Use of Terrestrial Laser Scanning (TLS) on crown and stem measuremntens in the survey and monitoring of mixed forests

PROGRAMA DE DOCTORADO EN CONSERVACION Y USO SOSTENIBLE DE SISTEMAS FORESTALES TESIS DOCTORAL: USE OF TERRESTRIAL LASER SCANNING (TLS) ON CROWN AND STEM MEASUREMNTENS IN THE SURVEY AND MONITORING OF MIXED FORESTS Presentada por Sara Uzquiano Pérez para optar al grado de Doctora por la Universidad de Valladolid Dirigida por: Dr. Felipe Bravo Oviedo Dr. Ignacio Barbeito Sánchez List of figures List of tables ........................................................................................................................................ 3 ......................................................................................................................................... 6 List of acronyms .................................................................................................................................... 9 Abstract Resumen ........................................................................................................................................….….10 .............................................................................................................................................. 12 Introduction ....................................................................................................................................... 14 · The present state of forests ........................................................................................................ 14 · The importance of mixed forests ................................................................................................. 15 · Models and TLS ............................................................................................................................ 16 · The crown information ................................................................................................................ 17 · The wood quality: Lean and sweep ............................................................................................. 17 · Pinus Sylvestris, Quercus Petraea and Quercus Pyrenaica …........................................................ 18 · Motivation of the study ............................................................................................................... 21 Objectives ........................................................................................................................................... 22 · General objective ·Specific objectives ......................................................................................................................... 22 …...................................................................................................................... 22 · Graphical approach ..................................................................................................................... 24 Study area ........................................................................................................................................... 26 · Pinus Sylvestris – Quercus Petraea (Site 1) ….................................................................................26 - Study area .............................................................................................................................. 26 - Experimental design ............................................................................................................... 27 · Pinus Sylvestris – Quercus Pyrenaica (Site 2) …............................................................................. 28 - Study area ............................................................................................................................... 28 - Experimental design ............................................................................................................... 28 Data collection · Field data ….................................................................................................................................. 30 ….................................................................................................................................. 30 · TLS data collection - Georeferencing ....................................................................................................................... 32 ...................................................................................................................... 32 - TLS data collection .................................................................................................................. 34 · TLS data processing ...................................................................................................................... 35 - Tree segmentation and variables extraction .......................................................................... 38 a) Pinus Sylvestris – Quercus Petraea …................................................................................ 38 b) Pinus Sylvestris – Quercus Pyrenaica …............................................................................ 42 Data analysis ....................................................................................................................................... 46 · Crown analysis · Wood quality .............................................................................................................................. 46 .............................................................................................................................. 49 · Creation and selection of models ................................................................................................ 49 -Pinus Sylvestris – Quercus Petraea -Pinus Sylvestris – Quercus Pyrenaica ...................................................................................... 49 ……................................................................................. 50 Results................................................................................................................................................. 51 TLS validation and sites comparison .................................................................................................... 51 Fitted crown models ........................................................................................................................... 51 · Pinus Sylvestris and Quercus Petraea · Pinus Sylvestris and Quercus Pyrenaica ........................................................................................ 51 ....................................................................................... 54 - Testing site 1 fitted models in site 2 (Analysis 1) .................................................................... 54 - Fitting models of site 1 to site 2 (Analysis 2) .......................................................................... 54 - Fitted models for site 2 (Analysis 3) ....................................................................................... 59 a) Comparison of models: Analyses 2 vs. 3 ......................................................................... 62 Fitted wood quality models ................................................................................................................ 65 · 3.1. Lean ....................................................................................................................................... 65 · 3.2. Sweep .................................................................................................................................... 66 Discussion ........................................................................................................................................... 68 · Fitted-Crown models ................................................................................................................... 68 - Size effect ............................................................................................................................... 70 - Density and Competition effect ............................................................................................. 71 - Mixture effect ......................................................................................................................... 72 - Site effect ................................................................................................................................ 74 - Ecology of species ................................................................................................................... 74 · Fitted wood quality models ......................................................................................................... 75 - Density, Competition, and Mixture effect .............................................................................. 75 - Asymmetry of the crown ........................................................................................................ 76 · Final remarks ............................................................................................................................... 76 Conclusion .......................................................................................................................................... 78 Conclusiones ....................................................................................................................................... 79 Acknowledgments .............................................................................................................................. 81 References .......................................................................................................................................... 85 Annex 1 ............................................................................................................................................. 103 Crown models of the mixture Pinus Sylvestris - Quercus Petraea applied in the mixture Pinus Sylvestris - Quercus Pyrenaica Annex 2 ............................................................................................................................................. 106 Residual analysis for the mixture Pinus Sylvestris – Quercus Pyrenaica (Analysis 2) Annex 3 ............................................................................................................................................. 115 Residuals analyses of the first 5 models with lower AIC that were developed for the mixture Pinus Sylvestris – Quercus Pyrenaica (Analysis 3) Annex 4 ............................................................................................................................................... 153 Residual analyses for Lean and Sweep models 3 LIST OF FIGURES Figure 1 ................................................................................................................................. 19 Area of distribution for Pinus Sylvestris, Quercus Petraea and mixed forest stands of both species in Spain. The study site is marked by black triangle. Figure 2 ................................................................................................................................. 19 Area of distribution for Pinus Sylvestris, Quercus Pyrenaica and mixed forest stands of both species in Spain. The study site is marked by black triangle. Figure 3 ................................................................................................................................. 24 Thesis workflow process of collecting and preparing TLS data for further analysis. Figure 4 ................................................................................................................................. 25 Thesis workflow process of TLS data analysis to obtain crown and wood quality models. Figure 5 ................................................................................................................................. 27 Triplets location. Distinguish by colors. White are triplets belonging to the Triplet 1, and yellow, triplets belonging to Triplet 2. Figure 6 ................................................................................................................................. 29 Experimental site of Palacio de Valdellorma, following a split-plot design. Rounded in red the three plots taken for this study. Figure 7 ................................................................................................................................. 33 From left to right. Sub-metric GPS Leica Model SR20. Sketch of the experimental plots of Valberzoso and Palacio de Valdellorma. Red circles represent the corners where GPS sub-metric was placed. Figure 8 ................................................................................................................................. 34 Characterization of GPS points in field (left) and identification of these points through the point clouds (right). Figure 9 ................................................................................................................................. 36 Figure 9. Recognition of at least three spheres in every scan image to be able to do the alignment and therefore convert panoramic images 2D of scans into point clouds 3D. Figure 10 ............................................................................................................................... 37 Scan positions performed in Faro Scene. Each scan position is characterized with one color. Image on the left shows one plot without be aligned, and on the right the scan positions well located after white has been recognized. 4 Figure 11 ............................................................................................................................... 38 TLS trees correlated with their correspondent ID in field after .txt file of UTM trees coordinates was overlapped on point clouds. Figure 12 ............................................................................................................................... 40 Variables computed for each tree by “Mathematica11” software. TH= Total Height; CL= Crown Length; CW=Crown Width; CBH= Crown Base Height; DBH= Diameter at Breast Height; CPA= Crown Projection Area; MCWH= Maximum Crown Width Height; CV=Crown Volume. Figure 13 ............................................................................................................................... 41 Schematic draft of a stem section. Where a represents the height of the tree on the y axis, b the longitude of the stem, d the lean of the stem and c the sweep of the stem. Image source: Höwler et al.(2017). Figure 14 ............................................................................................................................... 42 The great occlusion of the stands and the small diameter size of many oak trees made very difficult the isolation and identification of trees. Figure 15 ............................................................................................................................... 43 The plot density together with the steep and rugged ground made specially difficult the identification and isolation of trees. Figure 16 ............................................................................................................................... 44 (A)Creation of a subplot around trees with dendrometric bands, easy to identify from the point clouds (B). Figure 17 ............................................................................................................................... 45 Step by Step Isolation method performed by CompuTree. Figure 18 ............................................................................................................................... 45 Envelopes created in CompuTree every 10 cm around every tree. Figure 19 ............................................................................................................................... 48 Creation of circular subplots around each target tree with radius = 5, 7.5 and 10 m. Figure 20 ............................................................................................................................... 56 Predicted Vs. actual values for each variable, MCWH, CBH, CPA and CV for Pinus Sylvestris and its simultaneous linear hypothesis tests p-values. Figure 21 ............................................................................................................................... 57 Predicted Vs. actual values for each variable, MCWH, CBH, CPA and CV for Quercus sp. and its simultaneous linear hypothesis tests p-values. 5 Figure 22 ............................................................................................................................... 65 Residuals of fitted values of linear model for Lean variable followed a trumpet distribution. 6 LIST OF TABLES Table 1 ................................................................................................................................................ 