POLLEN–CLIMATE TRANSFER FUNCTIONS – PROBLEMS AND PITFALLS

1. POLLEN–CLIMATE TRANSFER FUNCTIONS – PROBLEMS AND PITFALLS John Birks University of Bergen & University College London NEPAL Sokli Workshop, Helsinki, 15 November 2007

2. Will actually talk on • POLLEN-CLIMATE TRANSFER FUNCTIONS – PRINCIPLES, PROBLEMS, PITFALLS, AND POTENTIALITIES AT SOKLI • Because • Some of the apparent ‘problems’ relate to the basic principles of pollen-climate transfer functions • Some of the ‘pitfalls’ relate to the data themselves • The potentialities at Sokli have not been fully exploited yet, at least from a general palaoecological viewpoint

3. Introduction • Assemblage Approach • Indicator Species Approach • Single species or taxon – univariate • Several taxa • Many taxa • All taxa – multivariate • Assumptions • Example • Problems • Pitfalls • Potentialities • Acknowledgements

4. INTRODUCTION • Aim of many palaeoecological studies is to reconstruct features of the past environment from fossil assemblages preserved in sediments • Flora or fauna – presence or absence • Populations – abundances • Communities • Landscapes • Environments including climate • Pollen analysis and plant macrofossils – mainly flora, communities and vegetation types, landscapes, and environments • Increasing need for quantification of past environment in response to demands for quantitative estimates of past environments as input to, or validation of, simulations by Earth System Models

5. Two main approaches to reconstructing quantitatively past environments from palaeobotanical data • 1. Assemblage approach • 2. Indicator species approach • Both need information about modern environmental requirements of taxa found as fossils

6. Basic assumption is methodological uniformitarianism, namely that modern-day observations and relationships can be used as a model for past conditions, and, more specifically, that organism-environment relationships have not changed with time, at least in the Late Quaternary. • Can only observe the realised niche of organisms. Assume that it is close to the potential and fundamental niches. Major assumption. • Remember that all reconstructions, qualitative or quantitative, are models. • All models are wrong, but how wrong are they?

7. ASSEMBLAGE APPROACH • Consider fossil assemblage as a whole and the proportions of its different fossil taxa. • Widely used in an intuitive non-quantitative way for many decades, e.g. pollen assemblages are interpreted as reflecting tundra, pine forest, or deciduous forest. Past environmental inferences are based on the present-day environment in which these vegetation types occur. Useful first essential step in vegetational or environmental interpretation. • Quantitative version is so-called modern analogue technique (MAT) and related response-surface approach.

8. Modern analog technique (MAT) = k-nearest neighbours (k-NN). Hutson (1980), Prell (1985), ter Braak (1995), et al. Compare fossil sample t with modern sample i Repeat for all modern samples Calculate DC between t and i Repeat for all fossil samples Value of k estimated by visual inspection, arbitrary rules (e.g., 10, 20, etc.), or cross-validation Select k-closest analogues for fossil sample t Estimate past environment for sample t as (weighted) mean of the environment of the k analogues

9. Response surface approach of Huntley, Bartlein, et al. is MAT but the modern pollen data are used to create a smooth ‘response surface’. Comparisons with fossil data involve a DC between smoothed modern pollen data i and fossil pollen spectrum t. • Limitations of MAT • Need for high-quality taxonomically consistent modern data from comparable sedimentary environments as fossil data and covering a wide environmental range • No means of deriving reliable error estimates for reconstructed values • How to define ‘good’, ‘poor’, or ‘no analogues’ • Choice of dissimilarity coefficient • Occurrence of ‘no analogues’ and ‘multiple analogues’

10. INDICATOR SPECIES APPROACH • Fossil occurrences of a taxon with known modern environmental tolerances provide a basis for environmental reconstruction • Assuming methodological uniformitarianism, the past environment is inferred to have been within the environmental range occupied by the taxon today • Require information about what environmental factors influence the distribution and abundance today of the taxon concerned

11. 1. Single taxon • Commonest means of obtaining such information - • Compare present-day distributions with selected climatic variables • Consider variables of potentially ecological or physiological significance • e.g. mean temperature of coldest month, maximum summer temperature If the geographical trend of an eco-climatic variable covaries with the taxon distribution in question, a cause-and-effect relationship is often assumed. e.g. – Dahl’s max summer temp isotherms for arctic-alpine taxa; Iversen, Kolstrup et al. for Filipendulaulmaria, Typha latifolia, Myriophyllum spicatum, etc.

