D.G. Frey and E.S. Deevey Review 1: Numerical tools in palaeolimnology – Progress, potentialities, and problems
 H.J.B. Birks,
 H.J.B Birks
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Abstract
In the last decade, palaeolimnology has shifted emphasis from being a predominantly qualitative, descriptive subject to being a quantitative, analytical science with the potential to address critical hypotheses concerning the impacts of environmental changes on limnic systems. This change has occurred because of (1) major developments in applied statistics, some of which have only become possible because of the extraordinary developments in computer technology, (2) increased concern about problem definition, research hypotheses, and project design, (3) the building up of high quality modern calibration datasets, and (4) the narrowing of temporal resolution in palaeolimnological studies from centuries to decades or even single years or individual seasons.
The most significant development in quantitative palaeolimnology has been the creation of many modern calibration datasets of biotic assemblages and associated environmental data. Such calibration sets, when analysed by appropriate numerical procedures, have the potential to transform fossil biostratigraphical data into quantitative estimates of the past environment. The relevant numerical techniques are now well developed, widely tested, and perform remarkably well. The properties of these techniques are becoming better known as a result of simulation studies. The advantages and disadvantages of the preferred technique (weighted averaging partial least squares) are reviewed and the problems in model selection are discussed. The need for evaluation and validation of reconstructions is emphasised. Several statistical surprises have emerged from calibration studies. Outstanding problems remain the need for a detailed and consistent taxonomy in the calibration sets, the quality, representativeness, and inherent variability of the environmental variables of interest, and the inherent bias in the calibration models. Besides biological environmental calibration sets, there is the potential to develop modern sedimentenvironment calibration sets to link sedimentary properties to catchment parameters. The adoption of a ‘dynamic calibration set’ approach may help to minimise the inherent bias in current calibration models. Modern regression techniques are available to explore the vast amount of unique ecological information about taxonenvironment relationships in calibration datasets.
Hypothesis testing in palaeolimnology can be attempted directly by careful project design to take account of ‘natural experiments’ or indirectly by means of statistical testing, often involving computer intensive permutation tests to evaluate specific null hypotheses. The validity of such tests depends on the type of permutation used in relation to the particular dataset being analysed, the sampling design, and the research questions being asked. Stratigraphical data require specific permutation tests. Several problems remain unsolved in devising permutation designs for fineresolution stratigraphical data and for combined spatial and temporal data. Constrained linear or nonlinear reduced rank regression techniques (e.g. redundancy analysis, canonical correspondence analysis and their partial counterparts) provide powerful tools for testing hypotheses in palaeolimnology. Work is needed, however, to extend their use to investigate and test for lag responses between biological assemblages and their environment.
Having developed modern calibration datasets, many palaeolimnologists are returning to the sedimentary record and are studying stratigraphical changes. In contrast to much palynological data, palaeolimnological data are often fineresolution and as a result are often noisy, large, and diverse. Recent developments for detecting and summarising patterns in such data are reviewed, including statistical evaluation of zones, summarisation by detrended correspondence analysis, and nonparametric regression (e.g. LOESS). Techniques of timeseries analysis that are free of many of the assumptions of conventional timeseries analysis due to the development of permutation tests to assess statistical significance are of considerable potential in analysing fineresolution palaeolimnological data. Such data also contain a wealth of palaeopopulation information. Robust statistical techniques are needed to help identify nonlinear deterministic dynamics (chaos) from noise or random effects in fineresolution palaeolimnological data.
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 Title
 D.G. Frey and E.S. Deevey Review 1: Numerical tools in palaeolimnology – Progress, potentialities, and problems
 Journal

Journal of Paleolimnology
Volume 20, Issue 4 , pp 307332
 Cover Date
 19981201
 DOI
 10.1023/A:1008038808690
 Print ISSN
 09212728
 Online ISSN
 15730417
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 calibration
 hypothesis testing
 permutation tests
 stratigraphical data analysis
 timeseries analysis
 weighted average partial least squares
 Industry Sectors
 Authors

 H.J.B. Birks ^{(1)}
 H.J.B Birks ^{(2)}
 Author Affiliations

 1. Botanical Institute, University of Bergen, Allégaten 41, N5007, Bergen, Norway Email
 2. Environmental Change Research Centre, University College London, 26 Bedford Way, London, WC1H 0AP, UK