28 Inventory data of oak-pine triplets where stand indicates plot condition (pure or mixed) and the letters Ps and Qp stand for Pinus Sylvestris and Quercus Petraea respectively. n/plot represents the total number of trees within each plot; n pines the number of Pinus Sylvestris, n oaks the number of Quercus Petraea, and n other the number of other species within the plots different from pines and oaks. Table 2 ................................................................................................................................................ 29 Inventory data of oak-pine of the experimental site of Palacio de Valdellorma. Where “treatment” indicates the intensity of thinning of that plot. n/plot represents the total number of trees within each plot; n pines the number of Pinus Sylvestris, n oaks the number of Quercus Pyrenaica, and n other the number of other species within the plots different from pines and oaks. Table 3 ................................................................................................................................................ 31 Stand characteristics of the study species. n stands for the number of total tree species. DBH is the Diameter at Breast Height in cm. TH is the total height of the tree in m. CBH is the Crown Base Height in m. CPA is the Crown Projection Area in cm2, and BA is the basal area in m2/ha. Table 4 ................................................................................................................................................ 35 Faro Focus 3D settings characteristics used to collect the data. Table 5 ................................................................................................................................................ 39 Total trees per plot (n/plot) compared to total point cloud trees isolated (TLS trees). Table 6 ................................................................................................................................................ 44 TLS trees isolated per plot and species and the total. Table 7 ................................................................................................................................................ 47 Crown models defined for this study. Response Variables are: Maximum Crown Width Height (MCWH), Crown Base Height (CBH), Crown Projection Area (CPA) and Crown Volume (CV) and Explanatory models classified in four categories. s= size, d= density, c= competition and m= mixture. Table 8 ................................................................................................................................................ 47 Categories and variables within each category we have used to define explanatory models. Table 9 ................................................................................................................................................ 49 Starting model equations for lean and sweep. Table 10 .............................................................................................................................................. 51 Mean Diameter Breast Height (DBH) in cm and Total Height (TH) in m of trees calculated with TLS separated by species and kind of plot (pure or mix).n total is the total number of trees measured. Table 11 .............................................................................................................................................. 53 Final equations for each species and crown response variable. . 7 Table 12 .............................................................................................................................................. 53 The explanatory models selected as the best fit according to their lowest Akaike index and biological criteria for each response variable (Variable) and species. r= radius of influence (5, 7.5 and 10 m); s = size; d=density; c= competition; m= mixture; α0= Intercept; α1-4= the coefficient numbers for each explanatory variable (size, density, competition, and mixture). AIC = Akaike, K-S test = P-value of Kolmogorov Smirnov Test for residuals, R2= coefficient of determination of the model. Table 13 .............................................................................................................................................. 55 Fitted models using variables defined for the first experimental site, fitting their coefficient for this second experimental site. Table 14 .............................................................................................................................................. 58 Difference coefficients for Pinus Sylvestris. Table 15 .............................................................................................................................................. 59 Statistical parameter comparison for analysis 1 and 2 for Pinus Sylvestris models. Table 16 .............................................................................................................................................. 59 Statistical parameter comparison for analysis 1 and 2 for Quercus sp. models. Table 17 .............................................................................................................................................. 61 Estimated parameter and statistical adjustment of the models. Table 18 .............................................................................................................................................. 62 K: the number of parameters in the model. AICc: information score of the model. ΔAICc: the difference in AIC score between the best model and the being compared. AICcWt: the proportion of the total amount of predictive power by the full set of models contained in the model being assessed. Cum.Wt: the sum of the AICc weights. LL: log-likelihood (how likely the model is, given the data) Table 19 .............................................................................................................................................. 63 AIC comparison analysis 2 and 3. Table 20 .............................................................................................................................................. 64 Comparison of analysis for Pinus sylvestris. The intercept B0 is not shown in this table since it was no significant for any of the models. Table 21 .............................................................................................................................................. 64 Comparison of analysis for Quercus Pyrenaica. Table 22 .............................................................................................................................................. 65 Fitted models for lean and sweep variable Table 23 .............................................................................................................................................. 66 The explanatory models for the response variable Lean for each species (Sp), selected as the best fit according to their lowest AIC index and residual analysis, Pinus sylvestris (Ps) and Quercus petraea (Qp). r = radius of influence (5 and 10 m); s = size; d = density; c = competition; m = mixture; μ = intercept; β1-4 = the coefficient numbers for each explanatory variable (size, density, competition, and mixture); AIC = Akaike and SSE= Residual Sum of Squares. 14 INTRODUCTION The present state of forests Within the last decade, the concern about the effects on Earth due to Climate Crisis has been increasing as it is already stressing food and forestry systems, directly impacting, among others, human health, ecosystem functioning, and forest structure (Prtner et al., 2022). For this reason, forests have received substantial political attention within the last COP26, since it is well known that forests can adapt to climate change, and thus, they are critically important to mitigate and conserve biodiversity (Vähänen, 2021) as they are well recognized to be one of our principal resources to obtain climate neutrality by 2050 (Lier et al., 2022). Nevertheless, maladaptation has been observed across many regions and systems and occurs for many reasons including inadequate knowledge and shortterm policies (Prtner et al., 2022). Forests also provide goods and ecosystem services (provisioning, regulating, and cultural) from plantations or cultivated forests (Pretzsch & Forrester, 2017; Uhl et al., 2015). Trends suggest social conscience of consuming products from sustainably managed forests is increasing (Europe, 2011). Based on this, management that is solely focused on wood production homogeneously throughout a plantation may miss opportunities to provide other ecosystem services (Himes & Puettmann, 2019) causing economic losses, as has already been experienced in Europe within the last 50 years, where the forests were impacted by extreme heat and drought impacting timber sales for example in Europe (Prtner et al., 2022). For that reason, understanding forest composition, structure, and functioning within a frame of climate change, is crucial to ensure ecosystem services to our society (Muñoz-Gálvez et al., 2021). Shifts in the temperature-precipitation domain that many species experienced during the last decade are likely to increase under a warmer and drier climate, and this may lead to directional, large-scale changes in forest composition (Hartmann et al., 2022) as forests are dependent on different abiotic factors (Bohn et al., 2014). Climate change scenarios project a worrisome increase of 2–5 ◦C in the 21st century coupled with a decrease in precipitation of up to 30%, and a higher frequency and intensity of extreme drought events (Muñoz-Gálvez et al., 2021). As an example, it is expected that, in the temperate zones, even in compliance with the Paris agreements (UNFCCC, 2015), forest productivity is estimated to drop by 23%, assuming forest management and composition are the same as we have nowadays (Bohn, 2021). Therefore, there is an urgent need for adequate management strategies to enhance long-term forest 15 resilience (Muñoz-Gálvez et al., 2021) as temperature changes could turn forests into carbon sinks or carbon sources (Bohn et al., 2014) without the proper management. For that reason, the objectives marked by the new European Union (EU) forest strategy for 2030 are focused on improving the quantity and quality of EU forests and strengthening their protection, restoration and resilience. The Importance of Mixed forests Forests cover almost one-third of the Earth’s land surface (Vähänen, 2021). Around 4% of these forests are undisturbed by human activity, while 29% of the managed forests are monocultures and 51% contain two or three species. In Europe, these mixed forests cover 23% of the pan-European region (UNECE & FAO, 2011). Under potential global warming effects, forest research has experimented with a shift from monospecific to more complex forest stands e.g. Aldea, 2018; Bravo-Oviedo et al., 2014; Bravo et al., 2021; Cattaneo et al., 2020; del Río et al., 2018, 2019; Merlin et al., 2015; Pretzsch & Schütze, 2021; Riofrio, 2018), not only because several studies have proved high biodiversity level is linked to mixed forests with high forests productivity (Bayer, Seifert, & Pretzsch, 2013; Forrester & Bauhus, 2016; Liang et al., 2016; Pretzsch & Forrester, 2017) compared to monocultures (Pretzsch & Schütze, 2014; Riofrío et al., 2017), but also because these stands present some advantages over monospecific ones concerning ecological functions and services (Forrester, 2017; Pretzsch & Forrester, 2017), showing to be more resilient, resistant, and recover faster from storms (Bravo et al., 2021; Pretzsch et al., 2017). Most recently, Rodríguez De Prado et al.(2022), proved, as well, that growth rates for mixed stands were higher than in pure stands. However, there is a need for more data and understanding to identify whether these observations represent a global trend (Hartmann et al., 2022; Heym et al., 2017), since different tree species compositions with different growth rates and final heights will likely develop more structurally diverse forests than those composed of only one or few species (Pretzsch & Forrester, 2017). As an example of this complexity, it is even difficult to reconcile all points of view and to describe mixed forests in a single definition (Bravo-Oviedo et al., 2014), because the understanding of tree species interaction in their structure and functioning is still poor (Pretzsch, 2014). Considering that mixed forest dynamics vary on a small scale (Metz et al., 2013) more studies are still needed across a variety of forest types to establish a sound theoretical approach across scales (Uzquiano et al., 2021). 16 Models and TLS To fully understand forest dynamics, especially in mixed forests, we need models that incorporate essential aspects such as emergent properties, multiple and multi-scale interactions or spatial, functional, and structural variability (Bravo et al., 2019), because it is well known in natural science that structures determine processes and that processes in return modify structures (Pommerening & Grabarnik, 2019). Diameter at Breast Height (DBH) and Total Tree Height (TH) are the two most common and easy variables for measuring, analyzing, and modeling forest stands (Pretzsch, 2009, Chapter 7). They are used separately or together in addition to tree species for estimating other important single-tree attributes such as the cross-sectional area, stem volume, or biomass (Luoma et al., 2019). Data of forest ecosystems are not only temporal but also spatial (Pommerening & Grabarnik, 2019). For this reason, Spatial systems analysis of forest ecosystems is therefore an important branch of ecological statistics integrating research on forest structure, sampling, monitoring, and modeling (Bravo et al., 2019; Pommerening & Grabarnik, 2019). However, the main limitation forestry models have traditionally dealt with is the reconstruction of spatial forest structure as they are usually based on approximations of the forest structure leading to large errors (Dassot et al., 2011), very hard to validate, and difficult to compare across other forest structures (Disney et al., 2018). In addition, forestry models ignore the three-dimensional nature of stand structure, its most important characteristic (Pretzsch, 2009, Chapter 7). Historically, in structure research, often, the necessary methods have been developed within the framework of mathematical statistics (Pommerening & Grabarnik, 2019). Nowadays, thanks to technological advances, this has enormously improved (Bravo et al., 2019) Terrestrial Laser Scanning (TLS) provides us with an accurate tree structure representation, enabling us to obtain detailed information at the tree or plot scales (Dassot et al., 2011). For this reason, TLS has become the main forest strategy to understand forest dynamics through its structure, which becomes even more complex in mixed forests (McElhinny et al., 2005). Since its implementation in forestry science, many authors have developed different studies based on mixed forest structures (e.g. (Martin-Ducup et al., 2016; Pretzsch & Zenner, 2017; Seidel et al., 2011; Wei et al., 2016) as species identity modifies the mixture outcomes (Bravo et al., 2021). This is why it is so necessary to study all possible species mixtures to define an appropriate management strategy for each species composition (Bravo et al., 2021) based on accurate and numerical analyses. 17 The Crown information The crowns of trees have been subjected to much less mensurational study (Hemery et al., 2005). However, as pointed out previously, due to the emerging society requirements, crowns are being further studied (e.g., Barbeito et al., 2017; Bicl-Sorlin & Bell, 2000; Fichtner et al., 2013; Hasenauer & Monserud, 1996; Zarnoch et al., 2004). The crown is a fundamental element of a tree, accomplishing multiple functions (W. Lin et al., 2017). For instance, crown size is closely related to the photosynthetic capacity of a tree (Hardiman et al., 2011; Hemery et al., 2005) and it may reflect the outcome of interspecific interactions (Seidel et al., 2011), looking to fully utilize limiting resources in different space and time (Bravo et al., 2021). In a mixed stand the inter and intra-specific competition effect between trees is shown through the crown (Barbeito et al., 2017; Cattaneo et al., 2020; Lin et al., 2017). The tree structure is highly dependent on the species composition of the competitors, and it can vary considerably from one species to another (del Río et al., 2019; Pretzsch & Schütze, 2014), but have been barely studied due to the difficulty in measuring and defining them accurately, as they were defined through geometric forms. Thus, more efficient algorithms need to be developed to calculate tree crown variables to facilitate the forest resource survey. (Lin et al., 2017). The wood quality: Lean and Sweep the straightening capacity of the stem and its mechanical stability (Lean and sweep) are other key variables in forest trees related to light capture (Sierra-de-Grado et al., 2022). despite their importance to the timber industry, they have not been considered (Thies et al., 2004). By studying these measurements we will understand the trade-off with other functions that may imply differential resource allocation patterns (Sierra-de-Grado et al., 2022) so that future wood resources can be better utilized (Höwler et al., 2017). Despite the necessity of study, the role of bark in the straightening process should be investigated in the longer term (Sierra-de-Grado et al., 2022). The information on inner wood quality is usually based on manipulative experiments at an early stage where data are not available before the trees are felled (Höwler et al., 2017) or they are based on subjective classification criteria, to avoid felling the tree (Thies et al., 2004). TLS allows to get around this problem and to obtain numerical measurements of wood quality such as the lean and the sweep of the stems objectively without felling the tree, thus, allowing longer-term experiments to understand how inter and intra-specific interaction acts on trees. 