# A Bayesian palaeoenvironmental transfer function model for acidified lakes

- 246 Downloads
- 11 Citations

## Abstract

A Bayesian approach to palaeoecological environmental reconstruction deriving from the unimodal responses generally exhibited by organisms to an environmental gradient is described. The approach uses Bayesian model selection to calculate a collection of probability-weighted, species-specific response curves (SRCs) for each taxon within a training set, with an explicit treatment for zero abundances. These SRCs are used to reconstruct the environmental variable from sub-fossilised assemblages. The approach enables a substantial increase in computational efficiency (several orders of magnitude) over existing Bayesian methodologies. The model is developed from the Surface Water Acidification Programme (SWAP) training set and is demonstrated to exhibit comparable predictive power to existing Weighted Averaging and Maximum Likelihood methodologies, though with improvements in bias; the additional explanatory power of the Bayesian approach lies in an explicit calculation of uncertainty for each individual reconstruction. The model is applied to reconstruct the Holocene acidification history of the Round Loch of Glenhead, including a reconstruction of recent recovery derived from sediment trap data.

The Bayesian reconstructions display similar trends to conventional (Weighted Averaging Partial Least Squares) reconstructions but provide a better reconstruction of extreme pH and are more sensitive to small changes in diatom assemblages. The validity of the posteriors as an apparently meaningful representation of assemblage-specific uncertainty and the high computational efficiency of the approach open up the possibility of highly constrained multiproxy reconstructions.

## Keywords

Environmental reconstruction Transfer functions Bayesian model selection Diatoms Acidification## Notes

### Acknowledgements

We are grateful to Devinder Sivia, John Birks and Richard Telford for useful discussions. We are additionally grateful for the constructive comments of both referees which have substantially improved the paper.

