D.G. Frey and E.S. Deevey Review 1: Numerical tools in palaeolimnology – Progress, potentialities, and problems

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 data-sets, 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 data-sets 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 sediment-environment 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 taxon-environment relationships in calibration data-sets. 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 data-set 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 fine-resolution stratigraphical data and for combined spatial and temporal data. Constrained linear or non-linear 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 data-sets, many palaeolimnologists are returning to the sedimentary record and are studying stratigraphical changes. In contrast to much palynological data, palaeolimnological data are often fine-resolution 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 non-parametric regression (e.g. LOESS). Techniques of time-series analysis that are free of many of the assumptions of conventional time-series analysis due to the development of permutation tests to assess statistical significance are of considerable potential in analysing fine-resolution palaeolimnological data. Such data also contain a wealth of palaeopopulation information. Robust statistical techniques are needed to help identify non-linear deterministic dynamics (chaos) from noise or random effects in fine-resolution palaeolimnological data.