With increasing site quality asymmetric competition and mortality reduces Scots pine (Pinus sylvestris L.) stand structuring across Europe

Forest Ecology and Management 520 (2022) 120365 Available online 21 June 2022 0378-1127/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/bync/4.0/). With increasing site quality asymmetric competition and mortality reduces Scots pine (Pinus sylvestris L.) stand structuring across Europe Hans Pretzsch a , d , * , Andr´ es Bravo-Oviedo b , Torben Hilmers a , Ricardo Ruiz-Peinado c , d , Lluís Coll e , f , Magnus L¨ of g , Shamim Ahmed a , Jorge Aldea g , Christian Ammer h , Admir Avdagi´ c i , Ignacio Barbeito j , Kamil Bielak k , Felipe Bravo d , l , Gediminas Brazaitis m , Jakub Cerný n , Catherine Collet o , Lars Dr¨ ossler p , Marek Fabrika q , Michael Heym a , r , Stig-Olof Holm s , Gro Hylen t , Aris Jansons u , Viktor Kurylyak v , Fabio Lombardi w , Bratislav Matovi´ c x , y , Marek Metslaid z , Renzo Motta aa , Thomas Nord-Larsen ab , Arne Nothdurft ac , Crist´ obal Ord´ o˜ nez d , l , Jan den Ouden ad , Maciej Pach ae , Marta Pardos c , Quentin Ponette af , Tomas P´ erot ag , Ditlev Otto Juel Reventlow ab , Roman Sitko q , Vit Sramek n , Mathias Steckel ah , Miroslav Svoboda ai , Enno Uhl a , r , Kris Verheyen aj , Sonja Vospernik ac , Barbara Wolff ak , Tzvetan Zlatanov al , Miren del Río c , d a Chair of Forest Growth and Yield Science, Department of Life Science Systems, TUM School of Life Sciences, Technical University of Munich, Hans-Carl-Von-CarlowitzPlatz 2, 85354 Freising, Germany b Dpt. Biogeography and Global Change, National Museum of Natural Sciences – CSIC, Serrano 115, 28006 Madrid, Spain c Forest Research Center, INIA-CSIC, Ctra. A Coru˜ na km 7.5, 28040 Madrid, Spain d iuFOR, Sustainable Forest Management Research Institute, University of Valladolid & INIA, Spain e Department of Agriculture and Forest Engineering (EAGROF), University of Lleida, Lleida, Spain f Joint Research Unit CTFC-AGROTECNIO-CERCA, Solsona, Spain g Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, Box 190, 23422 Lomma, Sweden h Silviculture and Forest Ecology of the Temperate Zones and Centre for Biodiversity and Sustainable Landuse, University of G¨ ottingen, Büsgenweg 1, G¨ ottingen, Germany i Faculty of Forestry, University of Sarajevo, Zagrebaˇ cka 20, 71000 Sarajevo, Bosnia and Herzegovina j Department of Forest Resources Management, Faculty of Forestry, The University of British Columbia, 2424 Main Mall, Vancouver, BC V6T 1Z4, Canada k Department of Silviculture, Institute of Forest Sciences, Warsaw University of Life Sciences, Nowoursynowska 159/34, 02776 Warsaw, Poland l Department of Plant Production and Forest Resources, Higher Technical School of Agricultural Engineering of Palencia, University of Valladolid, Spain m Vytautas Magnus University, Department of Forest Science, Studentu 11, Akademija LT-53361, Kaunas dist, Lithuania n Forestry and Game Management Research Institute, Strnady 136, 252 02 Jíloviˇ stˇ e, Czech Republic o Universit´ e de Lorraine, AgroParisTech, INRAE, UMR Silva, 54000, Nancy, France p School of Natural Sciences and Medicine, Ilia State, University, Kakutsa Cholokashvili Ave 3/5, 0162 Tbilisi, Georgia q Technical University in Zvolen, Faculty of Forestry, Department of Forest Resource Planning and Informatics, T. G. Masaryka 24, 96001 Zvolen, Slovakia r Bavarian State Institute of Forestry (LWF), Department Silviculture and Mountain Forest, Germany s Department of Ecology and Environmental Science, Umeå University, S-90187 Umeå, Sweden t NIBIO, Norwegian Institute of Bioeconomy Research, Pb 115. NO-143, Ås, Norway u Latvian State Forest Research Institute Silava, Rigas 111, Salaspils, Latvia v Institute of Forestry and Horticulture, Ukrainian National Forestry University, Lviv, Ukraine w Department of AGRARIA, Mediterranean University of Reggio Calabria, 89122 Reggio Calabria, Italy x University of Novi Sad, Institute of Lowland Forestry and Environment, Antona ˇ Cehova 13, 21000 Novi Sad, Serbia y University of East Sarajevo, Faculty of Agriculture, SP Forestry, Vuka Karadˇ zi´ ca 30, 71123 Istoˇ cno Sarajevo, Republika Srpska, Bosnia and Herzegovina z Chair of Silviculture and Forest Ecology, Institute of Forestry and Engineering, Estonian University of Life Sciences, Kreutzwaldi 5, 51006 Tartu, Estonia aa Dep. Agricultural, Forest and Food Sciences (DISAFA), University of Turin, Italy ab Department of Geosciences and Natural Resource Management, University of Copenhagen, Rolighedsvej 23, Frederiksberg C, Denmark ac Department of Forestand Soil Sciences, Institute of Forest Growth, BOKU, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Str. 82, A-1190 Vienna, Austria ad Forest Ecology and Forest Management, Wageningen University of Environmental Sciences, Wageningen, The Netherlands ae Department of Ecology and Silviculture, Faculty of Forestry, University of Agriculture in Krakow, al. 29-Listopada 46 31-425 Krak´ ow, Poland af UCLouvain - Universit´ e catholique de Louvain, Earth & Life Institute, Croix du Sud 2 box L7.05.09, 1348 Louvain-la-Neuve, Belgium * Corresponding author at: Chair of Forest Growth and Yield Science, Department of Life Science Systems, TUM School of Life Sciences, Technical University of Munich, Hans-Carl-Von-Carlowitz-Platz 2, 85354 Freising, Germany. E-mail address: [email protected] (H. Pretzsch). Contents lists available at ScienceDirect Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco https://doi.org/10.1016/j.foreco.2022.120365 Received 29 April 2022; Received in revised form 10 June 2022; Accepted 12 June 2022 Forest Ecology and Management 520 (2022) 120365 2 ag INRAE – UR EFNO - Centre de recherche Val de Loire, 45290 Nogent-Sur-Vernisson, France ah Forst Baden-Württemberg (A¨ oR), Forstbezirk Ulmer Alb, Schloßstr. 