12. 2. Several taxa • Often more realistic to consider distributions of several taxa in relation to two or more climatic variables.

13. Viscum album (mistletoe), Hedera helix (ivy), & Ilex aquifolium (holly) at or near their northern limits in Denmark (Iversen 1944) Considered occurrence, growth, and fruit production in relation to mean temperature of the coldest month and of the warmest month to delimit 'thermal limits'. Hedera helix

14. Mid-Holocene changes: ca. 2-2.5C warmer summers ca. 1-1.5C warmer winters Johs. Iversen Walther et al. (2005) show shifts in the northern limit of Ilex (holly) in last 50 years in response to climatic changes,confirming its sensitivity to climaticshifts. Viscum album Ilex aquifolium

15. 3. Many taxa Kühl et al. (2002) Quaternary Research 58; 381-392 Kühl (2003) Dissertations Botanicae 375; 149 pp. Kühl & Litt (2003) VHA 12; 205-214 Basic idea is to quantify the present-day distribution of plants that occur as Quaternary fossils (pollen and/or macrofossils) in terms of July & January temperature and probability density functions (pdf). Assuming statistical independence, a joint pdf can be calculated for a fossil assemblage as the product of the pdfs of the individual taxa. Each taxon is weighted by the extent of its climatic response range, so 'narrow' indicators receive 'high' weight. The maximum pdf is the most likely past climate and its confidence interval is the range of uncertainty. Can be used with pollen (+/-) and/or macrofossils (+/-).

16. Distribution of Ilex aquilifolium in combination with January temperature. Estimated probability density function of Ilex aquilifolium as an example for which the parametric normal distribution (solid line) fits well the non-parametric distribution (e.g. Kernel function (dashed line) histogram)

17. Estimated 1- and 2-dimensional pdfs of 4 species. The histograms (non-parametric pdf) and normal distributions (parametric pdf) on the left represent 1-dimensional pdfs. Crosses in the right-hand plots display the temperature values provided by the 0.5º x 0.5º gridded climatology (New et el., 1999). Black crosses = presence, grey crosses = absence of the specific taxon. A small red circle marks the mean  of the corresponding normal distribution and the ellipses represent 90% of the integral of the normal distribution centred on . Most sample points lie within this range. The interval may not necessarily include 90% of the data points. Carex secalina, an azonally distributed species, is an exception. A normal distribution seems an inappropriate estimating function for this species, therefore no normal distribution is indicated.

18. Climate dependencies of Carpinus (betulus) (C), Ilex (aquilifolium) (I), Hedera (helix) (H)& Tilia (T) & their combination. The pdf resulting from the product of the 4 individual pdfs (dotted) is similar to the ellipse calculated on the basis of the 216 points with common occurrences for the 4 taxa (dashed). No artificial narrowing of the uncertainty range is evident. Climate dependencies of Acer (A), Corylus (avellana) (C), Fraxinus (excelsior) (F)& Ulmus (U) & their combination. The pdf (dotted) resulting from the product of the 4 individual pdfs has a mean  very similar to the mean of the pdf (dashed) based on the 1667 points with common occurrences, but its variances are much smaller.

20. Reconstruction for the fossil assemblage of Gröbern. The thin ellipses indicate the pdfs of the individual taxa included in the reconstruction, and the thick ellipse the 90% uncertainty range of the reconstruction result.

21. Simplified pollen diagram from Gröbern (Litt 1994), reconstructed January & July temperature, and 18O (after Boettger et al. 2000).

