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Journal of Paleolimnology

, Volume 20, Issue 4, pp 307–332 | Cite as

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
Article

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.

calibration hypothesis testing permutation tests stratigraphical data analysis time-series analysis weighted average partial least squares 

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References

  1. Altman, D. G. & J. M. Bland, 1983. Measurement in medicine: the analysis of method comparison studies. The Statistician 32: 307–317.Google Scholar
  2. Altman, N.S., 1992. An introduction to kernel and nearest-neighbour nonparametric regression. Amer. Statistician 46: 175–185.Google Scholar
  3. Anderson, M. J. & N. A. Gribble, 1998. Partitioning the variation among spatial, temporal and environmental components in a multivariate data set. Austr. J. Ecol. 23: 158–167.Google Scholar
  4. Anderson, N. J., 1998. Variability of diatom inferred-phosphorus profiles in a small lake basin and its implications for histories of lake eutrophication. J. Paleolim. 20: 47–55.Google Scholar
  5. Anderson, N. J. & T. Korsman, 1990. Land-use change and lake acidification: Iron Age de-settlement in northern Sweden as a pre-industrial analogue. Phil. Trans. r. Soc., Lond. B 327: 373–376.Google Scholar
  6. Anderson, N. J., T. Korsman & I. Renberg, 1994. Spatial heterogeneity of diatom stratigraphy in varved and non-varved sediments of a small, boreal-forest lake. Aquatic Sciences 56: 40–58.Google Scholar
  7. Anderson, N. J., B. V. Odgaard, U. Segerströom & I. Renberg, 1996. Climate-lake interactions recorded in varved sediments from a Swedish boreal forest lake. Global Change Biology 2: 399–405.Google Scholar
  8. Anderson, N. J., I. Renberg & U. Segerströom, 1995. Diatom production responses to the development of early agriculture in a boreal forest lake-catchment (Kassjöon, northern Sweden). J. Ecol. 83: 809–822.Google Scholar
  9. Anderson, R. Y., 1992. Possible connection between surface winds, solar activity and the Earth' magnetic field. Nature 358: 51–53.Google Scholar
  10. Andersson, C., 1997. Transfer function vs. modern analog technique for estimating Pliocene sea-surface temperatures based on planktic foraminiferal data, western equatorial Pacific Ocean. J. Foram. Res. 27: 123–132.Google Scholar
  11. Andersson, G., P. Kaufmann & L. Renberg, 1996. Non-linear modelling with a coupled neural network-PLS regression system. J. Chemometrics 10: 605–614.Google Scholar
  12. Ascioti, F. A., E. Beltrami, T. O. Carroll & C. Wirick, 1993. Is there chaos in plankton dynamics? J. Plankton Res. 15: 603–617.Google Scholar
  13. Ball, I. R., 1975. Nature and formulation of biogeographic hypotheses. Syst. Zool. 24: 407–430.Google Scholar
  14. Barnett, V., 1994. Statistics and the long-term experiments: past achievements and future challenges. In R. A. Leigh & A. E. Johnston (eds.), Long-term Experiments in Agricultural and Ecological Sciences. CAB International, Wallingford: 165–183.Google Scholar
  15. Bartlein, P. J. & C. Whitlock, 1993. Paleoclimatic interpretation of the Elk Lake pollen record. In J. P. Bradbury & W. E. Dean (eds.), Elk Lake, Minnesota: Evidence for Rapid Climate Change in the North-Central United States. Geological Society of America Special Paper 276: 275–293.Google Scholar
  16. Battarbee, R. W., 1990. The causes of lake acidification, with special reference to the role of acidification. Phil. Trans. r. Soc., Lond. B 327: 339–347.Google Scholar
  17. Beebe, K. R. & B. R. Kowalski, 1987. An introduction to multivariate calibration and analysis. Anal. Chem. 59: 1007–1016.Google Scholar
  18. Beerling, D. J., H. H. Birks & F. I. Woodward, 1995. Rapid late-glacial atmospheric CO2 changes reconstructed from the stomatal density record of fossil leaves. J. Quat. Sci. 10: 379–384.Google Scholar
  19. Bennett, K. D., 1996. Determination of the number of zones in a biostratigraphical sequence. New Phytol. 132: 155–170.Google Scholar
  20. Bennion, H., S. Juggins & N. J. Anderson, 1996. Predicting epilimnetic phosphorus concentrations using an improved diatom-based transfer function and its application to lake eutrophication management. Envir. Sci. & Technol. 30: 2004–2007.Google Scholar
  21. Bennion, H., S. Wunsam & R. Schmidt, 1995. The validation of diatom-phosphorus transfer functions: an example from Mondsee, Austria. Freshwat. Biol. 34: 271–283.Google Scholar
  22. Bio, A. M. F., R. Alkemade & R. Barendregt, 1998. Determining alternative models for vegetation response analysis: a nonparametric approach. J. Veg. Sci. 9: 5–16.Google Scholar
  23. Birks, H. H., 1997. A reconstruction of the aquatic ecosystem development in Kråkenes Lake, Norway, during the late-glacial and early Holocene. Wüurzburger Geographische Manuskripte 41: 31–32.Google Scholar
  24. Birks, H. H. and 23 others, 1996. The Kråakenes late-glacial palaeoenvironmental project. J. Paleolim. 15: 281–286.Google Scholar