34, 89079 Ulm-Wiblingen, Germany ai Faculty of Forestry and Wood Sciences, Czech University of Life Sciences, Prague, Czech Republic aj Forest & Nature Lab, Ghent University, Melle-Gontrode, Belgium ak Hochschule für nachhaltige Entwicklung Eberswalde (HNEE), FG Waldinventur und Planung, Alfred-M¨ oller-Str.1, D 16225 Eberswalde, Germany al Institute of Biodiversity and Ecosystem Research, Bulgarian Academy of Sciences, 2 Gagarin Street, 1113 Sofia, Bulgaria ARTICLE INFO Keywords: Asymmetry of competition Size-dependent mortality Mode of competition Growth dominance coefficient Gini coefficient Structural heterogeneity ABSTRACT Heterogeneity of structure can increase mechanical stability, stress resistance and resilience, biodiversity and many other functions and services of forest stands. That is why many silvicultural measures aim at enhancing structural diversity. However, the effectiveness and potential of structuring may depend on the site conditions. Here, we revealed how the stand structure is determined by site quality and results from site-dependent partitioning of growth and mortality among the trees. We based our study on 90 mature, even-aged, fully stocked monocultures of Scots pine (Pinus sylvestris L.) sampled in 21 countries along a productivity gradient across Europe. A mini-simulation study further analyzed the site-dependency of the interplay between growth and mortality and the resulting stand structure. The overarching hypothesis was that the stand structure changes with site quality and results from the site-dependent asymmetry of competition and mortality. First, we show that Scots pine stands structure across Europe become more homogeneous with increasing site quality. The coefficient of variation and Gini coefficient of stem diameter and tree height continuously decreased, whereas Stand Density Index and stand basal area increased with site index. Second, we reveal a site-dependency of the growth distribution among the trees and the mortality. With increasing site index, the asymmetry of both competition and growth distribution increased and suggested, at first glance, an increase in stand heterogeneity. However, with increasing site index, mortality eliminates mainly small instead of all-sized trees, cancels the size variation and reduces the structural heterogeneity. Third, we modelled the site-dependent interplay between growth partitioning and mortality. By scenario runs for different site conditions, we can show how the site-dependent structure at the stand level emerges from the asymmetric competition and mortality at the tree level and how the interplay changes with increasing site quality across Europe. Our most interesting finding was that the growth partitioning became more asymmetric and structuring with increasing site quality, but that the mortality eliminated predominantly small trees, reduced their size variation and thus reversed the impact of site quality on the structure. Finally, the reverse effects of mode of growth partitioning and mortality on the stand structure resulted in the highest size variation on poor sites and decreased structural heterogeneity with increasing site quality. Since our results indicate where heterogeneous structures need silviculture interventions and where they emerge naturally, we conclude that these findings may improve system understanding and modelling and guide forest management aiming at structurally rich forests. 1. Introduction The structure of forest stands in terms of their variation in tree size is highly relevant for most ecosystem functions and services. Stand structure affects, among others, the productivity (Torresan et al. 2020, Dieler et al. 2017, Ishii et al. 2004, Juchheim et al. 2017), the mechanical stability (Dobbertin 2002) but also fire risk (Stephens and Moghaddas 2005), biodiversity (Bohn and Huth 2017, Archaux and Bakkaus 2007) and cultural services (Sutherland et al. 2016). For assessing the potential structural diversity, rating of an actual stand structure, and deriving silvicultural prescriptions, it is essential to know how the structure is pre-determined by the specific site conditions. A better understanding of the relationship between site quality and stand structure is of particular interest under changing site conditions. It may allow the prediction of how stands and associated functions and services will develop when growing conditions become harsher and how detrimental effects on stand structure may be remedied by silvicultural interventions (Schutz, 2002, Meyer 2000, Pretzsch 1996). Creation of structure by silvicultural interventions can, among others, increase mechanical stability (Griess and Knoke 2011), resistance against insect attacks (Jactel and Brockerhoff 2007) and drought stress (Pretzsch et al. 2022, 2013). However, the effectiveness and potential of size differentiation may depend on ecological preconditions such as tree species assemblage, the initial structure, and, finally, also on the site conditions. Starting with an initial tree size distribution, the stand structure results from the species-specific size growth and tree mortality. Site conditions may modulate both size growth and tree mortality partitioning. When dealing with the size distributions in the following, we will mainly consider the stem diameter distribution; but it should be noted that the distribution of tree height, stem basal area, or tree volume could also be used for describing a size distribution and can be derived from the stem diameter via allometric relationships. There is a growing body of evidence