18 The development of wood quality models can be used to characterize the Lean and Sweep of tree species, which will help in understanding the cost-benefit balance of the adaptive growth of the tree (Thies et al., 2004) as well as understanding the different influences between neighboring trees. Pinus sylvestris, Quercus petraea and Quercus pyrenaica Determining how the variability is influenced by tree inter or intra-specific interaction status in different species is particularly important for tree allometry applications in forest practice and modeling (del Río et al., 2019). For this reason, several studies have focused on pine-pine mixtures in different regions of the Iberian Peninsula (Riofrio, 2018), and some others on Scots pine-oak mixtures (Aldea Mallo, 2018; del Río & Sterba, 2009). In both cases, it was established that mixed stands support a greater increase in volume per occupied area compared to monoculture suggesting a species interaction with reduced levels of competition in the former (Aldea Mallo, 2018; del Río & Sterba, 2009). In either case, results from studies focused on Scots pine are quite distinct, probably due to the large distribution area of the species with high variability in its response to climatic conditions (Del Río et al., 2017). This research is focused on Scots pine (Pinus sylvestris L.), Sessile oak (Quercus petraea (Matt.) Liebl.), and Pyrenean oak (Quercus pyrenaica Willd.) to get a bit more insight into the ecology of these species. In the Iberian Peninsula, low altitudes sites are mainly dominated by Quercus spp., while higher and colder areas are dominated by conifers (mainly Pinus spp.). (Muñoz-Gálvez et al., 2021). However, it is very common to find them mixed (Figures 1 and 2). 19 Figure 1. Area of distribution for Pinus sylvestris, Quercus petraea, and mixed forest stands of both species in Spain. The study site is marked by a black triangle. Figure 2. Area of distribution for Pinus sylvestris, Quercus pyrenaica, and mixed forest stands of both species in Spain. The study site is marked by a black triangle. 20 Pinus sylvestris is the most widely distributed pine species in the world (Riofrio, 2018; Vallet & Perot, 2018), the species with the biggest area extension in Europe (Aldea Mallo, 2018; Montero et al., 2008), and the species with a wide silviculture tradition due to its multiple functions as productive and protective species (Montero et al., 2008). In the Iberian Peninsula, Scots pine is mainly found in montane climates: 800-2000 m.a.s.l., 600-1200 mm mean annual precipitation, and summer precipitation above 100 mm (Montero et al., 2008) representing the southernmost distribution of this typical boreal species (Castro et al., 2004). It is a light-demanding pioneer species that can grow in half-light conditions (Riofrio, 2018). It has a deep root system with dominant oblique and long secondary roots that allow access to deeper soil horizons during drought (Hartmann et al., 2022). Quercus petraea is widespread in the temperate zone at an altitude between 0 and 1500 or even at 1800 m.a.s.l (Reque, 2008) and is one of the most ecologically and economically important hardwood tree species in Central Europe (Arsić et al., 2021). It is characterized by having deep secondary branches and taproot (Reque, 2008). It has an important protector value as montane species, being the habitat of important animal species as Ursus arctos arctos (Clevenger et al., 1992; Reque, 2008; Ruiz-Villar et al., 2019) and is considered well adapted for future climate scenarios (Arsić et al., 2021) thanks to its broad ecological amplitude (Stimm et al., 2021). Quercus pyrenaica is distributed throughout the western Atlantic Mediterranean regions: West France, Portugal, Spain, and North Morocco. In Spain, the largest area distribution of this species is located in Castilla y Leon, which occupies 67% of its natural distribution area. It is found in sub-humid and continental Mediterranean climates between 400-1600 m.a.s.l. with a mean annual precipitation of 600 mm. It has a powerful root system, a well-developed central axis, and numerous horizontal and superficial roots (J. A. Bravo et al., 2008). It has a short growing season, which may determine its distribution. Summer drought is one of its limiting factors, and it avoids the driest areas (Aldea Mallo, 2018). The Pyrenean oak forests have been widely managed as coppice with silvopastoral uses, such as firewood, livestock grazing, and charcoal. Finally, the changes in land use are making it important to establish a forest-based management production (Bravo et al., 2008) for this species. Scots Pine and both oaks (Sessile oak and Pyrenean oak) usually establish spontaneous mixed stands where their natural distribution area is the same (Figure 1 and 2). Our study areas, like so many other areas of this type, are the result of forest management strategies during the second half of the twentieth century that included re-introducing pine into oak coppice stands as a method of forest restoration and to increase stand productivity (Aldea Mallo, 2018). However, the abandonment of traditional forest uses and the lack of subsequent management have resulted in structurally and 21 functionally homogeneous dense stands, which are particularly vulnerable to climate changeassociated disturbances (Fernández-de-Uña et al., 2015). In this kind of mixed stand, the successional processes are slower and wildlife biodiversity is reduced (Maestre & Cortina, 2004; Ruano et al., 2013). For this reason, the study and comprehension of mixed forests are crucial for their sustainable management. Motivation of the study TLS allows us to quantify the admixture effect that varies so much across sites and species (Muñoz- Gálvez et al., 2021). Recent studies related to the application of terrestrial 3D laser scanning systems in forestry focused on the measurement of the crown projection area and crown volume based on the point-cloud data; however, most studies used the laser scanning software only to process the data (W. Lin et al., 2017). Motivated by the still lack of scientific insights into specific advantages of mixedspecies forest (Pretzsch & Forrester, 2017) and all the potential TLS can provide us, in this research, we have evaluated two widespread mixtures in Spain, Pinus sylvestris – Quercus petraea and Pinus sylvestris – Quercus pyrenaica where the complementarity or competition between species may cause overgrow one over the other (Pretzsch & Forrester, 2017) making proper management of these forests difficult. With TLS we can collect accurate data in a way that does not destroy the forest and that allows us to fit new models that take into account the interaction between species, which is a fundamental part of forest management planning to support decision-making (Janowiak et al., 2017; Luoma et al., 2019). The resulting models aim to quantify these two species' composition mixtures and thus, managers can anticipate potential future conditions (Janowiak et al., 2017). This will serve as a tool to support the most appropriate decision-making to be able to do sustainably use of these stands. At the same time, the quantification of these species compositions will also help the work of policymakers and other stakeholders involved in land management. 22 OBJECTIVES General Objective The main objective of this thesis is to determine how inter and intra-specific competition affects crown shape on the individual crown structure and wood quality in a mixed stand composed of Pinus sylvestris – Quercus petraea and Pinus Sylvestris – Quercus pyrenaica to gain insight on management of these forests. Specific Objectives 1. To obtain accurate crown and wood quality data through TLS To characterize the crown and wood quality of every tree within the studied plots we used TLS. We firstly hypothesize that TLS techniques allow foresters to obtain high-quality information as traditional approaches do (e.g. through tools such as calipers and hypsometers). Thereafter, we developed several methods to obtain accurate and objective variables of the crown and the stem from TLS point clouds. 2. Determine a good approach to study the inter and intra-specific competition To determine the extent of influence of the surrounding trees around the target tree, we determined the three radii of influence (5, 7.5, and 10 m), thus we were able to analyze the density, competition, and mixture effect of the trees as a continuous variable. 3. Expanding and fitting crown and wood quality models To determine and quantify how species composition affects the crown shape of the trees, we selected crown models and expanded using explanatory variables of size, density, competition, and mixture and tested whether they had positive or negative relationships in their four crown variables (response variables): Maximum Crown Width Height (MCWH), Crown Base Height (CBH), Crown Projection Area (CPA), and Crown Volume (CV). We followed the same methodology for wood quality analysis, selecting the Lean and the Sweep of the stem as the response variables. 4. To test the robustness of crown fitted models To verify the robustness of the first models fitted for Pinus sylvestris-Quercus petraea, we 23 conducted three analyses: (1) we applied the models to the data of the mixture Pinus sylvestris-Quercus pyrenaica, (2) we fitted the coefficient of the models for this second mixture, and (3) we fitted models specifically for our second mixture Pinus sylvestris-Quercus pyrenaica. We then compared all of them using residual analyses and the AIC index. 30 DATA COLLECTION Field data For both sites, all trees belonging to the plots were labeled (tree ID), and each tree position (Cartesian x and y coordinates) was recorded with a Total Station (Topcon 220). Diameter at breast height (DBH) above 7.5 cm was measured with a caliper, and total height (TH) of the tree was measured with a hypsometer Vertex III (Haglöf Sweden) for all of the trees. In addition, for the experimental site of Valberzoso, Crown at Breast Height (CBH) was measured with Vertex III, and the projection radii (in four directions: N, E, S, W) were measured with tape to the closest cm. Tables 3 and 4 summarize the stand characteristics for each species and each experimental site 1 and 2, respectively. 31 Table 3. Stand characteristics of the study species. n stands for the number of total tree species. DBH is the Diameter at Breast Height in cm. TH is the total height of the tree in m. CBH is the Crown Base Height in m. CPA is the Crown Projection Area in cm2, and BA is the basal area in m2/ha. Main tree species Pine Oak n= 254 n= 480 min 13.60 7.20 DBH (cm) mean (± SD) 29.69 ± 6.61 19.91 ± 6.51 Median 29.73 19.65 Max 53.35 60.50 min 10.50 4.00 TH (m) mean (± SD) 18.23 ± 1.90 17.32 ± 2.93 Median 18.60 18.00 Max 23.90 23.70 min 1.10 2.00 mean (± SD) 12.56 ± 2.08 11.67 ± 2.21 CBH (m) Median 12.70 12.00 Max 17.50 16.70 min 0.59 0.14 mean (± SD) 12.50 ± 8.80 9.88 ± 9.37 CPA (cm2) Median 10.71 7.49 Max 56.61 114.20 min 0.17 0.06 mean ( ± SD) 0.92 ± 0.41 0.50 ± 0.40 BA (m2/ha) Median 0.90 0.43 Max 2.49 4.96 32 TLS data collection For both experimental sites, data collection was the same. The diagram of the following methodology is shown in Diagram 1. Diagram 1. Flowchart of Fieldwork data collection and the processing flowchart for TLS data. Georeferencing During scanning and as supporting material georeferenced plots corners were recorded with a submetric GPS Leica model SR20 frequency equipment with external antenna reception AT501. This equipment has an error margin of centimeters. This step was taken to speed up the tree identification process since data scans are metric, i.e. we can make use of TLS data to obtain the data of the densitometric variables but these data are not oriented, either referenced or locally or globally (UTM coordinates) so the correspondence between trees turns difficult. Thanks to this georeferencing we were able to minimize the error of the actual location of the plots, and therefore, make the correspondence of tree identification between field and point clouds easier. 33 For this purpose, for the first experimental site, we recorded three corners of each plot. Due to canopy cover, we have always chosen the corners closer to the road to ensure the GPS would find enough satellites (Figure 7). For the second experimental site, only five points were needed because plots were closer to each other, and connections between plots were possible to make (Figure 7). For each station, the GPS was located for 30 minutes, so that, the error was minimized. Figure 7. From left to right. Sub-metric GPS Leica Model SR20. Sketch of the experimental plots of Valberzoso and Palacio de Valdellorma. Red circles represent the corners where the GPS sub-metric was placed. As mentioned before, the perfect identification of these points is very important afterward in deskwork, thus, after each GPS station, the exact place was marked with one white sphere over a wooden pole (needed for the scanning process) and perfectly distinguished from the rest of white spheres (Figure 8). 34 Figure 8. Characterization of GPS points in the field (left) and identification of these points through the point clouds (right). TLS data collection Experimental site 1 (Valberzoso, Palencia) was scanned twice. The first time in September 2018, but after processing data, we observed that the quality of the data was not good enough to study tree architecture due to the leaves of the oak trees were obstructing the stem and crown information, therefore a second scan was performed between February and March 2020. Experimental site 2 (Palacio de Valdellorma, Leon) was scanned in March 2016. Previous to scanning and to assure the recording of all the trees belonging to the plots and to optimize battery scan life, a pre-design of a multiple-scan approach on each tree-plot map was done. However, the final amount of scanner positions varied depending on the plot density. For experimental site 1, where stand density was the same across all the plots, 12 scanner positions were needed in each plot. For experimental site 2, where different stand density existed the final amount of scan positions were 24 for plot A1 where the thinning intensity was 50% but for plots Z2 and A2, where the thinning intensity was 25% and 0%, respectively, 48 scan positions were needed. Terrestrial LiDAR data were captured by a Faro Focus 3D device. Panoramic spherical scans were captured, containing a horizontal angle from 0° to 360° and a vertical angle from -60° to 90°. The scan was mounted on a tripod at approximately 1.3 m above the ground. Each scan size was 8192x3414 points, that is to say, 28.0 million points per capture and spatial resolution of 7.670 mm at 10 m. The rest of the characteristics are defined in Table 4. 35 Table 4. Faro Focus 3D settings characteristics were used to collect the data. Angular Resolution 0.6135 milirad Horizontal field of view 0°  360° Quality 2x Vertical field of view -60°  90° Scan Duration (mm:ss) approx. 02:08 Point Distance 7.670 mm @ 10 m Scan Size (Pt) 8192x3414 Points captured per scan 28 M Faro Focus 3D had it owns 10 spheres of alignment which were 15 cm in diameter but based on previous experience (Uzquiano, 2014) to facilitate their recognition during processing data, we used 15 bigger spheres: 18 cm diameter cistern buoys, as reference points as they could be recognizable from farther away (Marcos, 2021). They were winded on a one-meter high wooden pole as is shown in Figure 8. During this process, to ensure the correct alignment of scans, we had to take care of two things: (1) The scanner should be able to recognize at least three of them in each scan position. (2) As the number of spheres was not enough to cover the entire plot at once assuring the visibility of three of them in each scan position, they had to be moved as we went scanning along with the plot, therefore we should take care the spheres were recorded in the same position from at least two scan positions. The total time needed for scanning each plot was about two hours, except for plots A2 and Z2 of Experimental site 2, where the final scanning time per plot was 5 hours each. TLS data processing To convert scan captions in point clouds we used a Workstation Intel CORE i7-5280K. hard disk SSD 256 GB Samsung 950 PPRO M S2. Hard disk SATA 4TB. WD Blank CPU INTEL 1022 CORE i7-5820K 3.3G. 6 CORE 6 CACHE. 