  25. Birks, H. J. B., 1985. Recent and possible future mathematical developments in quantitative palaeoecology. Palaeogeogr., Palaeoclim., Palaeoecol. 50: 107–147.Google Scholar
  26. Birks, H. J. B., 1990. Some reflections on the application of numerical methods in Quaternary palaeoecology. Publications of Karelian Institute, University of Joensuu, 102: 7–20.Google Scholar
  27. Birks, H. J. B., 1993a. Quaternary palaeoecology and vegetation science-current contributions and possible future developments. Rev. Palaeobot. Palynol. 79: 153–177.Google Scholar
  28. Birks, H. J. B., 1993b. Is the hypothesis of survival on glacial nunataks necessary to explain the present-day distributions of Norwegian mountain plants? Phytocoenologia 23: 399–426.Google Scholar
  29. Birks, H. J. B., 1994. The importance of pollen and diatom taxonomic precision in quantitative palaeoenvironmental reconstructions. Rev. Palaeobot. Palynol. 83: 107–117.Google Scholar
  30. Birks, H. J. B., 1995. Quantitative palaeoenvironmental reconstructions. In D. Maddy & J. S. Brew (eds.) Statistical Modelling of Quaternary Science Data. Technical Guide 5, Quaternary Research Association, Cambridge: 161–254.Google Scholar
  31. Birks, H. J. B., 1997. Reconstructing environmental impacts of fire from the Holocene sedimentary record. In J. S. Clark, H. Cachier, J. G. Goldammer & B. Stocks (eds.) Sediment Records of Biomass Burning and Global Change. Springer-Verlag, Berlin: 295–309.Google Scholar
  32. Birks, H. J. B., F. Berge, J. F. Boyle & B. F. Cumming, 1990c. A palaeoecological test of the land-use hypothesis for recent lake acidification in south-west Norway using hill-top lakes. J. Paleolim. 4: 69–85.Google Scholar
  33. Birks, H. J. B. & A. D. Gordon, 1985. Numerical methods in Quaternary pollen analysis. Academic Press, London, 317 pp.Google Scholar
  34. Birks, H. J. B., S. Juggins & J. M. Line, 1990b. Lake surface-water chemistry reconstructions from palaeolimnological data. In B. J. Mason (ed.), The Surface Waters Acidification Programme. Cambridge University Press, Cambridge: 301–313.Google Scholar
  35. Birks, H. J. B., J. M. Line, S. Juggins, A. C. Stevenson & C. J. F ter Braak, 1990a. Diatoms and pH reconstruction. Phil. Trans. r. Soc., Lond. B 327: 263–278.Google Scholar
  36. Birks, H. J. B. & A. F. Lotter, 1994. The impact of the Laacher See Volcano (11000 yr B.P.) on terrestrial vegetation and diatoms. J. Paleolim. 11: 313–322.Google Scholar
  37. Boddy, L., C. W. Morris, M. F. Wilkins, G. A. Tarran & P. H. Burkhill, 1994. Neural network analysis of flow cytometric data for 40 marine phytoplankton species. Cytometry 15: 283–293.Google Scholar
  38. Borcard, D., P. Legendre & P. Drapeau, 1992. Partialling out the spatial component of ecological variation. Ecology 73: 1045–1055.Google Scholar
  39. Borggaard, C. & H. T. Thodberg, 1992. Optimal minimal neural-interpretation of spectra. Analytical Chemistry 64: 545–551.Google Scholar
  40. Bowman, A. W. & A. Azzalini, 1997. Applied smoothing techniques for data analysis. Clarendon Press, Oxford, 193 pp.Google Scholar
  41. Breiman, L. & J. H. Friedman, 1997. Predicting multivariate responses in multiple linear regression (with discussion). J. r. Stat. Soc. B 59: 3–54.Google Scholar
  42. Brooks, S. J. & H. J. B. Birks, 1999. Chironomid-inferred late-glacial and early-Holocene mean July air temperatures for Kråakenes lake, western Norway. J. Paleolim. (in press).Google Scholar
  43. Brown, P. J., 1982, Multivariate calibration. J. r. Stat. Soc. B 44: 287–321.Google Scholar
  44. Brown, P. J., 1993. Measurement, regression, and calibration. Clarendon Press, Oxford, 201 pp.Google Scholar
  45. Buck, C. E., W. G. Cavanagh & C. D. Litton, 1996. Bayesian approach to interpreting archaeological data. J. Wiley & Sons, Chichester. 382 pp.Google Scholar
  46. Cameron, N. G., H. J. B. Birks, V. J. Jones, F. Berge, J. Catalan, R.J. Flower, J. Garcia, B. Kawecka, K. A. Koinig, A. Marchetto, P. Sáanchez-Castillo, R. Schmidt, M. ŚSiśsko, N. Solovieva, E. Stefkováa & M. Toro, 1999. Surface-sediment and epilithic diatom pH calibration sets for remote European mountain lakes (AL:PE project) and their comparison with the Surface Waters Acidification Programme (SWAP) calibration set. J. Paleolim. (in press).Google Scholar
  47. Chamberlain, T. C., 1965. The method of multiple working hypotheses. Science 148: 754–759.Google Scholar
  48. Cheng, B. & D. M. Titterington, 1994. Neural networks: a review from a statistical perspective. Statistical Science 9: 2–54.Google Scholar
  49. Chiu, S., 1989. Detecting periodic components in a white Gaussian time series. J. r. Stat. Soc. B 51: 249–259.Google Scholar
  50. Clark, J. S., J. Merkt & H. Müuller, 1989. Post-glacial fire, vegetation, and human history on the northern Alpine Forelands, southwestern Germany. J. Ecol. 77: 897–925.Google Scholar
  51. Cleveland, W. S., 1979. Robust locally weighted regression and smoothing scatterplots. J. am. Stat. Assoc. 74: 829–836.Google Scholar
  52. Cleveland, W. S., 1993. Visualizing data. Hobart Press, Summit, 360 pp.Google Scholar
