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Quantitative Environmental Reconstructions in Palaeoecology: Progress, current status, & future needs. John Birks University of Bergen, University College London, and University of Oxford. Tage Nilsson Lecture Centre for GeoBiosphere Science University of Lund, 7 March 2013. INTRODUCTION.
University of Bergen, University College London, and University of Oxford
Tage Nilsson Lecture
Centre for GeoBiosphere Science
University of Lund, 7 March 2013
Early attempts at quantitative environmental reconstructions used presence of one or more ‘indicator species’ (e.g. Andersson, Samuelsson, Iversen, Grichuk, Coope) or species groups (e.g. Hustedt, Nygaard). Major development in Quaternary science occurred in 1971 with publication of the classic paper by Imbrie & Kipp.
Paper laid the foundation of calibration functions (transfer functions) as a tool for the quantitative reconstruction of past environments using the whole fossil assemblage, not just a few indicator species. Paradigm shift, not only in palaeoceanography but also in quantitative palaeoecology.
Quickly followed by Webb & Bryson (1972) using pollen data in the Midwest, USA, to reconstruct climate. Used liner-based canonical correlation analysis. Palaeoclimatology
Marine planktonic foraminifera - Imbrie & Kipp 1971
Foraminifera are a function of sea-surface temperature (SST)
Foraminifera can be used to reconstruct past SST
Pollen is a function of regional vegetation – Webb & Bryson 1972
Regional vegetation is a function of climate
Pollen is an indirect function of climate and can be used to reconstruct past regional climate at a broad spatial scale
Chironomids (aquatic non-biting midges) are a function of lake-water temperature – Walker et al. 1991
Lake-water temperature is a function of climate
Chironomids are an indirect function of climate and can be used to reconstruct past climate but problems may arise
Freshwater diatoms are a function of lake-water chemistry – Renberg & Hellberg 1982
Diatoms can be used to reconstruct past lake-water chemistry
, m taxa
Fossil data (e.g. diatoms) ‘Proxy data’
Environmental variable (e.g. pH)
To be estimated or reconstructed
To solve for Xf, need modern data about species and pH from n samples
, m taxa
Modern biology (e.g. diatoms)
Modern environment (e.g. pH)
Model Ym in relation to Xm to derive modern calibration function Ûm
Apply Ûm to Yf to estimate past environment Xf
Imbrie & Kipp provided the basic theory and assumptions, a robust method, and modern and fossil data
Juggins & Birks (2012)
To solve for Xf, model Y0 in relation toX0, derive and apply calibration function F0 to Yf to estimate Xf
Fossil data (e.g. diatoms)
Environmental variable (e.g. pH)
, m taxa
Known from historical data
Unknown, to be reconstructed
All done at one site
Only consider Calibration-in-Space
In palaeolimnology, after Nygaard’s (1956) , , and indices and Merilainen’s (1967) calibration, first major step towards robust environmental reconstructions was made in 1982 by Renberg & Hellberg with their Index B
ind = indifferent species (either side of pH7) acp = acidophilous (pH<7) acb = acidobiontic (pH<7, optimum 5.5 or less)alk = alkaliphilous (pH7 or more) alb = alkalibiontic (pH>7)
Represented a great breakthrough, only 30 years ago
Discussed diatom-pH calibration functions in Lund with Rick Battarbee in 1986. Suggested how they might be improved
Major breakthrough occurred in 1989 as result of work of Cajo ter Braak with his 1987 doctoral thesis
Advances in Ecological Research 1988
Several important papers that have been very influential on quantitative palaeolimnology
Through his work at the Research Institute for Nature Management at Leersum, ter Braak advised ecologists about data analysis and developed many new techniques to help answer particular ecological questions.
One such ecologist was the diatomist Herman van Dam who was working on the impact of acidification on diatoms and water chemistry of Dutch moorland ponds (this work led ter Braak to publish his first paper on multivariate data analysis (principal component biplots) in 1982).
Changed the approaches to quantitative environmental reconstruction in palaeolimnology (and in much of palaeoecology)
Fortunately coincided with Surface Water Acidification Project’s (SWAP) Palaeolimnology Programme led by Rick Battarbee and Ingemar Renberg 1987-1990.
99 training-set diatom-pH samples; 61 independent test-set diatom samples. RMSEP is root mean squared error of prediction (‘standard error’). Generally want it as low as possible
Set the scene for weighted-averaging based methods – computationally simple, heuristic equivalents to the theoretically more rigorous maximum-likelihood methods.
