# Tree species growth response to climate in mixtures of Quercus robur/Quercus petraea and Pinus sylvestris across Europe - a dynamic, sensitive equilibrium

Sonja Vospernik, Michael Heym, Hans Pretzsch, Maciej Pach, Mathias

Steckel, Jorge Aldea, Gediminas Brazaitis, Andrés Bravo-Oviedo, Miren del
Rio, Magnus Löf, et al.

<figure><img src="image_1.png" /></figure>

To cite this version:

Sonja Vospernik, Michael Heym, Hans Pretzsch, Maciej Pach, Mathias Steckel, et al. Tree species growth response to climate in mixtures of Quercus robur/Quercus petraea and Pinus sylvestris across Europe - a dynamic, sensitive equilibrium. Forest Ecology and Management, 2023, 530, pp.120753. 10.1016/j.foreco.2022.120753. hal-04211027

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1 Tree species growth response to climate in mixtures of *Quercus robur*/*Quercus petraea*

2 and *Pinus sylvestris* across Europe - a dynamic, sensitive equilibrium

3 Sonja Vospernik<sup>a*</sup>, Michael Heym<sup>b</sup>, Hans Pretzsch<sup>c</sup>, Maciej Pach<sup>d</sup>, Mathias Steckel<sup>e</sup>, Jorge Aldea<sup>f</sup>, Gediminas

4 Brazaitis<sup>g</sup>, Andrés Bravo-Oviedo<sup>h</sup>, Miren Del Rio<sup>i</sup>, Magnus Löf<sup>f</sup>, Marta Pardos<sup>i</sup>, Kamil Bielak<sup>j</sup>, Felipe Bravo<sup>k</sup>

5 Lluís Coll<sup>l,m</sup>, Jakub Černý<sup>n</sup>, Lars Droessler<sup>o</sup>, Martin Ehbrecht<sup>p</sup>, Aris Jansons<sup>q</sup>, Nathalie Korboulewsky<sup>r</sup>, Marion

6 Jourdan<sup>s</sup>, Thomas Nord-Larsen<sup>t</sup>, Arne Nothdurft<sup>a</sup>, Ricardo Ruiz-Peinado<sup>i</sup>, Quentin Ponette<sup>u</sup>, Roman Sitko<sup>v</sup>

7 Miroslav Svoboda<sup>w</sup>, Barbara Wolff<sup>x</sup>

8 a Department of Forest- and Soil Sciences, Institute of Forest Growth, BOKU, University of Natural

9 Resources and Life Sciences Vienna, Peter-Jordan-Str. 82, A-1190 Vienna, Austria

10 b Bavarian State Institute of Forestry (LWF), Department Silviculture and Mountain Forest, Germany

11 c Chair of Forest Growth and Yield Science, Department of Life Science Systems, TUM School of

12 Life Sciences, Technical University of Munich. Hans-Carl-Von-Carlowitz-Platz 2, 85354 Freising.

13 Germany

14 d Department of Ecology and Silviculture, Faculty of Forestry, University of Agriculture in Krakow,

15 al. 29-Listopada 46 31-425 Kraków, Poland

16 e Forst Baden-Württemberg (AöR), Forstbezirk Ulmer Alb, Schloßstr. 34. 89079 Ulm-Wiblingen.

17 Germany

18 f Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, Box 190.

19 23422 Lomma, Sweden

20 g Vytautas Magnus University, Department of Forest Science, Studentu 11, Akademija LT-53361.

21 Kaunas dist, Lithuania

22 h Dpt. Biogeography and Global Change, National Museum of Natural Sciences – CSIC. Serrano 115.

23 28006 Madrid. Spain

24 i Instituto de Ciencias Forestales ICIFOR, INIA-CSIC, Ctra. A Coruña km 7.5. 28040 Madrid, Spain

25 j Department of Silviculture, Institute of Forest Sciences, Warsaw University of Life Sciences,

26 Nowoursynowska 159/34, 02776 Warsaw, Poland

27 k Department of Plant Production and Forest Resources, Higher Technical School of Agricultural

28 Engineering of Palencia, University of Valladolid, Spain

29 l Department of Agriculture and Forest Engineering (EAGROF), University of Lleida, Lleida, Spain

30 m Joint Research Unit CTFC-AGROTECNIO-CERCA, Solsona, Spain

31 n Forestry and Game Management Research Institute, Strnady 136, 252 02 Jíloviště, Czech Republic

32 o School of Natural Sciences and Medicine, Ilia State, University, Kakutsa Cholokashvili Ave 3/5.

33 0162 Tbilisi, Georgia
34 p Silviculture and Forest Ecology of the Temperate Zones and Centre for Biodiversity and Sustainable

35 Landuse, University of Göttingen, Büsgenweg 1, Göttingen, German

36 q Latvian State Forest Research Institute Silava, Rigas 111, Salaspils. Latvia

37 r French National Institute for Agriculture, Food. and Environment (INRAE), UR EFNO - Centre de

38 recherche Val de Loire, 45290 Nogent-Sur-Vernisson, France

39 s Université de Lorraine, AgroParisTech, INRAE, UMR Silva, 54000, Nancy, France

40 t Department of Geosciences and Natural Resource Management, University of Copenhagen,

41 Rolighedsvej 23, Frederiksberg C, Denmark

42 u UCLouvain - Université catholique de Louvain, Earth & Life Institute, Croix du Sud 2 box

43 L7.05.09. 1348 Louvain-la-Neuve. Belgium

44 v Technical University in Zvolen, Faculty of Forestry, Department of Forest Resource Planning and

45 Informatics, T. G. Masaryka 24, 96001 Zvolen, Slovakia

46 w Faculty of Forestry and Wood Sciences, Czech University of Life Sciences, Prague, Czech Republic

47 x Hochschule für nachhaltige Entwicklung Eberswalde (HNEE), FG Waldinventur und Planung,

48 Alfred-Möller-Str.1, D 16225 Eberswalde, Germany

49
50 *Corresponding author. Sonja Vospernik. University of Natural Resources and Life Sciences. Vienna.

51 Department of Forest and Soil Sciences. Institute of Forest Growth. Peter-Jordan-Str. 82. A-1190

52 Vienna. Austria

53 E-mail address: Sonja.Vospernik@boku.ac.at

54 Phone: ++43-1-47654/91412

55
56

Quercus robur/Quercus petraea and Pinus sylvestris are widely distributed and economically important tree species in Europe co-occurring on mesotrophic, xeric and mesic sites. Increasing dry conditions may reduce their growth, but growth reductions may be modified by mixture, competition and site conditions. The annual diameter growth in monospecific and mixed stands along an ecological gradient with mean annual temperatures ranging from 5.5°C to 11.5°C was investigated in this study. On 36 triplets (108 plots), trees were cored and the year-ring series were cross-dated, resulting in year-ring series of 785 and 804 trees for Q. spp. and P. sylvestris, respectively. A generalized additive model with a logarithmic link was fit to the data with random effects for the intercept at the triplet, year and tree level and a random slope for the covariate age for each tree; the Tweedie-distribution was used. The final model explained 87 % of the total variation in diameter increment for both tree species. Significant covariates were age, climate variables (long-term mean, monthly), local competition variables, relative dbh, mixture, stand structure and interactions thereof. Tree growth declined with age and local density and increased with social position. It was positively influenced by mixture and structural diversity (Gini coefficient); mixture effects were significant for P. sylvestris only. The influence of potential evapotranspiration (PET) in spring and autumn on tree growth was positive and non-linear, whereas tree growth sharply decreased with increasing PET in June, which proved to be the most influential month on tree growth along the whole ecological gradient. Interactions of PET with tree social position (relative dbh) were significant in July and September for Q. spp. and in April for P. sylvestris. Interactions of climate with density or mixture were not significant. Climatic effects found agree well with previous results from intra-annual growth studies and indicate that the model captures the causal factors for tree growth well. Furthermore, the interaction between climate and relative dbh might indicate a longer growth duration for trees of higher social classes. Analysis of
random effects across time and space showed highly dynamic patterns, with competitive advantages changing annually between species and spatial patterns showing no large-scale trends but pointing to the prevalence of local site factors. In mixed-species stands, the tree species have the same competitiveness in the long-term, which is modified by climate each year. Climate warming will shift the competitive advantages, but the direction will be highly site-specific.
1996 *Quercus* spp.