  53. Cleveland, W. S., 1994. The elements of graphing data (Revised edition). Hobart Press, Summit, 297 pp.Google Scholar
  54. Cleveland, W. S. & S. J. Devlin, 1988. Locally weighted regression: an approach to regression analysis by local fitting. J. am. Stat. Assoc. 83: 596–610.Google Scholar
  55. Connor, E. F., 1986. Time series analysis of the fossil record. In D. M. Raup & D. Jablonski (eds.), Patterns and Processes in the History of Life. Springer-Verlag, Berlin: 119–147.Google Scholar
  56. Crawley, M. J., 1993. GLIM for Ecologists. Blackwell Scientific Publications, Oxford, 379 pp.Google Scholar
  57. Cumming, B. F., J. P Smol & H. J. B. Birks, 1992. Scaled chrysophytes (Chrysophyceae and Synurophyceae) from Adirondack drainage lakes and their relationship to environmental variables. J. Phycol. 28: 162–178Google Scholar
  58. Dean, W. E., 1997. Rates, timing, and cyclicity of Holocene eolian activity in north-central United States: Evidence from varved lake sediments. Geology 25: 331–334.Google Scholar
  59. Deevey, E. S., 1969. Coaxing history to conduct experiments. BioScience 19: 40–43.Google Scholar
  60. Deevey, E. S., 1984. Stress, strain, and stability of lacustrine ecosystems. In E. Y. Haworth & J. W. G. Lund (eds.) Lake sediments and environmental history. Leicester University Press, Leicester: 203–229.Google Scholar
  61. de Jong, S., 1991. Chemometrical applications in an industrial food research laboratory. Mikrochimica Acta 2. 93–101.Google Scholar
  62. de Jong, S., 1993. PLS fits closer than PCR. J. Chemometrics 7: 551–557.Google Scholar
  63. Denham, M. C., 1997. Prediction intervals in partial least squares. J. Chemometrics 11: 39–52.Google Scholar
  64. Dennis, B., 1996. Discussion: Should ecologists become Bayesians? Ecol. Applic. 6: 1095–1103.Google Scholar
  65. Diggle, P. J., 1990. Time Series-A biostatistical introduction. Clarendon Press, Oxford, 257 pp.Google Scholar
  66. Duff, K. E., B. A. Zeeb & J. P. Smol, 1997. Chrysophyte cyst biogeographical and ecological distributions: a synthesis. J. Biogeogr. 24: 791-812.Google Scholar
  67. Dutilleul, P., 1995. Rhythms and autocorrelation analysis. Biological Rhythm Research 26: 173–193.Google Scholar
  68. Dutilleul, P. & B. Pinel-Alloul, 1996. A doubly multivariate model for statistical analysis of spatio-temporal environmental data. Environmetrics 7: 551–565.Google Scholar
  69. Efron, B., 1979. Computers and the theory of statistics: thinking the unthinkable. Society for Industrial and Applied Mathematics 21: 460–480.Google Scholar
  70. Efron, B. & R. Tibshirani, 1991. Statistical data analysis in the computer age. Science 253: 390–395.Google Scholar
  71. Ellison, A. M., 1996. An introduction to Bayesian inference for ecological research and environmental decision-making. Ecol. Applic. 6: 1036–1046.Google Scholar
  72. Eriksson, L., J. L. M. Hermens, E. Johansson, H. J. M. Verhaar & S. Wold, 1995. Multivariate analysis of toxicity data with PLS. Aquatic Sci. 57: 217–241.Google Scholar
  73. Flower, R. J., S. Juggins & R. W. Battarbee, 1997. Matching diatom assemblages in lake sediment cores and modern surface sediment samples: the implications for lake conservation and restoration with special reference to acidified systems. Hydrobiologia 344: 27–40.Google Scholar
  74. Frank, I. E. & J. H. Friedman, 1993. A statistical view of some chemometrics regression tools (with discussion). Technometrics 35: 109–148.Google Scholar
  75. Fritz, S. C., 1990. Twentieth-century salinity and water-level fluctuations in Devils Lake, North Dakota: Test of a diatombased transfer function. Limnol. Oceanogr. 35: 1771–1781.Google Scholar
  76. Fritz, S. C., D. R. Engstrom & B. J. Haskell, 1994. ‘Little Ice Age’ aridity in the North American Great Plains: a high-resolution reconstruction of salinity fluctuations from Devils Lake, North Dakota, USA. The Holocene 4: 69–73.Google Scholar
  77. Garthwaite, P. H., 1994. An interpretation of partial least squares. J. am. Stat. Assoc. 89: 122–127.Google Scholar
  78. Gasse, F., S. Juggins & L. Ben Khelifa, 1995. Diatom-based transfer functions for inferring past hydrochemical characteristics of African lakes. Palaeogeogr., Palaeoclim., Palaeoecol. 117: 31–54.Google Scholar
  79. Gauch, H. G., 1982. Noise reduction by eigenvector ordinations. Ecology 63: 1643–1649.Google Scholar
  80. Geladi, P., 1988. Notes on the history and nature of partial least squares (PLS) modelling. J. Chemometrics 2: 231–246.Google Scholar
  81. Geladi, P. & E. Dåaback, 1995. An overview of chemometrics applications in near infrared spectroscopy. J. Near Infrared Spectroscopy 3: 119–132.Google Scholar
  82. Geladi, P. & B. R. Kowalski, 1986. Partial least-squares regression. A tutorial. Analytica Chimica Acta 185: 1–17.Google Scholar
  83. Good, P., 1994. Permutation tests. A practical guide to resampling methods for testing hypotheses. Springer-Verlag, Berlin, 226 pp.Google Scholar
  84. Goodall, C., 1990. A survey of smoothing techniques. In J. Fox & J. S. Long (eds.), Modern methods of data analysis. Sage Publications, Newbury Park: 126–177.Google Scholar
