This script comprise the analysis of the paper entitled : No winter halt in belowground wood growth of four angisperm deciduous tree species

Lorène J. Marchand, Jožica Gričar, Paolo Zuccarini, Inge Dox, Bertold Mariën, Melanie Verlinden, Thilo Heinecke, Peter Prislan, Guillaume Marie, Holger Lange, Jan Van den Bulcke, Josep Penuelas, Patrick Fonti, Matteo Campioli

The analysis comprise (i) wood growth dataset, (ii) leaf phenology dataset (iii) climate dataset and (iv) fine root dataset

  1. Wood growth dataset contain all the measurements of xylogenesis of stem and roots for
  • Mature beech in 2018 (Belgium)
  • Mature beech and birch in 2020 (Belgium)
  • Sapling beech, birch, oak and poplar in 2017 (Belgium)
  • Sapling beech and birch in 2018 (Belgium)
  • Sapling beech and birch in 2018 (Spain)
  • Sapling beech and birch in 2018 (Norway)

The length of the layer of cell in enlargement is defined as “EC” , the length of the layer of cell in secondary cell wall of thickening is defined as “TH”, the total ring length is defined as “ring”

DOY_cumul reefers to cumulative DOY starting from the first year of measurement and continuing the following year.

  1. Phenology dataset contains the spring leaf, autumn leaf and fine root phenology observation for
  • Mature beech in 2018 (Belgium)
  • Mature beech and birch in 2020 (Belgium)
  • Sapling beech, birch, oak and poplar in 2017 (Belgium)
  • Sapling beech and birch in 2018 (Belgium)
  • Sapling beech and birch in 2018 (Spain)
  • Sapling beech and birch in 2018 (Norway)

file senescence_dataset.csv The autumn phenology variable “Senescence” is calculated with the formulate in Vitasse, Y., Porté, A. J., Kremer, A., Michalet, R. & Delzon, S. Responses of canopy duration to temperature changes in four temperate tree species: relative contributions of spring and autumn leaf phenology. Oecologia 161, 187–198 (2009).

file Bud_leaf_dev.csv The spring phenology variable “Bud_Leaf_dev” is calculated with the methods in Marchand, L. J. et al. Inter-individual variability in spring phenology of temperate deciduous trees depends on species, tree size and previous year autumn phenology. Agric. For. Meteorol. 290, 108031 (2020) and in Zuccarini, P. et al. Drivers and dynamics of foliar senescence in temperate deciduous forest trees at their southern limit of distribution in Europe. Agric. For. Meteorol. 342, 109716 (2023).

file fine_root.csv the fine root phenology from the file fine root dataset cumulative fine root surface is calculated form the formula in Mariën, B. et al. On the Below- and Aboveground Phenology in Deciduous Trees: Observing the Fine-Root Lifespan, Turnover Rate, and Phenology of Fagus sylvatica L., Quercus robur L., and Betula pendula Roth for Two Growing Seasons. Forests 12, 1680 (2021).

  1. Climate dataset contains in the file climate_soil_2017.csv the estimation of the soil temperature based on the sensor of another potted experiment with similar soil composition at the same site. Publiched in the following paper: https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15501. the file climate_2020.csv and climate_2018.csv contain soil and air temperature of the site of Brasschaat

Packages used

library(dplyr)
library(tidyr)
library(kableExtra)
library(mgcv)
library(ggeffects)
library(ggplot2)
library(patchwork)
library(cowplot)
library(rpart)
library(rpart.plot)

Xylogenesis dataset

xylogenesis<-read.table("xylogenesis.csv", header=T, sep=";", dec=",", na.strings = "NA")
xylogenesis$country<-as.factor(xylogenesis$country)
xylogenesis$species<-as.factor(xylogenesis$species)
xylogenesis$site<-as.factor(xylogenesis$site)
xylogenesis$plot<-as.factor(xylogenesis$plot)
xylogenesis$tree<-as.factor(xylogenesis$tree)
xylogenesis$organ<-as.factor(xylogenesis$organ)
xylogenesis$number<-as.factor(xylogenesis$number)
xylogenesis$date<-as.POSIXct(xylogenesis$date)
xylogenesis$DOY<-as.integer(xylogenesis$DOY)
xylogenesis$DOY_cumul<-as.integer(xylogenesis$DOY_cumul)
xylogenesis$exp<-as.factor(xylogenesis$exp)
xylogenesis$age<-as.factor(xylogenesis$age)
xylogenesis$lenght_EC<-as.numeric(xylogenesis$lenght_EC)
xylogenesis$lenght_TH<-as.numeric(xylogenesis$lenght_TH)
xylogenesis$lenght_ring<-as.numeric(xylogenesis$lenght_ring)
xylogenesis$code<-as.factor(xylogenesis$code)

Roots

we define the mean value per samples (4 measures) and create separate dataframe for each experiment

roots<-subset(xylogenesis, organ=="roots")

roots2 <- roots %>% 
  group_by(code) %>%
  dplyr::summarise(sample_size = n(), percent_TH = mean(((lenght_TH)/lenght_ring)*100), percent_EC = mean(((lenght_EC)/lenght_ring))*100)

roots2<-separate(roots2, "code" ,  sep ="_", into=c("country","species","plot","tree","type","number","DOY_cumul"))

