analog conditions. Failing this, the technique w ill have a consistent, predictable error response to increasing no-analog c onditions, as these are measured by a reliable index. The no-analog conditi ons that we used are a natural extension of the calibration conditions we c reated. Thus we test techniques for their response to shifting environmenta l conditions rather than for factors unrelated to the ecology of the taxa ( e.g. post-depositional fossil preservation). Five numerical techniques we t est with our hypothetical data are (1) multivariate regression of species p ercents, (2) correlation-based principal components with linear regression, (3) covariance-based principal components with linear regression, (4) corr elation-based principal components with non-linear regression, and (5) the Imbrie and Kipp technique. All the techniques show increasing estimation er ror as conditions depart from those of the calibration data set. There are two main causes of error in our estimates: (1) the distorting effects of ma trix closure on taxon abundances; and (2) generation of ratio no-analogs am ong species abundances because of non-linear responses to conditions depart ing progressively from the calibration range. With all the techniques, the distribution of error for no-analog conditions is complex. Non-linear regre ssion with factors shows the least predictable error response. We found tha t currently developed no-analog indicators do not have a good correlation t o estimation error. This means that better indicators, more closely linked to the accuracy of estimates, need to be developed. (C) 1999 Elsevier Scien ce B.V. All rights reserved.