Predicting the vessel lumen area tree-ring parameter of Quercus robur with linear and nonlinear machine learning algorithms

Open access

Abstract

Climate-growth relationships in Quercus robur chronologies for vessel lumen area (VLA) from two oak stands (QURO-1 and QURO-2) showed a consistent temperature signal: VLA is highly correlated with mean April temperature and the temperature at the end of the previous growing season. QURO-1 showed significant negative correlations with winter sums of precipitation. Selected climate variables were used as predictors of VLA in a comparison of various linear and nonlinear machine learning methods: Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), Model Trees (MT), Bagging of Model Trees (BMT) and Random Forests of Regression Trees (RF). ANN outperformed all the other regression algorithms at both sites. Good performance also characterised RF and BMT, while MLR, and especially MT, displayed weaker performance. Based on our results, advanced machine learning algorithms should be seriously considered in future climate reconstructions.

1 Introduction

Long systematic instrumental records of climate data are rare and spatially limited (for a review see Jones and Bradley, 1992). Natural archives are therefore used to extract information about the climate in the past. Tree-rings are among the most commonly used proxy records, especially in temperate zones, where seasonal growth results in annually resolved tree-rings.

The standard methodology which is usually used to study the relationship between climate (e.g., temperature, precipitation, moisture, cloudiness etc.) and tree-ring proxies is to apply (multiple) linear regression (MLR; Cook and Kairiukstis, 1992). However, while linear transfer functions usually fit data well, there are some concerns about predictions for data points close to the edge of observed data and points out of the calibration data. Linear models assume that the dependency between tree-ring parameters and climate changes linearly from the most favourable to the most unfavourable conditions. This assumption is contradictory to the well-accepted concept of ecological amplitudes (Braak and Gremmen, 1987; Fritts, 1976), and trees can thus grow only in a limited range of growing conditions. The relationship between tree-ring parameters and environmental factors should, therefore, change when approaching the edges of ecological amplitudes.

There is growing evidence that nonlinear techniques are better at describing the relationship between tree-ring proxies and climate variables (Balybina, 2010; D'Odorico et al., 2000; Helama et al., 2009; Jevšenak and Levanič, 2016; Ni et al., 2002; Zhang et al., 2000). Sun et al. (2017) showed a significant improvement over linear regression by using linear spline regression and a likelihood-based model to explain nonlinearity in the relationship between tree rings and precipitation. One of the most accurate and tested process-based models, the Vaganov-Shaskin model (VS model, Shishov et al., 2016; Vaganov et al., 2011), uses a piecewise linear function to model the relationship between daily environmental data and tree-rings. A similar idea is implemented in a simplified version of the VS model – the VS-Lite model (Tolwinski-Ward et al., 2011). The advantages of using nonlinear models have also been demonstrated in other studies using tree-ring data, such as predicting resilience to disturbance (Billings et al., 2015), modelling tree growth response after partial cuttings (Montoro Girona et al., 2017) and predicting the response of tree growth to climate change (Williams et al., 2010).

In this article, we compare various regression methods. To this end, we used Vessel Lumen Area (VLA) tree-ring chronologies of pedunculate oak (Quercus robur L.) from two lowland sites in Slovenia. VLA is gaining importance in dendroclimatological studies, especially at mesic sites, where earlywood conduits often have a better climatic signal than traditional tree-ring width (Campelo et al., 2010; Fonti and Garcia-Gonzalez, 2008; Jevšenak and Levanič, 2015).

The formation of earlywood vessels usually starts at the end of March or early April (Goršić, 2013; Gričar, 2010), when the temperature or moisture threshold, i.e., the degree-day sum, is surpassed. This threshold is site-and species-specific. The period of most intense xylem cell production in oaks from nearby areas is April-May (Gričar, 2010), when the relationship between earlywood conduits and climate is more or less linear. Again, in the period from middle May-June onward, we expect saturation of the function that describes the relationship between earlywood vessels and climate. The two functions that could model such relationships more accurately (as compared to linear regression) are the sigmoid-shaped and piecewise linear functions. Both were applied in our study.

The goals of our study were 1) to analyse the relationship between VLA and climate, 2) to select predictors of VLA based on the results of the climate-growth relationship and 3) to apply those predictors to compare MLR and four different nonlinear modelling techniques (ANN, MT, BMT and RF).

2 Material and methods

Study objects and wood-anatomical analysis

The two VLA chronologies used in our study were sampled from two lowland forest sites in Slovenia (Fig. 1). The selected sites are dominated by Quercus robur, but differ in some site-specific conditions (see Table 1). The two sites have approximately equal temperature distributions, while the QURO-2 site (meteorological station Ljubljana, Fig. 1C), gets slightly more precipitation than the QURO-1 site (meteorological station Maribor; Fig. 1D). Climate data for both meteorological stations were provided by the Slovenian Environment Agency (ARSO, 2017).

Fig. 1
Fig. 1

A) Locations of the research sites (circles) and the meteorological stations (triangles), B) location of Slovenia in Europe and climagraphs of C) Ljubljana and D) Maribor. The lines of climagraphs represent mean monthly temperature and the blocks represent monthly amounts of precipitation.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Table 1

General description of the analysed sites.