roots2$country<-as.factor(roots2$country)
roots2$species<-as.factor(roots2$species)
roots2$type<-as.factor(roots2$type)
roots2$DOY_cumul<-as.numeric(roots2$DOY_cumul)
roots2<-na.omit(roots2)
Root mature trees 2020
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula Military 2TC mature R1 232 4 4.018462 0.0000000
belgium Betula Military 2TC mature R1 246 4 1.472419 0.5153011
belgium Betula Military 2TC mature R1 260 4 9.743938 2.2904586
Root mature trees 2020
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Fagus Military 3MC mature R1 262 4 31.228717 10.045770
belgium Fagus Military 3MC mature R1 290 4 2.829133 1.057967
belgium Fagus Military 3MC mature R1 318 4 34.776442 0.000000
Root sapling 2017
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula 22 1 sapling R 292 4 3.459622 3.21722
belgium Betula 22 10 sapling R 314 4 4.012202 0.00000
belgium Betula 22 11 sapling R 279 4 1.101721 0.00000
Root sapling 2018 Belgium
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula 22 1 sapling R1 242 4 65.77996 0
belgium Betula 22 1 sapling R2 242 4 32.55413 0
belgium Betula 22 1 sapling R3 242 4 16.73598 0
Root sapling 2018 Spain
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
spain Betula A 1 sapling R1 255 4 13.76957 1.937926
spain Betula A 1 sapling R2 255 4 29.42329 8.844372
spain Betula A 1 sapling R3 255 4 33.56331 7.463675
Root sapling 2018 Norway
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
norway Betula B 10 sapling R1 273 4 6.174648 0.000000
norway Betula B 10 sapling R2 273 4 12.001504 0.000000
norway Betula B 10 sapling R3 273 4 25.624627 6.199426

Stems

we define the mean value per samples (3 measures) and create separate dataframe for each experiment

stem<-subset(xylogenesis, organ=="stem")

stem2 <- stem %>% 
  group_by(code) %>%
  dplyr::summarise(sample_size = n(),  percent_TH = mean(((lenght_TH)/lenght_ring)*100), percent_EC = mean(((lenght_EC)/lenght_ring))*100)

stem2<-separate(stem2, "code" ,  sep ="_", into=c("country","species","plot","tree","type","number","DOY_cumul"))

stem2$country<-as.factor(stem2$country)
stem2$species<-as.factor(stem2$species)
stem2$type<-as.factor(stem2$type)
stem2$DOY_cumul<-as.numeric(stem2$DOY_cumul)
stem2$number<-as.factor(stem2$number)
stem2<-na.omit(stem2)
Stem mature trees 2021 spring
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula Military 1XR mature S 470 3 0 100.00376
belgium Betula Military 1XR mature S 477 3 0 99.99846
belgium Betula Military 1XR mature S 484 3 0 99.99808
Stem mature trees 2020
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula Military 1XR mature S 217 3 0.2053874 0
belgium Betula Military 1XR mature S 225 3 0.3863606 0
belgium Betula Military 1XR mature S 232 3 0.2712426 0
Stem mature trees 2019 spring
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Fagus Military 3TC mature S 464 3 0 99.99976
belgium Fagus Military 3TC mature S 471 3 0 100.00188
belgium Fagus Military 3TC mature S 478 3 0 99.99826
Stem mature trees 2018
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Fagus Military 1MC mature S 233 3 0.2643709 0
belgium Fagus Military 1MC mature S 241 3 0.0000000 0
belgium Fagus Military 1MC mature S 248 3 0.2627119 0
Stem sapling 2017
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula 22 1 sapling S 292 3 0 0
belgium Betula 22 10 sapling S 314 3 0 0
belgium Betula 22 11 sapling S 279 3 0 0
Stem sapling 2018 Belgium
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
belgium Betula 22 1 sapling S1 242 3 95.36317 0
belgium Betula 22 12 sapling S1 299 3 0.00000 0
belgium Betula 22 14 sapling S1 299 3 0.00000 0
Stem sapling 2018 Spain
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
spain Betula A 10 sapling S1 313 3 0.000000 0.000000
spain Betula A 11 sapling S1 313 3 0.000000 0.000000
spain Betula A 12 sapling S1 235 3 6.770708 3.724248
Stem sapling 2018 Norway
country species plot tree type number DOY_cumul sample_size percent_TH percent_EC
norway Betula B 10 sapling S1 273 3 0.000000 0.000000
norway Betula B 12 sapling S1 290 3 0.000000 0.000000
norway Betula B 2 sapling S1 232 3 4.879942 1.514059

Temperature vs thickening

Temp_TH<-read.table("Temp_TH.csv", header=T, sep=";", dec=",", na.strings = "NA")
We create separate dataframe for each experiment
Temperature vs. ring thickening mature trees 2020
exp species organ DOY_cumul mean_persent_TH X10days_temp
21 exp_mat_2020_ Betula roots 232 7.530405 18.75
22 exp_mat_2020_ Betula roots 246 6.134205 16.54
23 exp_mat_2020_ Betula roots 260 10.891115 15.40
Temperature vs. ring thickening mature trees 2018
exp species organ DOY_cumul mean_persent_TH X10days_temp
21 exp_mat_2020_ Betula roots 232 7.530405 18.75
22 exp_mat_2020_ Betula roots 246 6.134205 16.54
23 exp_mat_2020_ Betula roots 260 10.891115 15.40
Temperature vs. ring thickening sapling 2017
exp species organ DOY_cumul mean_persent_TH X10days_temp
73 exp_young_bel_2017 Betula roots 257 17.70006 NA
74 exp_young_bel_2017 Betula roots 265 15.58598 NA
75 exp_young_bel_2017 Betula roots 272 11.13787 14.17
Temperature vs. ring thickening sapling 2018 belgium
exp species organ DOY_cumul mean_persent_TH X10days_temp
73 exp_young_bel_2017 Betula roots 257 17.70006 NA
74 exp_young_bel_2017 Betula roots 265 15.58598 NA
75 exp_young_bel_2017 Betula roots 272 11.13787 14.17

