MD dating: molecular decay (MD) in pinewood as a dating method

Dating of wood is a major task in historical research, archaeology and paleoclimatology. Currently, the most important dating techniques are dendrochronology and radiocarbon dating. Our approach is based on molecular decay over time under specific preservation conditions. In the models presented here, construction wood, cold soft waterlogged wood and wood from living trees are combined. Under these conditions, molecular decay as a usable clock for dating purposes takes place with comparable speed. Preservation conditions apart from those presented here are not covered by the model and cannot currently be dated with this method. For example, samples preserved in a clay matrix seem not to fit into the model. Other restrictions are discussed in the paper. One model presented covers 7,500 years with a root mean square error (RMSE) of 682 years for a single measurement. Another model reduced to the time period of the last 800 years results in a RMSE of 92 years. As multiple measurements can be performed on a single object, the total error for the whole object will be even lower.

Scientific RepoRtS | (2020) 10:11255 | https://doi.org/10.1038/s41598-020-68194-w www.nature.com/scientificreports/ The use of Scots pine and therefore its historical and current relevance is documented by the huge number of buildings constructed more or less out of pine wood 6,[27][28][29] . The production of tar out of birch and pine has been documented since Viking times 30 . The Sami people in northern Fennoscandia also used the inner bark as a comestible good without killing the trees 31,32 . In Alpine regions conifer needles (including from Scots pine, but predominantly from spruce) were also used for animal feed or litter in stables 33 .
The objective of this present work was the creation of a dating tool for Scots pine (Pinus sylvestris L.) wood covering the broad range of growth from Middle Europe to Scandinavia and including probably the oldest samples available with an age of about 14,000 years in Middle Europe and 7,500 years in northern Scandinavia. We hypothesize to find a useful model based on the molecular decay measured by means of infrared spectroscopy and evaluated by means of random forests.

MD-model with all samples.
A prediction model based on several sample sets of Scots pine wood has been built-up. Infrared spectra were measured and modelled with the dendrochronological reference. The maximal set contained 2,242 measurements on 232 wooden pieces. Sample sets and methods are given in the method section and supplementary material, respectively.
The molecular decay (MD)-model containing all samples revealed a similar effect as observed with the spruce model with samples from the salt environment 17 . Data are predicted with a systematic bias (Fig. 1). Waterlogged samples with an age of more than 3,000 BC are predicted above the line of perfect fit and thereby underestimated agewise. Samples around the BC/AD boundary are overestimated. This bending can be considered by a calibration step. However, as the Swiss samples from clay preservation conditions do not fit into this bending behavior they cannot be treated in a common model. We have to assume that clay preservation conditions lead to somehow different rates of molecular decay. Very specific sharp bands of clay minerals in the region between 3,700 and 3,500 cm −1 were missing in the spectra 34 . Therefore, we can be sure that no clay minerals entered pores or resin canals leading to spectral distortion. Moreover, apart from different preservation conditions the Swiss samples are also much older. Therefore, the comparison of the preservation conditions cannot be discussed conclusively. Further investigations and sample sets will have to be assessed for that purpose. For now the Swiss samples buried in clay deposits were taken out of the model and the modeling was repeated.
MD-model without Swiss samples preserved in a clay matrix. The resulting model was additionally subjected to a further calibration step according to Tintner et al. 17 . The modeling procedure used for this step is exactly the same as in the previous publication that presented models for different wood species. Furthermore, the time range is considerably extended, the spatial coverage of the samples included is far broader, and the depositional settings are more comprehensive (Fig. 2). The model quality is represented by the root mean square  Table 1 indicates the 30 most important wavenumbers arranged according to the four spectral regions included in the models. The wavenumbers of the spectrum reflect certain energy levels; its corresponding band height delivers information about specific molecular groups stimulated by that specific energy level. The first spectral region (2,970-2,800 cm −1 ) can be assigned to methyl and methylene groups; the second one (1,771-1,690 cm −1 ) is dominated by acetyl groups of hemicelluloses 35 . The third one (1,690-1,610 cm −1 ) can be assigned to resin acids 36 . The impact on this spectral region is relatively stronger than on the first spectral region. The last one (1,271-800 cm −1 ) contains different molecular compounds. Especially this last region contains lots of overlapping molecular vibrations from various chemical signals. In comparison to the four models presented in Tintner et al. 17 the different pine models are more comparable to the larch model (Larix decidua) than to the models of silver fir, spruce or oak. This result can be expected based on the wood chemistry of the species. Interestingly, the relevance of the resin band region decreases from the shortest time span (800 years) to the longest (approx. 13,500 years). The result could be interpreted as meaning that molecular changes and probably also the gradual disappearance of resin occur predominantly in the first centuries. At least for waterlogged samples from the Arctic zone, the depletion of resin was recognized even macroscopically. The Swiss samples in particular have better resin preservation, a fact that might stress the difference in preservation conditions in a clay matrix. In any case, the prediction of age is not affected by the systematic change of a single component. As resin compounds get more and more depleted, other wood chemical compounds become more relevant for the overall prediction. example procedure of model usage. In order to demonstrate the model usage for the prediction of a sample, two test sets of eight randomly selected samples each were sequently excluded from the data set and the model was built up again. Based on the recorded spectral features of the test set samples, their age was predicted Year (measured by dendrochronology) Year ( Table 2.
Most of the samples are predicted well, but also some wrong predictions far apart from the reference were recorded. Future work will have to identify the reasons, why these samples do not fit properly in the model.