that favourable environmental conditions modify the competition and growth distribution towards a more size-asymmetric mode on rich sites (Pretzsch et al. 2022, Pretzsch and Biber 2010, Wichmann 2002, Schwinning and Weiner 1998). This means that big trees grow overproportionally more than small trees. Their high growth rate may extend the right branch of the diameter distribution (large diameter side of the distribution). This asymmetric partitioning may be quantified by the steepness of the relationship between tree growth and tree size (Pretzsch and Biber 2010), by the Gini coefficient of tree growth (Latte et al. 2016, Metsaranta and Lieffers 2010, 2008, Nord-Larsen et al. 2006), or the growth dominance coefficient, GDC, (Binkley et al., 2006). Size inequality quantifies how stand density is distributed between different sizes of trees but does not quantify how individual tree growth is distributed among different sizes (Forrester 2019); this is why GDC is useful to known in combination with the Gini coefficient. However, mortality rates also often increase with site quality (Eid and Tuhus 2001). Thus, even if the growth partitioning became more asymmetric with increasing site quality, the stand structure may, in the end, be less heterogeneous (Gracia and Retana 1996, Aber et al. 1982). This means that despite a more unequal competition and growth distribution, the tree size structure may become more equal on rich and more unequal on poor sites. Whereas many studies dealt with the sitedependency of the mode of competition and partitioning of biomass, only little research is done about the site-dependency of the mode of mortality (the pattern of dropout of small compared to big trees) and its effect on size distribution in addition to the structuring effect of growth H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 3 partitioning (Bigler et al. 2007). In the following, we will use the term dropout trees for those trees that were dead at the time of the inventory. Both the partitioning of growth and mortality shape the size distribution dynamics; both may be site-dependent. Their interaction may result in the counterintuitive decrease of stand heterogeeity with increasing site quality despite the initial increase of inequality growth distribution. Against this background, the overarching hypothesis of this study was that the stand structure changes with site quality and results from site-dependent partitioning of both growth and mortality. We used a set of 90 medium and evenly aged, fully stocked Scots pine (Pinus sylvestris L.) stands distributed along a productivity gradient across Europe to answer the following questions: Q I: How does the stand structuring, characterized by, e.g. the coefficient of variation, and the Gini coefficient of stem diameter, change with increasing site quality across Europe? Q II: How does the inter-individual symmetry/asymmetry of competition, growth partitioning, and mortality depend on the site quality? Q III: How does the site-dependency of the stand structure result from the interplay between growth partitioning and mortality? 2. Material and methods 2.1. Material A series of EU funded projects such as EuMIXFOR, REFORM, and CARE4C backed by national projects of the included institutions, created a Trans-European network of triplets covering monoand mixed species stands of Scots pine and European beech (Fagus sylvatica L.; Pretzsch et al. 2015, 2016), Scots pine and Norway spruce (Picea abies (L.) Karst.; Ruiz-Peinado et al. 2021), and Scots pine and sessile and common oak (Quercus robur L., Quercus petraea (Matt.) Liebl.; Pretzsch et al. 2020a). The triplets are located in 21 countries (Austria, Belgium, BosniaHerzegovina, Bulgaria, Czech Republic, Denmark, Estonia, France, Georgia, Germany, Italy, Latvia, Lithuania, Norway, Poland, Serbia, Slovakia, Spain, Sweden, Netherlands, and Ukraine). Here, we used the 90 monospecific Scots pine stands established and inventoried in 2013–2017 in these countries across Europe (Fig. 1). The plots were established in mature, even-aged, fully stocked stands without signs of recent thinning interventions so that they represent stands close to maximum stand densities (Pretzsch et al. 2015). Most of the plots were established in even-aged plantation forests. Plot sizes were highly variable and ranged from 0.014 to 1.55 ha. On each plot, the diameter of all trees>7 cm was measured, and two increment cores per tree were taken at 1.3 m stem height in a sample of around 20 living trees per species and plot (covering the diameter range). For each standing tree, we recorded whether it was alive or dead. Annual ring widths were measured from each increment core, and the growth series were cross-dated using standardized dendrochronological techniques. Mean values of annual ring widths of the two cores per tree were used for further analysis. Using data from cored trees, tree diameter incrementdiameter models were fitted by year, species and plot to estimate diameter increments of non-cored trees for the studied period (Steckel et al. 2019). The studied 5-years growth periods were 2009–2013 for the Fig. 1. The locations of the 90 plots with monospecific Scots pine (black triangles) in Europe and the species distribution of Scots pine (grey) according to EUFORGEN (www.euforgen.org). H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 4 beech-pine transect and 2013–2017 for the oak-pine and the spruce-pine transects, the last year corresponding to triplet establishment. See Pretzsch et al. (2015, 2020) and Ruiz-Peinado et al. (2021) for more details on field measurements and main stand characteristics calculations. Note that stand state inventory