  85. Gotelli, N. J. & G. R. Graves, 1996. Null models in ecology. Smithsonian Institution Press, Washington, 368 pp.Google Scholar
  86. Green, D. G., 1981. Time series and postglacial forest ecology. Quat. Res. 15: 265–277.Google Scholar
  87. Grimm, E. C., 1987. CONISS: a FORTRAN 77 program for stratigraphically constrained cluster analysis by the method of incremental sum of squares. Comp. Geosci. 13: 13–35.Google Scholar
  88. Grimm, E. C. & G. L. Jacobson, 1992. Fossil-pollen evidence for abrupt climate changes during the past 18000 yrs in eastern North America. Clim. Dyn. 6: 179–184.Google Scholar
  89. Hall, R. I. & J. P. Smol, 1993. The influence of catchment size on lake trophic status during the hemlock decline and recovery (4800 to 3500 BP) in southern Ontario lakes. Hydrobiologia 269/270: 371–390.Google Scholar
  90. Hardy, D. R., R. S. Bradley & B. Zolitschka, 1996. The climate signal in varved sediments from Lake C2, northern Ellesmere Island, Canada. J. Paleolim. 16: 227–238.Google Scholar
  91. Hastie, T. & R. Tibshirani, 1990. Generalized additive models. Chapman & Hall, London, 335 pp.Google Scholar
  92. Heegaard, E., 1997. Ecology of Andreaea in western Norway. J. Bryol. 19: 527–636.Google Scholar
  93. Heikkinen, J. & H. Höogmander, 1994. Fully Bayesian approach to image restoration with an application in biogeography. Appl. Stat. 43: 569–582.Google Scholar
  94. Hill, M. O. & H. G. Gauch, 1980. Detrended correspondence analysis: an improved ordination technique. Vegetatio 42: 47–58.Google Scholar
  95. Hoerl, A. E. & R. W. Kennard, 1970. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 8: 27–51.Google Scholar
  96. Hofmann, W., 1998. Cladocerans and chironomids as indicators of lake level changes in north temperate lakes. J. Paleolim. 19: 55–62.Google Scholar
  97. Huffer, F. W. & H. Wu, 1998. Markov Chain Monte Carlo for autologistic regression models for application to the distribution of plant species. Biometrics 54: 509–524.Google Scholar
  98. Häardle, W., 1990. Applied nonparametric regression. Cambridge University Press, Cambridge, 333 pp.Google Scholar
  99. Häardle, W. & M. G. Schimek (Eds.), 1996. Statistical theory and computational aspects of smoothing. Physica-Verlag, Heidelberg, 265 pp.Google Scholar
  100. Jackson, D. A., 1993. Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches. Ecology 74: 2204–2214.Google Scholar
  101. Jacobson, G. L. & E. C. Grimm, 1986. A numerical analysis of Holocene forest and prairie vegetation in central Minnesota. Ecology 67: 958–966.Google Scholar
  102. Jacoby, W. G., 1997. Statistical graphics for univariate and bivariate data. Sage Publications, Thousand Oaks, 97 pp.Google Scholar
  103. Jassby, A. D. & T. M. Powell, 1990. Detecting changes in ecological time series. Ecology 71: 2044–2052.Google Scholar
  104. Jenkinson, D. S., J. M. Potts, J. N. Perry, V. Barnett, K. Coleman & A. E. Johnston, 1994. Trends in herbage yields over the last century on the Rothamsted Long-term Continuous Hay Experiment. J. Agric. Sci. 122: 365–374.Google Scholar
  105. Jolliffe, I. T., 1986. Principal component analysis. Springer-Verlag, New York, 271 pp.Google Scholar
  106. Jones, V. J. & S. Juggins, 1995. The construction of a diatom-base chlorophyll a transfer function and its application at three lakes on Signy Island (maritime Antarctic) subject to differing degrees of nutrient enrichment. Freshwat. Biol. 34: 433–445.Google Scholar
  107. Juggins, S., 1992. Diatoms in the Thames Estuary, England: Ecology, Palaeoecology, and Salinity Transfer Function. Bibliotheca Diatomologica 25: 216 pp.Google Scholar
  108. Juggins, S., R. W. Battarbee & S. C. Fritz, 1994. Diatom/salinity transfer functions and climate change: an assessment of methods and application to two Holocene sequences from the northern Great Plains, North America. In B. M. Funnell & R. L. F. Kay (eds.) Palaeoclimate of the Last Glacial/Interglacial Cycle, Special Publication 94/2, N.E.R.C. Earth Science Directorate, Swindon: 37–41.Google Scholar
  109. Kass, R. E., B. P. Carlin, A. Gelman & R. M Neal, 1998. Markov Chain Monte Carlo in practice: A roundtable discussion. Am. Statistician 52: 93–100.Google Scholar
  110. Kodama, K. P., J. C. Lyons, P. A. Siver & A-M. Lott, 1997. A mineral magnetic and scaled-chrysophyte paleolimnological study of two northeastern Pennsylvania lakes: records of fly ash deposition, land-use change, and paleorainfall variation. J. Paleolim. 17: 173–189.Google Scholar
  111. Korsman, T. & H. J. B. Birks, 1996. Diatom-based water chemistry reconstructions from northern Sweden: a comparison of reconstruction techniques. J. Paleolim. 15: 65–77.Google Scholar
  112. Korsman, T., M. Nilsson, J. öOhman & I. Renberg, 1992. Near-infrared reflectance spectroscopy of sediments: a potential method to infer the past pH of lakes. Envir. Sci. Technol. 26: 2122–2126.Google Scholar
  113. Korsman, T., I. Renberg & N. J. Anderson, 1994. A palaeolimnological test of the influence of Norway spruce (Picea abies) immigration on lake-water acidity. The Holocene 4: 132–140.Google Scholar