4 memories DIMM 8 GB DDR4. The first step needed was to convert the panoramic (2D) scans into 3D point clouds. Faro Focus 3D creates .fls files. This extension is only readable by Faro Focus 3D’s own software, Faro Scene (Faro Technologies Inc., Lake Marry, USA). We used Version 5.2 and 7.0 for experimental sites 2 and 1 respectively. Thanks to this software, we first made the alignment of scans, i.e. the scan placements, where every scan position is located in its actual position in the field by the recognition of, at least three white spheres with enough points (Figure 9), i.e. spheres were close enough to the scan position to be recognized as spheres if the sphere was 10 m far from the scanner, then we would have one 36 point every 7.67 mm (table 4), but if it was 20 m then we would have one point each 15.34 mm, the closer to the scan, the better. This processing of the scans can be done automatically using the option of Pre-processing (Marcos, 2021). Once the characteristics of the spheres were set into the software, the program searched for them automatically. This processing time varied depending on project size. Our projects varied between 5 and 10 Gb and therefore this processing time varied between 2 hours and 6 hours, respectively. After this pre-processing step is completed, it was executed a manual supervision scan to check the recognition of spheres was done correctly as sometimes it recognized other objects such as leaves or branches as if they were spheres or, on the contrary, did not recognize all the spheres in the scan. Once this process was done, scans were all aligned (Figure 10), and the project was saved as one single point cloud file with a .xyz extension. Therefore, we could edit the plot point clouds in other programs. Figure 9. Recognition of at least three spheres in every scanned image to be able to do the alignment and therefore convert 2D panoramic images of scans into 3D point clouds. 37 Figure 10. Scan positions performed in Faro Scene. Each scan position is characterized by one color. The image on the left shows one plot without being aligned, and on the right, the scan positions are well located after white spheres were recognized. To be able to identify each 3D tree with its corresponding ID the .xyz files were imported together with the georeferenced corner of the plots, which had a .txt format to the module IMispect from the software Polyworks Version 12.1.3 (InnovMetric Software Inc., Quebec, Canada) (Barbeito et al., 2017; Ferrarese et al., 2015; Hackenberg et al., 2015) and overlapped the point clouds layer (.xyz files) on the UTM points (the georeferenced corners). This process was done thanks to the characterization made during fieldwork, which let us know, which ones were the georeferenced points to be overlapped on the coordinates (Figure 8). Finally, we imported as text file (.txt format) UTM coordinates of all the trees belonging to the plots. This process was done manually. Since the project was already georeferenced, these points overlapped in their right position (Figure 11). 38 Figure 11. TLS trees correlated with their correspondent ID in the field after the .txt file of UTM tree coordinates was overlapped on point clouds. Tree segmentation and variable extraction Tree segmentation consists of obtaining one point cloud for each tree belonging to the plot, i.e. we should have as many point clouds as trees in the plot. This segmentation was done differently in the two experimental sites and is described below. Pinus sylvestris – Quercus petraea For our first experimental site, tree segmentation was done in two different ways. For Triplet 1, this isolation was conducted manually: we edited the original point cloud in IMispect selected each tree, and made a copy of the point cloud for each tree. Triplet 2 trees were based on density spatial clustering to detect individual-tree positions. This was performed within the programming environment of R (R Core Team, 2016) using the R packages rlas (Roussel & De Boissieu, 2020), dbscan (Hahsler et al., 2019), TreeLS (De Conto, 2020), and conicfit (Gama & Chernov, 2015), which automatized the method. For this method, only the x- and y-axes are used as input data. Firstly, the rlas package was used to convert our point cloud data into an interchange of 3-dimensional point cloud data process, next, dbscan was automatically able to detect each tree as a cluster, i.e., each recognized cluster (stem), and received a unique number and therefore, could be processed individually. Then each cluster was individually queried as to, which stem base cluster is closest in 39 distance and whether this distance is close enough (≤0.05m) to be classified as associated points. Stems were detected through the Hough Transformation, adapted by Olofsson et al. (2014), implemented in the R Package TreeLS. Followed by De Conto (2016) directions to remove the ground points, leaving only the stem. Finally, dead branches were removed by fitting an ellipse by R Package conicfit. After this step, each tree is visually checked for completeness. If necessary, unrecognized tree parts are added manually, and artifacts not belonging to the tree are removed using the software RiSCAN PRO. More detailed information is provided in (Jacobs et al., 2019). In both cases, final refined data for each tree were needed and it was performed manually in IMispect and the free software Cloud Compare Version 2.11 alpha (Anoia) by deleting points that were not part of the trees or by separating trees, that were identified as only one due to their crown proximity. For this experimental site, all the trees belonging to the study plots were identified, but due to canopy occlusion, especially in oak stands, which made tree separation impossible, the study was finally conducted with 91.2% of the total (Table 5). The total time for the Identification, isolation, and data refining of this experimental site took approximately 5 months. Table 5. Total trees per plot (n/plot) compared to total point cloud trees isolated (TLS trees) Triplet Plot type surface species n/plot TLS trees 1 1 pure 25x25 Pine 63 61 7 pure 25x25 Oak 87 75 4 mixed 30x30 Pine - Oak 48 - 55 47 - 53 2 2 pure 30x30 Pine 57 47 5 pure 20x30 Oak 81 74 6 mixed 30x30 Pine - Oak 44 - 63 38 - 54 Total 498 449 EXTRACTION OF VARIABLES For this experimental site, TLS dendrometric variables were extracted using the software “Mathematica 11” (Wolfram Research Inc., Champaign, IL, USA). In total, for each tree, we obtained eleven variables: Diameter at Breast Height (DBH), Total Height (TH), lean, sweep, and the crown metrics of Crown Base Height (CBH), Maximum Crown Width Height (MCWH), Maximum Area, Crown Volume (CV), Crown Surface Area (CSA), Crown Length (CL) (Figure 12), asymmetry of the crown concerning the stem (asymmetry) and as wood quality variables: Lean and Sweep (Figure 13). An extensive description of the computing process can be found in (Seidel et al., 2011) 46 DATA ANALYSIS Data analysis was conducted using Rstudio Inc. Version 1.1.453. Packages used were: dplyr (Hadley et al., 2020), data.table (Dowle & Srinivasan, 2020), lme4 (Bates et al., 2015), broom (Robinson et al., 2021), ggplot2 (Wickham, 2016), psych (Revelle, 2020), pastecs (Grosjean & Ibanez, 2018), car (Fox & Weisberg, 2019), gridExtra (Auguie, 2017), nls2 (Grothendieck, 2013), and tibble (Müller & Wickham, 2020). before proceeding with the analysis of the variables through TLS data, we analyzed their degree of affinity with the field data. Firstly, we compared TLS data distribution with Field data distribution with the Kolmogorov-Smirnov test. Following this, we applied Lin’s concordance correlation coefficient (CCC) (Lin, 1989) to compare TLS and Field measurements of the same variables. Crown analysis To determine the variables we needed for the analysis of the crown variables we based on usual forest modeling literature, and expanded the models following the methodology applied (Lizarralde, 2008) adding the mixture of explanatory variables (Table 7 and Table 8). Once we had the models, we were able to determine and adapt our data to our four categories of explanatory variables (size, density, competition, and, mixture) as shown in Table 8. For the Crown Volume, the explanatory variable d2h (squared diameter at breast height times height) was included as a size variable since this variable represents a proxy for tree volume. Furthermore, for the CPA response variable, the logarithmic transformation of the Basal Area was included as a density explanatory variable, (Ritter & Nothdurft, 2018). As for mixing variables, we used the Ratio variables of species, and due to the high correlation (ρ ≥ 0.9) to avoid multicollinearity problems, we decided to study only the ratio variables of pines, based on the more extensive bibliography on the subjects of pines mixture effect than oak mixture effects. 47 Table 7. Crown models were defined for this study. Response Variables are Maximum Crown Width height (MCWH), Crown Base Height (CBH), Crown Projection Area (CPA), and Crown Volume (CV), and explanatory models were classified into four categories. s= size, d= density, c= competition and m= mixture. Response Variables Equation Author MCWH 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1 + 𝑒𝛼1∗𝑠+𝛼2∗𝑑+𝛼3∗𝑐+𝛼4∗𝑚 (Pain & Hann, 1982) CBH 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1 + 𝑒𝛼1∗(𝑑 𝑠)+𝛼2∗𝑑+𝛼3∗𝑐+𝛼4∗𝑚 (Hann et al., 2003) CPA 𝐶𝑃𝐴 = 𝑒𝛼0+𝛼1𝑠+𝛼2∗𝑑+𝛼3∗𝑐+𝛼4∗𝑚 (Ritter & Nothdurft, 2018) CV 𝐶𝑉 = 𝛼0+ 𝛼1∗ 𝑠 + 𝛼2∗ 𝑑 + 𝛼3∗ 𝑐 + 𝛼4∗ 𝑚 (Sanquetta et al., 2015) Table 8. Categories and variables within each category we have used to define explanatory models Category Variable Response MCWH CBH CPA CV Explanatory - Size TH DBH d2h - Density BAtotal - Competition BALtotal BALpine BALoak Asymmetry C. I. - Mixture Ratio BApine Ratio BALpine Ratio npine We calculated the Basal area (BA) of each tree from their TLS point clouds and we analyzed the outliers for the variables: DBH, BA, TH, CBH, MCWH, CPA, and CV. Next, following Höwler et al. (2017) methodology, circular sample plots with a variable radius around each target tree were established. Radius size constraints were the size plots of the experimental site 1 (Table 1), the smallest plots we had. Thus, we determined three radii sizes at 5, 7.5, and 10m. Once radii sizes were defined, we used 48 R software to create point patterns (ppp) using the R package Spatstat (Baddeley & Turner, 2005) to first, delimit the plot size, followed by Siplab package (Garcia, 2014) to determine the Hegyi index (Hegyi, 1974), hereafter referred to as the Competition Index (C.I.), which was calculated according to Hegyi (1974) (Eq. 1) Eq. 1. 𝐻𝑒𝑔𝑦𝑖𝑖=∑𝐷𝐵𝐻 𝐷𝐵𝐻𝑖 ∙(𝑑𝑖𝑠𝑡𝑖𝑗+1) 𝑛 𝑗=1 Where i stands for target tree i, j for competitor tree, DBH for diameter at breast height, and distance between target tree and competitor tree are represented by “dist” within radii encompassing 5, 7.5, and 10. Within these circular plots, we also determined the BA, the Largest Basal Area (BAL), and the number of tree species around each target tree within each of the three circular subplots (Figure 19). Finally, response variables (CBH, MCWH, Crown Volume) and DBH and TH were compared between sites to see if there were significant differences between species that could explain possible differences in the results. Figure 19. Creation of circular subplots around each target tree with radii = 5, 7.5, and 10 m. 49 Wood Quality Wood quality was analyzed only for Experimental site 1. Through the trunk variables Lean and Sweep (Figure 13). No similar models were found in the literature, thus we decided to start applying linear models (Table 9) to see how our data fit. Table 9. Starting model equations for Lean and Sweep Response Variables Equation Lean 𝐿𝑒𝑎𝑛 = 𝛼0+ 𝛼1∗ 𝑠 + 𝛼2∗ 𝑑 + 𝛼3∗ 𝑐 + 𝛼4∗ 𝑚 Sweep 𝑆𝑤𝑒𝑒𝑝 = 𝛼0+ 𝛼1∗ 𝑠 + 𝛼2∗ 𝑑 + 𝛼3∗ 𝑐 + 𝛼4∗ 𝑚 Model Building and Selection Pinus sylvestris – Quercus petraea We worked with 193 pines and 256 oaks. For the response variables: MCWH, CBH, and CPA, non-linear regression models were performed using a brute force algorithm from the R package nls2 (Grothendieck, 2013). For the CV, lean, and sweep variables, simple linear regression was used. For each radius of influence considered (5, 7.5, and 10 m) all possible combinations of explanatory models (size, density, competition, and mixture) were tested. The total amount of models created for each variable varied depending on the number of explanatory variables within the script model. For MCWH and CBH we had 144 models, for CPA and CV where a third size variable (d2h), plus the Logarithm of BA as density variable, was included we obtained 216 models, and for Lean and Sweep we kept the logarithm of BA as a density variable, but we did not keep d2h as a size variable. We obtained a total of 180 models. To select the best model we followed the Akaike Information Criterion (AIC) (Eq. 2), which is a mathematical method for evaluating how well a model fits the data it was generated from. The bestfit model according to AIC is the one that explains the greatest amount of variation using the fewest possible independent variables (Bevans, 2021). Eq. 2. 𝐴𝐼𝐶 = 2𝐾 − 2𝑙𝑛 (𝐿) Where K is the number of independent variables used and L is the log-likelihood estimate. To compare AIC, we calculated the Akaike weight, which is interpreted as probabilities. If the Akaike weight approached 1 then, model was unambiguously supported by the data (Johnson & Omland, 2004). The top five models with the lowest AIC index were selected. 50 Finally, we analyzed the residuals of the top5 models for each response variable, and we calculated the sum of squares error (SSE) of every model to estimate the power of the regression, as well as their R2 to check the general explanatory power of the models. For non-linear models, we calculated the R2 (Nagelkerke, 1991). Finally, we created the histogram, density plot, and Q-Q plot for every model to analyze their residuals. Pinus sylvestris – Quercus pyrenaica For the analysis of Experimental site 2 we performed three models on 49 pines and 38 oaks. (1) we applied the models fitted in site 1 to this new site; (2) we used the models fitted for site 1 but modified their coefficients for this site 2; and (3) we fitted new models for this site following the same methodology as in Site 1. For (1) and (2), where we wanted to see the goodness-of-fit of the models fitted for site 1, we firstly created a graph of predicted vs. actual values adjusting a regression line, predicted = β0+ β1·actual. Next, we performed a simultaneity test to check regression line was significantly different from the bisector of the first quadrant (y=x) (Herrero et al., 2019; Huang. et al., 2003): - H0: b0=0 & b1=1 - H1: b0≠0 or b1≠1 Finally, we compared the AIC between the models to determine if the models fitted in site 1 are applicable to site 2 and thus, create a sound model for these variables or, on the contrary, we need to create a new model for each site. 51 RESULTS TLS validation and Sites comparison The Kolmogorov Smirnov test was not significant (𝛼 = 0.05) for all contrasted variables, which confirms the distribution of TLS data was not significantly different from the data taken in the field. Then, CCC was tested on the two tree size variables (DBH and TH) from which, the rest of the variables derive. We obtained very high rates for both of them which corroborates the confidence (CI) of our analysis: CCCDBH: 0.9766 (95% CI 0.9719 - 0.9806) and CCCTH: 0.7429 (95% CI 0.6984 - 0.7817). From here, the rest of the analysis was performed with TLS data. Firstly, descriptive statistics of all trees classified by species and pure and mixed-species plots were performed (Table 10). We have observed that oaks show similar tree heights, both in pure and mixed stands, but they are slightly thicker (DBH one cm higher) in the mix with pines than in pure conditions. Unlike pines, DBH is up to almost 3.5 cm thinner in the mix with pines but slightly taller (+0.5 m) compared to pure plots Table 10. Mean Diameter at Breast Height (DBH) in cm and Total height (TH) in m of trees calculated with TLS separated by species and kind of plot (pure or mix). n total is the total number of trees measured. Species Plot n total DBH (cm) TH (m) Max mean SD min Max mean SD min pine Pure 113 46.98 30.99 ± 2.07 5.68 26.44 17.33 ± 6.97 11.62 Mix 84 47.34 27.51 ± 2.13 13.96 22.36 18.04 ± 6.33 11.31 oak Pure 155 61.29 19.50 ± 3.38 7.56 23.20 17.38 ± 7.42 6.39 Mix 107 33.52 20.53 ± 2.41 10.07 20.85 17.31 ± 5.20 8.73 Fitted Crown models Pinus sylvestris and Quercus petraea Models were hierarchized according to the lowest Akaike Information Criterion (AIC). We analyzed the residuals and made the necessary changes in the structure of the models (Table 11) to assure models met the assumptions, and in the case they did not meet the assumptions after the transformation we rejected them. The best models for each crown variable, that we selected according to these criteria are shown in Table 12. For all cases, the model selected was the model with the lowest AIC index except for the MCWH variable in both species, where models with the second AIC index were selected due to residual analyses being slightly better in the second models. 