<figure><img src="image_3.png" /></figure>

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1996 *Pinus sylvestris*

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90 A random intercept for each triplet and year for *Quercus robur* and *Quercus petraea* (top) and *Pinus sylvestris*

91 (bottom) showing the inter-annual variation in diameter increment on different sites at the logarithmic scale in

92 mm
# 1. Introduction

Quercus robur/Quercus petraea (Q. spp. hereafter) and Pinus sylvestris are economically important tree species constituting a considerable proportion of the forest cover in Europe (Eaton et al. 2016, Durrant et al. 2016). All three species range from southern Europe (Iberian peninsula, Greece) to Scandinavia, but P. sylvestris grows on a wider latitudinal and longitudinal range (Eaton et al. 2016, Durrant et al. 2016) than Q. spp.. The two Quercus species naturally hybridize, forming fertile offspring, so that they are viewed as sub-species by some_authors (e.g. Roloff und Bärtels 2006). Because of their considerable range overlap, frequent hybridization and similar ecology, the two species are often investigated jointly.

Q. spp. and P. sylvestris are light-demanding tree species growing in a mixture on xeric and mesic, acidophilous sites where they represent the climatic climax (Muller 1992, Eaton et al. 2016, Durrant et al. 2016). The exigency for nutrients is lower for P. sylvestris than for Q. spp. (Mellert et al. 2012). Q. spp. are thermophilic, and they grow on sites with a minimum of 8.4°C during the growing season, while the temperature range of the pioneer species P. sylvestris is considerably larger (Vospernik 2021). All three tree species have been recognized as drought tolerant and with an efficient protection against high irradiance (Q. spp.: Epron and Dreyer 1993, Arend et al. 2011, Bose et al. 2021, Vitasse et al. 2019, P. sylvestris: Eilmann et al. 2006, Rigling et al. 2001). Q. spp. have deep penetrating tap roots and are an-isohydric tree species, known to keep their stomata open under drought conditions, showing a good resistance and resilience to drought and consequently a small decrease in tree growth in drought years (Trouvé et al. 2017, Leuzinger et al. 2005). Comparative studies on Q. robur and Q. petraea. reported only slight differences between the two species, with Q. petraea being more drought tolerant because of its higher intrinsic water-use efficiency (Epron and Dreyer 1993, Arend et al. 2011).
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*P. sylvestris* is also well adapted to a dry climate, but as conifer species, has a more conservative water use strategy. It can be classified as an iso-hydric species, closing its stomata earlier under drought conditions (Martín-Gómez et al. 2017, Zweifel 2009), which leads to carbon starvation and a long-term reduction of the needle mass (Rigling et al. 2001, Zweifel 2009). Subsequently, carbon starvation is thought to result in mortality, and higher mortality rates under drought were observed for *P. sylvestris* than for both *Q. spp.* (Bigler et al. 2006, Eilmann et al. 2006). In the last years, *P. sylvestris* has suffered tremendously from heat waves (Salomon et al. 2022), which may result in a species shift in favor of *Q. spp.* on dry sites with increasing climate warming (Eilmann et al. 2006).

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While tree growth in the South of Europe is limited by summer drought, imposed by the Mediterranean climate, tree growth in Central regions, exhibiting mesic growing conditions, is more dependent on the competitive potential (Ramírez-Valiente et al. 2020). In the Mediterranean climate, however, both *P. sylvestris* and *Q. spp.* show unimodal growth patterns. Tree growth starts in spring, showing a maximum around the summer solstice and a decline in late summer and autumn with the growing season being shorter on the more drought prone sites (Strieder and Vospernik 2021). As a consequence of this tree growth pattern, drought effects vary with season (Merlin et al. 2015), and spring or early summer droughts have a more substantial impact on tree growth (Bose et al. 2021). *P. sylvestris* is an evergreen conifer, which starts to grow when the temperature rises above 5 °C. As ring- porous trees, *Q. spp.* do not come into leaf until late April-May (Eaton et al. 2016), although their growth starts before budburst (Suzuki et al. 1996).

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Tree ring analysis is an important and frequently used way to investigate climate-growth relationships (Linderholm 2001, Mérian et al. 2013). Since the tree species studied here are widespread, many tree ring studies have been carried out to analyse their growth (e.g. Barsoum et al. 2015, Trouvé et al. 2017). Previous studies reported that *Q. spp.* and *P. sylvestris* respond to drought with reduced ring width, but fluctuations in ring width are less

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pronounced for *Q. spp.* because of its an-isohydric nature (Zweifel 2009) and tree growth at high elevations was reported to show less between year variation (Vospernik and Nothdurft 2018) than tree growth at lower ones; Similarly, a response to long-term drought was reported for higher elevations, whereas a response to short-term drought was observed at lower elevation sites (Bhuyan et al. 2017). These previous studies, however, focus on a specific area and do not encompass the whole climatic gradient where both *Q. spp.* and *P. sylvestris* co-occur, nor do they explicitly include mixture or competition effects, which may be prevalent in a temperate climate.

Growth related mixture effects for *Q. spp./P. sylvestris*, which occupy a similar ecological niche, are reported to be positive on average, with a range between 6-14% and considerable variation between sites (Steckel et al. 2019, Steckel et al. 2020a, Pretzsch et al. 2020). The competitive advantage for *P. sylvestris* in the mixture increases with site index and water supply, while it decreases with site index for *Q. spp.* (Pretzsch et al. 2020). Differences in productivity between monospecific and mixed stands at the stand level may result from higher stand densities, higher inequality of tree size distribution and growth-size relationships with stronger size asymmetry and emergent properties derived from effects at the tree level (Pretzsch and Schütze 2016). In contrast, at the individual tree level possible reasons for positive mixture effects are tree specific differences in the crown and root morphology, water and nutrient use strategy, different leaf and litter composition and tree phenology (Kelty et al. 1992, Pretzsch and Schütze 2016, Ammer 2019). At the individual tree level *Q. spp.* profited on average from the admixture of *P. sylvestris* (Toïgo et al. 2018) or behaved indifferently (Barsoum et al. 2015) or negative mixture effects were observed (Nothdurft and Engel 2020). However, interactions between a given pair of species are often dynamic, changing as resource availability and climate conditions change. It is not unusual for net complementary interactions between a given species pair to transform into net competitive interactions, or vice versa (Forrester 2014, Jacobs et al. 2022).
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At the individual tree level, species coexistence is driven by fine-scale spatial
patterns and the competitive ability of species (Collet et al. 2017). Even if species are mixed
at the stand scale, species may be segregated at the local scale. Such fine-scaled spatial
patterns may be captured by local competition indices and describe the physiological response
of trees in the interspecific and intraspecific neighbourhood (Höwler et al. 2019). Local
heterogeneity may also result from small-scale spatial heterogeneity of environmental factors
(micro-site) or interactions between species. Such local competition effects are rarely
included in tree-ring studies.

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Hypothesis

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In this study we analyse the climate-growth relationship of *Quercus* spp. and *P. sylvestris*
along a gradient across Europe in monospecific and mixed stands. We hypothesize that:

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(1) Tree growth reactions are site-specific. (i) Trees within the same bio-climatic regions show analogous tree growth patterns while patterns between different bio-climatic regions differ.

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(2) Tree growth reactions to drought are species, mixture and season specific (i) *Q. spp.* is more drought resistant (ii) *P. sylvestris* is more tolerant to cold, (iii) both species react more sensitively to drought on drought prone sites (iv) both species react less sensitive to drought in mixture compared to monocultures

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(3) Tree growth is influenced by mixture (i) mixture effects are positive for both tree species, (ii) mixture effects depend on local competition

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# 2. Material and Methods

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## 2.1 Material

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### 2.1.1 Study area and research sites

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This study builds on a comprehensive transect of 36 *Q. spp.* - *P. sylvestris* triplets located along an ecological gradient through Europe, reaching from nutrient-poorer and xeric to nutrient-richer and mesic sites (Fig. 1). The transect was initially established as part of the ERA-Net SUMFOREST project REFORM ("Resilience of FORest Mixtures", reform-mixing.eu) and is described in detail in previous studies focusing on stand productivity and tree drought resilience (Steckel et al. 2019, Pretzsch et al. 2020, Steckel et al. 2020a). Long-term mean temperature on triplets ranged between 5.5 °C and 11.5 °C, with long-term mean precipitation ranging from 456-929 mm (Table 1). By design, each triplet contains three sub-plots, representing one mixed *P. sylvestris* - *Q. spp.* stand and two monospecific stands of each species, respectively. In the sampling protocol stands were required to be even-aged, at maximum density and unthinned for at least 20 years and exhibit a more or less pronounced mono-layered structure. Stand age and stand density are given in Table 1.
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<figure><img src="image_5.png" /><figcaption>209 **Figure 1** Triplets (*Q. spp.*-P. *sylvestris*) distribution along European ecological gradient</figcaption></figure>
Table 1 Summary statistics of triplets. Tri = Triplet code; Lat = Latitude (degree); Long = Longitude (degree); Incl=Inclination (degree); Asp=Aspect (degree); P = long-term mean (1976-2015) annual precipitation (mm); T = long-term mean (1976-2015) annual temperature (Celsius degree); n = number of year rings observed on each plot; Age = Mean age of cored trees; QMD = quadratic mean diameter (cm); SDI = Stand density index for pure Quercus spp. (Q.) plots, pure Pinus sylvestris (P.) plots and mixed (M.) plots; id = average yearly diameter increment (mm) for Quercus spp. (Q.) and Pinus sylvestris (P.) in pure and mixed stands in the 20 years analysed; Note that one triplet was not included because no trees were available, were local competition variables could be calculated without edge effect