22. Kühl & Litt (2003) Reconstructed most probable mean January (blue) and July (red) temperature and 90% uncertainty range (dotted lines)

23. 4. All taxa – multivariate indicator species approach • How to use all the information, both presence-absence and proportions, in fossil pollen data? • Need estimates of environmental optima and tolerances of all taxa, not of the sporophyte generation of higher plants, but of the gametophyte generation.

24. A unimodal relation between the abundance value (y) of a species and an environmental variable (x). (u=optimum or mode; t=tolerance; c=maximum).

25. To estimate optima and tolerances, need extensive set of modern surface samples. 304 modern pollen samples Norway, northern Sweden, Finland (Sylvia Peglar, Heikki Seppä, John Birks, Arvid Odland)

27. Fossil data Climate variable (e.g., pollen, chironomids) (e.g., temperature) 'Proxy data' 1, ........... m taxa 1 YO XOUnknown. t t samples samples To be estimated or reconstructed To solve for XO, need modern data or 'training data' or 'calibration set' 1, ........... m taxa 1 Y X n n samples samples Modern biology Modern environment (e.g., pollen, chironomids) (e.g., temperature) Transfer function, in general terms, estimates the environmental optima (like Ellenberg indicator values) for all pollen taxa in the modern pollen data Allows us to solve:

28. In practice, use weighted-averaging partial least squares regression. (WA-PLS) Takes account of % data, ignores zero values, assumes unimodal responses, can handle several thousand species, and gives transfer functions of high precision (0.8ºC), low bias, and high robustness. X = g(Y1, Y2, Y3, ... ... ..., Ym) Modern data XO = g (YO1, YO2, YO3, ... ... ..., YOm) Fossil data g is our transfer function for X and Y where g is the estimate of the environmental ‘optima’ of all taxa (Y1 … Ym) today ^

29. Observed Inferred -logLik Modern responses 9 10 11 12 13 14 Temperature (ºC) ^ • Inferring past temperature from multivariate species composition • The reconstructed value x0 is a mean of the estimated optima weighted by the abundances of the taxa Modified from J. Oksanen (2002)

30. Assumptions • Basic biological assumption • Pollen • Pollen is a function of flora and vegetation • Flora and vegetation are a function of climate •  Pollen is a function of climate, at least at broad scales

31. Hidden basic assumptions • Taxa in training set (Y) are systematically related to the physical environment (X) in which they live • Environmental variable (X0 e.g. summer temp) to be reconstructed is, or is linearly related to, an ecologically important variable in the system • Taxa in the training set (Y) are the same as in the fossil data (Y0) and their ecological responses (Gm) have not changed significantly over the timespan represented • Mathematical methods used in regression and calibration adequately model the non-linear biological responses (Gm) to the environmental variable (X). • Other environmental variables than e.g. summer temperature have negligible influence or their joint distribution with summer temperature in the fossil set is the same as in the training set • In estimating the predictive power of the model, the test data are assumed to be independent of the modern data. Spatial autocorrelation seriously invalidates this assumption ^

32. Example of use and validation Björnfjelltjörn, N Norway

34. Björnfjelltjörn consensusreconstructions

36. Validate using another proxy – macrofossils of tree birch

37. Validate using a non-botanical proxy - chironomids Importance of multi-proxy studies & independent validation Challenges for the future!

38. PROBLEMS WITH PARTICULAR REFERENCE TO SOKLI PROJECT • Different reconstructions do not closely agree • chironomids about 12-13C mean July T • pollen about 10-12C mean July T • macro-remains about 7-13C min mean July T • Pollen-climate reconstructions need critical numerical evaluation using goodness-of-fit measures, proportion of taxa with poorly estimated optima, and presence of ‘no-analogues’ (Birks et al. 1990, Birks 1998) • How to evaluate ‘macro-remains’ ‘minimum mean July T’? • Do we make as many reconstructions as possible and use all our data, or do we split our data into reconstruction data and independent test or validation data? • Assumption of realised niche and hence environmental indicator value invariant in time, at least to OIS-3