52 Table 11. Final equations for each species and crown response variable. Equation MCWH Pine 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1 + 𝑒(−0.11·𝐶.𝐼.−0.13·𝑅𝑎𝑡𝑖𝑜𝐵𝐴𝐿𝑝𝑖𝑛𝑒) Oak 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1 + 𝑒(−0.0.9·𝑇𝐻+0.28·𝑅𝑎𝑡𝑖𝑜𝐵𝐴𝑝𝑖𝑛𝑒) CBH Pine 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1 + 𝑒(−22.9·𝐵𝐴𝑡𝑜𝑡𝑎𝑙 𝐷𝐵𝐻 −0.1·𝐵𝐴𝑝𝑖𝑛𝑒−0.41·𝑅𝐴𝑡𝑖𝑜𝐵𝐴𝐿𝑝𝑖𝑛𝑒) Oak 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1 + 𝑒(−14.43·𝐵𝐴𝑡𝑜𝑡𝑎𝑙 𝐷𝐵𝐻 +0.05·𝑙𝑛𝐵𝐴𝑡𝑜𝑡𝑎𝑙+0.04·𝐵𝐴𝐿𝑡𝑜𝑡𝑎𝑙+0.17·𝑅𝐴𝑡𝑖𝑜𝐵𝐴𝐿𝑝𝑖𝑛𝑒) CPA Pine 𝐶𝑃𝐴 = 𝑒0.07·𝐷𝐵𝐻+0.02·𝐵𝐴𝑡𝑜𝑡𝑎𝑙−0.1·𝐶.𝐼.) Oak 𝐶𝑃𝐴 = 𝑒0.9+0.04·𝐷𝐵𝐻+0.09·𝐵𝐴𝑡𝑜𝑡𝑎𝑙−0.1·𝐵𝐴𝐿.𝑡𝑜𝑡𝑎𝑙+1.15·𝑅𝑎𝑡𝑖𝑜 𝑛 𝑝𝑖𝑛𝑒) CV Pine 𝐶𝑉 = 1.5𝑒−3 · 𝑑2ℎ + 0.44 ·𝐵𝐴𝑡𝑜𝑡𝑎𝑙 − 2.35 · 𝐶. 𝐼. Oak 𝐶𝑉 = −20.28+0.003 · 𝑑2ℎ + 1.03 ·𝐵𝐴𝑡𝑜𝑡𝑎𝑙 − 4.29 · 𝐵𝐴𝐿𝑡𝑜𝑡𝑎𝑙 +46.92 · 𝑅𝑎𝑡𝑖𝑜𝐵𝐴𝑝𝑖𝑛𝑒) 53 Table 12. The explanatory models were selected as the best fit according to their lowest Akaike index and biological criteria for each response variable (Variable) and species. r= radius of influence (5, 7.5 and 10 m); s = size; d=density; c= competition; m= mixture; α0= Intercept; α1-4= the coefficient numbers for each explanatory variable (size, density, competition, and mixture). AIC = Akaike, K-S test = P-value of Kolmogorov Smirnov Test for residuals, R2= coefficient of determination of the model. Variable Species r s d c m α0 α1 α2 α3 α4 AIC K-S test R2 MCWH P. sylvestris 10 C.I. Ratio BALpine -0.11 -1.13 646.59 0.078 0.54 Q. petraea 10 TH Ratio BApine -0.095 0.273 890.47 0.007 0.78 CBH P. sylvestris 5 DBH BALpine Ratio BALpine -22.87 0.1 -0.41 557.21 0.227 0.71 Q. petraea 10 DBH ln(BAtotal) BALtotal Ratio BALpine -14.43 0.05 0.04 0.17 936.91 0.543 0.74 CPA P. sylvestris 10 DBH BAtotal C.I. 0.0655 0.0188 -0.0964 981.45 0.194 0.66 Q. petraea 7.5 DBH BAtotal BALtotal Ratio npine 0.81 0.039 0.089 -0.186 1.154 1203.11 0.001 0.70 CV P. sylvestris 10 d2H BAtotal C.I. 0.0015 0.44 2.35 1491.12 0.100 0.55 Q. petraea 7.5 d2H BAtotal BALpine Ratio BA -20.28 0.003 1.03 -4.29 46.92 1904.9 0.010 0.64 54 We observed that the size of the tree was a significant variable for all cases, with only one exception, MCWH for pines. In all the cases, tree size affected the crown shape, the bigger the tree, the higher the CBH and MCWH were, and the wider the CPA and CV too. That was, the bigger the tree, the higher and wide the crown. Competition boosted MCWH and CPA of pines, but it was observed for the rest of the variables that, the competition had a negative effect on crown shapes for both species, and crowns were shorter and narrower. The mixture variable was always statistically significant for oaks (Table 11). The presence of pines made the height of the oaks' crowns (MCWH and CBH) smaller, by contrast, it made their crown projection and volume larger. Pinus sylvestris and Quercus pyrenaica Testing site 1 fitted models in site 2 (Analysis 1) For this first analysis, we applied the models defined in Table 7 to our second experimental site, Palacio de Valdellorma. We studied how the predicted values fit against the actual values with these models. Models over estimated MCWH values of both pines and oaks, as well as oak CBH values. This was contrary to pine CBH and oak CPA values, which were underestimated. The best fit of models was for CV, nevertheless, all the simultaneous linear hypothesis tests were significantly different from zero and one (Annex 1). Fitting models of site 1 to site 2 (Analysis 2) The results for the second analysis with the statistical adjustments and fitted coefficients are shown in Table 13. 55 Table 13. Fitted models using variables defined for the first experimental site, fitting their coefficient for this second experimental site. Variable Species r s d c m α0 α1 α2 α3 α4 AIC SSE R2 MCWH P. sylvestris 10 NA NA C.I. Ratio BALp NA NA NA -0.02 -0.49 114.57 26.30 69.42 Q. petraea 10 TH NA NA Ratio BAp NA -0.03 NA NA -0.99 98.68 25.50 74.30 CBH P. sylvestris 5 DBH NA BALp Ratio BALp NA 3.82 NA -1.10 0.001 132.85 36.67 44.86 Q. petraea 10 DBH lnBAt BALt Ratio BALp NA 0.77 0.22 -1.52 0.87 115.77 35.98 40.57 CPA P. sylvestris 10 DBH BAt C.I. NA NA 0.12 -0.80 0.002 NA 217.31 205.54 69.68 Q. petraea 7.5 DBH BAt BALt Ratio np 0.15 0.02 2.46 -4.61 0.95 160.96 112.14 30.71 CV P. sylvestris 10 d2h BAt C.I. NA NA 0.01 -21.93 0.42 NA 365.48 4227.52 62.92 Q. petraea 7.5 d2h BAt BALp Ratio BAp -5.84 0.001 27.87 -37.49 11.18 251.58 1217.29 34.42 62 Finally, the Akaike weights (AICcWt) are shown in Table 18. The best-fitted model is for CPA where the models explained 78% and 94% of the variability for pines and oaks, respectively. On the contrary, the worst fitting models were those for the Crown Volume variable, for both species where only 27% and 39% of the variability for pine and oaks were explained by the model, respectively. For MCWH, the model was best fitted for oaks than for pines, but for CBH pines CBH data were better explained by the model than for oaks. Table 18. K: the number of parameters in the model. AICc: information score of the model. ΔAICc: the difference in AIC score between the best model and the being compared. AICcWt: the proportion of the total amount of predictive power by the full set of models contained in the model being assessed. Cum.Wt: the sum of the AICc weights. LL: log-likelihood (how likely the model is, given the data). Variable Species Mod. Selected K AICc AICcWt Cum.Wt LL MCWH pine [1] 4 106.95 0.30 0.30 -49.02 oak [1] 2 97.84 0.58 0.58 -46.75 CBH pine [1] 4 126.06 0.73 0.73 -58.58 oak [1] 3 111.62 0.34 0.34 -52.46 CPA pine [1] 3 209.26 0.78 0.78 -101.36 oak [1] 4 114.37 0.94 0.94 -52.58 CV pine [3] 5 357.50 0.27 0.27 -173.05 oak [1] 3 174.83 0.39 0.38 -84.03 Comparison of models: Analyses 2 Vs. 3 Comparing the two analyses, which fitted our data well, the models fitted specifically for the experimental site of Palacio de Valdellorma (Analysis 3) were always better than the models (Analysis 2) of the other experimental site with coefficients fitted for this second experimental site (Table 19). For Analysis 3, Akaike weight approaches were always up to 98% for both species, pines, and oaks. 63 Table 19. AIC comparison analyses 2 and 3. Species Variable Analysis K AICc Delta_AICc ModelLik AICcWt LL Cum. Wt Pine MCWH 3 4 107.2 0 1 0.98 -49.14 0.98 2 3 115.1 7.9 0.02 0.02 -54.28 1 CBH 3 4 126.07 0 1 0.98 -58.58 0.98 2 4 133.76 7.69 0.02 0.02 -62.42 1 CPA 3 3 213.8 0 1 0.9 -103.63 0.9 2 4 218.22 4.42 0.11 0.1 -104.66 1 CV 3 5 357.5 0 1 0.99 -173.05 0.99 2 4 366.39 8.88 0.01 0.01 -178.74 1 Oak MCWH 3 3 99.39 0 1 0.99 -46.34 0.99 2 2 109.85 10.46 0.01 0.01 -52.75 1 CBH 3 3 111.7 0 1 1 -52.5 1 2 5 219.51 107.81 3.88E-24 3.88E-24 -103.82 1 CPA 3 4 114.37 0 1 1 -52.58 1 2 5 161.66 47.28 5.40E-11 5.40E-11 -74.89 1 CV 3 3 244.93 0 1 0.996 -119.11 1 2 6 255.8 10.87 0.004 0.004 -120.55 1 Tables 20 and 21 show the models fitted with the two analyses with the best results for pines and oaks respectively showing, (1) Analysis 2, resulting models for site 1 with the specific coefficients for Palacio de Valdellorma, and (2) Analysis 3, resulting models developed specifically for site 2. For pines (Table 20), all resulting models for site 2 (Analysis 3) were fitted with fewer variables than the resulting models from site1 (Analysis 2). Nevertheless, the differences between their AIC were small, being the largest one 8% for MCWH. On the other hand, oaks (Table 21) had a higher variability between the models, reaching a difference in AIC among models of 42% and 41% for CV and CPA, respectively. 64 Table 20. Comparison of analysis for Pinus sylvestris. The intercept α0 is not shown in this table since it was not statistically significant for any of the models. Var. Analysis r s d c m AIC Δ AIC % dif R2 SSE α0 α1 α2 α3 α4 MCWH 3 10 DBH BAt NA Ratio BALp 106.05 8.52 8.04 75.33 21.22 NA 0.03 -0.66 NA -0.90 2 NA NA C.I. Ratio BALp 114.57 69.42 26.30 NA NA NA -0.02 -0.49 CBH 3 5 DBH lnBAt NA Ratio BAp 125.16 7.69 6.15 52.88 31.34 NA 12.09 -0.85 NA -0.94 2 DBH NA BALp Ratio BALp 132.85 44.86 36.67 NA 3.82 NA -1.10 0.003 CPA 3 5 DBH BAt NA NA 208.73 8.59 4.11 73.49 179.69 NA 0.12 -2.79 NA NA 2 10 DBH BAt C.I. NA 217.31 69.68 205.54 NA 0.12 -0.80 0.005 NA CV 3 5 d2h BAt BALt Ratio np 356.11 9.37 2.63 70.60 3352.25 NA 0.01 -131.45 99.12 -5.66 2 10 d2h BAt C.I. NA 366.39 62.92 4227.52 NA 0.01 -21.93 0.42 NA Table 21. Comparison of analysis for Quercus pyrenaica. Variable Analysis r s d c m AIC Δ AIC % dif R2 SSE α0 α1 α2 α3 α4 MCWH 3 10 NA NA NA Ratio BAp 97.50 1.19 1.22 73.74 26.05 NA NA NA NA -1.31 2 TH NA NA Ratio BAp 98.68 74.30 25.50 NA -0.03 NA NA -0.99 CBH 3 7.5 NA NA C.I. Ratio np 110.91 4.85 4.38 41.89 35.18 NA NA NA -0.05 0.53 2 10 DBH lnBAt BALt Ratio BALp 115.77 40.57 35.98 NA 0.77 0.22 -1.52 0.87 CPA 3 5 TH NA C.I. Ratio BALp 113.16 47.80 42.24 78.12 35.42 NA 0.22 NA -0.14 -0.49 2 7.5 DBH BAt BALt Ratio np 160.96 30.71 112.14 0.15 0.02 2.46 -4.61 0.95 CV 3 7.5 TH NA C.I. NA 178.52 73.06 40.93 39.43 254.12 NA 0.93 NA -0.35 NA 2 d2h BAt BALp Ratio BAp 251.58 34.42 1217.29 -5.84 0.001 27.87 -37.49 11.18 65 Fitted Wood Quality models Following the same methodology as for the crown variables, best models (Table 22) were selected according to the lowest AIC. The analyses of the residuals of the five models with the lowest AIC are shown in Annex 4. Table 22. Fitted models for Lean and Sweep variables, where is used Ø to represent models were the same for the three radii of influence. Response Variable Species Radius of influence Equation Lean Pine 10 𝐿𝑒𝑎𝑛 = 𝑒(−1.76−0.04·𝑇𝐻+0.003·𝐵𝐴𝑡.+0.1∙𝐴𝑠𝑦𝑚−0.26·𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝑝) Oak 5 𝐿𝑒𝑎𝑛 = −1 + 𝑒(0.23−0.01·𝑇𝐻−0.004·𝑙𝑛𝐵𝐴𝑡.+0.06∙𝐴𝑠𝑦𝑚+0.02·𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝑝) Sweep Pine Ø 𝑆𝑤𝑒𝑒𝑝 = 0.94 + 0.002 ∙𝑇𝐻 − 0.013 ∙ 𝐴𝑠𝑦𝑚 Oak Ø 𝑆𝑤𝑒𝑒𝑝 = 0.95 + 0.002 ∙𝑇𝐻 − 0.01 ∙ 𝐴𝑠𝑦𝑚 Lean Once the outliers are identified and removed, we work with 154 out of 190 possible outliers. With these 154 points, we fitted the linear models. We observed that the distribution of the errors followed a fan shape, in addition to other problems such as nonlinearity, as shown in Figure 22. Therefore, the resulting models were logarithmic. 𝑙𝑜𝑔(𝐿𝑒𝑎𝑛)= 𝛼0+ 𝛼1∙ 𝑠𝑖𝑧𝑒 + 𝛼2∙ 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 + 𝛼3∙ 𝐶𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 + 𝛼4∙ 𝑀𝑖𝑥𝑡𝑢𝑟𝑒 Figure 22. Residuals Vs. fitted values of the linear model for the Lean variable, violations of the equal variance and linearity assumptions. 66 For oaks the outlier analysis let us work with 221 out of 236 trees. For this species Lean values had values of zero, for that reason the final model is as follows: 𝑙𝑜𝑔(1 + 𝐿𝑒𝑎𝑛)= 𝛼0+ 𝛼1∙ 𝑠𝑖𝑧𝑒 + 𝛼2∙ 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 + 𝛼3∙ 𝐶𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 + 𝛼4∙ 𝑀𝑖𝑥𝑡𝑢𝑟𝑒 For both, pines and oaks all variables considered (size, density, competition and mixture) were statistically significant for the fitting of the Lean variable, but the radius of influence was bigger for pine (r = 10 m) than for oaks (r = 5m) (Table 23). Table 23. The explanatory models for the response variable Lean for each species (Sp), selected as the best fit according to their lowest AIC index and residual analysis, Pinus sylvestris (Ps) and Quercus petraea (Qp). r = radius of influence (5 and 10 m); s = size; d = density; c = competition; m = mixture; μ = intercept; β1-4 = the coefficient numbers for each explanatory variable (size, density, competition, and mixture); AIC = Akaike and SSE= Residual Sum of Squares. Var Sp r s d c m α0 α1 α2 α3 α4 AIC SSE K-S tes t L e a n Ps 10 TH BAt Asym Ratio BAp -1.76 -0.043 0.003 0.096 -0.256 -547.5 0.24 0.2 Qp 5 TH lnBAt Asym Ratio BAp 0.22 -0.012 -0.004 0.062 0.017 -646.1 0.66 0.7 The significant variable for size and competition were the total height of the tree and the asymmetry of the crown, respectively. The sign of the parameters for each variable indicated that the higher the tree and the less asymmetrical the crown, the more straight the stem for both pines and oaks. The density variable was different for each species, total basal area for pines, and the logarithm of total basal area for oaks. Nevertheless, the effect on the lean was the same, the higher the density around the tree, the straighter the tree. Finally, both species were affected by the mixture but in a different sense and radius of influence. For pines the bigger ratio of BA of pines within a radius of 10m the straighter the pine, but for oaks, it was the other way around, the bigger the ratio of Basal Area of pines in a radio of 5m the leaner were the oaks. Sweep For this variable, the residual analysis indicated a good model fit for the linear models. In this case, and after the outlier analysis we have worked with 178 pine trees out of 190 and with 202 oak data, out of 236 data. The best model selected is shown in Table 24. For this response variable, the resulting models were the same for all three radii of influence studied, r= 5, 7.5, and 10m. The sweep of the tree was only affected by the total height of the tree (size) and the asymmetry of the crown (competition), for both, pines and oaks, in the same way. The higher the 67 tree and the more asymmetric the crown concerning its trunk center, the less bent (sweep) the tree was. Table 24. The explanatory models for the response variable, Sweep, for each species (Sp), were selected as the best fit according to their lowest AIC index and residual analysis. Pinus sylvestris (Ps) and Quercus petraea (Qp). r = radius of influence (5 and 10 m); s = size; d = density; c = competition; m = mixture; μ = intercept; β1-4 = the coefficient numbers for each explanatory variable (size, density, competition, and mixture); AIC = Akaike and SSE= Residual Sum of Squares. Var Sp r s d c m α0 α1 α2 α3 α4 AIC SSE K-S test S w e e p Ps TH NA Asym NA 0.94 2.11E-03 NA -0.013 NA - 965.83 0.04 0.44 Qp TH NA Asym NA 0.95 2.37E-03 NA -0.013 NA - 1128.36 0.04 0.8 68 DISCUSSION Fitted Crown models In this study, we analyzed four crown variables: MCWH, CBH, CPA, and CV on a total of 242 Scots pines and 294 oaks Sp. through TLS in two experimental sites located in two different climate conditions (Atlantic and Continental Mediterranean climate) and analyzed them by linear and non-linear regression using as explanatory variables tree size, stand density, competition, and mixture proportion. Our results showed these variables affect significantly crown shape (Table 13, 20, and 21), creating a complex structure where the crown of pines are higher and narrower and the crown of oaks is shorter but wider, tending to occupy the gaps in the stand. Stand dynamics model development is a breakthrough in sustainable forest management (Lizarralde, 2008b) within the last years, many studies have focused on mixed forests dynamics searching for a better understanding of forest species interactions (Aldea, 2018; Cattaneo et al., 2020; Himes & Puettmann, 2020; Juchheim et al., 2020; Riofrio, 2018; Rodríguez De Prado et al., 2022) to understand mixing effects and develop more precise forest practice applications (del Río et al., 2019). Within this regard, the characterization of crown species is crucial, because it gives us information on how species tend to occupy the stand canopy and helps to quantify their plasticity (Cattaneo et al., 2018). Moreover, the crown characterization is a fundamental element in the development of forest dynamics models (Fichtner et al., 2013; Lizarralde, 2008b). On the one hand, the crown provides us with information about the health of the forest, large dense crowns have been associated with vigorous growth rates, while trees with small and sparsely foliated crowns show a declining state with little or no growth (Zarnoch et al., 2004). On the other hand, the response of tree crowns to changes in canopy structure or competition occurs over a shorter period (del Río et al., 2019), thus a comprehensive understanding of crown structure can give us an insight into tree species interaction determination and thus, in decision-making and forest planning. Del Río et al. (2019) stated that the admixed speciesdependent effects on tree allometry highlight the importance of considering species composition instead of species diversity since tree allometry can be influenced by between-species interactions. For this reason, in this study we have characterized the crown of one pine species (Pinus sylvestris L.) in combination with two oak species (Quercus petraea L. and Quercus pyrenaica Willd), considering each study individual neighbors within three radii of influence (5,7.5 and 10m), i.e. the species composition affecting the target tree within three specific circular plots. In this way, we have been able to analyze the inter and intra-interaction as a continuous variable and not based on pure and mixed stand assumptions as has been done traditionally (e.g. (Aldea, 2018; Cattaneo, 2018; del Río et al., 2019; Riofrío et al., 2017). Developing tree allometry models depending on intra- and inter-specific 69 interaction is crucial when evaluating mixing effects (Forrester and Pretzsch 2015), as they allow upscaling of results from tree to stand level (del Río et al., 2019). The value of this study is based on the analysis of costly measurement of tree crown variables in inventories, which usually relies on the human ability to identify precisely where the crown begins on individual trees, most of the time, this difficulty in obtaining crown data limits the studies to a specific DBH size of the tree (Zarnoch et al., 2004). Traditionally, crown data availability comes from studies that measure the crown height with a hypsometer and the crown diameter with a tape by standing under the estimated drip-line of the crown at the ends of each of these axes and measuring the horizontal distances (Zarnoch et al., 2004). Other crown studies are based on National Forest Inventories (NFI) average data, to develop crown models for species-specific crown shapes (Pretzsch, 2009). Although NFI data are a good first approach providing valuable insight, it is important to consider certain limitations inherent to them, as not all species are considered (del Río et al., 2019). Most of the important references we have nowadays to understand crown dynamics are based on these approaches (e.g. Assmann, 1961; Badoux, 1946), creating a compact geometric form in twodimensional space (Ritter & Nothdurft, 2018) and developing Weibull distribution or non-linear regressions to quantify the crown profile. More recent studies formulated models that track vertical crown development. All of them are acknowledged to be smoothed and simplistic approximations of crown shapes that, in reality, are more irregular with fractal dimensions (Pretzsch, 2009; Ritter & Nothdurft, 2018). Thanks to TLS, we have been able to obtain more accurate crown metrics (Barbeito et al., 2017), and represent a much more efficient usage of the growing space than the maps derived from the traditional allometric models enabling us to develop more complex approaches like quantitative structure models (QSMs) (Ritter & Nothdurft, 2018) and consequently, to gain deeper insight into tree crowns' response to pines and oaks mixture, focusing on the crown structural pattern in great detail fitting our models considering the real three-dimensional shape of the crowns. Within the last two decades, many studies have focused on analyses of the mixture of certain species with Pinus sylvestris e.g. (Cattaneo, 2018; Jacobs et al., 2019; Juchheim et al., 2020; Lizarralde, 2008; Riofrío et al., 2017; Seidel et al., 2013) and Quercus petraea e.g (Bicl-Sorlin & Bell, 2000; Petritan et al., 2014) both in pure and mixed stands, but only recently studies have been focused on Quercus petraea together with Pinus Sylvestris(Forrester, 2017; Michelot, et al., 2012; Perkins et al., 2018; Pretzsch et al., 2020; Steckel et al., 2020) despite their great distribution throughout Europe. On the other hand, little is known about both mixed and pure conditions of the crown structure of Quercus pyrenaica (e.g. Adame et al., 2010; Condés & Sterba, 2005; del Río & Sterba, 2009), a very important species in Spain due to forestry vocation as multiple-use forest systems (Pedrosa Meca Ferreira de Castro, 2004). 70 Our results suggest there is an inter and intra-specific interaction that modifies the crown shapes of pines and oaks (Table 13, 20, and 21). The differences we found between the mixtures (Pinus sylvestris- Quercus Petraea and Pinus sylvestris-Quercus pyrenaica) support what has been noted in previous studies, mixture effect on species productivity in temperate mixed deciduous-coniferous forests can depend more on species composition than on functional type (Toïgo et al., 2018). Structural complexity necessarily involves the interaction between many different attributes (variables) (McElhinny et al., 2005). Tree DBH, stand density, and stand age are known to be correlated with the crown diameter and other crown parameters (Zarnoch et al., 2004). For that reason, in this study, we have expanded and fitted the crown models fitted by Pain & Hann, 1982; Hann et al., 2003; Sanquetta et al., 2015; and Ritter & Nothdurft, 2018 for other species. In agreement with (Lizarralde, 2008) we observed the general structures of the models were robust enough to be used on our studied species at different locations. Nevertheless, in accordance with Ritter & Nothdurft (2018), It became evident that each study site needs its own allometric models since the models fitted for Site 1, did not fit for Site 2. (Annex 1). After having adjusted the coefficients we observed the data were better fitted to the models (Figures 20 and 21) but when comparing these models with new coefficient vs. models fitted specifically for Site 2, the AIC index (Table 19) showed us clearly that data were better explained by models developed for each site. Size effect The relationship between crown diameter (CPA and CV) and tree size was positive in all the cases; the bigger the tree the bigger the crown diameter. Similar to Bonnor (1964) and Sprinz & Burkhart (1987), who found a strong relationship between crown diameter and DBH for Pinus contorta Dougl, our results showed that DBH was a good predictor together with BA for Pinus sylvestris. This relationship was also found for Quercus petraea but for Quercus pyrenaica the wider crown dimensions were related to the TH of the tree. Smith (1986) found that trees exhibiting the greatest height growth are usually the largest in all dimensions, including crown size. Pommering & Grabarnik (2019) found that, the more growing space a tree is granted, the longer is its crown and the smaller its height diameter ratio. Our models suggest the same, as we found a positive effect in the crown width (CPA and CV) of every tree species when increasing the DBH or TH of the tree, but a negative effect for crown length (MCWH and CBH), i.e. the smaller the tree, the larger their crowns but wider. 71 Density and Competition effect Our results are partially in agreement with Pretzsch & Biber (2016) who found that due to a better supply and more efficient use of resources, maximum stand density can be larger in mixed species. An increase in stand density had a positive effect for Quercus petraea when growing with Pinus sylvestris but not the opposite. Nevertheless, Pinus sylvestris did show a positive effect on its crown when in mixture with Quercus pyrenaica. The relationship between density and competition we found for the mixture Pinus sylvestris-Quercus petraea, in line with Pretzsch et al. (2017) interspecific competition effect on tree allometry was more relevant for crown projection area and Crown Volume than for the other allometric relationships. These two variables were opposite for both species, which suggests increased inter-competition when decreasing total density. For Quercus petraea, this same relationship was also found for the CBH variable. This apparent rapport between oaks growing together with pines may agree with relaxing resources competition in mixed forests that lead tree species to temporal diversification and spatial niche partitioning as suggested by Williams et al. (2017) and Aldea (2018). Juchheim et al. (2017), found in a mixture between Pinus sylvestris with Picea Abies and Fagus sylvatica lower BA exhibited a greater Stand Structural Complexity Index. For the Pine-oak mixture, we found, the same results for pines, a decrease in BA resulted in wider crowns increasing the inter-competition. Nevertheless, our results suggest the mixture benefits Quercus petraea where we found the opposite relationship, crowns were wider when increasing the mixture with pines and thus, their BA, decreasing the competition, creating a more heterogeneous and complex stand structure agreeing with (del Río & Sterba, 2009), which found that Scots pine-oak mixed stands support higher volume increment per occupied area compared to pure stands, i.e. pine did not act as a real competitor and, therefore, the oak had larger crown dimension when mixed with pine (del Río et al., 2019). The seeming complementarity between density and competition showed in our models are in line with other studies (Hemery et al., 2005; Jucker et al., 2015; Ritter & Nothdurft, 2018), which have shown that, especially in mixed-species stands, crown plasticity enables trees to optimize canopy packing, to reduce inter-tree competition, and to maximize the utilization of available photoactive radiation. The competition reduction and facilitation mechanisms found in these mixtures lead to admixture positive effects on forest productivity and are commonly interpreted on the basis of complementarity (Ammer, 2019). McElhinny et al. (2005) found the density of shade-intolerant tree species to be the most significant 78 CONCLUSIONS 1. TLS is very useful for nondestructively examining external crown and stem characteristics of this tree species, which can substantially reduce fieldwork data collection. TLS is very easy to use and capable of adapting to any kind of terrain with batteries that last a long time. It was proven that not much resolution is needed to obtain good data, although they should be taken during periods of dormancy to ensure good visualization of the tree canopy. However, its greatest limitation to being perfectly incorporated as a forest management tool remains in the data processing time, which is still very time consuming and still only semi-automatic making manual intervention needed. This need for manual intervention grately limits the advantages that this device has in terms of data acquisition. In the last two years, much new software has been developed that can maybe help to solve this limitation, and thus, TLS will be perfectly integrated as a tool in forest management, but, for now, TLS is a great research tool as it allowed us to assess and quantify the crown and timber quality of three tree species. 2. It was shown, that fitted crown models should be specific for every site and mixture. However, models of one site can work for other sites. When comparing the models with the AIC index, we saw models for each of the sites were able to explain in all cases more than 90% of data and adjusted coefficient no more than 5%. 3. Our results suggest a complementarity in canopy space occupation, which creates a multilayered canopy (stem diameter and height variety) in oak-pine stands in Northern Spain. We hypothesize that multi-layered canopies are produced by the mixture complementarity of crown shapes of pines and oaks due to their differential crown architecture and the combination of shade-tolerant and shade-intolerant, resulting in oaks with wider crowns and pines with larger stems to be able to capture the light above oaks. 4. This research has given us a comprehensive work focused on the crown structure of Pinus sylvestris – Quercus petraea and Pinus sylvestris – Quercus pyrenaica mixture. Showing more positive effects for oaks due to the mixture than for pines, and proving inter and intra-specific relations between species. Similarities between Quercus Sp. were bigger than Pinus sylvestris across sites, we hypothesize this is due to site conditions. 5. We developed two models for analyzing wood quality in Pinus sylvestris and Quercus petraea through Lean and Sweep of stems. We found crown asymmetry is an important factor that compromises the straightness of the stem, adding, this way, another important value to the crown architecture of trees. Finally, based on our results, we hypothesized the Lean of the stems is determined by an interspecific relationship, but the Sweep of the stems seem to be an intrinsic condition of the tree. 79 CONCLUSIONES 1. El TLS resulto ser un aparato muy útil para examinar las características externas de la copa y el tronco sin tener que apear el árbol y además reduce significativamente el trabajo de toma de datos en campo. Es muy fácil de usar y, capaz de adaptarse a cualquier tipo de terreno con baterías muy duraderas, y quedó comprobado que no se necesita mucha resolución para obtener buenos datos, aunque deben tomarse en periodos de letargo para asegurar una buena visualización del dosel arbóreo. Si bien, su gran limitación para incorporarse perfectamente como herramienta de gestión forestal sigue estando en el tiempo de procesado de los datos, que es muy lento ya que se trata todavía de un proceso semiautomático por lo que se necesita la intervención manual, descompensando totalmente la gran ventaja que tiene este dispositivo en cuanto a la adquisición de datos. En los dos últimos años se han desarrollado muchos programas informáticos nuevos que puede que ayuden a incorporar de forma definitiva el TLS en la gestión forestal, pero, por ahora, es una gran herramienta de investigación, ya que nos permitió evaluar y cuantificar los efectos de la interacción de tres especies arbóreas en su copa y en la calidad de la madera. 2. Quedó demostrado que los modelos ajustados de copa deben ser específicos para cada sitio y mezcla. Aunque los modelos de un sitio pueden funcionar bastante bien para otros sitios, al comparar los modelos con el índice AIC vimos que los modelos para cada uno de los sitios eran capaces de explicar en todos los casos más del 90% de los datos y el coeficiente ajustado no superaba el 5%. 3. Nuestros resultados sugieren una complementariedad en la ocupación del espacio del dosel, que crea un dosel complejo con diferentes alturas y tamaños (variedad en el diámetro y altura del árbol) en las masas mixtas de pino y roble del norte de España. Nuestra hipótesis es que esta diferencia de alturas en el dosel arboreo mixto de pinos y robles se producen por la complementariedad de sus formas de, debido a su arquitectura diferencial de copas y a la combinación temperamentos, tolerantes y no tolerantes a la sombra, lo que da como resultado robles con copas más anchas y pinos con troncos más largos para poder captar la luz por encima de los robles. 4. Esta investigación nos ha proporcionado un trabajo exhaustivo centrado en la estructura de la copa de la mezcla Pinus sylvestris - Quercus petraea y Pinus sylvestris - Quercus pyrenaica. Mostrando efectos más positivos para los robles debido a la mezcla que para los pinos, y probando las relaciones inter e intraespecíficas entre las especies. Las similitudes entre Quercus Sp. fueron mayores que las de Pinus sylvestris en todos los emplazamientos, lo que, según nuestra hipótesis, se debe a las condiciones del lugar. 80 5. Desarrollamos dos modelos para analizar la calidad de la madera mediante la inclinación y el retorcimiento de los troncos. Encontramos que la asimetría de la copa es un factor importante que compromete la rectitud del tronco, añadiendo, de esta manera, otro valor importante a la arquitectura de la copa de los árboles y que asi como la inclinacion de los troncos si que viene determinada por la relacion interespecifica, el retorcimiento de los troncos parece ser una condicion intrinseca del arbol. 