A straight line displays the linear relation between the abundance value (y) of a species and an environmental variable (x). Modelled by linear regression.
A unimodal relation between the abundance value (y) of a species and an environmental variable (x). (u=optimum or mode; t=tolerance; c=maximum). Modelled by Gaussian logit regression (GLR)
Since 1971, calibration functions widely used in palaeoceanography, terrestrial palaeoecology, and palaeolimnology
Used with wide range of biological proxies
Now many different numerical reconstruction methods – at least 26 methods published, many minor variants of established methods
Reconstruction methods can be divided into three main types(Birks et al. 2010)
Concentrate on calibration-function approach
1. Basic Numerical Models
Y = f(X) + error
Estimate f by some mathematical procedure and 'invert' estimated (f) to find unknown past environment Xffrom fossil data Yf
Can be difficult computationally
In practice, for various mathematical reasons, do an inverse regression or calibration
X = g(Y) + error
Xf = g(Yf)
Obtain 'plug-in' estimate of past environment Xf from fossil data Yf
f or g are calibration functions
Easier to compute g and nearly always performs as well as classical approach
Birks et al. (2010)
I = inverse; C = classical
L = linear; U = unimodal; NA = not assumed;
R = reduced dimensionality; F = full dimensionality;
G = global parametric estimation; Ln = local non-parametric estimation
CF = calibration-function based; S = similarity-based
Good reasons for preferring methods with assumed biological response model, full dimensionality, and global parametric estimation(ter Braak (1995), ter Braak et al. (1993), etc.)
“To make sense of an observation, everyone needs a model … whether he or she knows it or not” Marc Kéry (2010)
4. Need 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 and sound methods for model selection.
5. Need means of establishing if reconstruction is statistically significant.
6. Need statistical estimation of standard errors of prediction for each reconstructed value.
7. Need statistical and ecological evaluation and validation of the reconstruction and of each reconstructed value.
Birks et al. (1990)
Early Methods Used
Principal components regression (PCR) = Imbrie & Kipp (1971) approach
Multiple linear regression or quadratic regression of Xm on PC1, PC2, PC3, etc, to derive Ûm. Express Yf as principal components and apply Ûm to estimate Xf
Principal components maximise variance withinYmonly
Selection of PCA components done visually until recently. Now cross-validation is used to select model with fewest components, lowest root mean squared error of prediction (RMSEP), & lowest maximum bias. ‘Minimal adequate model’ in statistical modelling
Inverse, linear, reduced dimensionality, global estimation. Linear response model is assumed, although non-linear responses are possible.
Index B (Um) Xf
Inverse, linear, reduced dimensionality, global parametric estimation. Needs a priori taxon groupings
Related inverse multiple linear regression approach (Davis & Berge 1980, Charles 1982, Davis et al. 1983, Davis & Anderson 1984, Flower 1986)
+ Xm Um Xf
Inverse, linear, reduced dimensionality, global parametric estimation. Linear model is assumed, although non-linear responses are possible. Can be done with a priori species groups or individual taxa (forward selection).
Gaussian logit regression (GLR) and maximum likelihood (ML) calibration
ter Braak & van Dam (1989)
b0, b1, b2
Ym + Xm
b0, b1, b2
b0, b1, b2
taxon GLR regression coefficients for all taxa Ûm
Classical, unimodal, full dimensionality, global estimation. Robust to spatial autocorrelation. Can be computationally difficult. ML finds the most likely value of Xf that maximises the likelihood function given Yf and Ûm
ter Braak & van Dam (1989); Birks et al. (1990)
Ym + Xm
taxa WA optima ‘calibration function’ Ûm
Inverse, unimodal, full dimensionality, global parametric estimation. Robust to spatial autocorrelation. First used in Quaternary science by Lynts and Judd (1971) Science 171: 1143-1144
Ecologically plausible – based on unimodal species response model.
J. Oksanen (2002)
2. Disregards residual correlations in biological data.
Can extend WA to WA-partial least squares to include residual correlations in biological data in an attempt to improve estimates of taxon optima
Weighted averaging partial least squares regression and calibration (WA-PLS)ter Braak & Juggins (1993) and ter Braak et al. (1993)
Components selected to maximise covariance between taxon weighted averages and environmental variable X
Selection of number of PLS components to include based on cross-validation. Model selected should have fewest components possible and low RMSEP and maximum bias – minimal adequate model. Inverse, unimodal, reduced dimensionality, global parametric estimation. Can be sensitive to spatial autocorrelation.