data from the year of plot establishment was available for all 90 Scots pine plots. In contrast, retrospective growth data was limited to 88 plots due to inconsistent measurements. A description of the main tree and stand characteristics is presented in Table 1. T, P: mean annual temperature and annual precipitation based on annual climate data were obtained from meteorological weather stations near each plot. When local station data were not available, or observations did not cover the studied period, gridded data provided by national meteorological services or the Climatic Research Unit (CRU) Time-Series (TS) Version 3.10 database (Harris et al. 2020) were used. MA: For characterizing the climatic conditions in the last 30 years before the plot establishment, we used the de Martonne aridity index (M =P/(T +10)) (Martonne 1926). We selected these annual climate variables as it describes in a simple way the large variability of climates covered by study sites, from Mediterranean to boreal climates, and is related to productivity variation at large scales (Huang and Xia 2019) (Table 1). SI: For site indexing (Table 1), we used the mean tree height at age 100 and applied the yield table (moderate thinning) for Scots pine by Wiedemann (1943), as this yield table covers the most fertile but also the poorest sites of Scots pine in Europe. When calculating the mean tree height we followed the standard procedure by Johann (1993); we first calculated the quadratic mean stem diameter (d q ), second derived the current diameter-height curve by regression (h-d relationship), and third entered with d q into the h-d relationship to read off the mean height h q which was used for site indexing. In this way trees of all sizes are considered when deriving the mean tree height of the stands and the respective SI (Kramer and Akça 1995). 2.2. Measures and metrics 2.2.1. Classical tree and stand variables For characterizing and analyzing the effect of site conditions on the tree and stand growth and structure, we used the following tree and stand characteristics (Table 1): d, h: measured individual stem diameter at 1.30 m above ground level and tree height. v: merchantable stem volume (>7 cm at the smaller end) calculated based on stem diameter, tree height and form factors according to Franz et al. (1973). dq, hq: quadratic mean stem diameter and height of the tree with dq. do, ho: mean stem diameter do of the 100 largest stem diameter trees per hectare and height of the trees with do. N, BA: tree number and stand basal area per hectare. SDI: stand density index according to Reineke (1933) calculated with exponent −1.593 according to Pretzsch and Biber (2005). V: Standing stem volume of the stand. 2.2.2. Characteristics of size distribution and partitioning of growth and mortality For characterizing the size distribution and partitioning of growth and mortality on the plots we used the following variables and metrics (Table 1): CVd, CVh, CVba: coefficient of variation of stem diameter, tree height, and stem basal area. GINId, GINIh, GINIba: Gini coefficient of stem diameter, tree height, and stem basal area. The Gini coefficient for a cumulative stock of trees is generally calculated as follows GINI =∑n i−1∑n j=1xi−xj 2n(n−1)×x (see de Camino, 1976, Kramer, 1988, p 82). Variables xi and xj denote size or growth (or other tree characteristics) for the ith and the jth tree in the stand with i and j=1…n trees (see Supplementary Fig. 1). skew, kurt: skewness and kurtosis of stem diameter distribution. GDCba: Growth Dominance Coefficient based on stem basal area and basal area growth (Binkley et al., 2006). The GDC can be calculated directly based on the individual tree records of stem basal area and stem basal area growth of all trees of a population sorted by size as GDC =1−∑n k=1(bak−bak−1)(ibak+ibak−1)(see Supplementary Fig. 1). a0, a1: intercept and slope of the plotwise linear regression id =a0+ a1×d, with id being the stem diameter increment in a given 5-yearsperiod and d being the stem diameter at the beginning of this period. dratio: the ratio between the mean stem diameter of the dropped out trees (dmort) caused by natural mortality and the mean stem diameter (dtotal) of all trees of a stand. As we inventoried both the stem diameters of the standing dead and living trees, we were able to calculate the variable dratio. The collective of dropped out trees included only dead trees that were still standing. Our study covered mainly medium-aged stands; we did not strive for analysing the change of structure with increasing stand age. We nevertheless included stand age and quadratic mean stand diameter in the regression models. However, as expected, these two variables proved to be not significant due to the sampling of mainly medium aged stands. 2.2.3. Overview of the empirical basis of this study Due to their location across Mediterranean, Atlantic, temperate, and continental regions, the mean values of annual temperature and precipitation show a very wide range; this results in site index (SI) values at age 100 from SI =14.44 to 35.74 m (Table 1). The mean individual stem diameters (23.6 cm), tree heights (20.2 m), and stem volumes (0.55 m 3 ) but also mean and variation of stand age reflect that our study stands cover mainly medium-aged trees. The standard deviation, the minimum and maximum values show a Table 1 Characteristics of the 90 plots in monospecific Scots pine stands with altogether 8610 sample trees measured in 2013–2017 used in this study (see variable explanation in sections 2.2.1 and 2.2.2). variable unit mean sd. dev min max site conditions T ◦C 8.09 1.30 2.80 11.47 P mm yr −1 735.72 172.78 456.02 1250.03 MA mm ◦C −1 40.98 10.49 21.24 69.23 SI m 25.55 4.47 14.44 35.74 tree characteristics d cm 23.59 9.83 0.70 72.70 h m 20.22 6.23 0.60 40.00 v m 3 0.55 0.60 0.001 6.61 stand characteristics plot size m 2 1332.97 1882.34 140.00 15500.00 stand age yr 66.49 22.58 40.00 150.00 dq cm 21.77 5.62 11.70 40.58 hq m 19.21 4.03 8.56 30.39 do cm 34.20 10.33 19.26 71.94 ho m 24.10 4.91 10.60 38.00 N ha −1 839 604 50 3200 BA m 2 ha −1 35.66 15.41 4.35 83.08 SDI ha −1 688.35 302.97 87.02 1561.56 V m 3 ha −1 382.41 191.19 44.17 959.33 stand structure CVd ./. 