## References

- Allott TEH, Harriman R, Battarbee RW (1992) Reversibility of lake acidification at the Round Loch of Glenhead, Galloway, Scotland. Environ Pollut 77:219–225CrossRefGoogle Scholar
- Battarbee RW, Juggins S, Gasse F, Anderson NJ, Bennion H, Cameron NG, Ryves DB, Pailles C, Chalie F, Telford R (2001) European Diatom Database (EDDI). An information system for palaeoenvironmental reconstruction. ECRC Research Report No. 81, 94 ppGoogle Scholar
- Battarbee RW, Monteith DT, Juggins S, Evans CD, Jenkins A, Simpson GL (2005) Reconstructing pre-acidification pH for an acidified Scottish loch: a comparison of palaeolimnological and modelling approaches. Environ Pollut 137:135–150CrossRefGoogle Scholar
- Birks HJB (1994) The importance of pollen and diatom taxonomic precision in quantitative palaeoenvironmental reconstructions. Rev Palaeobot Palynol 83:107–117CrossRefGoogle Scholar
- Birks HJB (1995) Quantitative palaeoenvironmental reconstructions. In: Maddy D, Brew JS (eds) Statistical modelling of quaternary science data. Technical guide 5. Quaternary Research Association, Cambridge, pp 161–254Google Scholar
- Birks HJB (1998) Numerical tools in palaeolimnology: progress, potentialities and problems. J Paleolimnol 20:307–332CrossRefGoogle Scholar
- Birks HJB (2003) Quantitative palaeoenvironmental reconstructions from Holocene biological data. In: Mackay AW, Battarbee RW, Birks HJB, Oldfield F (eds) Global change in the Holocene. Hodder Arnold, New York, pp 107–123Google Scholar
- Birks HH, Birks HJB (2003) Reconstructing Holocene climates from pollen and plant macrofossils. In: Mackay AW, Battarbee RW, Birks HJB, Oldfield F (eds) Global change in the Holocene. Hodder Arnold, New York, pp 342–357Google Scholar
- Birks HJB, Line JM, Juggins S, Stevenson AC, ter Braak CJF (1990) Diatoms and pH reconstruction. Philos Trans R Soc Lond 327:263–278CrossRefGoogle Scholar
- Box CEP, Tiao GC (1992) Bayesian inference in statistical analysis. Wiley-Interscience, New York, pp 608Google Scholar
- Cosby BJ, Ferrier RC, Jenkins A, Wright RF (2001) Modelling the effects of acid deposition: refinements, adjustments and inclusion of nitrogen dynamics in the MAGIC model. Hydrol Earth Syst Sci 5:499–517CrossRefGoogle Scholar
- Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74:829–836CrossRefGoogle Scholar
- Dennis B (1996) Discussion: should ecologists become Bayesians? Ecol Appl 6:1095–1103CrossRefGoogle Scholar
- Efron B (1983) Estimating the error rate of a prediction rule: improvement on cross-validation. J Am Stat Assoc 78:316–330CrossRefGoogle Scholar
- Flower RJ, Battarbee RW (1983) Diatom evidence for the acidification of two Scottish Lochs. Nature 305:130–133CrossRefGoogle Scholar
- Flower RJ, Battarbee RW, Appleby PB (1987) The recent palaeolimnology of acid lakes in Galloway, south-west Scotland. Diatom analysis, pH trends, and the role of afforestation. J Ecol 75:797–824CrossRefGoogle Scholar
- Haslett J, Whiley M, Bhattacharya S, Salter-Townshend M, Wilson SP, Allen JRM, Huntley B, Mitchell FJG (2006) Bayesian palaeoclimate reconstruction. J R Stati Soc A 169:395–438CrossRefGoogle Scholar
- Huntley B (1993) The use of climate response surfaces to reconstruct palaeoclimate from quaternary pollen and plant macrofossil data. Philos Trans R Soc Lond B 341:215–223CrossRefGoogle Scholar
- Imbrie J, Kipp NG (1971) A new micropaleontological method for quantitative paleoclimatology: application to a late Pleistocene Carribean core. In: Turekian KK (ed) The late cenozoic glacial ages. Yale University Press, New Haven and London, pp 71–181Google Scholar
- Jones VJ, Flower RJ (1986) Spatial and temporal variability in periphytic diatom communities: palaeoecological significance in an acidified lake. In: Smol JP, Battarbee RW, Davis RB, Meriläinen J (eds) Diatoms and Lake Acidity. Dr W. Junk Publishers, Dordrecht, pp 87–94Google Scholar
- Jones VJ, Stevenson AC, Battarbee RW (1989) Acidification of lakes in Galloway, south west Scotland—a diatom and pollen study of the post-glacial history of the Round Loch of Glenhead. J Ecol 77:1–23CrossRefGoogle Scholar
- Juggins S (2003) C
^{2}user guide. Software for ecological and palaeoecological data analysis and visualisation. University of Newcastle, Newcastle upon Tyne, UK, 69 ppGoogle Scholar - Korhola A, Vasko K, Toivonen HTT, Olander H (2002) Holocene temperature changes in northern Fennoscadia reconstructed from chironomids using Bayesian modeling. Quaternary Sci Rev 21:1841–1860CrossRefGoogle Scholar
- Köster D, Racca JMJ, Pienitz R (2004) Diatom-based inference models and reconstruction revisited: methods and transformation. J Paleolimnol 32:233–246CrossRefGoogle Scholar
- Kühl N, Gebhardt C, Litt T, Hense A (2002) Probability Density Functions as botanical-climatological transfer functions for climate reconstruction. Quaternary Res 58:381–392CrossRefGoogle Scholar
- Lancaster J, Belyea LR (2006) Defining the limits to local density: alternative views of abundance-environment relationships. Freshw Biol 51:783–796CrossRefGoogle Scholar
- Monteith DT, Evans CD (2005) The United Kingdom acid waters monitoring network: a review of the first 15 years and introduction to the special issue. Environ Pollut 137:3–13CrossRefGoogle Scholar
- Monteith DT, Hildrew AG, Flower RJ, Raven PJ, Beaumont WRB, Collen P, Kreiser AM, Shilland EM, Winterbottom JH (2005) Biological responses to the chemical recovery of acidified freshwaters in the UK. Environ Pollut 137:83–102CrossRefGoogle Scholar
- Munro MAR, Kreiser AM, Battarbee RW, Juggins S, Stevenson AC, Anderson DS, Anderson NJ, Berge F, Birks HJB, Davis RB, Flower RJ, Fritz SC, Haworth EY, Jones VJ, Kingston JC, Renberg I (1990) Diatom quality control and data handling. Philos Trans R Soc Lond B 327:257–261CrossRefGoogle Scholar
- Racca JMJ, Wild M, Birks HJB, Prairie YT (2002) Separating wheat from chaff: Diatom taxon selection using an artificial neural network pruning algorithm. J Paleolimnol 29:123–133CrossRefGoogle Scholar
- Rymer L (1978) The use of uniformitariansim and analogy in palaeoecology, particularly pollen analysis. In: D Walker JC Guppy (eds) Biology and quaternary environments. Australian Academy of Sciences, Canberra, pp 245–258Google Scholar
- Stevenson AC, Juggins S, Birks HJB, Anderson DS, Anderson NJ, Battarbee RW, Berge F, Davis RB, Flower RJ, Haworth EY, Jones VJ, Kingston VJ, Kreiser AM, Line JM, Munro MAR, Renberg I (1991) The surface waters acidification project palaeolimnology program: modern diatom/lake-water chemistry set. ENSIS, London, 86 ppGoogle Scholar
- ter Braak CJF (1995) Non linear models for multivariate statistical calibration and their use in palaeoecology; a comparison of inverse k-nearest neighhbours, partial least squares and weighted averaging partial least squares, and classical approaches. Chemomet Intell Lab 28:165–180CrossRefGoogle Scholar
- ter Braak CJF, Juggins S (1993) Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages. Hydrobiologica 269/270:485–502CrossRefGoogle Scholar
- ter Braak CJF, van Dam H (1989) Inferring pH from diatoms: a comparison of old and new calibration methods. Hydrobiologia 178:209–233CrossRefGoogle Scholar
- ter Braak CJF, Juggins S, Birks HJB, van der Voet H (1993) Weighted averaging partial least squares regression (WA-PLS): definition and comparison with other methods for species-environment calibration. In: GP Patil CR Roa (eds) Multivariate environmental statistics. Elsevier Science Publishers, Amsterdam, pp 525–560Google Scholar
- Vasko K, Toivonen HTT, Korhola A (2000) A Bayesian multinomial response model for organism-based environmental reconstruction. J Paleolimnol 24:243–250CrossRefGoogle Scholar