Location / Site denotationYear of samplingLatitudeLongitudeElevation (m)BedrockForest soil typeMeteorological stationAverage age of measured tree
Mlace/ QURO-12012N46°18′21′′E15°30′35′′280–315MarlEutric brown soilMaribor150
Sorsko Plain / QURO-22015N46°11′23′′E14°25′26′′360–365Alluvial loams and claysDystric brown soilLjubljana90

From each site, 6–8 mature and dominant trees (see Table 2, Fig. 2) were sampled for wood-anatomical analysis with a 10-mm increment borer. One core per tree was taken at breast height of 1.30 m. The extracted wooden cores were air dried, radially oriented and fitted in wooden holders. They were then sanded to a high polish in a laboratory, as suggested by Fonti et al. (2010). The sanding process starts with coarse 80-grit and ends with fine 1000-grit sanding paper. After sanding, vessels were filled with chalk, and high-quality images were taken with the ATRICS system (Levanič, 2007). ATRICS is an automated image acquisition system based on a motorised stage and a high-resolution microscope camera, which captures images and stitches them into a single, long image of the entire core. The captured images were analysed using the ImageJ program (Schindelin et al., 2012), combined with macro EWVA (Fig. 3; Jevšenak and Levanič, 2014). First, the contrast between the vessels and the adjacent surface was enhanced, based on the selected black and white threshold. Each group of vessels was then recognised as a consecutive year and, finally, vessel lumens were measured. In each tree-ring, all vessel lumens were measured, and the parameter vessel lumen area (VLA) was subsequently calculated, considering only vessels with an area greater than 10,000 μm2. The same threshold was used by Fonti and Garcia-Gonzalez (2008). VLA chronologies were not detrended, since we did not observe any age-related trend (see Fig. 4).

Fig. 2
Fig. 2

Individual sample lengths. The shaded area represents the analysed period used for model comparison for QURO-1 and QURO-2.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Fig. 3
Fig. 3

An example of a workflow of earlywood vessel analysis with ImageJ and macro EWVA: A) original image, B) image converted to a black and white mask for segmentation of the original image, vessels below the threshold were excluded from the analysis, C) recognised groups of earlywood vessels belonging to different years overlaid over the original image and D) measured earlywood vessels.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Fig. 4
Fig. 4

Chronologies of vessel lumen area (VLA) for QURO-1 and QURO-2 with 95% confidence interval of the mean.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Table 2

Characteristics of site chronologies: number of samples (N), chronology span, mean and standard deviation (Std) of vessel areas, minimum and maximum range of vessel areas (Min – Max), rbar (r̄) and autocorrelation with lag 1, 2 and 3 (AC).

Mean ± StdMin – Max
SiteNChronology span(μm2 104)(μm2 104)AC_1AC_2AC_3
QURO-162012–19616.259 ± 0.6035.133–7.7430.440.420.400.31
QURO-282015–19614.691 ± 0.3954.072–5.7560.320.610.520.46

Nonlinear machine learning methods

The nonlinear methods used in our study belong to the field of machine learning. We used a single layer perceptron as an artificial neural network (ANN) (Bishop, 1995; Hastie et al., 2009), which we trained with the Bayesian regularization training algorithm (Burden and Winkler, 2008). The described ANN method is available in the brnn R package (Pérez-Rodríguez and Gianola, 2016; Pérez-Rodríguez et al., 2013) and usually fits a sigmoid-shaped transfer function.

Model trees (MT; Quinlan, 1992) are tree-structured models in which each terminal node in the tree contains a prediction in the form of a linear equation. A model tree is equivalent to a piecewise linear function and, when visualised, offers some interpretable features, such as the relative importance of predictors and the different linear equations used in the different terminal nodes.

In order to further improve the predictive capabilities of MT, bagged model trees (BMT) were used, which are derived by the ensemble method of bagging (Breiman, 1996). Bagging involves the construction of several bootstrap samples of data obtained through random sampling with a replacement, and learning an MT from each bootstrap sample. Combining the predictions of individual MTs in the ensemble prevents overfitting the data.

Random Forests (RF; Breiman, 2001; Ho, 1995) of regression trees is an ensemble method that applies a randomised regression tree construction algorithm to each of the bootstrap samples. In regression trees, the predictions in the terminal nodes are real value constants, rather than linear models. The randomised algorithm considers only a small number of randomly selected predictors at each step of tree construction. We used the MT, BMT and RF algorithms for learning from the RWeka R package (Hornik et al., 2009).

ANN, MT, BMT and RF are advanced algorithms used in the field of machine learning. These algorithms can also find linear relationships, in cases in which the dependency to be modelled is linear. We hypothesised that nonlinear techniques would provide better models,

which means more explained variance and lower error on validation data.

Modelling strategy and comparison of nonlinear methods for VLA prediction

Pearson correlation coefficients were used to analyse the climate-growth relationship between climate data and VLA chronologies to get a first impression of patterns in the climate signal. Secondly, based on the results of the climate-growth relationship, climate variables were selected to be used as predictors for VLA. MLR models were then fitted by using these predictors, and the statistical properties of these models were assessed. To fit MLR models, stepwise selection of predictors with backward elimination was used. In addition, model trees (MT) were fitted to explore the understandable rules for VLA predictions. Finally, the performance of linear and nonlinear machine learning regression methods was evaluated by 3-fold cross-validation (Witten et al., 2011), which is implemented in the compare_methods() function of the dendroTools R package (Jevšenak and Levanič, 2018).

In 3-fold cross-validation, the datasets were randomly split into 3 equal parts (folds) and models were systematically calibrated (learned) on 2 folds and validated on the remaining fold that had not been used for calibration (learning). To minimise coincidence due to specific train and test splits, cross-validation was repeated 100 times, and the mean and standard deviation of the performance metrics across all repeats of cross-validation were shown. To ensure objective comparison, the cross-validation splits were identical for all nonlinear and MLR models, which was achieved by using the set.seed() function in R (R Core Team, 2018).

In addition, for each individual cross-validation split, the different models were ranked in terms of the calculated performance metrics, with rank 1 representing the best performance. The ties.method argument from the rank() function in R was set to ‘min’. Both models with the same performance metrics values were therefore given the lowest rank. The sum of shares of rank 1 consequently does not necessarily equal 1. The mean ranks and shares of rank 1 for each method are reported in the Results section.