  114. Korsman, T. & U. Segerströom, 1998. Forest fire and lake-water acidity in a northern Swedish boreal area: Holocene changes in lake-water quality at Makkassjöon. J. Ecol. 86: 113–124.Google Scholar
  115. Kowalski, B.R. & C.F. Bender, 1972. The K-Nearest Neighbor classification rule (pattern recognition) applied to nuclear magnetic resonance spectral interpretation. Anal. Chem. 44: 1405–1411.Google Scholar
  116. Laird, K. R., S. C. Fritz, E. C. Grimm & P. G. Mueller, 1996a. Century-scale paleoclimatic reconstruction from Moon Lake, a closed-basin lake in the northern Great Plains. Limnol. Oceanogr. 41: 890–902.Google Scholar
  117. Laird, K. R., S. C. Fritz, K. A. Maasch & B. F. Cumming, 1996b. Greater drought intensity and frequency before AD 1200 in the Northern Great Plains, USA. Nature 384: 552–554.Google Scholar
  118. Laird, K. R., S. C. Fritz, B. F. Cumming & E. C. Grimm, 1998. Early-Holocene limnological and climatic variability in the Northern Great Plains. The Holocene 8: 275–285.Google Scholar
  119. Le, J. & N. J. Shackleton, 1994. Estimation of palaeoenvironment by transfer functions: simulation with hypothetical data. Mar. Micropaleontol. 24: 187–199.Google Scholar
  120. Leeman, A. & F. Niessen, 1994. Varve formation and the climatic record in an Alpine proglacial lake: calibrating annuallylaminated sediments against hydrological and meteorological data. The Holocene 4: 1–8.Google Scholar
  121. Legendre, P., N. L. Oden, R. R. Sokal, A. Vaudor & J. Kim, 1990. Approximate analysis of variance of spatially autocorrelated regional data. J. Classif. 7: 53–75.Google Scholar
  122. Lek, S., A. Belaud, P. Baran, I. Dimopoulos & M. Delacoste, 1996a. Role of some environmental variables in trout abundance models using neural networks. Aquatic Living Resources 9: 23–29.Google Scholar
  123. Lek, S., M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga & S. Aulagnier, 1996b. Application of neural networks to modelling nonlinear relationships in ecology. Ecol. Modelling 90: 39–52.Google Scholar
  124. Lek, S., I. Dimopoulos & A. Fabre, 1996. Predicting phosphorus concentration and phosphorus load from watershed characteristics using back propagation neutral networks. Acta Oecologia 17: 43–53.Google Scholar
  125. Line, J. M. & H. J. B. Birks, 1990. WACALIB version 2.1-a computer program to reconstruct environmental variables from fossil assemblages by weighted averaging. J. Paleolim. 3: 170–173.Google Scholar
  126. Line, J. M., C. J. F. ter Braak & H. J. B. Birks, 1994. WACALIB version 3.3-a computer program to reconstruct environmental variables from fossil assemblages by weighted averaging and to derive sample-specific errors of prediction. J. Paleolim. 10: 147–152.Google Scholar
  127. Liu, Q., 1997. Variation partitioning by partial redundancy analysis (RDA). Environmetrics 8: 75–85.Google Scholar
  128. Liu, Q. & S. Bråakenhielm, 1995. A statistical approach to decompose ecological variation. Wat., Air Soil Pollut. 85: 1587–1592.Google Scholar
  129. Livingstone, D. M. & A. F. Lotter, 1998. The relationship between air and water temperatures in lakes of the Swiss Plateau: a case study with palaeolimnological implications. J. Paleolim. 19: 181–198.Google Scholar
  130. Lorber, A., L. E. Wangen & B. R. Kowalski, 1987. A theoretical foundation for the PLS algorithm. J. Chemometrics 1: 19–31.Google Scholar
  131. Lotter, A. F., 1998. The recent eutrophication of Baldeggersee (Switzerland) as assessed by fossil diatom assemblages. The Holocene 8: 395–405.Google Scholar
  132. Lotter, A. F., B. Ammann & M. Sturm, 1992. Rates of change and chronological problems during the late-glacial period. Clim. Dyn. 6: 233–239.Google Scholar
  133. Lotter, A. F. & H. J. B. Birks, 1993. The impact of the Laacher See Tephra on terrestrial and aquatic ecosystems in the Black Forest, southern Germany. J. Quat. Sci. 8: 263–276.Google Scholar
  134. Lotter, A. F. & H. J. B. Birks, 1997. The separation of the influence of nutrients and climate on the varve time-series of Baldeggersee, Switzerland. Aquatic Sciences 59: 362–375.Google Scholar
  135. Lotter, A. F., H. J. B. Birks, W. Hofmann & A. Marchetto, 1997. Modern diatom, cladocera, chironomid, and chrysophyte cyst assemblages as quantitative indicators for the reconstruction of past environmental conditions in the Alps. I. Climate. J. Paleolimn. 18: 395–420.Google Scholar
  136. Lotter, A. F., H. J. B. Birks, W. Hofmann & A. Marchetto, 1998a. Modern diatom, cladocera, chironomid, and chrysophyte cyst assemblages as quantitative indicators for the reconstruction of past environmental conditions in the Alps. II. Nutrients. J. Paleolim. 18: 443–463.Google Scholar
  137. Lotter, A. F., H. J. B. Birks & B. Zolitschka, 1995. Late-glacial pollen and diatom changes in response to two different environmental perturbations: volcanic eruption and Younger Dryas cooling. J. Paleolim. 14: 23–47.Google Scholar