Discussion
The models presented here provide a strong evidence that molecular decay can be used in a meaningful way to predict the age of Scots pine wood. They develop further what has been started by the publication of Tintner et al. 17 . In comparison to previous models, they provide several advanced insights into the applicability and usage of dating via MD. On the one hand we present a new species and in doing so we have selected a species widely found in the archaeological and historic context. Its preservation is proven to be good. Especially in the Arctic zone Pinus sylvestris is the only species, whose wood remains over time 37 . The impact of different climatic regions, or specific preservation conditions on the chemical decay and the resulting age determination provide a wide range of applications in different scientific fields-historical research, archaeology, and climatology. With a prediction quality of some one hundred years, MD-dating will be relevant in cases in which plenty of material is available and dendrochronology fails for any reason (for example low number of tree rings). The combination of both methods might also help to include also weak results obtained by dendrochronology into a sample set.
Results in Figs. 1 and 2 also display that within-sample variation cannot be described well by the molecular decay. Other effects randomly influence the estimated age, so vertically stacked data points can be seen in the figures. It has been proven that for young samples aging on the living tree and in wooden artefacts corresponds better (Fig. 3), but further investigations will have to separate effects of within-sample variation from aging effects driven by the preservation conditions. For practical purposes the problem is less critical: The use of MD-dating is basically based on analyzing a sample on a series of rings and takes the average as the age estimation.   17 . Brittle parts and a half centimeter range next the outer face of the wood in construction wood cannot be used. A limited set of preservation conditions is covered by our model, namely: dry conditions of construction wood, dry conditions in open areas in a cold climate, waterlogged wood in cold soft water with a neutral pH value. Other preservation conditions have to be investigated in the future. Preservation in clay seems to affect the molecular decay changing the clock we use for our dating model. This might be explained by ion exchange effects that are in principal well known for wood [38][39][40] . Tintner et al. 17 presented a different behavior of molecular decay preserved in a salty clay environment in Hallstatt, Upper Austria. We assume that corresponding effects are responsible. In order to answer that question more samples preserved in a clay matrix with ages comparable to our other samples will be necessary. Preservation conditions at the sampling sites. The Finnish samples comprise living tree and subfossil tree-ring materials originating from seven sites (lakes) in north-east Finnish Lapland from the counties of Utsjoki (Ailigasjärvi, Lohikoste, Vetsijärvi) and Inari (Juomusjärvi, Kompsiojärvi, Luolajärvi, Selkäjärvi). These sites were previously described in Eronen et al. 37,41 and Helama et al. 42,43 . According to available data the pH of the lake water was near to neutral.

Methods
The  46 . The pH of both lakes might be affected by calcareous bedrock.
The Swiss subfossil samples originated from the north-eastern flank of Uetliberg in Zurich, Switzerland. Covered in an up to eight-meter-deep homogenous clay package, the excavated in situ stumps have been well preserved under undisturbed, anaerobic conditions. They were covered by clay and were found at a depth of eight meters 47 . After discovery the samples were dried, leading to increased cell decomposition especially within the outer sapwood.
The Austrian construction wood originated from six different sites (castles and churches) in the two regions Waldviertel and Weinviertel of the Austrian state of Lower Austria. The recent samples originated from two different sites, one in each of these regions [48][49][50] .
The Polish samples originated from seven churches situated along an N-S transect through Poland from the Baltic Sea to the southern border with the Czech Republic and Austria. Another analyzed object was a wooden water pipe discovered and lifted at archaeological excavations in Pleszew (central Poland). Living trees originated from two research sites-forests Włocławek and Ojców National Park. Table 2. Results of two test sets for validation; each line represents one sample; "observed" refers to the dendrochronological reference of the last tree ring measured by means of FTIR; "predicted mean" and "standard deviation" comprise the predictions of each measurement per sample.  [50][51][52] . The Finnish samples were dendrochronologically cross-dated against the existing Scots pine tree-ring chronologies from the same region 4,37,42,43,53 . The Polish samples were cross-dated against the existing Scots pine chronologies from the same region 54,55 . The Swiss samples were selected from a floating Zurich Late Glacial ring width chronology, containing more than 300 trees, which have been dated through radiocarbon measurements. The Austrian samples were cross-dated against the regional pine-chronologies (Waldviertel and Weinviertel).
Fourier Transform Infrared (FTIR) spectroscopy. FTIR spectra were recorded in the ATR (attenuated total reflection) mode in the mid infrared area (4,000-400 cm −1 ) with an optical crystal of a BRUKER Helios FTIR micro sampler (Tensor 27). This device allows spot measurements with a spatial resolution of 250 microm. 32 scans were collected at a spectral resolution of 4 cm −1 . Spectra were vector normalized using the OPUS (version 7.2) software. Smoothing and second derivative spectra were obtained using The Unscrambler X 10.1 (CAMO) by applying the Savitzky-Golay algorithm 56 . Only the smoothed second derivative spectra were further processed.
Statistical methods. The model was established in the same way as the models presented in Tintner et al. 17 . The same band regions of the model for larch (Larix decidua) were used: 2,970-2,800 cm −1 , 1,771-1,690 cm −1 , 1,690-1,610 cm −1 , 1,270-800 cm −1 . Additionally the band from 880 to 865 cm −1 has been kept out of analyses. This band is assigned to calcite 57 originating from remnants of chalk that was used to make tree rings more visible. All statistical analysis was done using the statistical computer software language R 58 . The R package randomForest 59 was used to fit a random forest model to the data. Models were tenfold cross-validated.

Data availability
All code and result data in this study to perform the analyses and to create the figures can be made available upon request to the corresponding author. Original data are provided as supplementary material.