For each cross-validation split, MLR was fitted by a stepwise selection of predictors with backward elimination. For each individual MLR model, therefore, only statistically significant and non-correlated predictors were used. One of the major strengths of machine learning algorithms is that they can be run with a large set of predictors with no a priori assumptions regarding which predictors are most important, or the underlying nature of the relationship between the response and predictor variables. ML models were therefore trained using all available predictors.

In the preliminary experimentation phase, different parameter settings of the four nonlinear algorithms were explored. We optimised our methods by experimentation and with the caret R package (Kuhn et al., 2017). The train function from the caret R package sets up a grid of tuning parameter’s values for a number of regression routines, fits each model and calculates a resampling-based performance measure. The final models were tuned for each dataset separately and used to compare the performance of different regression algorithms. A list with tuned parameter values is presented in Supplementary Table S1.

The measures of performance used in our study were the correlation coefficient (r), the root mean squared error (RMSE; Willmott, 1981), the root relative squared error (RRSE; Witten et al., 2011), the index of agreement (d; Willmott, 1981), the reduction of error (RE; Fritts, 1976; Lorenz, 1956), the coefficient of efficiency (CE; Briffa et al., 1988) and the detrended efficiency (DE; Helama et al., 2018). Models with higher validation (testing) values of r, d, RE, CE and DE and lower values of RMSE and RRSE were considered to have better predictive capabilities. In addition, to address potential over- or under-prediction associated with a given approach, bias was calculated as the difference between observed and estimated mean response for the validation data. Bias is reported in the form of histograms for each method.

3 Results

Chronology characteristics and the climate-growth relationship

The two site chronologies had a common increasing trend in VLA in the last 2–3 decades (Fig. 4). Even though the trees considered differed in terms of age (Table 1, Fig. 2) and were sampled from sites with different site characteristics, the increasing trend in VLA was obvious and consistent for both sites. The values of VLA in the QURO-1 chronologies ranged from 5.133–7.743 μm2104, while VLA values for QURO-2 ranged from 4.072–5.756 μm2104. Higher coherence between individual VLA chronologies was observed for QURO-1 (r̄= 0.44),while QURO-2 had less coherent individual chronologies (r̄= 0.32). Autocorrelation was significant in both analysed chronologies. On average, the vessels with the largest area were those from the QURO-1 site (Table 2).

VLA chronologies were compared to mean monthly temperatures and monthly sums of precipitation (Table 3). The two sites showed a very similar temperature pattern – VLA was significantly correlated with mean spring temperatures and mean temperatures from the previous growing season. Analysing only individual months of the current growing season, April had the strongest correlation coefficient at both sites. For the previous growing season, QURO-1 was correlated with temperatures from July to September, while QURO-2 correlated with temperatures from July to November. Only QURO-2 had significant correlations between the sum of precipitation and the VLA chronologies. Winter precipitation showed negative correlations with VLA from QURO-2.

Table 3

Pearson correlation coefficients between vessel lumen area (VLA) and climate data: mean monthly temperatures (TEMP) and sum of monthly precipitation (PREC) for QURO-1 and QURO-2. Months with capital letters refer to the current growing season, while months with lowercase letters refer to the year of the previous growing season. Only correlation coefficients with p ≤ 0.01 are shown.

MonthQURO-1QURO-2
TEMPPRECTEMPPREC
Previous growing seasonJul0.450.53
Aug0.490.46
Sep0.370.38
Oct0.35
Nov0.37
Dec
Jul–Sep0.57
Jul–Nov0.71
Current growing seasonJAN–0.410.44
FEB
MAR0.38–0.33
APR0.600.63
MAY0.320.47
JUN0.470.50
JAN–MAR–0.43

Based on the correlation analysis, the predictors of VLA were selected for each site individually. All months with significant correlations from the previous growing season were averaged, so we obtained a single additional predictor representing the previous growing season temperatures. Precipitation values for the months from January to March were summed, so we obtained a single additional winter precipitation predictor for the QURO-1 site. All the monthly temperature variables from the current growing season with significant correlations were kept as individual predictors. The strongest linear relationship between VLA and monthly temperatures was observed for April, thus we expected to observe a more nonlinear relationship by adding temperature information for March and May. The final list of predictors for QURO-1 and QURO-2 is given in Table 4.

The predictors were fitted by the multiple regression method, using the stepwise selection of predictors (Table 5). None of the diagnostic plots of the linear regression models for the two sites showed any problematic patterns (see Fig. S1). As in the correlation analysis (Table 3), April temperatures were the most significant variables. Both models showed some similar patterns: 1) they excluded May temperatures as a significant predictor, 2) both models explained a similar amount of variance, 0.63 with QURO-1 and 0.62 with QURO-2 and 3) both models had a similar value for the coefficient for temperatures from the previous growing season.

For both sites, model trees (MT) were fitted to extract rules for predicting the VLA at each of the analysed sites (Fig. 5). For each instance (year), the values of its predictors determine which linear equation will be used to make the final prediction. For example, for QURO-1, if the mean April temperature (T_APR) is smaller than 9.97 °C, linear equation 1 (LM1) is used. Otherwise, the January-March sum of precipitation (P_JAN-MAR) is considered, with the threshold to select linear equation 2 (LM2) or 3 (LM3) set to 56.9 mm. This threshold indicates the point at which the relationship between VLA and the climate

Fig. 5
Fig. 5

Examples of the Model Tree (MT) for A) QURO-1 and B) QURO-2 sites.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Table 4

Description of predictors of the VLA for QURO-1 and QURO-2.