0.31 0.09 0.10 0.56 CVh ./. 0.20 0.10 0.04 0.45 CVba ./. 0.51 0.16 0.14 0.82 GINId ./. 0.17 0.05 0.06 0.31 GINIh ./. 0.11 0.05 0.02 0.25 GINIba ./. 0.33 0.09 0.15 0.55 skew ./. −0.01 0.56 −1.98 2.04 kurt ./. 2.88 1.23 1.39 9.52 partitioning GDCba ./. 0.00 0.09 −0.43 0.20 a0 ./. 1.17 0.77 −0.43 2.85 a1 ./. 0.57 0.25 0.12 1.10 dratio ./. 0.80 0.21 0.48 1.39 H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 5 considerable variation in size, indicating a variation of the stand structure. The upscaling from small plot sizes to hectare values may cause overor underestimation of stand values. The plots represent unthinned and fully stocked stands; the various measures of stand density such as tree number, stand basal area, SDI or standing volume indicate the wide range of covered site conditions. All stand structural characteristics show a wide variation; e.g. the coefficient of variation of the stem diameter was 0.31 on average. However, it was very low in homogeneous stands (CVd =0.10) or even 5-fold in heterogeneous stands (CVd =0.56). The variation of CVh, GINId, GINIba was even wider. The shape of the diameter distribution was nearly symmetric on average (skew =-0.01) but reached from strongly left-skewed (skew =-1.98) to right-skewed (skew =2.04). The variation of growth and mortality partitioning was of particular interest. The GDC based on the individual stem basal area indicated sizeproportional partitioning on average (mean GDCba =0); however, there were stands with an overproportional contribution of small trees to the stand growth (GDCba =-0.43) and stands with clear growth dominance of big trees (GDCba =0.20). The intercept (a0) and slope (a1) of the plot-specific id-d relationships corroborated this wide variation of growth partitioning; e.g., a0-values could be far below zero (a0 =-0.43), indicating size-asymmetric partitioning with a preference of big trees but also far above zero (a0 =2.85) indicating size-asymmetric partitioning with a preference of small trees. The dratios were 0.80 on average and covered a range between dratio =0.48 and 1.39; this means that on some plots, mortality eliminated mainly small trees with a mean diameter below the average stem diameter; on other plots, mortality eliminated mostly big trees. 2.3. Statistical analysis To analyze how the stand structure is modified by the site conditions (Q I), we scrutinized by ordinary linear regression how the Coefficients of variation of the stem diameter and tree height distribution, CVd, and CVh, and the Gini Coefficient of stem diameter and tree height, GINId, GINIh depend on the site index, SI, of the stands. We used the climate variables T, P, and MA to characterize the range of site conditions of the plots; however, these variables did not significantly contribute to explaining the variation of the stand structure along the transect across Europe. ln(CVdk) = a0+a1×ln(SIk) + ε k(1a) ln(CVhk) = a0+a1×ln(SIk) + ε k(1b) ln(GINIdk) = a0+a1×ln(SIk) + ε k(1c) ln(GINIhk) = a0+a1×ln(SIk) + ε k(1d) where ε k∼N(0, σ 2)is the residual for the kth forest plot. We chose double-logarithmic relationships in all four cases (models 1a-1d) as they appeared biologically more plausible than linear relationships and they also resulted in higher R 2 values. To analyze how the stem diameter growth and the partitioning of growth and mortality change with site index (Q II), we fitted models 2–7 to the data. Model 2 was fitted to quantify the plotwise relationship between the stem diameter increment in a given 5-years-period and d being the stem diameter at the beginning of this period. The evaluations resulted in the plotwise intercepts and slopes a0 and a1, respectively. In models 3–5, we tested the potential influence of site index and quadratic mean diameter (as an indicator of the stand stage development) on growth partitioning. In model 3, we explored these relationships using all the tree data by expanding the id-d model. In models 4–5, we tested the effect of site index and quadratic mean diameter on the intercepts and slopes of plotwise id-d relationships. We also tested the interactions between the variables and included them in case of significant contribution at p<0.05. idk=a0+a1×dk+ ε k(2) idik =a0+a1×dik+a2×SIik+a3×dqik +bi+ ε ik (3) a0=a0+a1×SIk+a2×dqk+a3×SIqk×dqk+ ε k(4) a1=a0+a1×SIk+a2×dqk+a3×SIqk×dqk+ ε k(5) Notice that in models (1) - (7), we used a0−a3 as regression coefficients, whereas a0 and a1 in models (4) and (5) are dependent variables. We tested the effects of all available stand variables and their respective interactions on dratio; only the following two models, 6 and 7, yielded significant results. dratiok=a0+a1×SIk+a2×dqk+ ε k(6) dratiok=a0+a1×GDCk+ ε k(7) We applied ordinary linear regression (models 1–2 and 4–7) and linear mixed effect models (3). The lower letters i and k represent the kth observation on the ith triplet in the previous equations. All fitted models were subject to the usual visual residual diagnostics. For all models, the residuals were plotted against the fitted values. In no case, the plots suggested a violation of variance homogeneity. Likewise, the normality of errors was verified by making normal q-q plots of the residuals. In model 3, a random effect bi∼N(0, τ 2)was implemented at the plot level to consider the hierarchical data structure, and that we sampled several trees on the same plot. In this way, we covered any spatial correlation between the neighbouring trees on a given plot. With ε ik ∼N(0, σ 2)we denoted independently and identically distributed errors. In all equations a0,…,an are the fixed effects parameters. For all calculations, we used the libraries nlme (Pinheiro et al., 2021) and lme4 (Bates et al. 2015) within the statistical software environment R 4.1.0 (R Core Team, 2021). 