Imbrie & Kipp (1971) data
Model performance statistic is root mean squared error of prediction (RMSEP) based on leave-one-out cross-validation
Shows importance of using a unimodal-based method(ter Braak et al. (1993))
Besides the development of new methods for deriving calibration functions and of modern calibration data-sets, there have been major developments in model evaluation and selection and in reconstruction assessment, namely statistics of calibration functions and in understanding the strengths and weaknesses of different methods and in their underlying theory
See Juggins (2013 QSR)
Tendency to use several different methods and to select so-called ‘best’ method. Resulted in a shift from an obsession with the model with lowest RMSEP or, even worse, the highest r2.
More concern with model performance statistics including estimates of bias and number of components fitted (e.g. in WA-PLS).
Model performance usually based on some form of internal cross-validation (leave-one-out, n-fold cross-validation, or bootstrapping) or external cross-validation with independent test-set.
Juggins & Birks (2012)
Birks & Simpson (2013) revisited the classical SWAP 167-sample diatom-pH calibration-set using modern methods (WA, WAPLS, GLR, MAT, etc.)
1. Internal cross-validation, done 50 times
167 samples 110 training-set samples
20 optimisation-samples (no. WAPLS components etc.
2. External cross-validation, done 50 times
167 samples 167 training-set samples
23 external optimisation-samples
50 external test-samples
Birks & Simpson (2013)
Birks & Simpson (2013)
(I = inverse; C = classical; M = monotonic; T = Tolerance downweighting)
WAI = WAC= WAM= WTM
< WATI = WATC = MAT < WAPLS < GLR
GLR < WAM= WTM < WAI = WAPLS
< WAC < WATI < MAT < WATC
Which to use as a guide to model selection?
External cross-validation involving independent test-set samples is ‘the appropriate benchmark to compare methods’ because all sources of error are considered (ter Braak & van Dam 1989)
van der Voet (1994) randomisation test of models helps find ‘minimal adequate model’ (MAM).
Model with good performance statistics and fewest number of fitted parameters. May be more than one MAM.
More work needed on model selection using criteria like Akaike Information Criterion (AIC) where unnecessary parameters are penalised. Active research area in ecology and evolutionary biology today.
Of course, performance of modern model is being assessed with other modern data, not with fossil data! Major problem. External cross-validation provides as rigorous a test as possible of performance.
Estimating model performance in terms of RMSEP, r2, maximum bias, etc, assumes that the test-set is statistically independent of the training-set. Cross-validation in presence of spatial autocorrelation violates this assumption as test samples are not spatially and statistically independent.
Spatial autocorrelation property of almost all environmental data and much ecological and biological data.
Telford & Birks (2005) Quat. Sci. Rev. 24: 2173-2179
Telford (2006) Quat. Sci. Rev. 25: 1375-1382
Telford & Birks (2009) Quat. Sci. Rev. 28: 1309-1316
Telford & Birks (2011) Quat. Sci. Rev. 30: 3210-3213
Results show the apparent performance of some models is enhanced as a result of spatial autocorrelation in oceans and on land
Problems in finding spatially independent test-sets to test inference models
Telford & Birks (2009) have developed methods for cross-validating a calibration function in presence of spatial autocorrelation, h-block cross-validation
Spatial autocorrelation does not appear to be a problem in many palaeolimnological calibration-sets. May be a problem in within-lake calibration-sets developed for water-level reconstructions (Velle et al. 2012)
Model uncertainty commonly expressed as RMSEP
Can only hope to reduce RMSEP by 20-25%
4. Testing the statistical significance of a quantitative palaeoenvironmental reconstruction
All calibration-function programs will produce output or ‘reconstruction’
Does the resulting reconstruction explain more of the variance in the fossil data than most (say 95%) reconstructions derived from calibration functions trained on random environmental data?
If it does, then it is statistically significant.
Global test of significance
Telford & Birks 2011 Quat. Sci. Rev. 30: 1272-1278
H.H. Birks et al. 2012 Quat. Sci. Rev. 33: 100-120
Telford & Birks (2011)
Can test if more than one reconstruction made from one biological data-set is statistically significant.
Chukchi Sea dinoflagellates – summer sea-surface temperature; sea-ice duration; summer salinity
Summer salinity not significant (p = 0.146)
What about ice duration and SST?
Telford & Birks (2011)
Partial out SST first as it explains marginally more of the variance (p = 0.003). Ice no longer significant when SST is allowed first. No significant independent information.