<table><thead><tr><th rowspan="2">Tri</th><th rowspan="2">Lat</th><th rowspan="2">Long</th><th rowspan="2">Incl</th><th rowspan="2">Asp</th><th rowspan="2">P</th><th rowspan="2">T</th><th rowspan="2">n</th><th rowspan="2">Age</th><th rowspan="2">QMD</th><th colspan="3">SDI</th><th colspan="4">id</th></tr><tr><th>Q.</th><th>P.</th><th>M.</th><th>Q.</th><th>P.</th><th>Q.</th><th>P.</th></tr></thead><tbody><tr><td>AT 1</td><td>48.6</td><td>15.8</td><td>0.0</td><td>180</td><td>658</td><td>8.7</td><td>1452</td><td>103</td><td>30.5</td><td>556</td><td>1024</td><td>785</td><td>0.266</td><td>0.150</td><td>0.177</td><td>0.161</td></tr><tr><td>AT 2</td><td>48.6</td><td>15.8</td><td>0.0</td><td>180</td><td>658</td><td>8.7</td><td>1249</td><td>56</td><td>26.3</td><td>643</td><td>1152</td><td>876</td><td>0.222</td><td>0.229</td><td>0.209</td><td>0.207</td></tr><tr><td>BE 1</td><td>50.2</td><td>4.7</td><td>0.0</td><td>180</td><td>929</td><td>9.3</td><td>1298</td><td>69</td><td>26.0</td><td>413</td><td>477</td><td>534</td><td>0.265</td><td>0.459</td><td>0.318</td><td>0.332</td></tr><tr><td>CZ 1</td><td>50.2</td><td>16.0</td><td>0.0</td><td>180</td><td>620</td><td>9.2</td><td>1012</td><td>95</td><td>26.2</td><td>632</td><td>900</td><td>962</td><td>0.225</td><td>0.176</td><td>0.207</td><td>0.195</td></tr><tr><td>CZ 2</td><td>49.9</td><td>13.5</td><td>0.0</td><td>180</td><td>573</td><td>8.7</td><td>726</td><td>76</td><td>21.2</td><td>937</td><td>1327</td><td>1053</td><td>0.235</td><td>0.250</td><td>0.178</td><td>0.327</td></tr><tr><td>DE 1</td><td>49.9</td><td>10.8</td><td>28.8</td><td>225</td><td>615</td><td>8.5</td><td>1122</td><td>108</td><td>27.5</td><td>1049</td><td>1034</td><td>1045</td><td>0.217</td><td>0.200</td><td>0.206</td><td>0.221</td></tr><tr><td>DE 2</td><td>49.9</td><td>10.8</td><td>27.6</td><td>225</td><td>615</td><td>8.5</td><td>858</td><td>108</td><td>26.4</td><td>1007</td><td>1060</td><td>1168</td><td>0.179</td><td>0.215</td><td>0.257</td><td>0.163</td></tr><tr><td>DE 3</td><td>49.7</td><td>11.0</td><td>23.6</td><td>315</td><td>663</td><td>8.4</td><td>22</td><td>110</td><td>29.7</td><td>836</td><td></td><td></td><td></td><td>0.092</td><td></td><td></td><td></td></tr><tr><td>DE 4</td><td>49.2</td><td>10.6</td><td>6.4</td><td>180</td><td>718</td><td>8.1</td><td>748</td><td>48</td><td>20.0</td><td></td><td>1144</td><td>921</td><td></td><td></td><td>0.219</td><td>0.541</td><td>0.440</td></tr><tr><td>DE 5</td><td>49.2</td><td>10.6</td><td>4.8</td><td>180</td><td>718</td><td>8.1</td><td>1078</td><td>46</td><td>20.7</td><td>864</td><td>1076</td><td>879</td><td>0.470</td><td>0.325</td><td>0.525</td><td>0.510</td></tr><tr><td>DE 6</td><td>52.9</td><td>14.1</td><td>0.0</td><td>180</td><td>558</td><td>9.4</td><td>1496</td><td>82</td><td>30.0</td><td>765</td><td>897</td><td>816</td><td>0.336</td><td>0.306</td><td>0.301</td><td>0.396</td></tr><tr><td>DE 7</td><td>51.5</td><td>11.2</td><td>53.2</td><td>202</td><td>503</td><td>9.5</td><td>946</td><td>80</td><td>21.0</td><td>1459</td><td>1715</td><td>1429</td><td>0.251</td><td>0.114</td><td>0.187</td><td>0.191</td></tr><tr><td>DK 1</td><td>56.0</td><td>12.1</td><td>0.0</td><td>180</td><td>667</td><td>8.0</td><td>462</td><td>50</td><td>27.1</td><td>833</td><td>1014</td><td>795</td><td>0.330</td><td>0.321</td><td>0.409</td><td>0.550</td></tr><tr><td>ES 1</td><td>43.0</td><td>3.8</td><td>45.3</td><td>236</td><td>819</td><td>11.4</td><td>503</td><td>45</td><td>20.6</td><td>1210</td><td>1517</td><td>1526</td><td>0.114</td><td>0.343</td><td>0.243</td><td>0.273</td></tr><tr><td>ES 2</td><td>43.0</td><td>3.8</td><td>41.9</td><td>259</td><td>819</td><td>11.4</td><td>374</td><td>45</td><td>21.5</td><td>1126</td><td>1461</td><td>1513</td><td>0.214</td><td>0.451</td><td>0.288</td><td>0.199</td></tr><tr><td>ES 3</td><td>42.0</td><td>2.0</td><td>27.0</td><td>180</td><td>586</td><td>10.0</td><td>660</td><td>61</td><td>24.9</td><td>911</td><td>1158</td><td></td><td></td><td>0.152</td><td>0.503</td><td></td><td></td></tr><tr><td>ES 4</td><td>42.3</td><td>2.1</td><td>60.7</td><td>22</td><td>846</td><td>10.9</td><td>861</td><td>53</td><td>17.9</td><td>637</td><td>395</td><td></td><td></td><td>0.143</td><td>0.312</td><td></td><td></td></tr><tr><td>ES 5</td><td>42.9</td><td>4.2</td><td>26.4</td><td>45</td><td>793</td><td>9.9</td><td>902</td><td>55</td><td>25.4</td><td>1258</td><td>1444</td><td>1412</td><td>0.206</td><td>0.373</td><td>0.259</td><td>0.310</td></tr><tr><td>FR 1</td><td>47.8</td><td>2.5</td><td>0.0</td><td>180</td><td>724</td><td>11.0</td><td>1332</td><td>64</td><td>28.7</td><td>651</td><td>867</td><td>705</td><td>0.288</td><td>0.361</td><td>0.246</td><td>0.319</td></tr><tr><td>FR 2</td><td>49.0</td><td>7.5</td><td>25.4</td><td>45</td><td>893</td><td>9.8</td><td>1496</td><td>112</td><td>37.3</td><td>413</td><td>792</td><td>519</td><td>0.296</td><td>0.190</td><td>0.255</td><td>0.185</td></tr><tr><td>GE 1</td><td>43.0</td><td>41.6</td><td>15.1</td><td>79</td><td>456</td><td>11.5</td><td>532</td><td>83</td><td>21.0</td><td>608</td><td>694</td><td>1419</td><td>0.130</td><td>0.189</td><td>0.174</td><td>0.333</td></tr><tr><td>LT 1</td><td>54.8</td><td>24.1</td><td>0.0</td><td>180</td><td>614</td><td>6.6</td><td>792</td><td>59</td><td>26.7</td><td>1093</td><td>632</td><td>871</td><td>0.349</td><td>0.290</td><td>0.242</td><td>0.298</td></tr><tr><td>LT 2</td><td>54.8</td><td>24.1</td><td>0.0</td><td>180</td><td>614</td><td>6.6</td><td>968</td><td>86</td><td>31.3</td><td>811</td><td>927</td><td>864</td><td>0.270</td><td>0.254</td><td>0.295</td><td>0.367</td></tr><tr><td>LV 1</td><td>57.5</td><td>24.8</td><td>0.0</td><td>180</td><td>657</td><td>5.5</td><td>1254</td><td>70</td><td>28.9</td><td>565</td><td>835</td><td>801</td><td>0.196</td><td>0.304</td><td>0.181</td><td>0.430</td></tr><tr><td>PL 1</td><td>53.0</td><td>14.3</td><td>10.4</td><td>180</td><td>604</td><td>9.1</td><td>946</td><td>55</td><td>23.1</td><td>863</td><td>1071</td><td>1054</td><td>0.240</td><td>0.333</td><td>0.254</td><td>0.374</td></tr><tr><td>PL 2</td><td>53.0</td><td>14.3</td><td>7.4</td><td>180</td><td>604</td><td>9.1</td><td>1034</td><td>56</td><td>24.2</td><td>899</td><td>1086</td><td>901</td><td>0.230</td><td>0.301</td><td>0.237</td><td>0.397</td></tr><tr><td>PL 3</td><td>51.8</td><td>19.9</td><td>0.0</td><td>180</td><td>554</td><td>8.1</td><td>1100</td><td>74</td><td>29.7</td><td>893</td><td>905</td><td>880</td><td>0.211</td><td>0.362</td><td>0.355</td><td>0.354</td></tr><tr><td>PL 4</td><td>51.8</td><td>19.9</td><td>0.0</td><td>180</td><td>554</td><td>8.1</td><td>1144</td><td>75</td><td>31.3</td><td>808</td><td>944</td><td>750</td><td>0.304</td><td>0.329</td><td>0.419</td><td>0.404</td></tr><tr><td>PL 5</td><td>50.1</td><td>20.3</td><td>0.0</td><td>180</td><td>671</td><td>8.4</td><td>1716</td><td>65</td><td>29.0</td><td>845</td><td>1020</td><td>999</td><td>0.287</td><td>0.352</td><td>0.421</td><td>0.323</td></tr><tr><td>PL 6</td><td>50.1</td><td>20.3</td><td>0.0</td><td>180</td><td>671</td><td>8.4</td><td>1606</td><td>65</td><td>29.5</td><td>854</td><td>1155</td><td>907</td><td>0.291</td><td>0.378</td><td>0.327</td><td>0.340</td></tr><tr><td>PL 7</td><td>50.0</td><td>20.4</td><td>0.0</td><td>180</td><td>680</td><td>8.4</td><td>1705</td><td>75</td><td>36.2</td><td>747</td><td>1218</td><td>804</td><td>0.452</td><td>0.282</td><td>0.357</td><td>0.298</td></tr><tr><td>PL 8</td><td>50.0</td><td>20.4</td><td>0.0</td><td>180</td><td>680</td><td>8.4</td><td>858</td><td>85</td><td>39.2</td><td>763</td><td>868</td><td></td><td></td><td>0.260</td><td>0.266</td><td></td><td></td></tr><tr><td>SE 1</td><td>57.5</td><td>12.4</td><td>6.0</td><td>202</td><td>891</td><td>7.2</td><td>962</td><td>86</td><td>26.2</td><td>505</td><td>883</td><td>568</td><td>0.336</td><td>0.199</td><td>0.380</td><td>0.322</td></tr><tr><td>SE 2</td><td>58.0</td><td>15.6</td><td>38.1</td><td>169</td><td>598</td><td>6.0</td><td>738</td><td>127</td><td>27.4</td><td>876</td><td>1149</td><td>876</td><td>0.147</td><td>0.088</td><td>0.155</td><td>0.096</td></tr><tr><td>SK 1</td><td>48.7</td><td>17.1</td><td>0.0</td><td>180</td><td>580</td><td>9.8</td><td>814</td><td>66</td><td>27.6</td><td>678</td><td>1051</td><td>728</td><td>0.166</td><td>0.202</td><td>0.182</td><td>0.220</td></tr></tbody></table>
220 2.1.2 Data collection and preparation