2.4. Model development and scenario analyses In addition to the empirical analyses, we developed and applied a simulation model to understand better the effect of both partitioning of growth and mortality between the trees on the size structure of the stand (Q III). The model was used to study the interplay between the sitedependency of the partitioning of growth and mortality. It was applied to answer Question 3, i.e., how the partitioning of mortality (in terms of the size distribution of dropout trees and its dependency on site conditions) in addition to the growth partitioning shapes the size variation and thereby the stand structure. The main model components were algorithms to generate the initial size distributions, model the growth partitioning between the trees depending on the site conditions, and model the mortality depending on site conditions. The initial size distribution was generated by random numbers from Gaussian normal distribution with a defined tree number, mean stem diameters and standard deviation using the R routine rnorm (). The whole model was developed as a script in R. We used realistic start parameters extracted from the empirical dataset of the 90 Scots pine plots. For the growth partitioning, we used equation (3), which estimates the annual stem diameter growth depending on the stem diameter at the beginning of the period, the quadratic mean stem diameter, and the site index, SI. The mortality was modelled in two steps; first, we estimated the number of dropout trees based on the selfthinning line and second, we selected the dropout trees from the size distribution. As the self-thinning line, we applied the equation ln(N) = 12−1.593 ×ln(dq). The intercept was based on an SDI =1000, and for the exponent, we chose the species-specific value reported by Pretzsch and Biber (2005). We implemented a uniform selection of the number of dropout trees (number of trees exceeding the self-thinning line) within defined diameter ranges of the stand. So, the simulation model allowed selecting H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 6 the dropout trees from different percentiles of the diameter distribution or over the whole range. In this way, we could analyze how different modes of mortality (e.g., dropout only at the smaller end or over the entire range of the distribution) affect the size variation of the stand in addition to the growth partitioning. In accordance with the empirical analyses, we assumed a restriction to the smaller end of the size distribution on rich sites, a wider range on medium sites, and mortality covering uniformly the whole diameter range on poor sites. In annual steps, the resulting scenario runs show how various (default values) assumptions of site-dependent partitioning of growth and mortality shape stand characteristics such as the GINI and GDC coefficient, the variation coefficient of stem diameter distribution, and the relationships between these values for different SI values. 3. Results 3.1. Overview of tree and stand characteristics The metrics for the stand structure, such as coefficient of variation (CVd, CVh, and CVba), GINI, and GDC, showed that the 90 Scots pine plots vary considerably in stand heterogeneity, size distribution, and growth partitioning (Table 1). Fig. 2 visualizes this finding by the Gini coefficients of (a) cumulative stem basal area and (b) basal area growth, plotted against the cumulative tree number, ordered after increasing tree size. The bundle of curves reveals the broad range of size and growth partitioning patterns on the 90 plots. The curves close to the bisecting line reflect an equal size or size growth distribution on the plots; the further the curves deviate from the bisecting line, the stronger the inequality of size or growth on the respective plots. The Growth Dominance coefficient can be visualized by the cumulative distribution of stem basal area growth over stem basal area, e.g., stem basal area growth over the initial stem basal area (Fig. 2c). For this purpose, all trees of a stand are ranked from smallest to largest basal area; the cumulative basal area of the trees is registered on the abscissa, their cumulative basal area growth on the ordinate. The resulting curves illustrate how tree size distribution contributes to total stand growth. The lines in Supplement Fig. 1c indicate a growth dominance of big trees (lower curve, GDC >0), small trees (upper curve, GDC <0), or a proportional contribution of growth according to their size (straight line, GDC =0). The 90 Scots pine plots include stands where small trees grow overproportionally related to their share in the stand (Fig. 2c, curves above the bisecting line) and stands where trees of all sizes grow proportional to their relative share of the stand basal area (curves close to the bisecting line). The curves below the bisecting line represent stands with an overproportional growth partitioning favouring big trees. The stands also varied considerably in the partition of mortality. The mean stem diameters on the plots (Fig. 3a) vary