Telford & Birks (2011)
Applicable to almost all reconstruction methods, not just WA or WA-PLS
Assuming overall reconstruction is statistically significant, some individual estimates may be less reliable than others (poor preservation, unusual composition or peak, etc). Need to evaluate individual reconstructed values. Local evaluation
Has a statistically significant (p=0.009) reconstruction but there is also a continuous overlap in RMSEP. Problems of temporal autocorrelation in assessing RMSEP for samples.
Birks & Peglar (unpub.)
6. Highlighting ‘signal’ from ‘noise’ in reconstructions
Use of LOESS smoother a great help
Seppä & Birks (2002)
Brooks & Birks (2001)
Compare reconstructed values with historical data. Rarely possible as few historical data exist.
Renberg & Hultberg (1992)
But when done, sometimes the model that gives the closest correspondence is not the model with lowest RMSEP or maximum bias!
Conflict between model performance and selection based on cross-validation of modern data and validation results using independent historical test-sets
Birks & Ammann (2000)
Similar trends, different absolute values. Not surprising, given different biology of different groups of organisms
Assumptions in quantitative palaeoenvironmental reconstructions
Multiple-variable reconstructions – what variables can be reconstructed?
Increasing tendency to reconstruct 2 or 3, even 7-8, environmental variables that on the basis of current ecological knowledge of, e.g., vegetation, chironomids, or diatoms, cannot all be ‘ecologically important’ (assumption 2)
e.g. mean January, mean July, mean annual temperature, growing degree days above 0C and above 5C, annual precipitation, and evaporation : potential evaporation.
Ecological data are not usually influenced by 8 independent ‘ecologically important’ variables. Usually only 1-3 significant ordination axes.
All variables may be statistically significant in a RDA or CCA when considered individually(‘marginal’ effects) but almost certainly not significant when considered together (‘conditional’ effects, high multicollinearity, variance inflation factors). Many reconstructions of, for example, ‘distance to littoral vegetation’ suspect.
Basic statistical error (Juggins 2013)
Other potentially powerful approach is hierarchical partitioning (HP)
HP is designed to overcome multicollinearity problems by using a mathematical theorem by which the explanatory capacities of a set of predictor environmental variables can be estimated. Uses goodness-of-fit measures for each of the 2k possible models for k independent variable. In HP, the variances are partitioned so that the independent contribution (I) of a given environmental variable is estimated. Furthermore, the variation shared with another environmental variable (conjoint contribution J) can be computed.
HP allows differentiation between those environmental variables whose independent, as distinct from partial, correlation with the response variable may be important from those variables that have little or no independent effect on the responses (hier.part in R).
Used by Steve Juggins with diatom data and encouraging results (2013)
3. Confounding effects of correlated environmental variables (assumptions 2 and 5)
Present in all studies, starting with Imbrie & Kipp (1971) with reconstructions of summer and winter sea-surface temperature and salinity.
Covarying environmental variables e.g. temperature and lake trophic status (e.g. total N or P) or temperature and lake depth and chironomids. Is the fossil chironomid signal temperature or trophic status?
Broderson & Anderson (2002)
In almost all ecological systems, assemblages are a complex function of multiple climatic, edaphic, land-use, biotic, and historical factors.
First part of assumption 5 (environmental variables other than the variable being reconstructed have negligible influence) is therefore almost never met. Need very careful design of modern training-set and rigorous statistical analysis to establish what can reliably and significantly be reconstructed.
Second part of assumption 5 (the joint distribution of additional variables with the variable of interest does not change with time) is also violated in many cases.
Climate model and glaciological results suggest that the joint distribution between summer temperature and winter accumulation has not been the same in the past 11,000 years.
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. pH-climate relationship changed with time.
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 in Norway to occur mainly at high altitudes and hence at low temperatures. In the past after deglaciation, almost all lakes had a higher pH than today, so the pH-temperature relationship in the past was different than today.
4. Assumption 3 “Taxa in the training-set are the same as in the fossil data and their ecological responses have not changed significantly over the timespan represented by the fossil assemblage”
Assumption not unique to calibration functions. Basic assumption of all Quaternary palaeoecology, namely uniformitarianism.
Considerable interest in niche-conservatism amongst biogeographers and conservation and evolutionary biologists. Increasing evidence for conservatism of ecological niche characteristics in the timespan of last 20,000 years.
Problems of ‘cryptic’ species and of taxa like Saxifraga oppositifolia-type in environmental reconstructions currently unresolved.
5. Use of different proxies can give different reconstructions
Mean July temp, Bjørnfjell
p = 0.001
p = 0.183 ns
Validate using another proxy – e.g. macrofossils of tree birch
Validate using second proxy – e.g. chironomids
Importance of independent validation and establishing what is statistically significant
Quantitative palaeoenvironmental reconstructions in the context of Quaternary palaeoecology are not really an end in themselves (in contrast to Quaternary palaeoclimatology) but they are a meansto an end.