PredictorDescription
QURO-1T_Jul_SepAverage temperature from July to September, previous growing season
T_MARAverage March temperature, current growing season
T_APRAverage April temperature, current growing season
T_MAYAverage May temperature, current growing season
T_JUNAverage June temperature, current growing season
P_JAN-MARSum of precipitation from January to March, current growing season
QURO-2T_Jul-NovAverage temperature from July to November, previous growing season
T_JANAverage January temperature, current growing season
T_APRAverage April temperature, current growing season
T_MAYAverage May temperature, current growing season
T_JUNAverage June temperature, current growing season
Table 5

Multiple linear regression summary statistics for QURO-1 and QURO-2.

VariableCoefficientst valuep value
QURO-1Intercept0.4961640.4180.67767
T_Jul–Sep0.1654912.6170.01196
T_MAR0.0424911.4370.15744
T_APR0.1595523.4740.00113
T_JUN0.0649031.4220.16164
P_JAN–MAR–0.00598–2.2940.02639
R2Adj R2
0.63040.5903
QURO-2Intercept1.083241.7920.07914
T_Jul–Nov0.128122.5700.01319
T_JAN0.037922.5010.01569
T_APR0.082732.8790.00586
T_ JUN0.046691.8000.07782
R2Adj R2
0.62410.5941

variables changes. While for QURO-1, T_APR is the most important predictor, for QURO-2 temperatures from the previous growing season (T_Jul-Nov) are in the root of MT. If T_Jul-Nov is greater than 14.77°C, linear equation 3 (LM3) is used; otherwise T_APR is considered. Finally, if T_APR is greater than 10.55 mm, MT will use LM1; otherwise LM2 is applied to make the final prediction.

Comparison of different ML algorithms for VLA prediction

MLR, ANN, MT, BMT and RF were used to model the relationship between VLA and the selected climate predictors (Table 4). The models were primarily evaluated in terms of their performance metrics on validation data (Table 6), which can be considered to be objective indicators. For QURO-1, ANN provided the best performance in 53% of individual cross-validation splits. ANN showed superior results for all mean validation statistics. RF, MLR and BMT showed similar performance at QURO-1, while MT had the worst validation performance. The statistical bias for validation data (Fig. 6) is reflected in the results from Table 6. Bias, with the highest count of values at 0, is an indication of no systematic over- or under-estimation of VLA. Histograms with a peak at 0 were obtained for BMT, ANN and RF, while for MLR and MT, the peak at 0 was not so obvious.

Fig. 6
Fig. 6

Histograms of mean bias, calculated as the difference between observed and estimated mean responses for validation data.

Citation: Geochronometria 45, 1; 10.1515/geochr-2015-0097

Table 6

Comparison of the performance of five predictive modelling methods for A) QURO_1 and B) QURO_2 sites. Methods were evaluated by 3-fold cross-validation repeated 100 times. The five predictive modelling methods were Multiple Linear Regression (MLR), Artificial Neural Networks (ANN), Model Trees (MT), Bagging of Model Trees (BMT) and Random Forests of Regression Trees (RF). The performance measures were the correlation coefficient (r), root relative squared error (RRSE), root mean squared error (RMSE), index of agreement (d), reduction of error (RE), coefficient of efficiency (CE) and detrended efficiency (DE), calculated on the training (train) and testing (test) data of cross-validation splits. Across the 100 runs of cross-validation, we present the mean, standard deviations (Std), mean rank and share of rank 1 for each performance measure. The best values of each performance measure on the test set are highlighted in bold.

MLRANNMTBMTRF
meanstdmeanstdmeanstdmeanstdmeanstd
(A) QURO-1
rtrain0.7970.0370.8150.0430.7890.0590.8100.0300.8980.018
rtest0.6940.1030.7260.0950.6330.1340.6920.1120.6890.097
RMSEtrain0.3560.0270.3430.0420.3590.0470.3600.0250.3020.022
RMSEtest0.4530.0630.4280.0660.4880.0790.4470.0650.4530.066
RRSEtrain0.6010.0480.5800.0770.6060.0800.6080.0410.5100.035
RRSEtest0.7860.1340.7410.1230.8450.1480.7710.1060.7780.083
dtrain0.8770.0260.8780.0590.8710.0420.8510.0300.8980.019
dtest0.7940.0660.8080.0730.7530.0810.7570.0670.7230.069
REtest0.4050.2270.4730.1840.3120.2570.4350.1580.4290.110
CEtest0.3640.2370.4360.2020.2650.2730.3940.1740.3870.132
DEtest0.3170.2490.3940.2150.2100.2890.3480.1880.3390.155
rankrank1rankrank1rankrank1rankrank1rankrank1
rtrain3.920.002.670.024.160.032.950.001.050.95
rtest2.910.111.850.503.930.062.930.153.120.20
RMSEtrain3.450.002.330.053.930.073.900.001.130.88
RMSEtest2.950.141.890.493.860.062.820.123.220.21
RRSEtrain3.450.002.330.053.930.073.900.001.130.88
RRSEtest2.950.141.890.493.860.062.820.123.220.21
dtrain2.640.072.520.133.390.134.710.001.490.68
dtest2.180.241.500.653.320.093.450.024.290.03
REtest2.960.141.890.493.860.062.820.123.220.21
CEtest2.960.141.890.493.860.062.820.123.220.21
DEtest2.950.141.890.493.860.062.820.123.220.21
Overalltrain3.370.022.460.063.850.083.860.001.200.85
Overalltest2.750.161.790.533.740.073.000.113.460.16
(B) QURO-2
rtrain0.7960.0440.8430.0350.8000.0390.8390.0280.9070.020
rtest0.7170.0930.7810.0840.6870.1040.7400.0870.7470.094
RMSEtrain0.2320.0190.2090.0270.2320.0190.2160.0150.1800.013
RMSEtest0.2930.0410.2570.0420.2970.0400.2780.0400.2740.043
RRSEtrain0.6010.0580.5410.0800.6020.0520.5600.0440.4650.044
RRSEtest0.7920.1640.6940.1500.8010.1470.7450.1260.7330.107
dtrain0.8740.0320.8990.0590.8660.0300.8830.0240.9210.018
dtest0.7930.0570.8390.0770.7650.0680.7890.0520.7820.058
REtest0.4100.2530.5460.2020.4010.2340.4830.1890.5030.142
CEtest0.3460.2990.4960.2480.3370.2830.4280.2300.4510.179
DEtest0.2970.3560.4570.2950.2860.3590.3840.3000.4090.236
rankrank1rankrank1rankrank1rankrank1rankrank1
rtrain4.540.002.440.004.300.002.720.001.001.00
rtest3.610.061.700.614.210.042.820.072.650.22
RMSEtrain4.420.002.220.014.260.003.080.001.010.99
RMSEtest3.700.031.750.644.050.032.780.112.720.20
RRSEtrain4.420.002.220.014.260.003.080.001.010.99
RRSEtest3.700.031.750.644.050.032.780.112.720.20
dtrain4.050.001.990.114.340.003.490.001.130.89
dtest3.090.031.300.854.020.033.150.043.440.05
REtest3.700.031.750.644.050.032.780.112.720.20
CEtest3.700.031.750.644.050.032.780.112.720.20
DEtest3.700.031.750.644.050.032.780.112.720.20
Overalltrain4.360.002.220.034.290.003.090.001.040.97
Overalltest3.530.041.620.684.080.032.880.082.880.17

