QUANTITATIVE METHODS IN PALAEOECOLOGY AND PALAEOCLIMATOLOGY

1. QUANTITATIVE METHODS IN PALAEOECOLOGY AND PALAEOCLIMATOLOGY Class 3 Analysis of Stratigraphical Data Espegrend August 2008

2. CONTENTS Introduction to temporal stratigraphical data Single sequence Partitioning or zonation Sequence splitting Rate-of-change analysis Gradient analysis and summarisation Analogue matching Relationships between two or more sets of variables in same sequence Two or more sequences Sequence comparison and correlation Combined scaling Difference diagrams Mapping Locally weighted regression (LOWESS) INQUA Commission for the Study of the Holocene Summary

3. INTRODUCTION In ecology, analysis of quadrats, lakes, streams, etc. Assume no autocorrelation, namely cannot predict the values of a variable at some point in space from known values at other sampling points. PALAEOCOLOGY – fixed sample order in time. strong autocorrelation – temporal autocorrelation STRATIGRAPHICAL DATA biostratigraphic, lithostratigraphic, geochemical, geophysical, morphometric, isotopic multivariate continuous or discontinuous time series ordering very important – display, partitioning, trends, interpretation

4. Numerical Techniques in Palaeoecology Range of numerical of data-analytical techniques available for the summarisation, synthesis, and interpretation of palaeoecological data Main purposes • Detect major patterns in complex data • Summarise data in terms of fossil zones, major trends, and groups of fossil types that covary • Identify ‘hidden’ features of data such as statistically significant splits in individual curves, rates of change, etc • Interpretation of data in terms of modern analogues (vegetation types) and past environment (e.g. climate) • Aid comparison and correlation of sequences from 1 or more sites • Display fossil data as maps to explore spatial patterns Numerical techniques are a useful part of the palaeoecologist’s ‘tool-kit’

5. SINGLE SEQUENCE Zonation or Partitioning of Stratigraphical Data Useful for: 1) description 2) discussion and interpretation 3) comparisons in time and space “sediment body with a broadly similar composition that differs from underlying and overlying sediment bodies in the kind and/or amount of its composition”.

6. CONSTRAINED CLASSIFICATIONS 1) Constrained agglomerative proceduresCONSLINK CONISS 2) Constrained binary divisive procedures Partition into g groups by placing g – 1 boundaries. Number of possibilities Compared with non-constrained situation. Criteria – within-group sum-of-squares or varianceSPLITLSQ – within-group information SPLITINF

7. 3) Constrained optimal divisive analysis OPTIMAL 2 group ______________________________ 3 group 4 group 4) Variable barriers approach BARRIER All methods in one program:ZONE n1 n2 n1 n2 n1 n3

8. Pollen diagram and numerical zonation analyses for the complete Abernethy Forest 1974 data set. Birks & Gordon 1985

9. What about CONISS in TILIA? CONISS = constrained incremental sum-of-squares (= constrained Word's minimum variance) TILIA ZONE

11. OPTIMAL SUM OF SQUARES PARTITIONS OF THE ABERNETHY FOREST 1974 DATA ZONE

12. HOW MANY ZONES? K D Bennett (1996) Determination of the number of zones in a biostratigraphical sequence. New Phytologist 132, 155-170 Broken stick model BSTICK

13. Ioannina Basin Tzedakis 1994 Pollen percentage diagram plotted against depth. Lithostratigraphic column is represented; symbols are based on Troels-Smith (1995).

14. Ioannina Basin Tzedakis 1994

15. Variance accounted for by the nth zone as a proportion of the total variance (fluctuating curve) compared with values from a broken-stick model (smooth curve): (a) randomized data set, (b) original data set. Zonation method: binary divisive using the information content statistic. Data set; Ioannina. Original data Broken stick model BSTICK

16. Bennett 1996

17. Sequence Splitting Walker & Wilson 1978 J Biogeog 5, 1–21 Walker & Pittelkow 1981 J Biogeog 8, 37–51 SPLIT, SPLIT2 BOUND2 Need statistically ‘independent’ curves   Pollen influx (grains cm–2 year–1) PCA or CA or DCA axes CANOCO Aitchison log-ratio transformation LOGRATIO where

22. Correlograms of sequence splits with charcoal, inorganic matter and total pollen influxes for three sections of the pollen record. The vertical scales give correlations; the horizontal scales give time lag in years (assuming a sampling interval of 50 years).