  138. Lotter, A. F., I. R. Walker & S. J. Brooks, 1998b. An intercontinental comparison of chironomid palaeotemperature inference models: Europe vs. North America. Quat. Sci. Rev. (in press).Google Scholar
  139. Maberly, S. C., C. S. Reynolds, D. G. George, E. Y. Haworth & J. W. G. Lund, 1994. The sensitivity of freshwater planktonic communities to environmental change: monitoring, mechanisms and models. In R. A. Leigh & A. E. Johnston (eds.), Long-term Experiments in Agricultural and Ecological Sciences. CAB International, Wallingford: 387–405.Google Scholar
  140. Malmgren, G. & U. Nordlund, 1996. Application of artificial neural networks to chemostratigraphy. Paleoceanography 11: 505–512.Google Scholar
  141. Malmgren, G. & U. Nordlund, 1997. Application of artificial neural networks to paleoceanographic data. Palaeogeogr. Palaeoclim. Palaeoecol. 136: 359–373.Google Scholar
  142. Manly, B. F. J., 1997. Randomisation, bootstrap and Monte Carlo methods in biology (2nd edition), Chapman & Hall, London. 399 pp.Google Scholar
  143. Marchetto, A. & R. Bettinetti, 1995. Reconstruction of the phosphorus history of two deep, subalpine Italian lakes from sedimentary diatoms, compared with long-term chemical measurements. Mem. Ist. ital. Idrobiol. 53: 27–38.Google Scholar
  144. Marron, J. S., 1996. A personal view of smoothing and statistics. In W. Häardle & M. G. Schimek (eds.), Statistical theory and computational aspects of smoothing. Physica-Verlag, Heidelberg: 1–9.Google Scholar
  145. Martens, H. & T. Næs, 1989. Multivariate calibration. J. Wiley & Sons, Chichester, 419 pp.Google Scholar
  146. McCullagh, P. & J. A. Nelder, 1989. Generalized linear models (2nd edition). Chapman & Hall, London, 511 pp.Google Scholar
  147. McQuoid, M. R. & L. A. Hobson, 1997. A 91-year record of seasonal and interannual variability of diatoms from laminated sediments in Saanich Inlet, British Columbia. J. Plankton Res. 19: 173–194.Google Scholar
  148. Minchin, P. R., 1987. Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio 71: 145–156.Google Scholar
  149. Moore, D. A., 1997. Bayes for Beginners? Some reasons to hesitate. Amer. Statistician 51: 254–261.Google Scholar
  150. Nilsson, M. B., E. Dåabakk, T. Korsman & I. Renberg, 1996. Quantifying relationships between near-infrared reflectance spectra of lake sediments and water chemistry. Envir. Sci. Technol. 30: 2586–2590.Google Scholar
  151. Noon, P. E., 1997a. Recent environmental change at Signy Island, maritime Antarctica: quantitative lake-sediment studies as a basis for reconstructing catchment ice-cover. Doctoral Thesis, University of London, 460 pp.Google Scholar
  152. Noon, P. E., 1997b. A sediment-based transfer function to reconstruct recent climatic change in Antarctica. Wüurzburger Geographische Manuskripte 41: 149–150.Google Scholar
  153. Nüurnberg, G. K., 1995. Quantifying anoxia in lakes. Limnol. Oceanogr. 40: 1100–1111.Google Scholar
  154. Oehlert, G. W., 1988. Interval estimates for diatom-inferred lake pH histories. Can. J. Statistics 16: 51–60.Google Scholar
  155. Ohlendorf, C., F. Niessen & H. Weissert, 1997. Glacial varve thickness and 127 years of instrumental climate data: a comparison. Climatic Change 36: 391–411.Google Scholar
  156. Oksanen, J., E. Läaaräa, P. Huttunen & J. Meriläainen, 1988. Estimation of pH optima and tolerances of diatoms in lake sediments by the methods of weighted averaging, least squares and maximum likelihood, and their use for the prediction of lake acidity. J. Paleolim. 1: 39–49.Google Scholar
  157. Oksanen, J., E. Läaäaräa, P. Huttunen & J. Meriläainen, 1990. Maximum likelihood prediction of lake acidity based on sedimented diatoms. J. Veg. Sci. 1: 49–56.Google Scholar
  158. Oksanen, J. & P. R. Minchin, 1997. Instability of ordination results under changes in input data order: explanations and remedies. J. Veg. Sci. 8: 447–454.Google Scholar
  159. Palmer, M. W. & P. M. Dixon, 1990. Small-scale environmental heterogeneity and the analysis of species distributions along gradients. J. Veg. Sci. 1: 57–65.Google Scholar
  160. Paruelo, J. M. & F. Tomasel, 1997. Prediction of functional characteristics of ecosystems: a comparison of artificial neural networks and regression models. Ecological Modelling 98: 173–186.Google Scholar
  161. Pflaumann, U., J. Duprat, C. Pujol & L. D. Labeyrie, 1996. SIMMAX: A modern analog technique to deduce Atlantic sea surface temperatures from planktonic foraminifera in deep-sea sediments. Paleoceanography 11: 15–35.Google Scholar
  162. Phatak, A. & S. de Jong, S. 1997. The geometry of partial least squares. J. Chemometrics 11: 311–338.Google Scholar
  163. Pinel-Allou, B., N. Bourbonnais & P. Dutilleul, 1996. Among-lake and within-lake variations of autotrophic pico-and nanoplankton biomass in six Quebec lakes. Can. J. Fish. aquat. Sci. 53: 2433–2445.Google Scholar
  164. Poff, N. L., S. Tokar & P. Johnson, 1996. Stream hydrological and ecological responses to climate change assessed with an artificial neural network. Limnol. Oceanogr. 41: 857–858.Google Scholar
