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

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

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

	Predictor	Description
QURO-1	T_Jul_Sep	Average temperature from July to September, previous growing season
	T_MAR	Average March temperature, current growing season
	T_APR	Average April temperature, current growing season
	T_MAY	Average May temperature, current growing season
	T_JUN	Average June temperature, current growing season
	P_JAN-MAR	Sum of precipitation from January to March, current growing season
QURO-2	T_Jul-Nov	Average temperature from July to November, previous growing season
	T_JAN	Average January temperature, current growing season
	T_APR	Average April temperature, current growing season
	T_MAY	Average May temperature, current growing season
	T_JUN	Average June temperature, current growing season

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_

	Month	QURO-1		QURO-2
		TEMP	PREC	TEMP	PREC
Previous growing season	Jul	0.45		0.53
	Aug	0.49		0.46
	Sep	0.37		0.38
	Oct			0.35
	Nov			0.37
	Dec
	Jul–Sep	0.57
	Jul–Nov			0.71
Current growing season	JAN		–0.41	0.44
	FEB
	MAR	0.38	–0.33
	APR	0.60		0.63
	MAY	0.32		0.47
	JUN	0.47		0.50
	JAN–MAR		–0.43

General description of the analysed sites_

Location / Site denotation	Year of sampling	Latitude	Longitude	Elevation (m)	Bedrock	Forest soil type	Meteorological station	Average age of measured tree
Mlace/ QURO-1	2012	N46°18′21′′	E15°30′35′′	280–315	Marl	Eutric brown soil	Maribor	150
Sorsko Plain / QURO-2	2015	N46°11′23′′	E14°25′26′′	360–365	Alluvial loams and clays	Dystric brown soil	Ljubljana	90

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 ± Std	Min – Max
Site	N	Chronology span	(μm2 104)	(μm2 104)	r̄	AC_1	AC_2	AC_3
QURO-1	6	2012–1961	6.259 ± 0.603	5.133–7.743	0.44	0.42	0.40	0.31
QURO-2	8	2015–1961	4.691 ± 0.395	4.072–5.756	0.32	0.61	0.52	0.46