81 ACKNOWLEDGMENTS This Thesis was possible through the Doctoral contract to Sara Uzquiano by Junta de Castilla y León and the European Social Fund 2016–2021. Thanks to the CARE4C H2020-MSCA-RISE-2017 (Grant Agreement no 778322) for funding my research stay at Chair for Forest Growth and Yield Science - Technische Universität München (Germany). Thanks to the ERASMUS+ program, COST Action program EuMIXFOR [STSM FP1206-29214] for my internships at LERFOB-INRAE University of Lorraine (Nancy- France) The University of Sweeden (SLU), The University of Göttingen (Germany) and a very special thanks to The University of Valladolid and the International mentoring program IMFAHE for funding my research stay at the Earth And Planetary Science department (EAPS) at MIT (Cambridge-USA). And thank you to the external reviewers of this thesis whose comments have helped to improve this thesis. First of all, I would like to express my gratitude to my advisors Felipe Bravo and Ignacio Barbeito (Nacho), thanks for all you have taught me through these years of research. -special thanks to Felipe. I know, a Ph.D. is not only about the willingness to do research, you need to have a good professor next to you who provides you with experience and academic support to be able to start, and later on good networking to keep going and eventually finish the research. Thus I will be always very grateful to Prof. Felipe Bravo for trusting me and letting me do my Ph.D. under his supervision. Thank you also for introducing me to Nacho, who has been officially on board only for the last two years of this Ph.D., but his support in giving my ideas and sharing his experience with TLS has been with me since the very beginning of this thesis across Nancy-Lund and now Canada, thank you very much for that. I want to thank the Sustainable Forest Management Research Institute (iuFOR), basically for everything. From even before the beginning of this Ph.D. journey to the very end of it. Thank you for the support in all my field trips, especially to Cristobal, Ana, and Aitor. And a huge thank you to the Photogrammetry Laboratory (LFA) of the Architecture School of the University of Valladolid, Kuki, Juanjo, Monica and Alicia. And a very special thank you to Jose, David, and Luis for having had always time for me and giving me a hand during the scanning process, and especially during the endless data processing time. But most of all thank you for making me feel that I was also part of your team since the very same day we met in Montejo de Tiermes. I want to thank the program IMFAHE. Thank you for assigning me Shivang Dave as my mentor. Thank you Shivang for having been such a good mentor, and always has given me your honest opinion even when it was not very nice to hear. And to Dr. Adam Schloser, thank you for opening the doors to me to MIT and being my supervisor at the EAPS department, and for all the collaborations that came later on. I will always remember this stay as the most inspiring of my stays. I also want to thank Prof. Hand Pretzsch for all the ideas and nice talks. Thank you for sharing with me all your knowledge about forest dynamics and especially about mixed forests. I feel really privileged for this. Thank you very much as well, to Prof. Ammer, Dr. Ebrecht, and Dr. Seidel your help has been crucial in the development of this thesis. Y porque realmente una tesis no se hace sola, y sois muchas las personas que a lo largo de estos años habéis estado a mi lado queriéndome ayudar en todo lo que estaba en vuestra mano. Por eso de algún modo esta tesis también os pertenece. Quiero empezar agradeciendo a todos los que en su día hicisteis que realmente quisiera entrar a formar parte de este mundo de investigación: María Hdez., Diana, Carmen, Pablo, Gonzalo, Lu, Estela, Ana Ponce, Celia, Wilson. Y muchas gracias a todas las personas que durante todo este proceso habéis hecho que, después de todo, siempre vaya a recordar estos años de tesis en el Edificio E con mucha nostalgia por todos los buenos momentos vividos: Maria Operaria, Guille, Arca, Tamara, Aitor, Maria Casado, Yeisi, Ruth, Juan, Silvia, Maria Santos, David, Jony, Cristina, Irene, Alvaro, Wilson, Elena, Ana Martinez, Edu, Laura, Pili (gracias por tus fotos), Patricia, Sergio, Farooq y todas las personas que han pasado por el iuFOR en estos años. Mención especial a mis compis de la 2.17. La oficina donde he desarrollado la mayor parte de mi trabajo. Empezando por mis chicos lindos de la 2.17: Jorge, Jose y Nico, gracias por todas las risas, las cumbias, las clases de R y todas las lecciones de vida tan valiosas que me han dado y me han seguido dando a lo largo de todos estos años desde Ecuador, Suecia y Canadá/Noruega. A mis amores de hombres: Nacho, Ali, Gianluca, Eric, Frederico y Juncal, thanks for all the laughs and above all, thanks for the support in all my cuttings experiments and videos filmed. Y a Olaya, gracias por ser la más amiga de las compañeras. Gracias por todas las sesiones de fotos, todas las risas y sobre todo, todo el apoyo y comprensión que siempre me has mostrado. Y junto contigo, Ana, Daphne y Marina que aunque no compartíamos despacho, me habéis hecho un hueco en el vuestro cuando lo he necesitado (casas incluidas). Gracias por haber sido las mejores de las compañeras y por ser las mejores de las amigas. A mi compi Diego, muchas gracias por todos los madrugones y desayunos productivos. Por ayudarme a desatascarme cuando más atascada estaba. Por sacar siempre un hueco de donde sé que no tenías, para echarme una mano. Gracias de corazón. A Irene Ruano, las persona con la que me introduje en el mundo de la investigación. Gracias por haber sido siempre la cara más amable y ensenarme a relajarme desde el primero de los congresos hasta en esta última etapa de tesis. Muchas gracias a la ETSIIAA del Campus de Palencia y toda la gente que forma parte de ella. Gracias a los informáticos, Raúl, Tomas y Marcos por vuestra disponibilidad y vuestra paciencia ayudándome en 82 83 todos los problemas técnicos que me surgieron (virus incluidos). A todos mis profesores, ahora colegas de profesión, Carlos, Reque, Julio, Andrés, Enrique, Carolina, Pilar, Pablo, Charo, Chema, Belén, Francisco, Joaquín y todos los que durante estos años me habéis acompañado y me habéis hecho querer tanto esta nuestra profesión y a Celia Redondo, Inma y Rocío y a Sara y Josefina por toda vuestra paciencia y ayudarme siempre con todo el papeleo siempre tan burocrático. Y un gracias muy especial a Feli y Eve que habéis sido siempre mi refugio de alegría en la escuela hasta en los momentos más difíciles. En definitiva, GRACIAS a todos y todas los que habéis formado parte de mi día a día durante todos estos años y habéis hecho de mi lugar de trabajo un sitio al que realmente me gustaba ir. Os echare mucho de menos! A very special THANK YOU to all the people I have met during these years of research that made my stays abroad more pleasant and unforgettable: Martin, Francesco, Cristina, Laura, Ola, Tomas, and to everybody that even for a short time, has been important persons during the development of this thesis enriching my life. Y, muy especialmente a mi grupo de amigos investigadores de Cape Cod: Dafne, Jesús, Marian, Xaquin, Candela y Yolanda. Gracias por enseñarme a peinarme, por darme una cama donde dormir en Madrid, por los packs de emergencia inesperados los paseos y picnics por Palencia y Venta de Baños, y las llamadas de apoyo mutuo de horas y horas desde Valencia a Palencia y al revés. A mis amigos de hoy y siempre: Claudia, Nacho, Marisa, Maria Elena, Jaime, Alvaro, Josean, Melisa, Leire, Dani, compi Miriam, Nuria, Tania S., Laura y Tania Cobo por haber estado a mi lado durante todo este proceso y haber estado siempre dispuestos a echarme una mano siempre que lo he necesitado: corrigiendo mi inglés, ayudándome con el diseño de esta tesis e incluso dándome un espacio en las noticias de RTVE. Gracias por aportarme siempre ideas y soluciones y haberme hecho sentir que os tenia a mi lado siempre y que podía contar con vosotros incluso estando a miles de kilómetros. Thanks to my dearest Erasmus friends Silvia, Camille, and Victoire, for having given me all your support and always opening the doors of your homes to me in my travels during this Ph.D. Journey and be always checking on me how I was doing and encourage me to keep going. And finally, thank you very much to Marta, Christian, Mika, and Dinant which destiny has reunited us again in this very last period of my Ph.D. thank you guys for being so welcome to me in Amsterdam, and thank you for making me feel accompanied during the last moments fo the development of this thesis. And a + thank you to Mika for offering and having checked the English of my thesis. A mi amiga Sara, gracias por haber sido mi partner in pomodoro y mi constante en todo este tiempo. Disponible siempre para mí 24/7. Incluso acompañándome a hacer el trabajo de campo en aquel día de marzo cuando la pandemia ya nos estaba llamando a la puerta. Gracias, gracias, por siempre gracias amiga. 84 Gracias al Nuevo Fielato y a mi equipo Nerd, por haber sido siempre un lugar de oxígeno en todo este proceso y haber sido siempre la más divertida ventana de evasión A Roberto San Martin, una pieza clave en el desarrollo y sobre todo termino de esta tesis. Que más no quisiera yo tener todo el dinero que le debo (más de 150 fijo que es) para así poder sentir que de alguna manera te estoy agradeciendo lo suficiente todo el apoyo que me has dado con la parte más difícil de una tesis…La estadística. Gracias por todo el tiempo, incluso en tus vacaciones, que me has dedicado y siempre con tu buena disposicion y tu buen humor. Te estaré enternamente agradecida a la par que endeudada I don't want to finish this section without say a big THANKS to Land Life Company (Land Life) for giving me the last push I was needing to end this chapter of my life. Thank you for trusting me before even know me and giving me the kind of job I have been preparing for all this time and the one I always dreamed of. Y para concluir, quiero agradecer a mis padres y a mi hermana por haberme animado a seguir este camino y haberme dado siempre las palabras más sinceras que muchas veces no son las que uno quisiera escuchar, pero son las que te hacen aprender y mejorar en tu trabajo y en la vida. Gracias por enseñarme desde siempre que en la vida uno no deja nunca de estudiar y que hay que aprender a amar lo que uno hace. GRACIAS por haberme educado así. Por todo a todos y todas, MUCHAS GRACIAS! THANK YOU VERY MUCH! MERCI BEAUCOUP! DANKE SHÖN! DANK JE WEL! 85 REFERENCES Adame, P., Del Río, M., & Cañellas, I. (2010). Modeling individual-tree mortality in Pyrenean oak (Quercus pyrenaica Willd.) stands. Annales of Forest Science, 67, 810. https://doi.org/10.1051/forest/2010046 Aiba, M., & Nakashizuka, T. (2009). Architectural differences associated with adult stature and wood density in 30 temperate tree species. Functional Ecology, 23, 265–273. https://doi.org/10.1111/J.1365-2435.2007.01500.X Aldea Mallo, J. (2018). Tree Growth Dynamic and Thinning response in Mediterranean Pine-Oak Forest Stands [Universidad de Valladolid]. https://doi.org/10.35376/10324/30209 Ammer, C. (2019). Diversity and forest productivity in a changing climate. New Phytologist, 221(1), 50– 66. https://doi.org/10.1111/NPH.15263 Apiolaza, L. A., Butterfield, B., Chauhan, S. S., & Walker, J. C. F. (2011). Characterization of mechanically perturbed young stems: Can it be used for wood quality screening? Annals of Forest Science, 68(2), 407–414. https://doi.org/10.1007/S13595-011-0028-8/FIGURES/3 Arsić, J., Stojanović, M., Petrovičová, L., Noyer, E., Milanović, S., Světlík, J., Horáček, P., & Krejza, J. (2021). Increased wood biomass growth is associated with lower wood density in Quercus petraea (Matt.) Liebl. saplings growing under elevated CO2. PLOS ONE, 16(10), e0259054. https://doi.org/10.1371/JOURNAL.PONE.0259054 Assmann, E. (1961). The science of forest yield. The organic production, structure, increment and yield of forest stands. The Science of Forest Yield. The Organic Production, Structure, Increment and Yield of Forest Stands. https://www.cabdirect.org/cabdirect/abstract/19610604099 Auguie, B. (2017). gridExtra: Miscellaneous Functions for “Grid” Graphics. CRAN - Package GridExtra. https://cran.r-project.org/web/packages/gridExtra/index.html Baddeley, A., & Turner, R. (2005). Spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software, 12, 1–42. https://cran.r-project.org/web/packages/spatstat/index.html Badoux, E. (1946). ETH Library Relations entre le développement de la cime et l’accroissement chez le pin sylvestre contribution à l’étude de l’éclaircie [L’ÉCOLE POLYTECHNIQUE FÉDÉRALE]. https://doi.org/10.3929/ethz-a-000287615 86 Barbeito, I., Dassot, M., Bayer, D., Collet, C., Drössler, L., Löf, M., del Rio, M., Ruiz-Peinado, R., Forrester, D. I., Bravo-Oviedo, A., & Pretzsch, H. (2017). Terrestrial laser scanning reveals differences in crown structure of Fagus sylvatica in mixed vs. pure European forests. Forest Ecology and Management, 405(September), 381–390. https://doi.org/10.1016/j.foreco.2017.09.043 Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01 Bauhus, J., Forrester, D. I., & Pretzsch, H. (2017). Mixed-species forests: The development of a forest management paradigm. In Mixed-Species Forests: Ecology and Management (pp. 1–25). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-54553-9_1 Bayer, D., Seifert, S., & Pretzsch, H. (2013). Structural crown properties of Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.]) in mixed versus pure stands revealed by terrestrial laser scanning. Trees - Structure and Function, 27(4), 1035–1047. https://doi.org/10.1007/s00468-013-0854-4 Benneter, A., Forrester, D. I., Bouriaud, O., Dormann, C. F., & Bauhus, J. (2018). Tree species diversity does not compromise stem quality in major European forest types. Forest Ecology and Management, 422, 323–337. https://doi.org/10.1016/J.FORECO.2018.04.030 Bevans, R. (2021). Akaike Information Criterion | When & How to Use It. Scribbr. https://www.scribbr.com/statistics/akaike-information-criterion/ Bicl-Sorlin, G. H., & Bell, A. D. (2000). Crown architecture in Quercus petraea and Q. robur : the fate of buds and shoots in relation to age, position and environmental perturbation. Forestry: An International Journal of Forest Research, 73(4), 331–349. https://doi.org/10.1093/FORESTRY/73.4.331 Bohn, F. J. (2021). Forest ecosystems trends and innovation: satellite observation, simulations, and fire fighting. COP26. https://www.cop26eusideevents.eu/ Bohn, F. J., Frank, K., & Huth, A. (2014). Of climate and its resulting tree growth: Simulating the productivity of temperate forests. Ecological Modelling, 278, 9–17. https://doi.org/10.1016/J.ECOLMODEL.2014.01.021 Bonnor, G. M. (1964). THE INFLUENCE OF STAND DENSITY ON THE CORRELATION OF STEM DIAMETER WITH CROWN WIDTH AND HEIGHT FOR LODGEPOLE PINE. The Forestry Chronicle, 40(3), 347– 87 349. https://doi.org/10.5558/TFC40347-3 Bravo-Oviedo, A., Pretzsch, H., Ammer, C., Andenmatten, E., Barbati, A., Barreiro, S., Brang, P., Bravo, F., Coll, L., Corona, P., Ouden, J. den, Ducey, M. J., Forrester, D. I., Giergiczny, M., Jacobsen, J. B., Lesinski, J., Lf, M., Mason, W. L., Matovic, B., … Zlatanov, T. (2014). European Mixed Forests: definition and research perspectives. Forest Systems, 23(3), 518–533. https://doi.org/10.5424/FS/2014233-06256 Bravo, F., Ariza, A. M., Dugarsuren, N., & Ordóñez, C. (2021). Disentangling the Relationship between Tree Biomass Yield and Tree Diversity in Mediterranean Mixed Forests. Forests 2021, Vol. 12, Page 848, 12(7), 848. https://doi.org/10.3390/F12070848 Bravo, F., Fabrika, M., Ammer, C., Barreiro, S., Bielak, K., Coll, L., Fonseca, T., Kangur, A., Löf, M., Merganičová, K., Pach, M., Pretzsch, H., Stojanović, D., Schuler, L., Peric, S., Rtzer, T., Del Río, M., Dodan, M., & Bravo-Oviedo, A. (2019). Modelling approaches for mixed forests dynamics prognosis. Research gaps and opportunities. In Forest Systems (Vol. 28, Issue 1). Ministerio de Agricultura Pesca y Alimentacion. https://doi.org/10.5424/fs/2019281-14342 Bravo, J. A., Roig, S., & Serrada, R. (2008). Selvicultura en montes bajos y medios de Quercus ilex L., Q. pyrenaica Willd. y Q. faginea Lam. In Compendio de Selvicultura Aplicada en España. Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria-INIA (p. 88). Castro, J., Zamora, R., Hodar, J. A., & Gomez, J. M. (2004). Seedling establishment of a boreal tree species (Pinus sylvestris) at its southernmost distribution limit: consequences of being in a marginal Mediterranean habitat. Journal of Ecology, 92(2), 266–277. https://doi.org/10.1111/j.0022-0477.2004.00870.x Cattaneo, Nicolás. (2018). Competencia, productividad y cambios a nivel de copas en bosques mixtos de pinos mediterráneos, señales a nivel del árbol individual. Universidad de Valladolid. Cattaneo, Nicolás, Bravo-Oviedo, A., & Bravo, F. (2018). Analysis of tree interactions in a mixed Mediterranean pine stand using competition indices. European Journal of Forest Research, 137(1), 109–120. https://doi.org/10.1007/s10342-017-1094-8 Cattaneo, Nicolas, Schneider, R., Bravo, F., & Bravo-Oviedo, A. (2020). Inter-specific competition of tree congeners induces changes in crown architecture in Mediterranean pine mixtures. Forest Ecology and Management, 476, 118471. https://doi.org/10.1016/j.foreco.2020.118471 94 http://www.jstor.org/stable/2532051 REFERENCES Linked references are available on JSTOR for thi. Biomatrics, 45(1), 255–268. Lin, W., Meng, Y., Qiu, Z., Zhang, S., & Wu, J. (2017). Measurement and calculation of crown projection area and crown volume of individual trees based on 3D laser-scanned point-cloud data. Internation Journal Remote Sensing, 38(4), 1083–1100. https://doi.org/10.1080/01431161.2016.1265690 Lizarralde, I. (2008a). Dinámica de rodales y competencia en las masas de Pino silvestre (Pinus sylvestris) y Pino negral (Pino pinaster Ait.) de los Sistemas Central e Ibérico meridional. 