  165. Prager, M. H. & J. M. Hoenig, 1989. Superposed epoch analysis: a randomization test of environmental effects on recruitment with application to chub mackerel. Trans. am. Fish. Soc. 118: 608–618.Google Scholar
  166. Prager, M. H. & J. M. Hoenig, 1992. Can we determine the significance of key-event effects on a recruitment time series?-A power study of superposed epoch analysis. Trans. am. Fish. Soc. 121: 123–131.Google Scholar
  167. Pueyo, S., 1997. The study of chaotic dynamics by means of very short time series. Physica D 106: 57–65.Google Scholar
  168. Quinlan, R., J. P. Smol & R. I. Hall, 1998. Quantitative inferences of past hypolimnetic anoxia in south-central Ontario lakes using fossil midges (Diptera: Chironomidae). Can. J. Fish. aquat. Sci. 55: 587–596.Google Scholar
  169. Renberg, I. & R. W. Battarbee, 1990. The SWAP palaeolimnology programme: a synthesis. In B. J. Mason (ed.), The Surface Waters Acidification Programme. Cambridge University Press, Cambridge: 281–300.Google Scholar
  170. Renberg, I. & H. Hultberg, 1992. A paleolimnological assessment of acidification and liming effects on diatom assemblages in a Swedish lake. Can. J. Fish. aquat. Sci. 49: 65–72.Google Scholar
  171. Renberg, I., T. Korsman & H.J.B. Birks, 1993. Prehistoric increases in the pH of acid-sensitive Swedish lakes caused by land-use changes. Nature 362: 824–826.Google Scholar
  172. Renberg, I., U. Segerströom & J.-E. Wallin, 1984. Climatic reflection in varved lake sediments. In N.-A. Möorner & W. Karláen (eds.) Climatic Changes on a Yearly to Millennial Basis. Reidel, Dordrecht: 249–256.Google Scholar
  173. Robertson, I., D. Lucy, L. Baxter, A. M. Pollard, R. G. Aykroyd, A. C. Barker, A. H. C. Carter, V. R. Switsur & J. S. Waterhouse, 1999. A kernel-based Bayesian approach to climatic reconstruction. The Holocene (in press).Google Scholar
  174. Schulz, M. & K. Stattegger, 1997a. SPECTRUM: A PC-program for spectral analysis of unevenly spaced time series. INQUA Sub-Commission on Data-Handling Methods Newsletter 16: 3–4.Google Scholar
  175. Schulz, M. & K. Stattegger, 1997a. SPECTRUM: spectral analysis of unevenly spaced paleoclimatic time series. Comp. Geosci. 23: 929–945.Google Scholar
  176. Simola, H., I. Hanski & M. Liukkonen, 1990. Stratigraphy, species richness and seasonal dynamics of plankton diatoms during 418 years in Lake Lovajäarvi, south Finland. Ann. bot. fenn. 27: 241–259.Google Scholar
  177. Simonoff, J. S., 1996. Smoothing methods in statistics. Springer-Verlag, New York, 338 pp.Google Scholar
  178. Smilauer, P. & H. J. B. Birks, 1995. The use of generalised additive models in the description of diatom-environment response surfaces. Geological Survey of Denmark Service Report 7: 42–47.Google Scholar
  179. Stager, J. C., B. Cumming & L. Meeker, 1997. A high-resolution 11,400-Yr diatom record from Lake Victoria, East Africa. Quat. Res. 47: 81–89.Google Scholar
  180. Stern, H. S., 1996. Neural networks in applied statistics. Technometrics 38: 205–220.Google Scholar
  181. Stone, L. & S. Ezrati, 1996. Chaos, cycles and spatiotemporal dynamics in plant ecology. J. Ecol. 84: 279–291.Google Scholar
  182. Stone, M. & R. J. Brooks, 1990. Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression. J. r. Stat. Soc. B 52: 237–269.Google Scholar
  183. Sugihara, G., B. Greenfell & R. M. May, 1990. Distinguishing error from chaos in ecological time series. Phil. Trans. r. Soc., Lond. B 330: 235–251.Google Scholar
  184. Sugihara, G. & R. M. May, 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344: 734–741.Google Scholar
  185. Sundberg, R., 1985. When is the inverse regression estimator MSE superior to the standard regression estimator in multivariate controlled situations? Statistics and Probability Letters 3: 75–79.Google Scholar
  186. ter Braak, C. J. F., 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179.Google Scholar
  187. ter Braak, C. J. F., 1987. Unimodal models to relate species to environment. Doctoral thesis, University of Wageningen, 152 pp.Google Scholar
  188. ter Braak, C. J. F., 1990. Update notes: CANOCO version 3.10. Agricultural Mathematics Group, Wageningen, 35 pp.Google Scholar
  189. ter Braak, C. J. F., 1992. Permutation versus bootstrap significance tests in multiple regression and ANOVA. In K.-H. Jöockel, G. Rothe & W. Sendler (eds.) Bootstrapping and related techniques. Springer-Verlag, Berlin: 79–86.Google Scholar
  190. ter Braak, C. J. F., 1995. Non-linear methods for multivariate statistical calibration and their use in palaeoecology: a comparison of inverse (k-nearest neighbours, partial least squares and weighted averaging partial least squares) and classical approaches. Chemometrics and Intelligent Laboratory Systems 28: 165–180.Google Scholar
  191. ter Braak, C. J. F. & H. van Dam, 1989. Inferring pH from diatoms: a comparison of old and new calibration methods. Hydrobiologia 178: 209–223.Google Scholar
  192. ter Braak, C. J. F., H. van Dobben & G. di Bella, 1996. On inferring past environmental change from species composition data by nonlinear reduced rank models. XVIII International Biometric Conference July 1–5 1996, Amsterdam, Invited Papers: 65–70.Google Scholar
