A statistical approach for evaluating distance metrics and analog assignments for pollen records

D. G. Gavin, W. W. Oswald, E. R. Wahl, and J. W. Williams

2003 Quaternary Science Reviews in press

Abstract —  The modern analog technique typically uses a distance metric to determine the dissimilarity between fossil and modern biological assemblages.  Despite this quantitative approach, interpretation of distance metrics is usually qualitative and rules for selection of analogs tend to be ad hoc.  We present a statistical tool, the receiver-operating characteristic (ROC) curve, which provides a framework for identifying analogs from distance metrics.  If modern assemblages are placed into groups (e.g., biomes), this method can 1) evaluate the ability of different distance metrics to distinguish among groups, 2) objectively identify thresholds of the distance metric for determining analogs, and 3) compute a likelihood ratio and a Bayesian probability that a modern group is an analog for an unknown (fossil) assemblage.   Applied to a set of 1689 modern pollen assemblages from eastern North America classified into eight biomes, ROC analysis confirmed that the squared-chord distance (SCD) outperforms most other distance metrics.  The optimal threshold increased when comparing more dissimilar biomes.  The probability of an analog vs. no analog result (a likelihood ratio) increased sharply with decreasing SCD below the optimal threshold, indicating a nonlinear relationship between the SCD and the probability of analog.  Probabilities of analog computed for a post-glacial pollen record at Tannersville Bog (Pennsylvania USA) identified transitions between biomes and periods of no-analog.