23. Rate Of Change Analysis Amount of palynological compositional change per unit time. Calculate dissimilarity between pollen assemblages of two adjacent samples and standardise to constant time unit, e.g. 250 14C years. Jacobson & Grimm 1986 Ecology 67, 958-966 Grimm & Jacobson 1992 Climate Dynamics 6, 179-184 RATEPOL POLSTACK (TILIA)

24. Graph of distance (number of standard deviations) moved every 100 yr in the first three dimensions of the ordination vs age. Greater distance indicates greater change in pollen spectra in 100yr. Jacobson & Grimm 1986

26. Graph of distance (number of standard deviations) moved every 100 yr in the first three dimensions of the ordination vs. age. Greater distance indicates greater change in pollen spectra in 100 yr.

32. MANY PROXIES, ONE SITE

33. ONE PROXY, MANY SITES - fertile - poor Chord distance between samples at Solsø, Skånsø, and Kragsø, calculated on smoothed data with 35 taxa and interpolated at 400 year and 1,000 year intervals. - poor

34. Pollen percentages from Loch Lang, Western Isles, plotted against age (radiocarbon years BP). Data from Bennett (1990).

35. Pollen percentages from Hockham Mere, eastern England, plotted against age (radiocarbon years BP). Data from Bennett (1983).

36. Rate x5 that at Loch Lang Comparison of Holocene rates of change at Loch Lang and Hockham Mere, with 2 - 2 dissimilarity coefficient on unsmoothed data, with a radiocarbon timescale. High rates of change at Hockham Mere

37. Data Summarisation by Ordination or Gradient Analysis of Single Sequence Ordination methods CA/DCA or PCA joint plot biplot Sample summary CA/DCA/PCA Species arrangement CCA CA = correspondence analysis DCA = detrended correspondence analysis PCA = principal components analysis CCA = canonical correspondence analysis CANOCO R

38. PCA Biplot 74.6% Gordon 1982 Biplot of the Kirchner Marsh data; C2 = 0.746. The lengths of the Picea and Quercus vectors have been scaled down relative to the other vectors. Stratigraphically neighbouring levels are joined by a line.

39. CA Joint Plot 62% Gordon 1982 Correspondence analysis representation of the Kirchner Marsh data; C2 = 0.620. Stratigraphically neighbouring levels are joined by a line.

40. Stratigraphical plot of sample scores on the first correspondence analysis axis (left) and of rarefaction estimate of richness (E(Sn)) (right) for Diss Mere, England. Major pollen-stratigraphical and cultural levels are also shown. The vertical axis is depth (cm). The scale for sample scores runs from –1.0 (left) to + 1.2 (right).

41. DCS axes 1 and 2 for a south Finnish pollen sequence plotted (right) in relation to time.

42. The 1st and 2nd axis of the Detrended Correspondence Analysis for Laguna Oprasa and Laguna Facil plotted against calibrated calendar age (cal yr BP). The 1st axis contrasts taxa from warmer forested sites with cooler herbaceous sites. The 2nd axis contrasts taxa preferring wetter sites with those preferring drier sites Haberle & Bennett 2005

43. Species arrangement Percentage pollen and spore diagram from Abernethy Forest, Inverness-shire. The percentages are plotted against time, the age of each sample having been estimated from the deposition time. Nomenclatural conventions follow Birks (1973a) unless stated in Appendix 1. The sediment lithology is indicated on the left side, using the symbols of Troels-Smith (1995). The pollen sum, P, includes all non-aquatic taxa. Aquatic taxa, pteridophytes, and algae are calculated on the basis of P +  group as indicated.

44. CANOCO TRAN Pollen types re-arranged on the basis of the weighted average for depth

45. Analogue Analysis Modern training set – similar taxonomy   – similar sedimentary environment Compare fossil sample 1 with all modern samples, use appropriate DC, find sample in modern set ‘most like’ (i.e. lowest DC) fossil sample 1, call it ‘closest analogue’, repeat for fossil sample 2, etc. Overpeck et al. 1985 Quat Res 23, 87–108 ANALOG MATCH MAT

46. Compare fossil sample i with modern sample j. Calculate similarity between i and j Sij Find modern sample with highest similarity 'ANALOGUE‘ Repeat for all modern samples Repeat for all fossil samples ? Evaluation

47. Dissimilarity coefficients, radiocarbon dates, pollen zones, and vegetation types represented by the top ten analogues from the Lake West Okoboji site.

48. Maps of squared chord distance values with modern samples at selected time intervals

49. Plots of the minimum squared chord-distance for each fossil spectrum at each of the eight sites.

50. A schematic representation of how fossil diatom zones/samples in a sediment core from an acidified lake can be compared numerically with modern surface sediment samples collected from potential modern analogue lakes. In this space-for-time model the vertical axis represents sedimentary diatom zones defined by depth and time; the horizontal axis represents spatially distributed modern analogue lakes and the dotted lines indicate good floristic matches (dij = <0.65), as defined by the mean squared Chi-squared estimate of dissimilarity (SCD, see text). Flower et al. 1997