  193. ter Braak, C. J. F. & S. Juggins 1993. Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages. Hydrobiologia 269/270: 485–502.Google Scholar
  194. ter Braak, C. J. F., S. Juggins, H. J. B. Birks & H. van der Voet, 1993. Weighted averaging partial least squares regression (WAPLS): Definition and comparison with other methods for species-environment calibration. In G. P. Patil & C. R. Rao (eds.) Multivariate Environmental Statistics. Elsevier Science Publishers, Amsterdam: 525–560.Google Scholar
  195. ter Braak, C. J. F. & C. W. N. Looman, 1994. Biplots in reducedrank regression. Biometrics J. 36: 983–1003.Google Scholar
  196. ter Braak, C. J. F. & I. C. Prentice, 1988. A theory of gradient analysis. Adv. ecol. Res. 18: 271–317.Google Scholar
  197. ter Braak, C. J. F. & J. Wiertz, 1994. On the statistical analysis of vegetation change: a wetland affected by water extraction and soil acidification. J. Veg. Sci. 5: 361–372.Google Scholar
  198. Theiler, J., S. Eubank, A. Longtin, B. Galdrikian & J. D. Farmer, 1992. Testing for nonlinearity in time series: the method of surrogate data. Physica D 58: 77–84.Google Scholar
  199. Tilman, D., M. E. Dodd, J. Silvertown, P. R. Poulton, A. E. Johnston & M. J. Crawley, 1994. The Park Grass Experiment: Insights from the most long-term ecological study. In R. A. Leigh & A. E. Johnston (eds.), Long-term Experiments in Agricultural and Ecological Sciences. CAB International, Wallingford: 287–303.Google Scholar
  200. Turney, C. S. M., D. J. Beerling, D. D. Harkness, J. J. Lowe & E. M. Scott, 1997. Stable carbon isotope variations in northwest Europe during the last glacial-interglacial transition. J. Quat. Sci. 12: 329–334.Google Scholar
  201. van der Merwe, A. & J. V. Zidek, 1980. Multivariate regression analysis and canonical variates. Can. J. Statistics 8: 27–39.Google Scholar
  202. Verdonschot, P. F. M. & C. J. F. ter Braak, 1994. An experimental manipulation of oligochaete communities in mesocosms treated with chlorpyrifos or nutrient additions: multivariate analyses with Monte Carlo permutation tests. Hydrobiologia 278: 251–266.Google Scholar
  203. ver Hoef, J. M., 1996. Parametric empirical Bayes methods for ecological applications. Ecol. Applic. 6: 1047–1055.Google Scholar
  204. Vinebrooke, R. D., R. I. Hall, P. R. Leavitt & B. F. Cumming, 1998. Fossil pigments as indicators of phototrophic response to salinity and climate change in lakes of western Canada. Can. J. Fish. aquat. Sci. 55: 668–681.Google Scholar
  205. Vos, H., A. Sanchez, B. Zolitschka, A. Brauer & J. F. W. Negendank, 1997. Solar activity variations recorded in varved sediments from the crater lake of Holzmaar-a maar lake in the Westeifel volcanic field, Germany. Surveys in Geophysics 18: 163–182.Google Scholar
  206. Walker, D., 1990. Purpose and method in Quaternary palynology. Rev. Palaeobot. Palynol. 64: 13–27.Google Scholar
  207. Walker, I. R., A. J. Levesque, L. Cwynar & A. F. Lotter, 1997. An expanded surface-water palaeotemperature inference model for use with fossil midges from eastern Canada. J. Paleolim. 18: 165–178.Google Scholar
  208. Whitlock, C. & P. J. Bartlein, 1997. Vegetation and climate change in northwest America during the past 125 ka yr. Nature 388: 57–61.Google Scholar
  209. Wilson, S. E., B. F. Cumming & J. P. Smol, 1996. Assessing the reliability of salinity inference models from diatom assemblages: an examination of a 219-lake data set from western North America. Can. J. Fish. aquat. Sci. 53: 1580–1594.Google Scholar
  210. Xanthakis, J., I. Liritzis & C. Poulakos, 1995. Solar-climatic cycles in the 4,190-year Lake Saki mud layer thickness record. In C. W. Winkl, Jr. (ed.) Holocene Cycles-Climate, Sea Levels, and Sedimentation. Journal of Coastal Research Special Issue 17: 79–86.Google Scholar
  211. Yee, T. W. & N. D. Mitchell, 1991. Generalized additive models in plant ecology. J. Veg. Sci. 2: 587–602.Google Scholar
  212. Young, R., 1997. Time-series analysis and time-basis reconstruction in palaeoecology. Analyses of palaeoecological data from annually laminated sediments of Lake Go&015B;ci&0105;z, Poland. Doctoral thesis, University of Amsterdam, 158 pp.Google Scholar
  213. Young, S. G. & A. W. Bowman, 1995. Non-parametric analysis of covariance. Biometrics 51: 920–931.Google Scholar
  214. Zeeb, B. A., C. E. Christie, J. P. Smol, D. L. Findlay, H. J. Kling & H. J. B. Birks, 1994. Responses of diatom and chrysophyte assemblages in Lake 227 sediments to experimental manipulation. Can. J. Fish. aquat. Sci. 51: 2300–2311.Google Scholar
  215. Zolitschka, B., 1992. Climatic change evidence and lacustrine varves from maar lakes, Germany. Clim. Dyn. 6: 229–232.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • H.J.B. Birks
    • 1
  • H.J.B Birks
    • 2
  1. 1.Botanical Institute, University of BergenBergenNorway E-mail
  2. 2.Environmental Change Research CentreUniversity College LondonLondonUK

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