Use the reconstructions based on one proxy (e.g. chironomids) to provide an environmental history against which observed biological changes in another, independent proxy (e.g. pollen) can be viewed and interpreted as biological responses to environmental change.
Black portions = wet periods, grey = dry periods
Major change 1000 years ago towards drier conditions, decline in Fagus and rise in Pinus in charcoal
Climate vegetation fire frequency
These approaches involving environmental reconstructions independent of the main fossil record can be used as a long-term ecological observatory or laboratory to study long-term ecological dynamics under a range of environmental conditions, not all of which exist on Earth today (e.g. lowered CO2 concentrations, low human impact).
Can begin to study the Ecology of the Past.
Exciting prospect, many potentialities in future research, as outlined by Flessa and Jackson (2005)and discussed by Birks et al. (2010 Open Ecol J 3: 68-110)
Is the reconstruction a reconstruction of pH or climate?
5. Different methods can give very different reconstructions, even though they have similar modern model performances
6. There are increasing numbers of calibration data-sets (e.g. Norwegian, Swiss, Norwegian + Swiss, N Sweden, Finland 1 & 2 chironomid data-sets). How to select the ‘appropriate’ one?
Same July T range, different continentality (3), one with lower July T range. Similar but not identical RMSEP and maximum bias, all two-way WA
RMSEP (C) Max bias (C)
Salonen et al. (in press)
All reconstructions statistically significant (p<0.05). Likely explanation is that WA optima are different in areas of different continentality. Higher in areas of high continentality (e.g. Ulmus, Tilia, Quercus)
Basic problem in palaeoecology – really interested in the fundamental niche but can only study the realised niche as a result of confounding environmental variables. Realised niche may be different in different areas. Conflicts with assumptions 3 and 5.
8. Try to understand why results are seemingly inconsistent
9. Remember what the six basic assumptions of calibration functions are and try not to violate them or, even better, try to test them (e.g. niche conservatism)
Bayesian framework is an important future research direction but it presents very difficult and time-consuming computational problems. No available software (cf. DECORANA, CANOCO, WACALIB, CALIB, etc. philosophy)
Importance of continued research collaboration between palaeoecologists and applied statisticians
“All reconstructions are wrong, but some reconstructions may be useful”
The challenge is to identify the useful and reliable ones
It is a difficult task and one that has received surprisingly little attention until recently. Major challenge for the future.
Takes account of % data, ignores zero values, assumes unimodal responses, can handle several hundred species, and gives calibration functions of high precision (0.8ºC), low bias, and high robustness.
Xm = g(Y1, Y2, Y3, ... ... ..., Yp) Modern data WA regression
Xf = g(Yf1, Yf2, Yf3, ... ... ..., Yfp) Fossil data WA calibration
g is our calibration function for Xm and Ym
Simple, ecologically realistic, and robust
WA is robust to spatial autocorrelation, as are Gaussian logit regression and ML calibration. WA (with monotonic deshrinking) and GLR are, to me, the preferred methods
Lynts and Judd 1971 Science 171: 1143-1144
Late Pleistocene Paleotemperatures at Tongue of the Ocean, Bahamas
It too is 42 years old! Has 20 citations (cf. 652)
Major problem in all reconstructions are the effects of secondary variables, confounding variables, and non-causal environmental variables on resulting reconstructions.
Only recently beginning to receive attention – Juggins & Birks (2012) and Juggins (2013).
We must all give greater attention to what can and cannot be reconstructed and explicitly address the dangers of reconstructing surrogate variables (e.g. water depth) and confounding variables (e.g. climate and nutrients)
Cajo ter Braak
One cannot do calibration-function research without high quality data and these need skilled palaeoecologists. Many colleagues have contributed to the development of calibration functions by creating superb modern-environmental data sets
Only met Tage Nilsson once, in 1969, when we came to Lund to go to Blekinge with Björn and to Öland with Knix Königsson. The Lund lab then was very small with Tage Nilsson as Professor (1969-1971) and Björn Berglund and Gunnar Digerfeldt.
My next visit was in 1975. Great expansion with tree-ring lab, radiocarbon-dating lab, faunal research, and palaeomagnetism, as well as pollen and macrofossil analyses.
Tage Nilsson had laid the foundations for something great, namely the University of Lund Quaternary research centre. Proud to have been associated with Lund for over 40 years.