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_

	MLR		ANN		MT		BMT			RF
	mean	std	mean	std	mean	std	mean	std	mean		std
(A) QURO-1
rtrain	0.797	0.037	0.815	0.043	0.789	0.059	0.810	0.030	0.898		0.018
rtest	0.694	0.103	0.726	0.095	0.633	0.134	0.692	0.112	0.689		0.097
RMSEtrain	0.356	0.027	0.343	0.042	0.359	0.047	0.360	0.025	0.302		0.022
RMSEtest	0.453	0.063	0.428	0.066	0.488	0.079	0.447	0.065	0.453		0.066
RRSEtrain	0.601	0.048	0.580	0.077	0.606	0.080	0.608	0.041	0.510		0.035
RRSEtest	0.786	0.134	0.741	0.123	0.845	0.148	0.771	0.106	0.778		0.083
dtrain	0.877	0.026	0.878	0.059	0.871	0.042	0.851	0.030	0.898		0.019
dtest	0.794	0.066	0.808	0.073	0.753	0.081	0.757	0.067	0.723		0.069
REtest	0.405	0.227	0.473	0.184	0.312	0.257	0.435	0.158	0.429		0.110
CEtest	0.364	0.237	0.436	0.202	0.265	0.273	0.394	0.174	0.387		0.132
DEtest	0.317	0.249	0.394	0.215	0.210	0.289	0.348	0.188	0.339		0.155
	rank	rank1	rank	rank1	rank	rank1	rank	rank1	rank		rank1
rtrain	3.92	0.00	2.67	0.02	4.16	0.03	2.95	0.00	1.05		0.95
rtest	2.91	0.11	1.85	0.50	3.93	0.06	2.93	0.15	3.12		0.20
RMSEtrain	3.45	0.00	2.33	0.05	3.93	0.07	3.90	0.00	1.13		0.88
RMSEtest	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22		0.21
RRSEtrain	3.45	0.00	2.33	0.05	3.93	0.07	3.90	0.00	1.13		0.88
RRSEtest	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22		0.21
dtrain	2.64	0.07	2.52	0.13	3.39	0.13	4.71	0.00	1.49		0.68
dtest	2.18	0.24	1.50	0.65	3.32	0.09	3.45	0.02	4.29		0.03
REtest	2.96	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22		0.21
CEtest	2.96	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22		0.21
DEtest	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22		0.21
Overalltrain	3.37	0.02	2.46	0.06	3.85	0.08	3.86	0.00	1.20		0.85
Overalltest	2.75	0.16	1.79	0.53	3.74	0.07	3.00	0.11	3.46		0.16
(B) QURO-2
rtrain	0.796	0.044	0.843	0.035	0.800	0.039	0.839	0.028	0.907		0.020
rtest	0.717	0.093	0.781	0.084	0.687	0.104	0.740	0.087	0.747		0.094
RMSEtrain	0.232	0.019	0.209	0.027	0.232	0.019	0.216	0.015	0.180		0.013
RMSEtest	0.293	0.041	0.257	0.042	0.297	0.040	0.278	0.040	0.274		0.043
RRSEtrain	0.601	0.058	0.541	0.080	0.602	0.052	0.560	0.044	0.465		0.044
RRSEtest	0.792	0.164	0.694	0.150	0.801	0.147	0.745	0.126	0.733		0.107
dtrain	0.874	0.032	0.899	0.059	0.866	0.030	0.883	0.024	0.921		0.018
dtest	0.793	0.057	0.839	0.077	0.765	0.068	0.789	0.052	0.782		0.058
REtest	0.410	0.253	0.546	0.202	0.401	0.234	0.483	0.189	0.503		0.142
CEtest	0.346	0.299	0.496	0.248	0.337	0.283	0.428	0.230	0.451		0.179
DEtest	0.297	0.356	0.457	0.295	0.286	0.359	0.384	0.300	0.409		0.236
	rank	rank1	rank	rank1	rank	rank1	rank	rank1	rank		rank1
rtrain	4.54	0.00	2.44	0.00	4.30	0.00	2.72	0.00	1.00		1.00
rtest	3.61	0.06	1.70	0.61	4.21	0.04	2.82	0.07	2.65		0.22
RMSEtrain	4.42	0.00	2.22	0.01	4.26	0.00	3.08	0.00	1.01		0.99
RMSEtest	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72		0.20
RRSEtrain	4.42	0.00	2.22	0.01	4.26	0.00	3.08	0.00	1.01		0.99
RRSEtest	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72		0.20
dtrain	4.05	0.00	1.99	0.11	4.34	0.00	3.49	0.00	1.13		0.89
dtest	3.09	0.03	1.30	0.85	4.02	0.03	3.15	0.04	3.44		0.05
REtest	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72		0.20
CEtest	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72		0.20
DEtest	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72		0.20
Overalltrain	4.36	0.00	2.22	0.03	4.29	0.00	3.09	0.00	1.04		0.97
Overalltest	3.53	0.04	1.62	0.68	4.08	0.03	2.88	0.08	2.88		0.17

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

	Variable	Coefficients	t value	p value
QURO-1	Intercept	0.496164	0.418	0.67767
	T_Jul–Sep	0.165491	2.617	0.01196
	T_MAR	0.042491	1.437	0.15744
	T_APR	0.159552	3.474	0.00113
	T_JUN	0.064903	1.422	0.16164
	P_JAN–MAR	–0.00598	–2.294	0.02639
	R2	Adj R2
	0.6304	0.5903
QURO-2	Intercept	1.08324	1.792	0.07914
	T_Jul–Nov	0.12812	2.570	0.01319
	T_JAN	0.03792	2.501	0.01569
	T_APR	0.08273	2.879	0.00586
	T_ JUN	0.04669	1.800	0.07782
	R2	Adj R2
	0.6241	0.5941