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

Published online by Cambridge University Press:  20 January 2017

Daniel G Gavin*
Affiliation:
Department of Plant Biology, University of Illinois, Urbana, IL 61801, USA
W.Wyatt Oswald
Affiliation:
College of Forest Resources, University of Washington, Seattle, WA 98195, USA
Eugene R Wahl
Affiliation:
Environmental and Societal Impacts Group, National Center for Atmospheric Research, Boulder, CO 80301, USA
John W Williams
Affiliation:
National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, Santa Barbara, CA 93101, USA
*
*Corresponding author.E-mail address: dgavin@life.uiuc.edu (D.G. Gavin).

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 more dissimilar biomes were compared. The probability of an analog vs no-analog result (a likelihood ratio) increased sharply when SCD decreased below the optimal threshold, indicating a nonlinear relationship between SCD and the probability of analog. Probabilities of analog computed for a postglacial pollen record at Tannersville Bog (Pennsylvania, USA) identified transitions between biomes and periods of no analog.

Type
Research Article
Copyright
University of Washington

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