Similarly, as with QURO-1, ANN also had the best validation performance for QURO-2. The second-best performance was obtained by RF, followed by BMT. The worst validation results were recorded for MLR and MT, which performed the best only in 4% (MLR) and 3% (MT) of individual cross-validation splits (Table 6). Histograms of mean bias (Fig. 6) reflect the performance of models from Table 6. The histogram of mean bias for the ANN method shows the best performance, followed by RF and BMT, while the histograms of mean bias for MLR and MT display weaker performance. Based on the results from Table 6 and Fig. 6, the final selected models for both sites would be those learned by ANN.

4 Discussion

Climate signal in VLA

The main goal of our study was to compare various regression methods in the task of VLA prediction. To do so, we first analysed the climate signal of VLA chronologies to select predictors for different regression models. The correlation coefficients showed a similar pattern for both sites: the VLA tree-ring parameter was correlated with temperatures at the end of the previous growing season and temperatures at the time of earlywood formation. Many other studies have also reported positive correlations between mean temperatures and VLA (e.g., Fonti and Garcia-Gonzalez, 2008; Garcia-Gonzalez and Fonti, 2008; Matisons and Dauškane, 2009; Tumajer and Treml, 2016).

The April temperature signal is in accordance with xylogenetic studies from similar sites (e.g., Goršić, 2013; Gričar, 2010), which have reported an expansion of earlywood conduits in April. The spring temperature signal stored in vessel characteristics is related to the onset of cambial activity and the duration of the enlargement period before lignification of the vessel secondary wall

(Perez-de-Lis et al., 2016). Rising temperatures before bud break increase the expression of genes involved in polar auxin transport (Schrader et al., 2003), which induces radial growth. The onset of cambial activity starts approximately one month before bud swelling (Gonzalez-Gonzalez et al., 2013; Sass-Klaassen et al., 2011). Earlywood conduits are therefore mainly developed during the period with limited (or no) photosynthetic activity and trees use stored carbohydrates from the previous growing season, leading to the preservation of the temperature signal of the previous growing season in the vessel characteristics.

The correlation coefficients between the sum of monthly precipitation and VLA were negative and significant only for the QURO-1 site, but nevertheless lower than temperature correlations. Negative correlations between VLA and winter precipitation are usually attributed to the excess of water accumulated in the soil (e.g.; González-González et al., 2015). The QURO-1 site is in close proximity to small artificial lakes and water is, therefore, available throughout the year. Water saturation affects anatomical features, mainly the formation of smaller vessels (Ballesteros et al., 2010).

Temperature is, therefore, the most important limiting growth factor at both sites. However, many other studies have reported that earlywood vessel characteristics are mostly related to water availability (Copini et al., 2016; Garcia-Gonzalez and Eckstein, 2003; Garcia-Gonzalez and Fonti, 2008; Kames et al., 2016; St George and Nielsen, 2000). Based on literature published to date, there are no obvious site factors that would explain when VLA is more related to temperature and when to water availability.

Evaluation of various ML algorithms

To the best of our knowledge, our comparative study is the first in the dendroclimatological field to have used VLA tree-ring proxy and several climate predictors to compare different linear and nonlinear methods. In most previous comparative studies with tree-ring and climate data, ANN outperformed MLR (Balybina, 2010; D'Odorico et al., 2000; Jevšenak and Levanič, 2016; Zhang et al., 2000). We confirmed the high predictive abilities of ANN, which outperformed the other regression methods for both sites.

The high performance of nonlinear algorithms might be partially explained by the selection of predictors. By employing months with lower (linear) correlations, such as March and May, we allowed the nonlinear algorithms to use this information and explain the VLA more accurately. April had the strongest linear correlations with VLA at both sites, but temperatures in March and May probably cause nonlinear reactions in VLA. Advanced ML algorithms can use this information and model the relationship between climate and VLA more accurately. ML methods such as ANN should, therefore, become a more standard approach in dendroclimatology.

Despite the obvious outperformance of ANN over all the other regression methods used in our study, we recommend testing several different regression algorithms and selecting the optimal one for climate reconstruction. In a related study, Jevšenak et al. (2017) showed that different datasets favour different regression algorithms and that there is no single method that always outperforms the other regression methods. The methodological approach used in our study to compare different regression methods is implemented in the compare_methods() function from the dendroTools R package (Jevšenak and Levanič, 2018). This function could be used to find the optimal regression method for any dataset, prior to climate reconstruction.