Phenology

Senescence

senescence<-read.table("senescence_dataset.csv", header=T, sep=";", dec=",", na.strings = "NA")
We create separate dataframe for each experiment
Senescence mature trees 2020
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
9034 belgium 2020 TC Betula mature NA 2 232 0 0 0
9035 belgium 2020 TC Betula mature NA 2 239 0 0 0
9036 belgium 2020 TC Betula mature NA 2 246 2 3 5
Senescence mature trees 2020
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
8746 belgium 2018 TC Fagus mature NA 1 191 35 0 35
8747 belgium 2018 MC Fagus mature NA 1 191 15 0 15
8748 belgium 2018 TC Fagus mature NA 2 191 30 0 30
Senescence sapling 2017
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
belgium 2017 2 Populus sapling H 1 221 0 5 5
belgium 2017 2 Populus sapling H 2 221 0 2 2
belgium 2017 2 Populus sapling H 3 221 0 0 0
Senescence sapling 2018 Belgium
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
5601 belgium 2018 1 Betula sapling N 1 201 0 2 2
5602 belgium 2018 1 Betula sapling N 2 201 0 2 2
5603 belgium 2018 1 Betula sapling N 3 201 0 2 2
Senescence sapling 2018 Spain
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
7678 spain 2018 A Betula sapling high 4 243 0 0 0
7679 spain 2018 A Betula sapling high 7 243 0 0 0
7680 spain 2018 A Betula sapling high 10 243 0 0 0
Senescence sapling 2018 Norway
country year block species type FERTILISATION TREE_NUMBER DOY LEAFFAL NOTGREEN senescence
7990 norway 2018 A Fagus sapling L 4 219 0 0 5
7991 norway 2018 A Fagus sapling L 7 219 0 0 5
7992 norway 2018 A Fagus sapling L 10 219 0 0 20

bud and beaf development

bud<- read.table("Bud_Leaf_dev.csv", header=T, sep=";", dec=",", na.strings = "NA")
We create separate dataframe for each experiment
bud and leaf development mature trees 2021
country type year block species tree DOY DOY_cumul score
1905 belgium mature 2021 TC Betula 2 63 428 0.2
1906 belgium mature 2021 TC Betula 2 69 434 0.0
1907 belgium mature 2021 TC Betula 2 77 442 0.1
bud and leaf development mature trees 2019
country type year block species tree DOY DOY_cumul score
2009 belgium mature 2019 MC Fagus 3 75 440 0.0
2010 belgium mature 2019 MC Fagus 3 82 447 0.0
2011 belgium mature 2019 MC Fagus 3 86 451 0.5
bud and leaf development sapling 2018
country type year block species tree DOY DOY_cumul score
belgium sapling 2018 3 Quercus 1 73 438 0
belgium sapling 2018 3 Quercus 2 73 438 0
belgium sapling 2018 3 Quercus 3 73 438 0

fine roots

the cumulative root surface is calculated per day of measurements, for each site, species, tree, and tube.

fine_root<- read.table("fine_root.csv", header=T, sep=";", dec=",", na.strings = "NA")

fine_root_2 <- na.omit(fine_root)
fine_root_3 <-  fine_root_2 %>%
  group_by(Doy_tot, Site, Species, Tree_ID, Tube) %>%
  dplyr::summarise(cum.Root_surf = sum(TotSurfArea))
fine roots dataset 2020
Doy_tot Site Species Tree_ID Tube cum.Root_surf new_DOY
594 KS Betula pendula 1 13 123.0688 230
594 KS Betula pendula 1 14 84.3600 230
594 KS Betula pendula 1 15 6.1426 230

outup of the GAM model:

## 
## Family: Negative Binomial(1.381) 
## Link function: log 
## 
## Formula:
## cum.Root_surf ~ s(new_DOY, by = Species, k = 5) + Species
## 
## Parametric coefficients:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              3.5724     0.1030  34.698   <2e-16 ***
## SpeciesFagus sylvatica  -1.6091     0.1899  -8.474   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                   edf Ref.df Chi.sq p-value
## s(new_DOY):SpeciesBetula pendula    1      1  0.171   0.680
## s(new_DOY):SpeciesFagus sylvatica   1      1  0.039   0.844
## 
## R-sq.(adj) =  0.178   Deviance explained = 34.9%
## -REML =  430.6  Scale est. = 1         n = 105

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-7.488591e-05,0.0001235658]
## (score 430.6019 & scale 1).
## Hessian positive definite, eigenvalue range [6.968977e-05,49.62825].
## Model rank =  10 / 10 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                   k' edf k-index p-value  
## s(new_DOY):SpeciesBetula pendula   4   1     0.8    0.09 .
## s(new_DOY):SpeciesFagus sylvatica  4   1     0.8    0.05 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Climate

We create separate dataframe for each experiment
climate mature trees 2020
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
2020-07-31 20.96635 17.46242 18.04394 26.59321 17.20943 17.68603 213 2020 mature belgium
2020-08-01 17.92585 16.68914 14.68467 20.84016 16.25325 17.13565 214 2020 mature belgium
2020-08-02 15.65607 15.82741 12.21618 21.24378 15.32350 16.32500 215 2020 mature belgium
Climate mature trees 2020
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
297 2018-07-31 21.72062 16.43896 17.21 27.08 16.15 16.72 212 2018 mature belgium
298 2018-08-01 23.02688 16.43521 17.58 28.72 16.05 16.86 213 2018 mature belgium
299 2018-08-02 24.93521 16.64375 18.25 32.05 16.20 17.15 214 2018 mature belgium
Climate sapling 2017
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
561 2017-12-31 NA 6.136960 NA NA 4.452524 7.821396 365 2017 sapling belgium
562 2017-09-30 NA 12.886499 NA NA 11.200697 14.572301 273 2017 sapling belgium
563 2017-10-31 NA 9.741746 NA NA 8.059044 11.424448 304 2017 sapling belgium
Climate sapling 2018 Belgium
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
813 2018-09-30 10.79858 23.59412 6.204 19.008 21.86611 25.32214 273 2018 sapling belgium
814 2018-08-01 25.42616 24.90096 15.891 37.370 23.16455 26.63737 213 2018 sapling belgium
815 2018-08-02 26.83622 24.34193 16.177 40.085 22.60919 26.07467 214 2018 sapling belgium
Climate sapling 2018 Spain
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
947 NA 19.66291 NA 17.80661 21.51921 NA NA 182 2018 sapling spain
948 NA 19.66291 NA 17.80661 21.51921 NA NA 183 2018 sapling spain
949 NA 21.19753 NA 19.33810 23.05697 NA NA 184 2018 sapling spain
Climate sapling 2018 Norway
date mean_TA mean_TS min_TA max_TA min_TS max_TS DOY year type country
1131 NA 20.1 NA 15.7 24.7 NA NA 213 2018 sapling norway
1132 NA 18.9 NA 13.2 23.7 NA NA 214 2018 sapling norway
1133 NA 19.0 NA 12.8 23.9 NA NA 215 2018 sapling norway