221 Field sampling was carried out in late 2017 at the end of the growing season,
222 following a comprehensive standardized sampling protocol (Pretzsch et al. 2020). All trees on
223 each plot of the triplets were assessed and for each tree coordinates, dbh, height and height to
224 the crown base were recorded. On a sub-sample of trees, two increment cores were extracted
225 at breast height (1.3 m) from north and east cardinal directions, covering the entire diameter
226 distribution. A minimum of 20 dominant and 10 sub-dominant trees per species were sampled
227 on each plot, after removing damaged cores and trees sampled close to plot boundary, to
228 avoid edge effects in the calculation of local competition (see section 2.2.1 neighborhood
229 analysis), the resulting number of cores was 785 and 804 trees for Q. spp. and P. sylvestris,
230 respectively for the total gradient. The diameter at breast height (dbh) was also measured with
231 an accuracy of 0.1 cm, using a girth tape.

232 Annual ring-widths were measured from each increment core, using standardized
233 dendrochronological techniques (Speer 2010). Cross-dating was performed for the individual
234 plots of each triplet, guided by narrow ring widths in species-specific pointer years
235 (Schweingruber et al. 1990). Inter-series correlation ranged between 0.34-0.77 for Q. spp. and
236 0.39-0.74 for P. sylvestris. The expressed population signal, estimating how well the
237 particular sample of cores at hand represents the theoretical population chronology from
238 which it is drawn based on the inter-series correlation (Wigley et al. 1984), ranged from 0.61-
239 0.96 and 0.84-0.99 for Q. spp. and P. sylvestris, respectively. Thus, it was above the
240 recommended threshold value of 0.85 for P. sylvestris on all sites, but below this threshold on
241 some sites for Q. spp.. To reflect the current competitive status, only year-ring series from
242 1996-2017, a period with no silvicultural interventions, were used in this analysis.

243

244 2.1.3 Climate data
245

Meteorological information (monthly mean temperature (T) and monthly
precipitation total (P)) was obtained from local meteorological stations. It was assumed that
the observations from meteorological stations reflect local site conditions as well as possible.

Meteorological stations used were located in close proximity to the research sites in question.

Such sites did not exhibit any regional topographical peculiarities that would prohibit such an
approach.

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In cases where no suitable local station data was available (no coverage at all or
distance to site considered too far), interpolated observations as gridded data sets as provided
by national meteorological services or the CRU (Climatic Research Unit) 0.5° (Harris et al.
2020). In general, such modelled data used was cross-checked with station measurements
(where possible) to evaluate the comparability of data sources. Monthly meteorological
data were subsequently further aggregated to annual values or multi-annual means. From the
gridded temperature and precipitation data, the potential evapotranspiration (PET) according
to Thornthwaite (1948) and the climatic water balance (P-PET) were derived for each month.

In addition, different drought indices were calculated: the De Martonne aridity index (DMI)
(Martonne 1926), the standardized precipitation index (SPI) (McKee et al. 1993), and the
standardized precipitation and evapotranspiration index (SPEI) (Vicente-Serrano et al. 2010).

The climate growth relationship was analyzed from August of the previous year to September
of the year of tree-ring formation based on previous dendroecological and intra-annual growth
studies (e.g. Sánchez-Salguero et al. 2013).

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## 2.2 Methods

267

### 2.2.1 Neighbourhood analysis

268

We analyzed the competitive constellation of every cored tree on the plot to reveal
how the local inter- and intra-specific environment modify tree growth. First, a circle with the

269
270

recommended radius of r = 7 m (Biging and Dobbertin 1992, Biging and Dobbertin 1995)
271 around the stem coordinate of each cored tree was constructed and all trees within the circle
272 were used in the neighbourhood analyses. Circles of this size include 8-9 trees on average and
273 at least the 5–6 most impactful neighbors (Prodan 1968a, Prodan 1968b).

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For the neighbourhood analysis, we calculated the tree's specific competition index
according to Hegyi (1974), with $ci_j = \sum_{i \neq j}^{n} \left( \frac{d_i}{d_j} \times \frac{1}{dst_{ij}} \right)$, which quantifies the competition of
central tree j based on its stem diameter ($d_j$), the stem diameters of its neighbours (n) $d_{i,i=1...n}$,
and the distance ($dst_{ij}$) between the central tree j and the respective neighbors and the local
Stand Density Index, SDI, (Reineke 1933): $SDI = N \times (\frac{25}{d_g})^\alpha$, where N is the stem number
within the 7 m radius, dg is the quadratic mean diameter within the radius and $\alpha$ is the
species-specific allometric exponent derived by Pretzsch and Biber (2010). We used the same
approach to calculate the tree's specific density, but did not include the tree of interest (central
tree).

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The trees sampled in the circle were also used to calculate the local mixing
proportions using all admixed tree species. The mixing proportions $m_1...m_n$ should reflect
the area proportions of the two or more species in the observed mixed stands (Dirnberger et
al. 2017, Pretzsch and Del Río 2020). Tree number, basal area or volume proportions are only
appropriate for this purpose if the mixed species have similar growing area requirements
(Pretzsch et al. 2017, pp. 137-140). The considered tree species vary per se in the growing
area requirement and maximum stand density in fully stocked stands. In order to standardize
the density and to calculate unbiased area related to mixing proportions we applied the
equivalence factors by Pretzsch and Biber (2016). The potential edge effect was considered
by simply removing all trees with search radii reaching beyond the edge of the plots.