The aggregate expression of the many interacting nonlinear, rate-limited processes within a tree is often effectively a linear response to local climate in its ring widths (Cook and Pederson, 2011). Linearity is, therefore, possible on a smaller part of the entire interval of climate-growth response but, when approaching the edge of this spectrum, the relationship between tree growth and climate is likely to become more or less nonlinear. In addition, in most climate reconstruction models, the reconstruction process estimates data points out of calibration data, i.e., in the spectrum of the climate-tree response, which is expected to react nonlinearly. This is an additional argument in favour of nonlinear methods being used in dendroclimatology, since their predictions are likely to be more accurate.

Our comparative study showed that nonlinear algorithms can provide better models. Machine learning algorithms have several advantages, especially when a number of predictors, with a broader spectrum of climate and tree response data, are considered. In pursuit of more accurate climate reconstructions, it seems reasonable to switch from linear to advanced nonlinear algorithms.

5 Conclusions

We analysed the relationship between climate and the VLA parameter and used the results to select predictors to train and compare linear and nonlinear models. The two sites showed very similar results. ANN showed superior results for all mean validation statistics. The second-best models were RF and BMT, followed by MLR and MT. The question of whether it is reasonable to substitute the current gold standard arises. The current gold standard in the field of dendrochronological studies is MLR, but there are alternatives that might provide better predictions. The high performance of ANN was confirmed in our comparative study, but there is no reason to believe that ANN will always outperform other regression methods. We, therefore, suggest implementing our comparison strategy as a standard preliminary process, before using a selected method. To do so, there is a compare_methods() function available in the dendroTools R package.

Acknowledgements

The work of JJ was supported by the Pahernik Foundation and the Slovenian Academy of Sciences and Arts. Many thanks to the Institute of Lowland Forestry and the Environment from Novi Sad, where JJ was hosted at the time of writing this paper. TL and JJ were assisted by the following programmes and projects supported by the Slovenian Research Agency: Program and Research Group “Forest biology, ecology and technology” P4-0107, basic research projects J4-5519 “Paleoclimate data enhances drought prediction in the W Balkan Region” and J4-8216 “Mortality of lowland oak forests - consequence of lowering underground water or climate change?” SD was supported by the Slovenian Research Agency (grants P2-103, J4-7362, L2-7509, and N2-0056), the European Commission (projects LANDMARK and HBP SGA2) and ARVALIS (project BIODIV).

Supplementary material

Supplementary material, containing additional Table S1 and Figure S1, is available online at https://dx.doi.org/10.1515/geochr-2015-0097.

References

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    • Crossref
    • Export Citation
  • Balybina AS 2010. Reconstructing the air temperature from dendrochronological data from the Preolkhon area using the neural network method. Geography and Natural Resources 31(1): 30−33 DOI 10.1016/j.gnr.2010.03.006.

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    • Crossref
    • Export Citation
  • Breiman L 1996. Bagging predictors. Machine Learning 24(2): 123−140 DOI 10.1023/A:1018054314350.

  • Breiman L 2001. Random forests. Machine Learning 45(1): 5−32 DOI 10.1023/A:1010933404324.

  • Briffa KR Jones PD Pilcher JR and Hughes MK 1988. Reconstructing summer temperatures in northern Fennoscandinavia back to A.D.1700 using tree ring data from Scots Pine. Arctic and Alpine Research 20: 385–394 DOI 10.2307/1551336.

    • Crossref
    • Export Citation
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    • Crossref
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  • Jevšenak J and Levanič T 2014. Macro EWVA - an effective tool for analysis of earlywood conduits of ring porous species. Acta silvae et ligni 104: 15−24 DOI 10.20315/ASetL.104.2.

  • Jevšenak J and Levanič T 2015. Dendrochronological and wood-anatomical features of differently vital pedunculate oak Quercus robur L.) stands and their response to climate. Topola 195/196: 85−96.

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  • Jevšenak J and Levanič T 2018. dendroTools: R package for studying linear and nonlinear responses between tree-rings and daily environmental data. Dendrochronologia 48: 32−39 DOI 10.1016/j.dendro.2018.01.005.

  • Jones PD and Bradley RS 1992. Climatic variations in the longest instrumental records. In: Jones PD RS Bradley eds. Climate Since A.D. 1500 Routledge London: 246−268.

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    • Crossref
    • Export Citation
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    • Export Citation
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If the inline PDF is not rendering correctly, you can download the PDF file here.

  • ARSO 2017. Archive – observed and measured meteorological data in Slovenia. WEB Site: http://meteo.arso.gov.si/met/sl/archive/. Accesed: 2017 August 8.

  • Ballesteros JA Stoffel M Bollschweiler M Bodoque JM and Díez-Herrero A 2010. Flash-flood impacts cause changes in wood anatomy of Alnus glutinosa Fraxinus angustifolia and Quercus pyrenaica. Tree Physiology 30(6): 773–781 DOI 10.1093/treephys/tpq031.

    • Crossref
    • Export Citation
  • Balybina AS 2010. Reconstructing the air temperature from dendrochronological data from the Preolkhon area using the neural network method. Geography and Natural Resources 31(1): 30−33 DOI 10.1016/j.gnr.2010.03.006.

  • Billings SA Glaser SM Boone AS and Stephen FM 2015. Nonlinear tree growth dynamics predict resilience to disturbance. Ecosphere 6(11): 1–13 DOI 10.1890/ES15-00176.1.

  • Bishop CM 1995. Neural Networks for Pattern Recognition Oxford University Press Inc.: 482 pp.

  • Braak CJFT and Gremmen NJM 1987. Ecological Amplitudes of Plant Species and the Internal Consistency of Ellenberg's Indicator Values for Moisture. Vegetatio 69(1/3): 79–87 DOI 10.1007/BF00038689.