Analyse Fig. 3

A

output of the GAM model

Stem thickening saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -6.9463     0.9429  -7.367  1.3e-11 ***
## speciesFagus    -0.2470     1.4035  -0.176    0.861    
## speciesPopulus   0.2351     1.6624   0.141    0.888    
## speciesQuercus   0.5066     1.1744   0.431    0.667    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df      F  p-value    
## s(DOY_cumul):speciesBetula  1.000  1.000  2.626   0.1073    
## s(DOY_cumul):speciesFagus   1.000  1.000 11.111   0.0011 ** 
## s(DOY_cumul):speciesPopulus 1.767  1.946 29.065  < 2e-16 ***
## s(DOY_cumul):speciesQuercus 1.000  1.000 27.873 1.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.404   Deviance explained = 66.8%
## -REML = -190.78  Scale est. = 0.021918  n = 151

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-1.832858e-05,-6.092525e-09]
## (score -190.7834 & scale 0.02191819).
## Hessian positive definite, eigenvalue range [1.454247e-05,71.50118].
## Model rank =  12 / 12 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                               k'  edf k-index p-value
## s(DOY_cumul):speciesBetula  2.00 1.00    1.34       1
## s(DOY_cumul):speciesFagus   2.00 1.00    1.34       1
## s(DOY_cumul):speciesPopulus 2.00 1.77    1.34       1
## s(DOY_cumul):speciesQuercus 2.00 1.00    1.34       1

Senescence saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.26530    0.01622  -16.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                         edf Ref.df     F p-value    
## s(DOY):speciesBetula  1.998  2.000 877.5  <2e-16 ***
## s(DOY):speciesFagus   1.977  1.999 591.0  <2e-16 ***
## s(DOY):speciesPopulus 1.832  1.972 586.5  <2e-16 ***
## s(DOY):speciesQuercus 1.985  2.000 400.5  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.67   Deviance explained =   62%
## -REML = -1551.8  Scale est. = 0.21094   n = 5012

Bud development saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## score ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.9348     0.4471   8.801  < 2e-16 ***
## speciesFagus   -13.7813     2.4272  -5.678 1.68e-08 ***
## speciesPopulus  -7.3847     0.9945  -7.425 2.01e-13 ***
## speciesQuercus  -5.2867     0.8351  -6.331 3.34e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df     F p-value    
## s(DOY_cumul):speciesBetula  1.990  2.000 97.31  <2e-16 ***
## s(DOY_cumul):speciesFagus   1.930  1.995 91.22  <2e-16 ***
## s(DOY_cumul):speciesPopulus 1.880  1.986 37.73  <2e-16 ***
## s(DOY_cumul):speciesQuercus 1.911  1.992 85.11  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.898   Deviance explained = 86.7%
## -REML = -617.09  Scale est. = 0.31269   n = 1332

Senescence mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.29375    0.07583  -3.874 0.000142 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F p-value    
## s(DOY):speciesBetula 1.974  1.999 120.9  <2e-16 ***
## s(DOY):speciesFagus  1.978  2.000 111.7  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.848   Deviance explained = 78.7%
## -REML = -98.667  Scale est. = 0.13114   n = 224

Bud development mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## score/4 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    1.6476     0.1837   8.967 2.83e-16 ***
## speciesFagus  -2.5469     0.2110 -12.073  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F p-value    
## s(DOY_cumul):speciesBetula 1.281  1.484  64.08  <2e-16 ***
## s(DOY_cumul):speciesFagus  1.986  2.000 224.03  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.939   Deviance explained = 90.7%
## -REML = -150.85  Scale est. = 0.075632  n = 196

Stem thickening mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -6.0152     0.3759 -16.002   <2e-16 ***
## speciesFagus   0.1132     0.5679   0.199    0.842    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F p-value    
## s(DOY_cumul):speciesBetula 1.000  1.000 37.01  <2e-16 ***
## s(DOY_cumul):speciesFagus  1.454  1.702 58.56  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.452   Deviance explained = 61.7%
## -REML = -378.93  Scale est. = 0.024468  n = 239

## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-3.012335e-05,5.792129e-06]
## (score -378.9339 & scale 0.02446787).
## Hessian positive definite, eigenvalue range [2.28155e-05,117.5008].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value
## s(DOY_cumul):speciesBetula 2.00 1.00       1    0.75
## s(DOY_cumul):speciesFagus  2.00 1.45       1    0.68

Stem thickening mature trees spring 2021

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.5926     0.3492  -7.424 1.27e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(DOY_cumul):speciesBetula 1.000  1.000 34.48 1.37e-06 ***
## s(DOY_cumul):speciesFagus  1.862  1.981 10.40 0.000274 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.707   Deviance explained =   73%
## -REML = -22.306  Scale est. = 0.12634   n = 38

## 
## Method: REML   Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-1.197018e-05,3.279038e-05]
## (score -22.30589 & scale 0.1263375).
## Hessian positive definite, eigenvalue range [1.197269e-05,17.50937].
## Model rank =  5 / 5 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value
## s(DOY_cumul):speciesBetula 2.00 1.00    1.32    0.98
## s(DOY_cumul):speciesFagus  2.00 1.86    1.32    0.97