39. PITFALLS WITH PARTICULAR REFERENCE TO SOKLI PROJECT • Biological system with abundant fossils that is responsive and sensitive to environmental variables of interest • A large, high-quality training set of modern samples. Should be representative of the likely range of variables, be of consistent taxonomy and nomenclature, be of highest possible taxonomic detail, be of comparable quality (methodology, count size, etc) , and be from the same sedimentary environment Basic requirements in quantitative palaeoenvironmental reconstructions

40. Basic requirements in quantitative palaeoenvironmental reconstructions • Fossil set of comparable taxonomy, nomenclature, quality, and sedimentary environment • Robust statistical methods for regression and calibration that can adequately model taxa and their environment with the lowest possible error of prediction and the lowest bias possible • Statistical estimation of standard errors of prediction for each constructed value • Statistical and ecological evaluation and validation of the reconstructions (Birks et al. 1990)

41. Pollen and spore taxonomy and pollen sums not, at present, identical • e.g. Betula nana separated at Sokli • Pteridophytes outside the sum at Sokli • Some ‘wetland’ taxa at Sokli are in the modern pollen sum • Ericaceae, Apiaceae, etc, not divided at Sokli • Need careful taxonomic harmonisation and then re-run the modern WA-PLS model using a modern taxonomy comparable to Sokli

42. Will need to fuse Betula, tree birch and Betula cf. nana at Sokli to match modern Betula • Need identical pollen sums • Net result will not be very different from Helmens et al. (2007) as WA-PLS is very robust due to it inherent weightings and scalings, but it must be done • 2. Need to understand better how to interpret and use sample specific errors of reconstruction

43. Hidden assumption 5. 'Other environmental variables than, say, summer temperature have negligible influence or their joint distribution with summer temperature in the past is the same as the training set.’ • Climate model and glaciological results suggest that the joint distribution between summer temperature and winter accumulation has not been the same in the past. • Good evidence to suggest that lake-water pH has decreased naturally (soil deterioration) whilst summer temperature rose and then fell in the last 11,000 years. • In Norway today, lake-water pH is negatively correlated with summer temperature because lakes of pH 6-7.5 are on basic rock and this happens to occur mainly at high altitudes and hence at low temperatures. After deglaciation almost all lakes had higher pH than today, so the pH-temperature relationship was different than today.

44. POTENTIALITIES WITH PARTICULARL REFERENCE TO SOKLI PROJECT • Climate reconstructions based on several groups of fossils (pollen, macro-remains, chironomids, diatoms) • Potential to validate reconstructions based on different groups of organisms • Should not expect all reconstructions to be identical! Real world is more complex than that, as different organisms respond differently to the environment and to the very real interactions within the environment

45. Birks & Ammann (2000)

46. Environmental variable 2 Environmental variable 1 • 4. In a carefully implemented multi-proxy study in OIS-3, an opportunity to try to test ideas of realised niche changing with different climatic spaces. Basic and original contribution to theory of Quaternary palaeoecology Fundamental niche space Available environmental space Potential niche space Realised niche Jackson & Overpeck (2000)

47. Realised environmental space Jackson & Overpeck (2000)

48. Environmental variable 2 Environmental variable 1 Changes in realised space and species responses (a-e) to environmental change Fundamental niche Available environmental space, Time 1 Available environmental space, Time 2 a b c d e Jackson & Overpeck (2000)

49. Very tentative potentiality involving chironomids and inferred vegetation • Look at fossil and modern chironomid assemblages together numerically to see which modern vegetation types have chironomid assemblages that most closely resemble the fossil chironomid assemblages • Are they closest to modern low-arctic tundra chironomid assemblages (mean July temperature ca. 8-9C) or middle boreal forest (mean July temperature ca. 13C)? • In other words, explore the apparent discrepancies between chironomid inferences and palaeobotanical inferences. • Interesting challenge – should not be ignored. Differences are often more interesting than similarities!

50. ACKNOWLEDGEMENTS • Karin Helmens – co-ordinating Sokli project • Heikki Seppä – involving me in Sokli pollen data • Other Sokli colleagues - fruitful collaboration • NEPAL network – financial support • Hilary Birks and Kathy Willis – useful discussions • Cathy Jenks – much invaluable help