    • Crossref
    • Export Citation
  • Breiman L 1996. Bagging predictors. Machine Learning 24(2): 123−140 DOI 10.1023/A:1018054314350.

  • Breiman L 2001. Random forests. Machine Learning 45(1): 5−32 DOI 10.1023/A:1010933404324.

  • Briffa KR Jones PD Pilcher JR and Hughes MK 1988. Reconstructing summer temperatures in northern Fennoscandinavia back to A.D.1700 using tree ring data from Scots Pine. Arctic and Alpine Research 20: 385–394 DOI 10.2307/1551336.

    • Crossref
    • Export Citation
  • Burden F and Winkler D 2008. Bayesian regularization of neural networks. In: Livingstone DJ ed. Artificial Neural Networks: Methods and Applications Humana Press Totowa NJ 458: 23−42.

  • Campelo F Nabais C Gutierrez E Freitas H and Garcia-Gonzalez I 2010. Vessel features of Quercus ilex L. growing under Mediterranean climate have a better climatic signal than tree-ring width. Trees-Structure and Function 24(3): 463–470 DOI 10.1007/s00468-010-0414-0.

  • Cook ER and Kairiukstis LA 1992. Methods of Dendrochronology : Applications in the Environmental Sciences Dordrecht Kluwer Academic Publishers: 394 pp.

  • Cook ER and Pederson N 2011. Uncertainty Emergence and Statistics in Dendrochronology. In: Hughes MK TW Swetnam HF Diaz eds. Dendroclimatology: Progress and Prospects Springer Netherlands Dordrecht: 77−112.

  • Copini P den Ouden J Robert EMR Tardif JC Loesberg WA Goudzwaard L and Sass-Klaassen U 2016. Flood-Ring Formation and Root Development in Response to Experimental Flooding of Young Quercus robur Trees. Frontiers in Plant Science 7: 775 DOI 10.3389/fpls.2016.00775.

  • D'Odorico P Revelli R and Ridolfi L 2000. On the use of neural networks for dendroclimatic reconstructions. Geophysical Research Letters 27(6): 791−794 DOI 10.1029/1999GL011049.

  • Fonti P and Garcia-Gonzalez I 2008. Earlywood vessel size of oak as a potential proxy for spring precipitation in mesic sites. Journal of Biogeography 35(12): 2249−2257 DOI 10.1111/j.1365-2699.2008.01961.x.

  • Fonti P von Arx G Garcia-Gonzalez I Eilmann B Sass-Klaassen U Gartner H and Eckstein D 2010. Studying global change through investigation of the plastic responses of xylem anatomy in tree rings. New Phytologist 185(1): 42–53 DOI 10.1111/j.1469-8137.2009.03030.x.

    • Crossref
    • Export Citation
  • Fritts HC 1976. Tree Rings and Climate London Academic Press: 567 pp.

  • Garcia-Gonzalez I and Eckstein D 2003. Climatic signal of earlywood vessels of oak on a maritime site. Tree Physiology 23(7): 497–504 DOI 10.1093/treephys/23.7.497.

    • Crossref
    • Export Citation
  • Garcia-Gonzalez I and Fonti P 2008. Ensuring a representative sample of earlywood vessels for dendroecological studies: an example from two ring-porous species. Trees-Structure and Function 22(2): 237–244 DOI 10.1007/s00468-007-0180-9.

    • Crossref
    • Export Citation
  • Gonzalez-Gonzalez BD Garcia-Gonzalez I and Vazquez-Ruiz RA 2013. Comparative cambial dynamics and phenology of Quercus robur L. and Q-pyrenaica Willd. in an Atlantic forest of the northwestern Iberian Peninsula. Trees-Structure and Function 27(6): 1571–1585 DOI 10.1007/s00468-013-0905-x.

  • González-González BD Vázquez-Ruiz RA and García-González I 2015. Effects of climate on earlywood vessel formation of Quercus robur and Q. pyrenaica at a site in the northwestern Iberian Peninsula. Canadian Journal of Forest Research 45(6): 698–709 DOI 10.1139/cjfr-2014-0436.

  • Goršić E 2013. Diameter increment dynamics of pedunculate oak (Quercus robur L.) in Croatia. Ph.D. dissertation University of Zagreb Zagreb: 154 pp.

  • Gričar J 2010. Xylem and phloem formation in sessile oak from Slovenia in 2007. Wood Research 55(4): 15−22.

  • Hastie T Tibshirani R and Friedman JH 2009. The Elements of Statistical Learning : Data Mining Inference and Prediction. New York Springer: 745 pp.

  • Helama S Makarenko NG Karimova LM Kruglun OA Timonen M Holopainen J Merilainen J and Eronen M 2009. Dendroclimatic transfer functions revisited: Little Ice Age and Medieval Warm Period summer temperatures reconstructed using artificial neural networks and linear algorithms. Annales Geophysicae 27(3): 1097−1111 DOI 10.5194/angeo-27-1097-2009.

  • Helama S Sohar K Läänelaid A Bijak S and Jaagus J 2018. Reconstruction of precipitation variability in Estonia since the eighteenth century inferred from oak and spruce tree rings. Climate Dynamics 50(11): 4083–4101 DOI 10.1007/s00382-017-3862-z.

    • Crossref
    • Export Citation
  • Ho TK 1995. Random decision forests In Proceedings of the Third International Conference on Document Analysis and Recognition. Montreal Canada: 278−282 pp.

  • Hornik K Buchta C and Zeileis A 2009. Open-source machine learning: R meets Weka. Computational Statistics 24(2): 225−232 DOI 10.1007/s00180-008-0119-7.

  • Jevšenak J Džeroski S and Levanič T 2017. On the use of machine learning methods to study the relationships between tree-ring characteristics and the environment. Acta silvae et ligni 114: 21−29 DOI 10.20315/ASetL.114.2.