B

output of the GAM models

coarse roots thickening saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -2.8022     0.2170 -12.913  < 2e-16 ***
## speciesFagus     0.8465     0.2662   3.180  0.00170 ** 
## speciesPopulus   0.7629     0.2761   2.763  0.00625 ** 
## speciesQuercus   0.7385     0.2718   2.717  0.00714 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df      F  p-value    
## s(DOY_cumul):speciesBetula  1.752  1.938  5.827  0.00770 ** 
## s(DOY_cumul):speciesFagus   1.916  1.993 14.411 2.59e-06 ***
## s(DOY_cumul):speciesPopulus 1.895  1.989 14.186 4.68e-06 ***
## s(DOY_cumul):speciesQuercus 1.516  1.765  7.258  0.00642 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.333   Deviance explained = 35.6%
## -REML = -119.77  Scale est. = 0.12381   n = 217

## 
## Method: REML   Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-7.473892e-07,2.15553e-08]
## (score -119.7694 & scale 0.1238126).
## Hessian positive definite, eigenvalue range [0.1324954,104.5065].
## Model rank =  12 / 12 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                               k'  edf k-index p-value
## s(DOY_cumul):speciesBetula  2.00 1.75    0.94    0.26
## s(DOY_cumul):speciesFagus   2.00 1.92    0.94    0.24
## s(DOY_cumul):speciesPopulus 2.00 1.90    0.94    0.29
## s(DOY_cumul):speciesQuercus 2.00 1.52    0.94    0.20

coarse roots thickening mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.62679    0.09959 -26.375   <2e-16 ***
## speciesFagus -0.09531    0.14814  -0.643    0.521    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F  p-value    
## s(DOY_cumul):speciesBetula 1.001  1.002  8.197  0.00456 ** 
## s(DOY_cumul):speciesFagus  1.776  1.950 19.988 3.24e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.156   Deviance explained = 19.8%
## -REML = -206.62  Scale est. = 0.069802  n = 235

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-9.09653e-05,0.000330166]
## (score -206.6163 & scale 0.06980164).
## Hessian positive definite, eigenvalue range [9.11888e-05,115.5012].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value  
## s(DOY_cumul):speciesBetula 2.00 1.00    0.91    0.09 .
## s(DOY_cumul):speciesFagus  2.00 1.78    0.91    0.13  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pannel Fig.3

Analyse Fig. 4

A

output of the GAM models

Senescence mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.09684    0.07214  -1.342    0.181
## 
## Approximate significance of smooth terms:
##          edf Ref.df     F p-value    
## s(DOY) 1.975  1.999 147.3  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.67   Deviance explained = 61.1%
## -REML = -62.874  Scale est. = 0.23048   n = 288

Bud development mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## score/4 ~ s(DOY_cumul, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.7416     0.2261   3.281  0.00146 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df     F p-value    
## s(DOY_cumul) 1.957  1.998 99.48  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.921   Deviance explained = 88.7%
## -REML = -56.416  Scale est. = 0.1318    n = 96

Stem thickening mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -5.5784     0.5075  -10.99   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df    F  p-value    
## s(DOY_cumul) 1.723  1.923 14.1 8.71e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.206   Deviance explained = 41.7%
## -REML =   -123  Scale est. = 0.051917  n = 95

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-1.523382e-09,1.374303e-10]
## (score -122.9962 & scale 0.05191742).
## Hessian positive definite, eigenvalue range [0.2602423,46.50451].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                k'  edf k-index p-value
## s(DOY_cumul) 2.00 1.72    1.11    0.96

Stem thickening mature trees spring 2019

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.624      0.250  -6.497  1.8e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                             edf Ref.df     F p-value  
## s(DOY_cumul):speciesFagus 1.364  1.596 5.454  0.0117 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.246   Deviance explained = 26.7%
## -REML = -7.6328  Scale est. = 0.25041   n = 37

## 
## Method: REML   Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-5.380094e-06,2.989539e-06]
## (score -7.632802 & scale 0.2504064).
## Hessian positive definite, eigenvalue range [0.0391342,17.5011].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                             k'  edf k-index p-value
## s(DOY_cumul):speciesFagus 2.00 1.36    1.34    0.99

B

output of the GAM models

Coarse root thickening mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.66670    0.07619     -35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df     F p-value    
## s(DOY_cumul) 1.002  1.004 32.17  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.12   Deviance explained = 16.1%
## -REML = -204.78  Scale est. = 0.074562  n = 235

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-6.046205e-05,0.0007739654]
## (score -204.7787 & scale 0.07456161).
## Hessian positive definite, eigenvalue range [6.210505e-05,116.4992].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##              k' edf k-index p-value  
## s(DOY_cumul)  2   1    0.88    0.03 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pannel Fig.4

Analyse fig. 5

A

output og GAM models

relation coarse roots thickening and soil temperature mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3) + 
##     species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.65190    0.09237 -28.710 4.59e-14 ***
## speciesFagus -0.06319    0.13420  -0.471    0.645    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                 edf Ref.df      F  p-value    
## s(X10days_temp):speciesBetula 1.862  1.981  7.863  0.00694 ** 
## s(X10days_temp):speciesFagus  1.815  1.966 26.958 3.12e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.813   Deviance explained = 82.6%
## -REML = -37.471  Scale est. = 0.0048975  n = 20

## 
## Method: REML   Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-1.335988e-06,5.923017e-07]
## (score -37.47109 & scale 0.004897524).
## Hessian positive definite, eigenvalue range [0.2986393,8.04504].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                 k'  edf k-index p-value
## s(X10days_temp):speciesBetula 2.00 1.86    1.33    0.88
## s(X10days_temp):speciesFagus  2.00 1.82    1.33    0.88

relation stems thickening and air temperature mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3) + 
##     species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -5.1240     0.3222 -15.905 1.11e-14 ***
## speciesFagus  -0.8896     0.5565  -1.598    0.122    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                 edf Ref.df     F  p-value    
## s(X10days_temp):speciesBetula 1.713  1.917 17.55 8.22e-05 ***
## s(X10days_temp):speciesFagus  1.000  1.000 25.65 3.27e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.771   Deviance explained = 79.5%
## -REML = -64.146  Scale est. = 0.0054494  n = 30