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To describe forest structure, the Gini coefficient by basal area was calculated in the
local neighborhood with a radius of 7 m as suggested by Binkley et al. (2006). Furthermore,

294
the relative dbh was calculated by dividing individual tree dbh by quadratic mean diameter (dg) averaged over all species in the stand to characterize each tree's social position at the stand level.

298

## 2.2.1 Modeling

Diameter increment was modeled using the generalized additive models (GAMs). originally developed by Hastie and Tabshirani (1990) blending properties of additive models with generalized linear models. In generalized additive models, the expected value depends on unknown smooth functions of the predictor variables and the observed values are assumed to be of some exponential family distribution (Wood 2011, 2017).

GAMs were estimated using the mgcv-package (Wood 2011, 2017) in R (R Core Team 2018); Within the GAM-framework of mgcv, model-covariates may be specified: (a) in parametric form or (b) non-parametrically, as smooth functions. The smooth functions are made of basis functions, that added together compose the smooth terms, hence the name (Wood 2011, 2017). Each smooth $f_j$ is represented by a sum of k simpler, fixed basis functions ($b_{j,k}$), multiplied by corresponding coefficients $\beta_{j,k}$ which need to be estimated.

$$f_j(x_j) = \sum_{k=1}^{k} (\beta_{j,k} \cdot b_{j,k}(x_k)) \qquad (1)$$

Numerous different basis functions, such as cubic splines, circular splines or thin plate regression splines, are provided by the mgcv-package, and the type and number of basis functions can be set.

Given a matrix of known coefficients S, we can formally note a penalized likelihood function:

$$l_p(\beta) = l(\beta) - \frac{1}{2} \sum_j \lambda_j \beta^T S_j \beta$$
316

Where $l(\beta)$ is the usual GLM likelihood function and $\lambda_j$ are the smoothing parameters. The part of the function including $\lambda$ penalizes curvature in the function and controls the degree to which the model fits the data. As $\lambda \to \infty$, the estimator for $f_j$ becomes linear while $\lambda = 0$ would allow any $f$ that interpolates the data (Wood, 2006). Technically, it can be set, but it is usually determined programmatically by minimizing the least squares criterion subject to a roughness penalty based on second derivatives, i.e. if the second derivatives are zero, the function is linear and these departures from linearity (smoothness) are penalized, which avoids overfitting. The final complexity of the smooth is given by the effective degree of freedom (edf) and an edf of 1 is equivalent to a linear function. The model degrees of freedom are obtained by summing the effective degrees of freedom (Wood 2011, 2017).

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In addition, the mgcv-package also allows for the inclusion of random terms. Since the data set used in this study is a hierarchical data set with trees at the same plot and measurements at the same tree being correlated, random effects at the tree, triplet and year level for both intercept and slope were included, where necessary. Diameter increment was linked to the covariates with a logarithmic link function and as exponential family distribution, the Tweedie distribution was used, which allows for fitting the type of exponential distribution from the data via a parameter $p$, encompassing different exponential distributions such as the normal ($p=0$), Gamma ($p=2$) and inverse Gaussian distribution. Parametric terms were used for categorical covariates, whereas smooth functions were used for continuous covariates, with thin plate regression splines as basis functions. The number of basis functions used in model fitting was 10. The mgcv option “select” was set to TRUE, enabling shrinkage. Shrinkage adds an extra penalty and if the smoothing parameter $\lambda$, is large enough, the coefficients will shrink to zero. In this manner it can be assessed whether a predictor is adding anything to the model and it can be used as variable selection technique.
Enabling shrinkage helps to deal with concurvity of the covariates (Marra and Wood 2011).
Concurvity refers to the non-linear dependence of covariates in the GAM-framework, causing
unstable estimates similar to collinearity in the linear case. Interactions were included as
tensor product interactions, which can be used for variables that operate on different scales.
The specification “ti-interaction”, i.e. a tensor product interaction where variable 1, variable 2
and their combination are separate, was used. All covariates described in the data section were
included in model fitting and the best fitting model was selected based on Akaike’s
information criterion (AIC) (Akaike 1973). From the fitted model variance components for
smoothing parameters and random effects were extracted. Note the two variance components
for the tensor product smooth indicated by “ti”. The first is the variance component of the
tensor product smooth for the marginal basis of the first variable; the second is the variance
component of the tensor product smooth for the marginal basis of the second variable.

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355

# 3. Results

356

## 3.1 Overall model results

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364

365

The final fitted models for diameter increment for *P. sylvestris* and *Q. spp.* included
mixture effects at the plot level, age, relative dbh, local SDI, tree species specific Gini
coefficient, long-term mean temperature, evapotranspiration of the month of September of the
previous year and for each month from April-July (PET 4-7) of the current year and the
interaction thereof with relative dbh as fixed effects and triplet and tree specific random
effects (Equation 2). The climatic drivers differed slightly between species; PET in April
(PET 4) was significant for *P. sylvestris* only, PET in May (PET 5) for *Q. spp.*. The
interactions between climate and stand density index and climate and mixture were not
significant.
$$
\begin{array}{l}
366 \quad \ln(id_{ijk}) = \\
367 \quad \beta_o + \beta_1 \cdot \text{mixture} + f(\text{age}) + f(\text{local SDI}) + f(\text{gini ba}) + f(\text{relative dbh}) + \\
368 \quad f(\text{LTMT}) + f(\text{PET previous 9}) + f(\text{PET 4-7}) + f(\text{PET previous 9, relative dbh}) + \\
369 \quad f(\text{PET 4-7, relative dbh}) + \gamma_{1i} \cdot \text{Triplet} \cdot t_{ij} + \gamma_k \cdot \text{Tree}_k + \gamma_k \cdot \text{Tree}_k \cdot f(\text{age}) + e_{ijk} \\
370 \quad (2) \\
371
\end{array}
$$

372 $id_{ijkl}$ observed diameter increment for tree k, in season j, on triplet i

373 $\beta_o$ population mean of diameter increment

374 $\beta_1 \cdot \text{mixture}$ parametric mixture effect

375 $f(\text{age})$ smooth function for age

376 $f(\text{local SDI})$ smooth function for local SDI

377 $f(\text{gini ba})$ smooth function for species specific Gini coefficient

378 $f(\text{relative dbh})$ smooth function for relative dbh

379 $f(\text{LTMT})$ smooth function for long-term mean temperatures

380 $f(\text{PET previous 9})$ smooth function for monthly potential evapotranspiration for September of the previous year

381 $f(\text{PET4-7})$ smooth function for monthly potential evapotranspiration for each month from April - July

382 $\gamma_{1i} \cdot \text{Triplet} \cdot t_{ij}$ triplet and year specific random effect

385 $\gamma_k \cdot \text{Tree}_k$ tree specific random intercept

386 $y_k \cdot \text{Tree}_k \cdot f(\text{age})$ tree specific random slope, random effect of age within each level of tree

388 $\epsilon_{ijk}$ random error

390 Overall, the model explained 87.4 % and 87.0 % of the total variation for each of the two models (Table 2). Thereof, 41.9 % and 38.2 % were explained by the fixed part of the model for *Q. spp.* and *P. sylvestris*, respectively. The most important variables in the fixed part of the model were relative dbh, species-specific Gini coefficient, and long-term mean temperature for *Q. spp.* and relative dbh as indicated by the variance components (Table 3). In the random part of the model, tree-specific random effects explained more variation, than triplet- and year-specific random effects (Table 3).

397 For the parametric mixture effects the coefficient and the p-value are given; Table 2
398 contains the effective degrees of freedom and the p-value for the smooth terms. A high degree
399 of non-linearity for the fixed part of the model was found for age, relative dbh, and local SDI
400 whereas a linear decrease, as is indicated by effective degrees of freedom of 1, was found for
401 other variables, in particular for PET in various month for *P. sylvestris*.

402 **Table 2:** Coefficients for parametric effects (Estimate) and effective degrees of freedom for smooth terms (edf)

403 for *Quercus spp.* and *Pinus sylvestris*. The p-value indicates significance of terms. R², Akaike's information

404 criterion and the number of observations are given in the bottom lines. Tweedie p gives the estimate for the
405 shape parameter p of the Tweedie distribution. Note that mixture and LTM are not significant in the *Quercus*

406 *spp.* model and PET in May is not significant in the *Pinus sylvestris* model as is indicated by the italic font.