due to the strongly differing site conditions, although the stand ages are somewhat similar. We show both the mean stem diameters of the total and dropout trees (Fig. 3a and b) to stress that mortality does not operate exclusively at the smaller end of the diameter distribution. The ratios dratio =dmort/dtotal show that in many cases, the dropout trees’ stem diameter is, on average smaller than those of the total stand (points below the bisecting line in Fig. 3c). However, there are also plots on which the mortality eliminated trees with stem diameters that were, on average similar to or even larger than the trees of the total stand. This suggests that mortality modifies the size distribution in different ways. 3.2. Tree size variation depending on site quality (Q I) The coefficients of variation and the Gini coefficients of the stem diameter and tree height decreased with increasing site index (Fig. 4); i. e., the structural diversity decreased from poor to rich sites. To consider any additional changes in the structural diversity due to differences in the stand development phase, we also included stand age and quadratic mean stand diameter in the regression models. However, these two variables were not significant. The decrease of the height diversity reflected by the slopes of the CVh and GINIh coefficients (see a1-values in Table 2, models 1b and 1d) was stronger than the decrease of stem diameter diversity (see a1-values in Table 2, model 1a and 1c). This corroborated the dominance of monolayered stands on rich sites. 3.3. Mode of competition, growth distribution, and mortality depending on site quality (Q II) The plotwise fit of the model id =a0+a1×d to the measured stem diameter growth, id, and stem diameter at the beginning of the respective growth periods, d, (Fig. 5a) resulted in n =88 a0 and a1 values. Notice that the status data were available from 90 Scots pine plots, the growth data only from 88 plots. The a0 values (mean, min, max) werea0 =-0.003, −0.293, 0.478, and the a1 values a1 =0.009, −0.008, 0.028. In this context the intercept and slope of the id-d-relationship were not used for prediction but for characterization of the mode of growth partitioning between the trees in the stands. Straight lines with a0=0, i.e., lines through the origin would indicate size symmetric competition and resource partitioning, whereas lower and higher a0 values indicate overproportional and disproportional increase of growth with increasing size, respectively. The Fig. 2. Overview of size distribution and growth partitioning on the 90 Scots pine stands underlying this study. (a) The Gini coefficient of stem basal area distribution, GINIba, indicates the degree of size equality of trees in a forest stand. (b) The Gini coefficient of stem basal area growth distribution, GINIiba, indicates the degree of size growth equality of the trees in a forest stand. (c) the Growth Dominance Coefficient, GDCba, indicates the relative contribution of small compared with big trees to stand growth. In all cases, the bisecting line (dashed) represents equality of size or size growth. H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 7 a0-values from −0.293 to 0.478 indicate that the plots cover a broad spectrum of different modes of competition, ranging from sizeasymmetric competition with growth strongly overproportionally increasing with size (a0<0) to size-symmetric competition and partitioning (a0=0), and to size-asymmetric competition with growth disproportionally increasing with size (a0>0). Fig. 5b shows how the stem diameter growth depends on the initial individual stem diameter d, the developmental state of the stand, represented by dq, and on the site index. Latter significantly increases the level of growth and size-asymmetric partitioning in favour of big trees. The effects of d, SI, and dq were significant (see Table 2, model 3). The effect of the site index on the growth partitioning between the trees is further corroborated by Fig. 5c and d; the site quality decreases the intercept and increases the slope of the individual stands’ relationship between stem diameter growth and stem diameter at the beginning of the growth period. This indicates a strong increase in asymmetric growth partitioning favouring big trees on rich sites. Fig. 6a shows the dependency of dratio on the site index; the better the site conditions, the lower is dratio. This indicates that on poor sites, mortality eliminates more often bigger trees than on rich sites and this tendency increases with stand development state, represented by dq. Interestingly, there seems to be a trade-off between dratio and GDC (Fig. 6b). This finding underpins the observation that size-asymmetric growth partitioning favouring big trees (high GDC values) causes the Fig. 3. Overview of mortality characteristics of monospecific Scots pine stands underlying this study. (a) Mean stem diameter of the total stand, d total. (b) Mean stem diameter of the dropout trees, dmort and (c) dmort plotted over dtotal. Observations below the bisecting line in (c) indicate prevailing mortality of small trees. The vertical lines in (a) and (b) at a stem diameter of 30 cm do not represent the means of the respective distributions. Still, they serve as a reference for better comparing both distributions. The straight lines in (c) represent ratios of 0.5, 1.0, and 1.5 between the mean diameter of the trees dropping out due to mortality and the trees of the total stand. Fig. 4. Characteristic of stand structure and their dependency on stand and site conditions. (a and b) The coefficient of variation of stem diameter, CVd, and height, CVh, decreases with site index, SI. (c and d) Gini coefficient of stem diameter and tree height decreases with SI. The curves resulted from models 1, a-d; for statistical characteristics, see Table 2. H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 8 mortality of mainly small trees (low dratios). In contrast, more equal growth partitioning (low GDC values) is coupled with a more uniformly distributed mortality (higher dratios) that eliminates trees throughout the whole stem diameter range. 