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-1.835675e-05,1.134982e-06]
## (score -64.14605 & scale 0.005449361).
## Hessian positive definite, eigenvalue range [1.835596e-05,13.00716].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                 k'  edf k-index p-value
## s(X10days_temp):speciesBetula 2.00 1.71    0.84    0.14
## s(X10days_temp):speciesFagus  2.00 1.00    0.84    0.20

B

relation coarse roots thickening and soil temperature saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3) + 
##     species
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -2.9586     0.3594  -8.233 8.53e-10 ***
## speciesFagus     0.8941     0.4294   2.082   0.0445 *  
## speciesPopulus   0.9045     0.4379   2.065   0.0461 *  
## speciesQuercus   0.8586     0.4299   1.997   0.0534 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                edf Ref.df     F p-value  
## s(X10days_temp):speciesBetula    1      1 2.280  0.1398  
## s(X10days_temp):speciesFagus     1      1 1.593  0.2150  
## s(X10days_temp):speciesPopulus   1      1 7.077  0.0116 *
## s(X10days_temp):speciesQuercus   1      1 0.692  0.4111  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.197   Deviance explained = 36.1%
## -REML = -40.871  Scale est. = 0.05859   n = 44

## 
## Method: REML   Optimizer: outer newton
## full convergence after 12 iterations.
## Gradient range [-4.582348e-06,3.295469e-06]
## (score -40.87065 & scale 0.05859002).
## Hessian positive definite, eigenvalue range [7.520812e-07,18].
## Model rank =  12 / 12 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                k' edf k-index p-value  
## s(X10days_temp):speciesBetula   2   1    0.81   0.065 .
## s(X10days_temp):speciesFagus    2   1    0.81   0.070 .
## s(X10days_temp):speciesPopulus  2   1    0.81   0.090 .
## s(X10days_temp):speciesQuercus  2   1    0.81   0.065 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

relation stems thickening and air temperature saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3) + 
##     species
## 
## Parametric coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -7.7993     1.8440  -4.229 0.000362 ***
## speciesFagus      0.1513     2.2119   0.068 0.946100    
## speciesPopulus -102.1380    28.2781  -3.612 0.001598 ** 
## speciesQuercus    0.9141     2.1184   0.431 0.670426    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                  edf Ref.df     F p-value   
## s(X10days_temp):speciesBetula  1.657  1.882 0.362 0.74312   
## s(X10days_temp):speciesFagus   1.000  1.000 0.020 0.88884   
## s(X10days_temp):speciesPopulus 1.930  1.995 7.213 0.00407 **
## s(X10days_temp):speciesQuercus 1.000  1.000 0.760 0.39318   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.826   Deviance explained = 83.2%
## -REML = -71.399  Scale est. = 0.0056269  n = 31

## 
## Method: REML   Optimizer: outer newton
## full convergence after 15 iterations.
## Gradient range [-2.059792e-06,1.415258e-07]
## (score -71.39885 & scale 0.005626888).
## Hessian positive definite, eigenvalue range [1.15875e-06,11.51528].
## Model rank =  12 / 12 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                  k'  edf k-index p-value  
## s(X10days_temp):speciesBetula  2.00 1.66    0.82   0.085 .
## s(X10days_temp):speciesFagus   2.00 1.00    0.82   0.120  
## s(X10days_temp):speciesPopulus 2.00 1.93    0.82   0.090 .
## s(X10days_temp):speciesQuercus 2.00 1.00    0.82   0.100 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pannel 5

Analyse Fig. 6

A

output of GAM models

Senecence saplings Belgium 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.91723    0.03759   -24.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F p-value    
## s(DOY):speciesBetula 1.877  1.985 573.3  <2e-16 ***
## s(DOY):speciesFagus  1.966  1.999 696.7  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.77   Deviance explained =   72%
## -REML = -611.89  Scale est. = 0.21954   n = 2026

Stem thickening saplings Belgium 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -5.277      0.242  -21.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F  p-value    
## s(DOY_cumul):speciesBetula 1.000  1.000 413.78  < 2e-16 ***
## s(DOY_cumul):speciesFagus  1.126  1.236  19.79 5.87e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.908   Deviance explained = 89.7%
## -REML = -70.594  Scale est. = 0.013452  n = 61

B

output of GAM models

Senecence saplings Spain 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.46656    0.07301   -6.39 6.14e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F p-value    
## s(DOY):speciesBetula 1.982  2.000 157.6  <2e-16 ***
## s(DOY):speciesFagus  1.958  1.998 154.0  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.831   Deviance explained = 79.1%
## -REML = -136.01  Scale est. = 0.14834   n = 312

Stem thickening saplings Spain 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -4.9028     0.7985   -6.14 2.67e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F  p-value    
## s(DOY_cumul):speciesBetula 1.868  1.982  4.689 0.018354 *  
## s(DOY_cumul):speciesFagus  1.877  1.984 10.759 0.000232 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.569   Deviance explained = 61.5%
## -REML = -39.351  Scale est. = 0.11534   n = 46

C

output of GAM models

Senecence saplings Norway 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## senescence/100 ~ s(DOY, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.64597    0.04655  -13.88   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F p-value    
## s(DOY):speciesBetula 1.970  1.999 205.5  <2e-16 ***
## s(DOY):speciesFagus  1.985  2.000 143.3  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.672   Deviance explained = 61.9%
## -REML = -210.63  Scale est. = 0.22083   n = 756

Stem thickening saplings Norway 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -5.1989     0.4349  -11.95 8.61e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(DOY_cumul):speciesBetula 1.444  1.691 21.61 4.63e-05 ***
## s(DOY_cumul):speciesFagus  1.000  1.000 17.72 0.000115 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.349   Deviance explained = 57.4%
## -REML = -68.423  Scale est. = 0.025826  n = 50