407 Variables modelled as random effects are indicated in bold letters

<table><thead><tr><th rowspan="2">Variable</th><th colspan="2">Quercus spp.</th><th colspan="2">Pinus syl.</th></tr><tr><th>Estimate</th><th>p.value</th><th>Estimate</th><th>p.value</th></tr></thead><tbody><tr><td>Intercept</td><td>-1.66</td><td>0.000</td><td>-2.03</td><td>0.000</td></tr><tr><td>Mixture</td><td>0.05</td><td>0.574</td><td>0.24</td><td>0.030</td></tr><tr><th>Variable</th><th>edf</th><th>p.value</th><th>edf</th><th>p.value</th></tr><tr><td>s(age)</td><td>7.53</td><td>0.000</td><td>6.80</td><td>0.000</td></tr><tr><td>s(local SDI)</td><td>6.08</td><td>0.000</td><td>7.83</td><td>0.000</td></tr><tr><td>s(rel. dbh)</td><td>6.28</td><td>0.000</td><td>6.95</td><td>0.000</td></tr><tr><td>s(Gini coefficient)</td><td>4.32</td><td>0.010</td><td>6.12</td><td>0.004</td></tr><tr><td>s(LTM temp)</td><td>2.44</td><td>0.057</td><td>1.00</td><td>0.020</td></tr><tr><td>s(PET Sept. prev)</td><td>1.79</td><td>0.000</td><td>4.45</td><td>0.003</td></tr><tr><td>s(PET April)</td><td>-</td><td>-</td><td>1.00</td><td>0.001</td></tr><tr><td>s(PET May)</td><td>2.37</td><td>0.000</td><td>1.00</td><td>0.100</td></tr><tr><td>s(PET June)</td><td>1.67</td><td>0.000</td><td>1.28</td><td>0.001</td></tr><tr><td>s(PET July)</td><td>2.04</td><td>0.000</td><td>3.66</td><td>0.000</td></tr><tr><td>s(PET April, rel. dbh)</td><td>-</td><td>-</td><td>6.01</td><td>0.010</td></tr><tr><td>s(PET July, rel. dbh)</td><td>7.23</td><td>0.000</td><td>-</td><td>-</td></tr><tr><td>s(PET Sept, prev. rel.dbh)</td><td>5.06</td><td>0.000</td><td>-</td><td>-</td></tr><tr><td>sTree ID</td><td>641.94</td><td>0.000</td><td>700.33</td><td>0.000</td></tr><tr><td>s Tree ID, age</td><td>653.24</td><td>0.000</td><td>706.16</td><td>0.000</td></tr><tr><td>s(Triplet, Year)</td><td>645.99</td><td>0.000</td><td>641.47</td><td>0.000</td></tr><tr><td>R<sup>2</sup></td><td colspan="2">0.874</td><td colspan="2">0.870</td></tr><tr><td>AIC</td><td colspan="2">-52605.71</td><td colspan="2">-47896.73</td></tr><tr><td>n</td><td colspan="2">16696</td><td colspan="2">17284</td></tr><tr><td>Tweedie (p)</td><td colspan="2">1.651</td><td colspan="2">1.347</td></tr></tbody></table>
<table><caption>**Table 3:** Variance components (as standard deviation) and their upper and lower confidence limits for the models of *Quercus spp.* and *Pinus sylvestris*. Note the two variance components for the tensor product smooth indicated by ti. The first is the variance component of the tensor product smooth for the marginal basis of the first variable, the second is the variance component of the tensor product smooth for the marginal basis of the second variable. Variables modelled as random effects are indicated in bold letters.</caption><thead><tr><th rowspan="2">Variable</th><th colspan="3">Quercus spp.</th><th colspan="3">Pinus sylvestris</th></tr><tr><th>std.dev</th><th>lower</th><th>upper</th><th>std.dev</th><th>lower</th><th>upper</th></tr></thead><tbody><tr><td>s(age)</td><td>0.0031</td><td>0.0016</td><td>0.0064</td><td>0.0026</td><td>0.0014</td><td>0.0049</td></tr><tr><td>s(local SDI)</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0001</td></tr><tr><td>s(rel. dbh)</td><td>0.8516</td><td>0.1435</td><td>5.0527</td><td>0.9739</td><td>0.9736</td><td>0.9742</td></tr><tr><td>s(Gini coefficient)</td><td>1.9878</td><td>1.1261</td><td>3.5090</td><td>4.4684</td><td>2.3557</td><td>8.4760</td></tr><tr><td>s(LTM temp)</td><td>0.1728</td><td>0.0115</td><td>2.6057</td><td>0.0003</td><td>0.0000</td><td>1069e+107</td></tr><tr><td>s(PET Sep. prev)</td><td>0.0004</td><td>0.0001</td><td>0.0012</td><td>0.0024</td><td>0.0000</td><td>0.0101</td></tr><tr><td>s(PET April)</td><td>-</td><td>-</td><td>-</td><td>0.0000</td><td>0.0000</td><td>1055e+263</td></tr><tr><td>s(PET May)</td><td>0.0006</td><td>0.0000</td><td>0.0133</td><td>0.0000</td><td>0.0000</td><td>0.0033</td></tr><tr><td>s(PET June)</td><td>0.0003</td><td>0.0000</td><td>0.0021</td><td>0.0002</td><td>0.0001</td><td>0.0005</td></tr><tr><td>s(PET July)</td><td>0.0003</td><td>0.0001</td><td>0.0012</td><td>0.0010</td><td>0.0003</td><td>0.0033</td></tr><tr><td>ti(PET Sep. prev, rel. dbh)1</td><td>0.0201</td><td>0.0054</td><td>0.0749</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ti(PET Sep. prev, rel. dbh)2</td><td>0.0014</td><td>0.0013</td><td>0.0015</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ti(PET April, rel. dbh)1</td><td>-</td><td>-</td><td>-</td><td>0.0083</td><td>0.0028</td><td>0.0248</td></tr><tr><td>ti(PET April, rel. dbh)2</td><td>-</td><td>-</td><td>-</td><td>0.0248</td><td>0.0043</td><td>0.0049</td></tr><tr><td>ti(PET July, rel.dbh)1</td><td>0.0087</td><td>0.0032</td><td>0.0235</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ti(PET July, rel.dbh)1</td><td>0.0093</td><td>0.0009</td><td>0.0934</td><td>-</td><td>-</td><td>-</td></tr><tr><td>s(Tree ID)</td><td>1.0398</td><td>0.9760</td><td>1.1077</td><td>1.3867</td><td>1.3078</td><td>1.4704</td></tr><tr><td>s(Tree ID, age)</td><td>0.0161</td><td>0.0152</td><td>0.0171</td><td>0.0220</td><td>0.0208</td><td>0.0234</td></tr><tr><td>s(Triplet, Year)</td><td>0.1580</td><td>0.0895</td><td>0.2789</td><td>0.1761</td><td>0.0928</td><td>0.3340</td></tr><tr><td>Residual</td><td>0.1517</td><td>0.1494</td><td>0.1540</td><td>0.1350</td><td>0.1330</td><td>0.1370</td></tr></tbody></table>

## 3.2 Fixed effects - parametric and smooth terms

The species mixture increased diameter increment for both *Q. spp.* and *P. sylvestris* (Table 2), but the effect was significant for *P. sylvestris* only. Both tree species showed a decrease in diameter increment with age (Fig. 2) and local SDI (Fig. 3). The decrease being sharper for *P. sylvestris* than for *Q. spp.* (Fig. 2,3). Confidence intervals were narrow for age for the total range of values, but became very large for high SDI values.
<figure><img src="image_6.png" /><figcaption>**Figure 2:** Effect of age on diameter increment for *Quercus robur* and *Quercus petraea* (left) and *Pinus sylvestris* (right). Solid line: prediction, dashed lines: confidence interval. Note that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate age.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 3:** Effect of local SDI on diameter increment for *Quercus robur* and *Quercus petraea* (left) and *Pinus sylvestris* (right). Solid line: prediction, dashed lines: confidence interval. Note that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate local SDI.</figcaption></figure>

Both species showed an almost linear increase in diameter increment with relative dbh; Thus trees in the stand upper layer had higher increment rates (Fig. 4).
<figure><img src="image_8.png" /><figcaption>**Figure 4:** Effect of relative dbh (dbh divided by quadratic mean diameter) on diameter increment for *Quercus robur* and *Quercus petraea* (left) and *Pinus sylvestris* (right). Solid line: prediction, dashed lines confidence interval. Note that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate relative dbh.</figcaption></figure>

Non-linear patterns were observed for the relationship between Gini coefficient and diameter increment and the patterns for the two tree species differed (Figure 5). It might point to the fact, that this variable captures different tree structures in the observed data, but that this pattern might not be generalizable.

<figure><img src="image_9.png" /><figcaption>**Figure 5:** Effect of Gini coefficient on diameter increment for *Quercus robur* and *Quercus petraea* (left) and *Pinus sylvestris* (right). Solid line: prediction, dashed lines confidence interval. Note that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate Gini coefficient.</figcaption></figure>

The effect of long-term mean temperature for both tree species is illustrated in Fig. 6, but the effect was significant for *P. sylvestris* only. Effects differed for the two tree species:
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the growth of *Q. spp.* indicated an optimum temperature at 7° C, but the *P. sylvestris* growth
showed a linear decrease with temperature (Fig. 6). Both relationships have very large
confidence intervals.