  • Jevšenak J and Levanič T 2014. Macro EWVA - an effective tool for analysis of earlywood conduits of ring porous species. Acta silvae et ligni 104: 15−24 DOI 10.20315/ASetL.104.2.

  • Jevšenak J and Levanič T 2015. Dendrochronological and wood-anatomical features of differently vital pedunculate oak Quercus robur L.) stands and their response to climate. Topola 195/196: 85−96.

  • Jevšenak J and Levanič T 2016. Should artificial neural networks replace linear models in tree ring based climate reconstructions? Dendrochronologia 40: 102−109 DOI 10.1016/j.dendro.2016.08.002.

  • Jevšenak J and Levanič T 2018. dendroTools: R package for studying linear and nonlinear responses between tree-rings and daily environmental data. Dendrochronologia 48: 32−39 DOI 10.1016/j.dendro.2018.01.005.

  • Jones PD and Bradley RS 1992. Climatic variations in the longest instrumental records. In: Jones PD RS Bradley eds. Climate Since A.D. 1500 Routledge London: 246−268.

  • Kames S Tardif JC and Bergeron Y 2016. Continuous earlywood vessels chronologies in floodplain ring-porous species can improve dendrohydrological reconstructions of spring high flows and flood levels. Journal of Hydrology 534: 377–389 DOI 10.1016/j.jhydrol.2016.01.002.

    • Crossref
    • Export Citation
  • Kuhn M Wing J Weston S Williams A Keefer C Engelhardt A Cooper T Mayer Z Kenkel B Benesty M Lescarbeau R Ziem A Scrucca L Tang Y Candan C Hunt T and the R Core Team 2017. caret: Classification and Regression Training. R package version 6.0-76 WEB Site: https://CRAN.R-project.org/package=caret. Accesed: 2017 August 10.

  • Levanič T 2007. ATRICS - A new system for image acquisition in dendrochronology. Tree-Ring Research 63(2): 117−122 DOI 10.3959/1536-1098-63.2.117.

  • Lorenz EN 1956. Empirical Orthogonal Functions and Statistical Weather Prediction Massachusetts Massachusetts Institute of Technology Department of Meteorology: 49 pp.

  • Matisons R and Dauškane I 2009. Influence of climate on earlywood vessel formation of Quercus robur at its northern distribution range in central regions of Latvia. Acta Universitatis Latviensis 753: 49–58.

  • Montoro Girona M Rossi S Lussier J-M Walsh D and Morin H 2017. Understanding tree growth responses after partial cuttings: A new approach. PLoS ONE 12(2): e0172653 DOI 10.1371/journal.pone.0172653.

    • Crossref
    • Export Citation
  • Ni FB Cavazos T Hughes MK Comrie AC and Funkhouser G 2002. Cool-season precipitation in the southwestern USA since AD 1000: Comparison of linear and nonlinear techniques for reconstruction. International Journal of Climatology 22(13): 1645−1662 DOI 10.1002/joc.804.

  • Perez-de-Lis G Rossi S Vazquez-Ruiz RA Rozas V and Garcia-Gonzalez I 2016. Do changes in spring phenology affect earlywood vessels? Perspective from the xylogenesis monitoring of two sympatric ring-porous oaks. New Phytologist 209(2): 521–530 DOI 10.1111/nph.13610.

    • Crossref
    • Export Citation
  • Pérez-Rodríguez P and Gianola D 2016. Brnn: Brnn (Bayesian Regularization forFeed-forward Neural Networks). R package version 0.6 WEB Site: http://CRAN.R-project.org/package=brnn. Accesed: 2017 April 20.

  • Pérez-Rodríguez P Gianola D Weigel KA Rosa GJM and Crossa J 2013. Technical Note: An R package for fitting Bayesian regularized neural networks with applications in animal breeding. Journal of Animal Science 91(8): 3522–3531 DOI 10.2527/jas.2012-6162.

    • Crossref
    • Export Citation
  • Quinlan JR 1992. Learning with continuous classes In Proceedings of the 5th Australian Joint Conference on Artificial Intelligence (AI '92). Hobart: 343−348 pp.

  • R Core Team 2018. R: A language and environment for statistical computing. R Foundation for Statistical Computing WEB Site: http://www.R-project.org/. Accesed: 2017 November 15.

  • Sass-Klaassen U Sabajo CR and den Ouden J 2011. Vessel formation in relation to leaf phenology in pedunculate oak and European ash. Dendrochronologia 29(3): 171–175 DOI 10.1016/j.dendro.2011.01.002.

    • Crossref
    • Export Citation
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IMPACT FACTOR 2018: 0.865
5-year IMPACT FACTOR: 1.623

CiteScore 2018: 1.12

SCImago Journal Rank (SJR) 2018: 0.584
Source Normalized Impact per Paper (SNIP) 2018: 0.514

Figures
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    A) Locations of the research sites (circles) and the meteorological stations (triangles), B) location of Slovenia in Europe and climagraphs of C) Ljubljana and D) Maribor. The lines of climagraphs represent mean monthly temperature and the blocks represent monthly amounts of precipitation.

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    Individual sample lengths. The shaded area represents the analysed period used for model comparison for QURO-1 and QURO-2.

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    An example of a workflow of earlywood vessel analysis with ImageJ and macro EWVA: A) original image, B) image converted to a black and white mask for segmentation of the original image, vessels below the threshold were excluded from the analysis, C) recognised groups of earlywood vessels belonging to different years overlaid over the original image and D) measured earlywood vessels.

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    Chronologies of vessel lumen area (VLA) for QURO-1 and QURO-2 with 95% confidence interval of the mean.

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    Examples of the Model Tree (MT) for A) QURO-1 and B) QURO-2 sites.

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    Histograms of mean bias, calculated as the difference between observed and estimated mean responses for validation data.

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