3.4. Effect of the growth and mortality of trees on the size variation at the stand level revealed by scenario simulations (Q III) Among the many scenario runs, we selected the ones shown in Fig. 7 as they convey the main results. Scenarios 1–3 reflect the net effect of the overlay of partitioning of growth and mortality for poor (black curves), medium (red curves), and rich site conditions (green curves) (SI =15, 25, 35 m height at age 100). To reproduce and demonstrate the effects of both partitioning of growth and mortality on the stand structure, we assumed a characteristic initial diameter distribution and modes of growth and mortality for poor, medium, and rich sites. Then, using the model introduced in section 2.4, we simulated the stand development in terms of SDI, GDC, dratio, CVd and other variables. The model functions were based on the 90 Scots pine stands that were middle aged but did not include really old stands. The diameter growth function (see model 3, Table 2) reflects that the level of the id ~ d relationship decreases with progressing stand development. However, it does not reflect that the Table 2 Statistical characteristics of the main models used in this study for answering questions Q I-Q II. The equation numbers refer to the models introduced in statistical models section 2.3 (Statistical models). For reasons of space limitation, the table reports only the fixed effect variables of the respective models. For variable explanation, see section 2.2 and Table 1. All regression coefficients and models that were significant, at least at the level of p<0.05, were set in bold letters. model variables n a 0 std (a 0 ) p-value a 1 std (a 1 ) p-value a 2 std (a 2 ) p-value a 3 std (a 3 ) p-value Q I: 1a ln(CVd) ~ ln(SI) 90 0.98 0.49 0.048 −0.69 0.15 <0.001 1b ln(CVh) ~ ln(SI) 90 2.19 0.84 0.011 −1.22 0.26 <0.001 1c ln(GINId) ~ ln(SI) 90 0.46 0.50 0.272 −0.71 0.15 <0.001 1d ln(GINIh) ~ ln(SI) 90 1.80 0.83 0.033 −1.29 0.26 <0.001 Q II: 2 id ~ d see section 3.3 3 id ~ d, SI, dq 88 0.11 0.01 <0.001 0.01 0.0001 <0.001 0.002 0.0002 <0.001 −0.007 0.0003 <0.001 4 a0 ~ SI, dq, SI × dq 88 0.97 0.36 0.008 −0.04 0.01 0.002 −0.03 0.02 0.03 0.002 0.0006 0.009 5 a1 ~ SI, dq, SI × dq 88 −0.003 0.015 0.047 0.0002 0.0005 <0.001 0.001 0.0005 0.09 −0.00007 −0.00007 0.007 6 dratio ~ SI, dq 34 0.76 0.18 <0.001 −0.02 0.005 0.003 0.02 0.005 <0.001 7 dratio ~ GDC 34 0.85 0.03 <0.001 −0.54 0.16 0.002 Fig. 5. Visualization of the relationship between annual stem diameter growth, id, initial stem diameter, d, and covariables site index, SI, and quadratic mean stem diameter of the stand, dq. (a) Individual tree measurements of id and d (black points) and plotwise relationships id =a 0+a1×d fitted by linear regression (see model 2 and model coefficients a0 and a1 reported at the beginning of section 3.3). (b) Overall model 3 for the stem diameter growth depending on d, dq, and SI (model 3, coefficients see Table 2). (c and d) Dependency of the model coefficients a0 and a1 of the plotwise relationships between id and SI and dq (models 4 and 5, coefficients see Table 2). H. Pretzsch et al. Forest Ecology and Management 520 (2022) 120365 9 slope of the id ~ d relationship can flatten continuously or even become negative in old stands. The age (mean ±standard deviation) of the underlying stands was 66.5 ±22.6 years (see Table 1); thus the trajectories beyond stand age 90 represent extrapolations and should be interpreted cautiously. Fig. 7 shows the mean course of 10 replications for each scenario (in the case of CVd means ±SE). To keep the scenario results simple, we added the confidence bands (±SE) only in the case of the most interesting output variable CVd (see Supplement Fig. 2 for analogous representations of variables SDI, GDC, and dratio). All three scenarios start with the same diameter distribution (2000 trees ha −1 , mean diameter 15 cm, standard deviation 5 cm). After about 20 years, the stand approached the assigned maximum stand density of SDI =1200 trees ha −1 at dq =25 cm and followed this line until advanced age (Fig. 7a). The default id-d relationships for poor, medium, and rich sites result in the GDC developments shown in Fig. 7b. The growth dominance (the inequality of growth partitioning indicated by the GDC) continuously increased in all three scenarios. However, the growth dominance was permanently higher on richer sites than on poorer ones. The GDC remained below the 0-line into advanced age on poor sites, indicating an always relatively equal growth distribution (Fig. 7b). The scenarios of dratio reveal that on poor sites, the diameter of the dropout trees is similar to the mean diameter of the total stand. In contrast, the mortality eliminates smaller trees on medium and rich sites Fig. 6. Mode of mortality in terms of the ratio d ratio =dmort/dtotal depending on (a) site index, SI, and (b) the Growth Dominance Coefficient, GDC. For underlying models and statistical characteristics, see Table 1. Fig. 7. Results of three scenario runs (means ±SE of 10 replications each) assuming the site-specific growth and mortality partitioning on poor, medium, and rich sites (underlying assumptions see Fig. 6. Development of (a) SDI, (b) GDC, (c) dratio, and (d) CVd. H. Pretzsch et al.