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**Figure 6:** Effect of long-term mean temperature (ltm temp.) from the years 1976-2015 on diameter increment for *Quercus robur* and *Quercus petraea* (left) and *Pinus sylvestris* (right). Solid line: prediction, dashed lines confidence interval. Note that the p-value for *Q. spp.* is 0.1. Note also that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate ltm temp. The relationship between the linear predictor and ltm temp. is linear and could also be represented by a parametric linear term.

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In addition to long-term mean temperature, both species responded to
evapotranspiration in different months. In general, autumn of the previous year and spring and
summer of the current year influenced tree growth. Influential months differed between
species. For both species, the influential months were September of the previous year and
June and July of the current year (Fig. 7, Fig. 8); An additional month of the current year had
also a significant influence: May for *Q. spp.* and April for *P. sylvestris*. Patterns significantly
differed between months and often showed opposite trends. The diameter increment showed a
decrease with increasing PET of September of the previous for *Q. spp.* and was highly non-
linear for *P. sylvestris*. In spring, at the onset of growth, tree growth increased with increasing
PET for both species, which switched to a sharp decrease in June. Note the very different
scales of observed PET values on the x-axis for various months and the different scale for the
linear predictor. A larger effect of climate on diameter increment was observed in spring
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compared to autumn, but effects for both tree species had a similar magnitude for the same month. June is the most influential month for both tree species. Interactions of PET with relative dbh were significant for September of the previous year and July of the current year for *Q. spp.* (Fig. 9) and with PET in April of the current year for *P. sylvestris* (Fig. 10). The climate-growth relationship shown in the figures (Fig. 9, Fig. 10) differs for trees of different social position (the most dominant and suppressed trees) in particular at the beginning and the end of the growing season. These are the only significant interactions at the logarithmic scale of diameter increment. Such interactions are, however, significant for all months, when modelling diameter increments on a linear scale; As the fit of a concurrent linear model showed, different social classes behave differently to the climate in a specific month.

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<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

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<figure><img src="image_13.png" /><figcaption>**Figure 7:** Effect of potential evapotranspiration (PET) in the month of September of the previous year and April–July of the current year on diameter increment for *Quercus robur* and *Quercus petraea*. Solid line: prediction, dashed lines confidence interval. Note that the linear predictor (`(ln(diameter increment))`) is zero at the mean of the covariate PET in the respective month.</figcaption></figure>

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<figure><img src="image_15.png" /></figure>

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<figure><img src="image_16.png" /><figcaption>**Figure 8:** Effect of potential evapotranspiration (PET) in the month of September of the previous year and April—July of the current year on diameter increment for *Pinus sylvestris*. Solid line: prediction, dashed lines confidence interval. Note that the linear predictor (ln(diameter increment)) is zero at the mean of the covariate PET in the respective month.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 9:** Interaction between potential evapotranspiration in the month September of previous year (left) and July from current year (right) for *Quercus robur* and *Quercus petraea* with relative dbh (dbh divided by quadratic mean diameter). Z-values (top of graph) represent the linear predictor (ln(diameter increment)). Dots indicate observed data points. White parts indicate regions with no data points.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 10:** Interaction between potential evapotranspiration in the month from April of the current year for *Pinus sylvestris* with relative dbh (dbh divided by quadratic mean diameter). Z-values (top of graph) represent the linear predictor (ln(diameter increment)). Dots indicate observed data points. White parts indicate regions with no data points.</figcaption></figure>

**3.3 Random effects**

The temporal trends for both tree species at the same site (Figure 11: two selected plots. Supplementary material 1: all plots) clearly indicate the same growth reaction for both tree genera in some years, but in the years investigated, contrasting patterns prevail at all sites. Similarly, random effects vary between triplets and the triplet effect is year specific (Figure 12: two selected years for *Q. spp.*. Supplementary material 2 and 3: all years for both species). The regional site- specific effect is not correlated with the classification in the three broad

<figure><img src="image_19.png" /></figure>
527 climatic classes: Mediterranean climate, temperate climate and boreal climate. Residual

528 diagnostics (Supplementary material 4) indicate an adequate model fit.

529 **Figure 11: Random temporal trend for two selected plots. Left: Austria, Plot 2017, 0. Right: Georgia, Plot 2011**

530 0. RanEf=Random effects (ln(diameter increment))

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<figure><img src="image_20.png" /></figure>

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<figure><img src="image_21.png" /></figure>

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<caption>**Figure 12:** Random triplet effects for *Quercus robur* and *Quercus petraea* for 1996 and 2017. Z-Values represent the linear predictor (ln(diameter increment))</caption>

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4. Discussion
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4.1 Long-term climate and site effects on tree growth

Large-scale spatial patterns drive the occurrence of tree species and the occurrence of specific mixtures or ecotones (Thurm et al. 2018). With climate warming, many tree species will shift their centroids of occurrence and migrate northward (Thurm et al. 2018). Also, tree growth depends on long-term climate (Vospernik 2021), which was also confirmed in this study. However, only long-term mean temperature was included to represent climatic effects in the best model since the data does not cover all combinations of temperature and precipitation, though covering a large gradient of the single variables. Since not all combinations were covered, long term precipitation was shrunk to the null-space because of concurvity with long-term temperature.

Other site factors, such as soil type, soil water holding capacity, solar radiation or aspect were represented by the random triplet and plot effects accounting for site-specific growth response. Local soil conditions and local climate between plots within a year are very diverse. The site can be highly contrasting even at small spatial scales (Oberhuber et al. 1998).

The overall variation explained by the models is 87 %, which is considerably more
than 30-70 % reviewed for tree ring studies in an opinion paper by Wilmking et al. (2020).
This result indicates that it is important to account for the site and the hierarchical structure of
the data by including random effects. Influential factors at the tree level, considered by the
random effects, could be tree genetics, management history, or defoliation elicited by insects,
which explain a larger proportion of the variation than the site-level random effects.

## 4.2 Climate during the growing season

Climate during the growing season and tree growth are well correlated, as confirmed
by many tree ring studies (Linderholm 2001, Bose et al. 2021, Gillner et al. 2013). The tricky
part might be to define the growing season correctly in data sets that span large environmental gradients. Frequently, the period from August of the previous year to September of the current year is considered (Sánchez-Salguero et al. 2013). Surprisingly, significant months found in this study were rather consistent across sites with the influential month being the same on all plots. Tree growth in our study was related to PET in September of the previous year and PET in April-July, whereas PET in late summer and autumn of the current year were not significant. Variables related to ring-width in other tree ring studies were temperature and precipitation (Linderholm and Linderholm 2004, Nothdurft and Engel 2020, Vospernik 2021a, Jacobs et al. 2022), PET (Toïgo et al. 2018), vapour pressure deficit (Timofeeva et al. 2017, Lindner et al. 2010) or climatic water balance (Árvai et al. 2018) and drought indices (Gomes Marques et al. 2018, Marqués et al. 2021). In our study, PET resulted in the highest R² and lowest AIC, but model fit with other climatic variables resulted in a similar model performance except for models including drought indices, with the choice between climate variables being almost arbitrary. Thus, in our study the climate variables themselves are better suited to explain tree growth, then the tested drought indices (De Martonne-index (Martonne 1926), SPI (McKee et al. 1993), SPEI (Vicente-Serrano et al. 2010). Models including climate variables have a slightly higher R² and lower AIC than models including drought indices. The better overall performance of climate variables may be due to the fact that climate-growth patterns in spring are mainly temperature limited, which in turn might not be well captured by drought indices. The better performance of climate variables is in line with results from temperate sites (Linderholm and Linderholm 2004, Nothdurft and Engel 2020, Vospernik 2021a, Toïgo et al. 2018, Timofeeva et al. 2017, Lindner et al. 2010); whereas on Mediterranean sites, drought indices are used in tree ring studies (Gomes Marques et al. 2018, Marqués et al. 2021). We did, however, not detect a dependence of random site effects on the bio-climatic region, and thus think that PET accurately describes tree growth even on Mediterranean sites.
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*Quercus-Pinus* sites are mostly xeric sites, where water availability is a more
important limiting factor for tree growth than temperature (Bose et al. 2021), but the
importance of different climatic factors varies throughout the year and is tightly linked to tree
ring formation. Tree growth was positively related with higher PET in the spring and early
summer month. With sufficient soil moisture from winter rainfall, warm conditions are
favourable for tree growth, whereas this pattern switches to a sharp decrease of growth in
June with increasing PET. Surprisingly, the climatic influence is again opposite already in
July, possibly because of a switch to late-wood production in this month (Rathgeber et al.
2016).