D

Coarse root thickening saplings Belgium 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -2.0036     0.1363 -14.700  < 2e-16 ***
## speciesFagus   0.6107     0.1654   3.692 0.000289 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                            edf Ref.df      F p-value    
## s(DOY_cumul):speciesBetula   1      1 39.346  <2e-16 ***
## s(DOY_cumul):speciesFagus    1      1  2.881  0.0912 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.199   Deviance explained = 22.3%
## -REML = -85.452  Scale est. = 0.14519   n = 197

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-1.214706e-05,4.313095e-06]
## (score -85.45225 & scale 0.1451868).
## Hessian positive definite, eigenvalue range [1.079767e-05,96.5].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                            k' edf k-index p-value    
## s(DOY_cumul):speciesBetula  2   1    0.69  <2e-16 ***
## s(DOY_cumul):speciesFagus   2   1    0.69  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

E

Coarse root thickening saplings Spain 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.27414    0.08634 -14.757  < 2e-16 ***
## speciesFagus -0.48750    0.14545  -3.352  0.00104 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F p-value    
## s(DOY_cumul):speciesBetula 1.877  1.985  5.586 0.00774 ** 
## s(DOY_cumul):speciesFagus  1.000  1.001 47.727 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.313   Deviance explained = 34.2%
## -REML =    -90  Scale est. = 0.095513  n = 142

## 
## Method: REML   Optimizer: outer newton
## full convergence after 11 iterations.
## Gradient range [-2.724611e-05,0.0001644394]
## (score -89.99961 & scale 0.09551259).
## Hessian positive definite, eigenvalue range [2.730224e-05,69.00271].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value   
## s(DOY_cumul):speciesBetula 2.00 1.88    0.77   0.005 **
## s(DOY_cumul):speciesFagus  2.00 1.00    0.77   0.005 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

F

Coarse root thickening saplings Norway 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_TH/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.31600    0.08886 -14.809  < 2e-16 ***
## speciesFagus -0.37209    0.13219  -2.815  0.00553 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(DOY_cumul):speciesBetula 1.200  1.361 6.964 0.003638 ** 
## s(DOY_cumul):speciesFagus  1.729  1.926 9.231 0.000843 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.161   Deviance explained = 18.2%
## -REML = -94.357  Scale est. = 0.096752  n = 156

## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-0.000168264,0.0002208678]
## (score -94.35738 & scale 0.09675166).
## Hessian positive definite, eigenvalue range [0.01768467,76.00184].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value    
## s(DOY_cumul):speciesBetula 2.00 1.20    0.56  <2e-16 ***
## s(DOY_cumul):speciesFagus  2.00 1.73    0.56  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pannel 6

SEPPLEMENTARY

Analyse supp data Fig. 4

A

Output GAM models

Coarse root enlargement mature trees 2020

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_EC/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -3.7664     0.1374 -27.420  < 2e-16 ***
## speciesFagus  -1.3538     0.3413  -3.966 9.75e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F p-value   
## s(DOY_cumul):speciesBetula 1.000  1.001 0.929  0.3361   
## s(DOY_cumul):speciesFagus  1.702  1.911 8.214  0.0019 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.0983   Deviance explained = 17.2%
## -REML = -276.48  Scale est. = 0.048313  n = 235

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-5.19665e-05,0.0001298861]
## (score -276.4779 & scale 0.04831275).
## Hessian positive definite, eigenvalue range [5.199871e-05,115.5016].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                             k' edf k-index p-value
## s(DOY_cumul):speciesBetula 2.0 1.0    0.87    0.14
## s(DOY_cumul):speciesFagus  2.0 1.7    0.87    0.16

B

Coarse root enlargement mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_EC/100 ~ s(DOY_cumul, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -5.4595     0.6501  -8.399 5.89e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df     F p-value  
## s(DOY_cumul) 1.469  1.718 5.248  0.0284 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.119   Deviance explained = 27.6%
## -REML = -113.11  Scale est. = 0.080379  n = 93

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-6.113341e-06,7.147707e-07]
## (score -113.1098 & scale 0.08037892).
## Hessian positive definite, eigenvalue range [0.06780577,45.50057].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                k'  edf k-index p-value
## s(DOY_cumul) 2.00 1.47    0.98    0.68

C

Coarse root enlargement saplings 2017

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_EC/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -4.19434    0.23938 -17.522   <2e-16 ***
## speciesFagus   -0.97646    0.46748  -2.089   0.0379 *  
## speciesPopulus  0.20725    0.35191   0.589   0.5565    
## speciesQuercus  0.05527    0.34605   0.160   0.8733    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df     F p-value  
## s(DOY_cumul):speciesBetula  1.769  1.947 1.390  0.2929  
## s(DOY_cumul):speciesFagus   1.000  1.000 0.843  0.3597  
## s(DOY_cumul):speciesPopulus 1.000  1.000 5.241  0.0231 *
## s(DOY_cumul):speciesQuercus 1.000  1.000 1.352  0.2462  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.0496   Deviance explained = 13.5%
## -REML = -250.8  Scale est. = 0.046646  n = 217

## 
## Method: REML   Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-5.685153e-05,1.147608e-06]
## (score -250.8045 & scale 0.04664647).
## Hessian positive definite, eigenvalue range [1.975501e-05,104.5011].
## Model rank =  12 / 12 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                               k'  edf k-index p-value
## s(DOY_cumul):speciesBetula  2.00 1.77    0.89    0.23
## s(DOY_cumul):speciesFagus   2.00 1.00    0.89    0.20
## s(DOY_cumul):speciesPopulus 2.00 1.00    0.89    0.22
## s(DOY_cumul):speciesQuercus 2.00 1.00    0.89    0.20

D

Coarse root enlargement saplings Belgium 2018

## 
## Family: Negative Binomial(0.27) 
## Link function: log 
## 
## Formula:
## EC_poisson ~ s(DOY_cumul, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -6.660      1.932  -3.448 0.000565 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df Chi.sq p-value   
## s(DOY_cumul):speciesBetula 1.000  1.000  9.191 0.00243 **
## s(DOY_cumul):speciesFagus  1.841  1.975 12.629 0.00341 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.125   Deviance explained = 55.8%
## -REML = 66.162  Scale est. = 1         n = 197

## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-5.894138e-06,1.475478e-05]
## (score 66.16159 & scale 1).
## Hessian positive definite, eigenvalue range [5.313892e-06,4.984712].
## Model rank =  5 / 5 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value    
## s(DOY_cumul):speciesBetula 2.00 1.00    0.67  <2e-16 ***
## s(DOY_cumul):speciesFagus  2.00 1.84    0.67  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

E

Coarse root enlargement saplings Spain 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_EC/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -3.2452     0.1828 -17.755   <2e-16 ***
## speciesFagus  -0.5738     0.3185  -1.802   0.0738 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F p-value   
## s(DOY_cumul):speciesBetula 1.000  1.000 5.115  0.0253 * 
## s(DOY_cumul):speciesFagus  1.833  1.972 5.645  0.0057 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.0915   Deviance explained = 18.5%
## -REML = -136.2  Scale est. = 0.084356  n = 142

## 
## Method: REML   Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-4.143248e-05,2.988675e-05]
## (score -136.2043 & scale 0.08435622).
## Hessian positive definite, eigenvalue range [4.143132e-05,69.00276].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value    
## s(DOY_cumul):speciesBetula 2.00 1.00    0.67  <2e-16 ***
## s(DOY_cumul):speciesFagus  2.00 1.83    0.67  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

F

Coarse root enlargement saplings Norway 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## percent_EC/100 ~ s(DOY_cumul, by = species, k = 3) + species
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -3.3312     0.1648  -20.21   <2e-16 ***
## speciesFagus  -0.1329     0.2334   -0.57     0.57    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(DOY_cumul):speciesBetula 1.000  1.000 17.15 5.74e-05 ***
## s(DOY_cumul):speciesFagus  1.874  1.984 11.44 3.70e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.205   Deviance explained = 25.2%
## -REML = -153.74  Scale est. = 0.056268  n = 156

## 
## Method: REML   Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-3.945162e-05,3.310582e-08]
## (score -153.7356 & scale 0.05626796).
## Hessian positive definite, eigenvalue range [3.944856e-05,76.00284].
## Model rank =  6 / 6 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                              k'  edf k-index p-value    
## s(DOY_cumul):speciesBetula 2.00 1.00    0.66  <2e-16 ***
## s(DOY_cumul):speciesFagus  2.00 1.87    0.66  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Panel supp data 2

Analyse supp data fig. 3

A

B

C

D

E

F

Pannel supp data Fig. 4

Analyse supp data Fig. 5

A

Output GAM models

relation coarse roots thickening and soil temperature mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.3204     0.2727  -8.508 0.000144 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                 edf Ref.df     F p-value  
## s(X10days_temp)   1      1 13.03  0.0112 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.663   Deviance explained = 71.3%
## -REML = -8.9528  Scale est. = 0.037541  n = 8

## 
## Method: REML   Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-4.559549e-06,2.688536e-06]
## (score -8.952766 & scale 0.03754137).
## Hessian positive definite, eigenvalue range [4.559539e-06,2.999997].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                 k' edf k-index p-value
## s(X10days_temp)  2   1    1.31    0.63

relation stem thickening and air temperature mature trees 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -4.806      0.379  -12.68 3.83e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf Ref.df     F p-value    
## s(X10days_temp) 1.779  1.951 24.17   5e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.924   Deviance explained = 84.9%
## -REML = -22.002  Scale est. = 0.0079383  n = 12

## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-4.789263e-06,-1.933828e-06]
## (score -22.00186 & scale 0.00793832).
## Hessian positive definite, eigenvalue range [0.2076955,5.071474].
## Model rank =  3 / 3 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                   k'  edf k-index p-value
## s(X10days_temp) 2.00 1.78    1.43    0.92

B

relation coarse roots thickening and soil temperature saplings Belgium 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.6062     0.1827  -8.791 1.03e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df     F p-value  
## s(X10days_temp):speciesBetula   1      1 5.832  0.0389 *
## s(X10days_temp):speciesFagus    1      1 0.784  0.3989  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.241   Deviance explained = 44.5%
## -REML = -11.73  Scale est. = 0.051577  n = 12

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-7.020143e-06,1.953047e-06]
## (score -11.73045 & scale 0.05157694).
## Hessian positive definite, eigenvalue range [8.741088e-07,4.499998].
## Model rank =  5 / 5 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                               k' edf k-index p-value
## s(X10days_temp):speciesBetula  2   1    1.26    0.70
## s(X10days_temp):speciesFagus   2   1    1.26    0.76

relation stem thickening and air temperature saplings Belgium 2018

## 
## Family: quasibinomial 
## Link function: logit 
## 
## Formula:
## mean_persent_TH/100 ~ s(X10days_temp, by = species, k = 3)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -20.003      1.126  -17.76 8.05e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                 edf Ref.df     F p-value    
## s(X10days_temp):speciesBetula 1.823  1.969 367.1  <2e-16 ***
## s(X10days_temp):speciesFagus  1.000  1.000 201.4  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.843   Deviance explained = 89.1%
## -REML = -13.634  Scale est. = 0.00086352  n = 12

## 
## Method: REML   Optimizer: outer newton
## step failed after 8 iterations.
## Gradient range [-0.01044635,0.03061406]
## (score -13.63354 & scale 0.0008635237).
## eigenvalue range [-3.920443e-07,4.495246].
## Model rank =  5 / 5 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                 k'  edf k-index p-value
## s(X10days_temp):speciesBetula 2.00 1.82    0.76    0.17
## s(X10days_temp):speciesFagus  2.00 1.00    0.76    0.16

Pannel supp data Fig.5

Pannel supp data Fig. 6

Pannel supp data Fig. 7

Pannel supp data Fig. 9