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*Quercus*, as ring-porous species, re-establish their vessels from stored carbohydrates
early in spring before leaf-unfolding (Morecroft and Roberts 1999). *P. sylvestris* is
anatomically very different and, as conifer species can do photosynthesis during warm periods
in winter (Pakharkova et al. 2016). Nevertheless, the beginning of cell formation and tree
growth for *P. sylvestris* are also linked to increasing temperatures in spring (e.g. Strieder and
Vospernik 2021), with the beginning of tree growth of *P. sylvestris* being sometimes earlier at
the same site than for *Q. spp.* (Michelot et al. 2012a), which is confirmed by the significant
influence of PET in April for the *P. sylvestris* model and no significant effect of April climate
on ring width for *Q. spp.*. With increasing spring temperatures, cell formation and growth
rates increase, and maximum growth rates are often observed around the summer solstice (e.g.
Strieder and Vospernik 2021). Cell formation takes several weeks (Rathgeber et al. 2016), and
for *Q. spp.* there can be a 50-day delay from leaf-unfolding till the trees reach maximum
photosynthetic capacity (Morecroft and Roberts 1999). As a consequence, June PET has the
most considerable influence on tree growth in our model across all sites. This behaviour is
also supported by the fact that spring and early summer droughts are usually crucial for tree
growth and better correlated with ring width (Bose et al. 2021, Gillner et al. 2013) than
summer or autumn droughts. Subsequently, in July, trees switch from early-wood formation
to late-wood formation, and the production of new cells ceases in time before winter to protect the sensitive cambium from frost (Rathgeber et al. 2016). Photosynthetic products from autumn are stored and affect next years' tree ring formation in *Quercus*, but less so for *P. sylvestris* (Michelot et al. 2012b). In line with this physiological behaviour, tree ring width for both tree genera (*Quercus*, *Pinus*) is influenced by September PET, but patterns are more evident for *Q. spp.* Such correlations with last years' temperature are likewise reported in other studies (*Quercus* (e.g. Gillner et al. 2013); *Pinus* (e.g. Sánchez-Salguero et al. 2013)). Similarly, to the lagged influence of autumn climate, growth reductions due to drought are also observed in the following years (Bose et al. 2021, Gillner et al. 2013), but the long-term impact of drought must be considered marginal for *Quercus spp.* (Gillner et al. 2013) since post-drought effects for *Quercus spp.* are observed for 1-2 years (Gillner et al. 2013, Vitasse et al. 2019). In contrast, growth of conifers is enduringly reduced by spring drought (Vitasse et al. 2019) and recovery from drought spells for *P. sylvestris* is reported to be slower (more > 5 years) (Galiano et al. 2011) than for *Quercus*. Moreover, results by Bose et al. 2020 indicate that *P. sylvestris* trees that experienced more frequent droughts (e.g. series of drought years like 2015, 2018, 2019 in Europe) over the long-term are less resistant to extreme droughts. Thus, more frequent and longer predicted drought periods in the future may overstrain *P. sylvestris* potential for acclimation. This, however, could be buffered to some extent by favoring *Quercus-Pinus* mixed forest stands over monocultures of both tree species on mesotrophic xeric and mesic sites (Steckel et al. 2020a).

### 4.3 Age, competition and social position

Tree growth declined with age; this age trend was modelled for the whole population and tree ring series specific. Modelling or removing the age trend is key in studying the climate-growth relationship and is the standard in tree ring research (e.g. Linderholm 2001, Bose et al. 2021, Gillner et al. 2013, Schmitt et al. 2020). In this study, we opted for modelling the age trend, since we were interested in the trend itself. The age trend was
consistent, showing a steady decline with age. This is because the stands investigated are all at an age past the maximum of individual tree diameter increment. Similarly, we included other factors such as competition and social position, which are treated as noise in tree ring studies and a smooth from tree ring series using splines. From the various competition indices tested, local SDI was included in the final model. This index resulted in the highest R² and lowest AIC, although differences were almost identical (<0.01 difference in R²) compared to potential models including different competition indices. The major advantage of local SDI is that it showed consistent patterns in many model formulations, indicating little concurvity with other variables. In particular, its independence of age facilitates the development of multivariate models (e.g. Burkhart and Tomé 2012). The relationship found for studied tree species is quite similar in both magnitude and form, with a stronger decrease for *P. sylvestris* at higher densities. We refrained from including dbh in the model since tree size increases with both age and social position making it difficult to separate the respective effects. Social position is known to significantly affect growth duration, with suppressed trees having a shorter period of growth than dominant ones (e.g. Rathgeber et al. 2011, Strieder and Vospernik 2021). Interactions between social position and climate found in this study might reflect this different behavior observed in studies on intra-annual growth.

## 4.4 Mixture and stand structure

Positive mixture effects on productivity at the stand level were reported for the *Quercus-Pinus* triplet gradient (Pretzsch et al. 2020, Steckel et al. 2020a, del Rio et al. 2022). At the individual tree level, positive mixture effects are also observed, but are only significant for *P. sylvestris*, once the overall model accounts for stand density and structure. Beneficial mixture effects at the individual tree level result from higher nutrient availability (Thelin et al. 2002, Aubert et al. 2006, Nickmans et al. 2015), hydraulic lift (Muñoz-Gálvez et al. 2021) and complementary light use efficiency because of different crown structure and leave phenology (Kelty et al. 1992, Pretzsch and Schütze 2016, Ammer 2019) all of which seem to affect *Pinus*
mainly positively. This behavior is in line with the ecophysiology of the two genera since *Q.*
*spp.* has the more nutrient-rich leaves (Yuste et al. 2005) and a deeper rooting system.
Differences in stand density between species and differences in stand structure may be
important reasons why the effects of mixture on productivity differ between stand and
individual tree levels (Pretzsch and Schütze 2016). For the species investigated here, *P.*
*sylvestris* has a considerably higher maximum density than *Q.* spp. (Vospernik and Sterba
2015) and this higher potential density of *P. sylvestris* may be an important reason for
differing results at the stand level and the individual tree levels, because it indicates different
use of space of the two species. The temporal patterns of the random effects show that trees
species-specific effects can strongly vary between tree species at the same site and for
particular years. Other studies also reported varying between-year effects (Strieder and
Vospernik 2021). Given the 20-years analyzed in this study, the population results reported
characterize tree species behavior, but also show that caution needs to be exercised when
analyzing shorter periods since effects strongly fluctuate. There was no consistent interaction
effect between climate and mixture. Thus, the mitigating effect of mixture on growth for the
species investigated could not be shown.

# 5. Conclusions

The relationship between tree growth and climate change is an important
contemporary question at large spatial scales. Inference from single case studies is complex.
and pooling Europe-wide data or data from different sources is needed to enhance
understanding of the climate growth relationship and facilitate growth prognosis at larger
scales. This study shows that tree ring data can be modelled over large environmental
gradients by accounting for random tree and site effects, explaining 87% of the total
variation. This correct statistical specification results in climate – growth relationships that are
well in line with our current physiological understanding from more detailed dendrometer
studies. Climate reactions across Europe have a standard population signal, and the most significant influence of climate on tree growth is in June, at the maximum day length, but the direction and magnitude of climatic effects vary throughout the growing seasons. This varying strength and direction of seasonal climatic effects are rarely accounted for in modelling tree growth response, where the average climate for the whole growing season is often included. In future studies, accounting for a monthly or daily climate in forest growth models should receive more emphasis.

An interesting finding is the high temporal dynamic at the same site, emphasizing the importance of considering several years in tree growth analysis. Tree species mixture has a positive effect on productivity. However, this effect is small compared to the climatic impacts. Thus, the mixture may only partly mitigate growth reductions due to drought. Rather large effects on diameter increment are observed due to stand structure but cannot be systematically explained in this study or related to silvicultural management.

Growth factors are manifold and interrelated, and tree ring models are thus prone to concurvity. Nevertheless, we advocate an overall model approach, which in contrast to dendrochronological studies, allows testing other growth factors and interactions thereof with climate. Concurvity can be well avoided by including variables that are considered free of the influence of other growth factors.

708

709 Acknowledgements

The authors thank the European Union for funding the project "Mixed species forest management. Lowering risk, increasing resilience (REFORM)" under the framework of Sumforest ERA-NET. All contributors thank their national funding institutions to establish, measure and analyze data from the triplets. The Polish State Forests Enterprise also supported one of the Polish co-authors (Grant No: OR.271.3.15.2017). The Orléans site, OPTMix was
installed thanks to ONF (National Forest Service, France), belongs to research infrastructure
ANAEE-F; it is also included in the SOERE TEMPO, ZAL (LTSER Zone Atelier Loire) and
the GIS oop network. This work was also supported by grant APVV-18-0347 (Slovakia). We
acknowledge Institutional support MZE-RO0118 from the Ministry of Agriculture of the
Czech Republic, partly funding the field measurements at Czech triplets.

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