230. Lizarralde, I. (2008b). Dinamica de Rodales y competencia en las masas de Pino silvestre (Pinus sylvestris L.) y Pino negral (Pinus pinaster Ait.) de los Sistemas Centrales e Iberico Meridional. Universidad de Valladolid. Longuetaud, F., Piboule, A., Wernsdörfer, H., & Collet, C. (2013). Crown plasticity reduces inter-tree competition in a mixed broadleaved forest. European Journal of Forest Research, 132(4), 621– 634. https://doi.org/10.1007/S10342-013-0699-9/FIGURES/8 Lopez Leiva, C., Espinosa Rincón, J., & Bongoa, J. (2009). Mapa de Vegetacion de Castilla y Leon. Sintesis 1:400.000. Junta de Castilla y León. Consejería de Medio Ambiente, Ed. Luoma, V., Saarinen, N., Kankare, V., Tanhuanpää, T., Kaartinen, H., Kukko, A., Holopainen, M., Hyyppä, J., & Vastaranta, M. (2019). Examining changes in stem taper and volume growth with two-date 3D point clouds. Forests, 10(5), 14. https://doi.org/10.3390/f10050382 Maestre, F. T., & Cortina, J. (2004). Are Pinus halepensis plantations useful as a restoration tool in semiarid Mediterranean areas? Forest Ecology and Management, 198, 303–317. https://doi.org/10.1016/j.foreco.2004.05.040 Marcos, D. (2021). Virtualización del patrimonio. Definicion de una metodologia y documentacion y difusion del patrimonio arquitectonico. Universidad de Valldolid. Martin-Ducup, O., Robert, S., Fournier, R. A. R. A., Olivier, M. D., Robert, S., & Fournier, R. A. R. A. (2016). Response of sugar maple (Acer saccharum, Marsh.) tree crown structure to competition in pure versus mixed stands. Forest Ecology and Management, 374, 20–32. https://doi.org/10.1016/j.foreco.2016.04.047 95 McElhinny, C., Gibbons, P., Brack, C., & Bauhus, J. (2005). Forest and woodland stand structural complexity: Its definition and measurement. Forest Ecology and Management, 218(1–3), 1–24. https://doi.org/10.1016/J.FORECO.2005.08.034 Merlin, M., Perot, T., Perret, S., Korboulewsky, N., & Vallet, P. (2015). Effects of stand composition and tree size on resistance and resilience to drought in sessile oak and Scots pine. Forest Ecology and Management, 339, 22–33. https://doi.org/10.1016/j.foreco.2014.11.032 Metz, J. Ô., Seidel, D., Schall, P., Scheffer, D., Schulze, E. D., & Ammer, C. (2013). Crown modeling by terrestrial laser scanning as an approach to assess the effect of aboveground intra- and interspecific competition on tree growth. Forest Ecology and Management, 310, 275–288. https://doi.org/10.1016/j.foreco.2013.08.014 Michelot, A., Simard, S., Rathgeber, C., Dufrêne, E., & Damesin, C. (2012). Comparing the intra-annual wood formation of three European species (Fagus sylvatica, Quercus petraea and Pinus sylvestris) as related to leaf phenology and non-structural carbohydrate dynamics. Tree Physiology, 32(8), 1033–1045. https://doi.org/10.1093/treephys/tps052 Montero, G., del Río, M., Roig, S., & Rojo, A. (2008). Selvicultura de Pinus sylvestris L. In Compendio de Selvicultura Aplicada en España. Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria-INIA (pp. 503–534). Moulia, B., Bastien, R., Chauvet-Thiry, H., & Leblanc-Fournier, N. (2019). Posture control in land plants: growth, position sensing, proprioception, balance, and elasticity. Journal of Experimental Botany, 70(14), 3467–3494. https://doi.org/10.1093/jxb/erz278 Moulia, B., & Fournier, M. (2009). The power and control of gravitropic movements in plants: a biomechanical and systems biology view. Journal of Experimental Botany, 60(2), 461–486. https://doi.org/10.1093/jxb/ern341 Müller, K., & Wickham, H. (2020). tibble: Simple Data Frames. CRAN - Package Tibble. https://cran.rproject.org/web/packages/tibble/index.html Muñoz-Gálvez, F. J., Herrero, A., Esther Pérez-Corona, M., & Andivia, E. (2021). Are pine-oak mixed stands in Mediterranean mountains more resilient to drought than their monospecific counterparts? Forest Ecology and Management, 484, 118955. https://doi.org/10.1016/J.FORECO.2021.118955 96 Nagelkerke, N. J. D. (1991). A Note on a General Definition of the Coefficient of Determination. Biometrika, 78(3), 691–692. Olofsson, K., Holmgren, J., & Olsson, H. (2014). Tree Stem and Height Measurements using Terrestrial Laser Scanning and the RANSAC Algorithm. Remote Sensing, 6(12), 4323–4344. https://doi.org/10.3390/rs6054323 Pain, D. P., & Hann, D. W. (1982). Maximum crown-width equations for southwestern oregon tree species. Forest Research Lab, 46, 20. http://cips.forestry.oregonstate.edu/sites/cips/files/FRL_RP46_SW1.pdf Pedrosa Meca Ferreira de Castro, M. M. (2004). Analisis de la interaccion vegetacion-herbivoro en sistemas silvopastorales basados en Quercus pyrenaica. Universidad de Alcala. Perkins, D., Uhl, E., Biber, P., Toit, B. Du, Carraro, V., Rötzer, T., Pretzsch, H., du Toit, B., Carraro, V., Rötzer, T., & Pretzsch, H. (2018). Impact of Climate Trends and Drought Events on the Growth of Oaks (Quercus robur L. and Quercus petraea (Matt.) Liebl.) within and beyond Their Natural Range. 9(3), 108. http://www.mdpi.com/1999-4907/9/3/108 Petritan, I. C., Marzano, R., Petritan, A. M., & Lingua, E. (2014). Overstory succession in a mixed Quercus petraea–Fagus sylvatica old growth forest revealed through the spatial pattern of competition and mortality. Forest Ecology and Management, 326, 9–17. https://doi.org/10.1016/J.FORECO.2014.04.017 Pommerening, A., & Grabarnik, P. (2019). Individual-based Methods in Forest Ecology and Management. Springer International Publishing. https://doi.org/10.1007/978-3-030-24528-3 Prtner, H. O., Roberts, D. C., Adams, H., Adler, C., Aldunce, P., Ali, E., & Ibrahim, Z. Z. (2022). IPCC. Technical Summary Climate change 2022: impacts, adaptation and vulnerability. https://research.wur.nl/en/publications/climate-change-2022-impacts-adaptation-and- vulnerability Poyatos, R., Llorens, P., Piñol, J., & Rubio, C. (2008). Response of Scots pine ( Pinus sylvestris L.) and pubescent oak ( Quercus pubescens Willd.) to soil and atmospheric water deficits under Mediterranean mountain climate. Annals of Forest Science, 65(3), 306. https://doi.org/10.1051/forest:2008003 Pretzsch, H., del Río, M., Schütze, G., Ammer, C., Annighöfer, P., Avdagic, A., Barbeito, I., Bielak, K., 97 Brazaitis, G., Coll, L., Drössler, L., Fabrika, M., Forrester, D. I., Kurylyak, V., Löf, M., Lombardi, F., Matović, B., Mohren, F., Motta, R., … Bravo-Oviedo, A. (2016). Mixing of Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) enhances structural heterogeneity, And the effect increases with water availability. Forest Ecology and Management, 373, 149–166. https://doi.org/10.1016/j.foreco.2016.04.043 Pretzsch, H., Steckel, M., Heym, M., Biber, P., Ammer, C., Ehbrecht, M., Bielak, K., Bravo, F., Ordóñez, C., Collet, C., Vast, F., Drössler, L., Brazaitis, G., Godvod, K., Jansons, A., de-Dios-García, J., Löf, M., Aldea, J., Korboulewsky, N., … del Río, M. (2020). Stand growth and structure of mixed-species and monospecific stands of Scots pine (Pinus sylvestris L.) and oak (Q. robur L., Quercus petraea (Matt.) Liebl.) analysed along a productivity gradient through Europe. European Journal of Forest Research, 139(3), 349–367. https://doi.org/10.1007/s10342-019-01233-y Pretzsch, H, & Schütze, G. (2021). Tree species mixing can increase stand productivity, density and growth efficiency and attenuate the trade-off between density and growth throughout the whole rotation. Annals of Botany, 128(6), 767–786. https://doi.org/10.1093/AOB/MCAB077 Pretzsch, Hans. (2009). Forest Dynamics, Growth and Yield. In Forest Dynamics, Growth and Yield. https://doi.org/10.1007/978-3-540-88307-4 Pretzsch, Hans. (2014). Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures. Forest Ecology and Management, 327, 251–264. https://doi.org/10.1016/j.foreco.2014.04.027 Pretzsch, Hans, & Biber, P. (2016). Tree species mixing can increase maximum stand density. Canadian Journal of Forest Research, 46(10), 1179–1193. https://doi.org/10.1139/CJFR-2015- 0413/ASSET/IMAGES/LARGE/CJFR-2015-0413F7.JPEG Pretzsch, Hans, & Forrester, D. I. (n.d.). Mixed-Species Forests. Pretzsch, Hans, & Forrester, D. I. (2017). Stand Dynamics of Mixed-Species Stands Compared with Monocultures. In Hans Pretzsch, D. I. Forrester, & J. Bauhus (Eds.), Mixed-Species Forests. Ecology and Management (pp. 117–209). Springer Nature. https://doi.org/10.1007/978-3-662-54553-9 Pretzsch, Hans, Forrester, D. I., & Bauhus, J. (2017). Mixed-Species Forests: Ecology and Management (Hans Pretzsch, D. I. Forrester, & J. Bauhus (eds.)). Springer. https://doi.org/10.1007/978-3-662- 54553-9 98 Pretzsch, Hans, & Rais, A. (2016). Wood quality in complex forests versus even-aged monocultures: review and perspectives. Wood Science and Technology, 50(4), 845–880. https://doi.org/10.1007/S00226-016-0827-Z/FIGURES/13 Pretzsch, Hans, & Schütze, G. (2009). Transgressive overyielding in mixed compared with pure stands of Norway spruce and European beech in Central Europe: Evidence on stand level and explanation on individual tree level. European Journal of Forest Research, 128(2), 183–204. https://doi.org/10.1007/s10342-008-0215-9 Pretzsch, Hans, & Schütze, G. (2014). Size-structure dynamics of mixed versus pure forest stands. Forest Systems, 23(3), 560–572. https://doi.org/10.5424/FS/2014233-06112 Pretzsch, Hans, & Zenner, E. K. (2017). Toward managing mixed-species stands: from parametrization to prescription. Forest Ecosystems, 4(1), 1–17. https://doi.org/10.1186/S40663-017-0105- Z/FIGURES/10 R Core Team. (2016). R: a language and environment for statistical computing. R Foundation for Statistical Computing. https://www.r-project.org/ Reque, J. A. (2008). Selvicultura de Quercus petraea L . y Quercus robur L . In Compendio de Selvicultura Aplicada en España. Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria-INIA (p. 27). Revelle, W. (2020). psych: Procedures for Psychological, Psychometric, and Personality Research. CRAN - Package Psych. https://cran.r-project.org/web/packages/psych/index.html Riofrio, J. (2018). Mixed stands growth dynamics of Scots pine and Maritime pine. Species complementarity relationships and growth effects. Universidad de Valladolid. Riofrío, J., Del Río, M., & Bravo, F. (2017). Mixing effects on growth efficiency in mixed pine forests. Forestry, 90(3), 381–392. https://doi.org/10.1093/FORESTRY/CPW056 Ritter, T., & Nothdurft, A. (2018). Automatic assessment of crown projection area on single trees and stand-level, based on three-dimensional point clouds derived from terrestrial laser-scanning. Forests, 9(5), 237. https://doi.org/10.3390/f9050237 Robinson, D., Hayes, A., & Couch, S. (2021). broom: Convert Statistical Objects into Tidy Tibbles. CRAN - Package Broom. https://cran.r-project.org/web/packages/broom/index.html 99 Rodríguez De Prado, D., Riofrío, J., Aldea, J. orge, Mcdermott, J., Bravo, F., & Herrero De Aza, C. (2022). Species Mixing Proportion and Aridity Influence in the Height-Diameter Relationship for Different Species Mixtures in Mediterranean Forests. Forests 2022, Vol. 13, Page 119, 13(1), 119. https://doi.org/10.3390/F13010119 Roussel, J.-R., & De Boissieu, F. (2020). rlas: Read and Write “las” and “laz” Binary File Formats Used for Remote Sensing Data. R package version 1.3.7. Ruano, I., Rodríguez-García, E., & Bravo, F. (2013). Effects of pre-commercial thinning on growth and reproduction in post-fire regeneration of Pinus halepensis Mill. Annals of Forest Science, 70(4), 357–366. https://doi.org/10.1007/S13595-013-0271-2/FIGURES/5 Ruiz-Villar, H., Morales-González, A., Bombieri, G., Zarzo-Arias, A., & Penteriani, V. (2019). Characterization of a brown bear aggregation during the hyperphagia period in the Cantabrian Mountains, NW Spain. Ursus, 29(2), 93–100. https://doi.org/10.2192/URSU-D-29-1.1 Sánchez-Gómez, D., Valladares, F., & Zavala, M. A. (2006). Functional traits and plasticity in response to light in seedlings of four Iberian forest tree species. Tree Physiology, 26(11), 1425–1433. https://doi.org/10.1093/TREEPHYS/26.11.1425 Sanquetta, C. R., Behling, A., Dalla Corte, A. P., Arlindo Simon, A., Lourenco Rodrigues, A., Camacho Cadori, G., & Costa Junior, S. (2015). Modelling crown volume in Acacia mearnsii stands. African Journal of Agricultural Research, 10(28), 2756–2762. https://doi.org/10.5897/ajar2015.9778 Schüler, O., Hemmersbach, R., & Böhmer, M. (2015). A bird’s-eye view of molecular changes in plant gravitropism using omics techniques. Frontiers in Plant Science, 6, 1176. https://doi.org/10.3389/FPLS.2015.01176/BIBTEX Seidel, D., Leuschner, C., Müller, A., & Krause, B. (2011). Crown plasticity in mixed forests—Quantifying asymmetry as a measure of competition using terrestrial laser scanning. Forest Ecology and Management, 261(11), 2123–2132. https://doi.org/10.1016/j.foreco.2011.03.008 Seidel, D., Leuschner, C., Scherber, C., Beyer, F., Wommelsdorf, T., Cashman, M. J., & Fehrmann, L. (2013). The relationship between tree species richness, canopy space exploration and productivity in a temperate broad-leaf mixed forest. Forest Ecology and Management, 310, 366– 374. https://doi.org/10.1016/j.foreco.2013.08.058 Sierra-de-Grado, R., Pando, V., Voltas, J., Zas, R., Majada, J., & Climent, J. (2022). Straightening the 100 crooked: intraspecific divergence of stem posture control and associated trade-offs in a model conifer. Journal of Experimental Botany, 73(4), 1222–1235. https://doi.org/10.1093/JXB/ERAB535 Smith, D. M. (1986). The practice of silviculture. https://bibliotecadigital.infor.cl/handle/20.500.12220/1265 Sprinz, P. T., & Burkhart, H. E. (1987). Relationships between tree crown, stem, and stand characteristics in unthinned loblolly pine plantations. Canadian Journal of Forest Research, 17(6), 534–538. https://doi.org/10.1139/X87-089 Steckel, M., del Río, M., Heym, M., Aldea, J., Bielak, K., Brazaitis, G., Černý, J., Coll, L., Collet, C., Ehbrecht, M., Jansons, A., Nothdurft, A., Pach, M., Pardos, M., Ponette, Q., Reventlow, D. O. J., Sitko, R., Svoboda, M., Vallet, P., … Pretzsch, H. (2020). Species mixing reduces drought susceptibility of Scots pine (Pinus sylvestris L.) and oak (Quercus robur L., Quercus petraea (Matt.) Liebl.) – Site water supply and fertility modify the mixing effect. Forest Ecology and Management, 461. https://doi.org/10.1016/J.FORECO.2020.117908 Sterba, H., Río, M. del, Brunner, A., & Condés, S. (2014). Effect of species proportion definition on the evaluation of growth in pure vs. mixed stands. Forest Systems, 23(3), 547–559. http://revistas.inia.es/index.php/fs/article/view/6051 Stimm, K., Heym, M., Uhl, E., Tretter, S., & Pretzsch, H. (2021). Height growth-related competitiveness of oak (Quercus petraea (Matt.) Liebl. and Quercus robur L.) under climate change in Central Europe. Is silvicultural assistance still required in mixed-species stands? Forest Ecology and Management, 482. https://doi.org/10.1016/J.FORECO.2020.118780 Thies, M., Pfeifer, N., Winterhalder, D., & Gorte, B. G. H. (2004). Three-dimensional reconstruction of stems for assessment of taper, sweep and lean based on laser scanning of standing trees. Scandinavian Journal of Forest Research, 19(6), 571–581. https://doi.org/10.1080/02827580410019562 Toïgo, M., Perot, T., Courbaud, B., Castagneyrol, B., Gégout, J. C., Longuetaud, F., Jactel, H., & Vallet, P. (2018). Difference in shade tolerance drives the mixture effect on oak productivity. Journal of Ecology, 106(3), 1073–1082. https://doi.org/10.1111/1365-2745.12811 Uhl, E., Biber, P., Ulbricht, M., Heym, M., Horváth, T., Lakatos, F., Gál, J., Steinacker, L., Tonon, G., Ventura, M., & Pretzsch, H. (2015). Analysing the effect of stand density and site conditions on 101 structure and growth of oak species using Nelder trials along an environmental gradient: Experimental design, evaluation methods, and results. Forest Ecosystems, 2(1). https://doi.org/10.1186/s40663-015-0041-8 UNECE, & FAO. (2011). FOREST EUROPE: State of Europe’s Forests 2011. In Status and Trends in Sustainable Forest Management in Europe. UNFCCC (2015). Adoption of the Paris Agreement. Proposal by the President. Conference of the Parties Twenty-first session Paris, 30 November to 11 December 2015. Uzquiano. (2016). Terrestrial Laser Scanning Data Processing: Development of a New Methodology applied to Mixed Forests. Universidad de Valladolid. Uzquiano, S. (2014). Mediciones Dendrometricas y Dasometricas Mediante Tecnicas LiDAR y Fotogametricas. Universidad de Valladolid. Uzquiano, S., Barbeito, I., San Martín, R., Ehbrecht, M., Seidel, D., & Bravo, F. (2021). Quantifying Crown Morphology of Mixed Pine-Oak Forests Using Terrestrial Laser Scanning. Remote Sensing, 13(23), 4955. https://doi.org/10.3390/rs13234955 Vähänen, T. (FAO). (2021). Forest ecosystems trends and innovation: satellite observation, simulations, and fire fighting - YouTube. COP 26. https://www.youtube.com/watch?v=JaA3bcN_n_s Valladares, F., & Niinemets, Ü. (2008). Shade Tolerance, a Key Plant Feature of Complex Nature and Consequences. Annual Review of Ecology, Evolution, and Systematics, 39, 237–257. https://doi.org/10.1146/ANNUREV.ECOLSYS.39.110707.173506 Vallet, P., & Perot, T. (2018). Coupling transversal and longitudinal models to better predict Quercus petraea and Pinus sylvestris stand growth under climate change. Agricultural and Forest Meteorology, 263, 258–266. https://doi.org/10.1016/j.agrformet.2018.08.021 Wei, T., Lin, Y., Yan, L., & Zhang, L. (2016). Tree species classification based on stem-related feature parameters derived from static terrestrial laser scanning data. International Journal of Remote Sensing, 37(18), 4420–4440. https://doi.org/10.1080/01431161.2016.1213920 Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis. CRAN - Package Ggplot2. https://cran.r-project.org/web/packages/ggplot2/index.html Williams, L. J., Paquette, A., Cavender-Bares, J., Messier, C., & Reich, P. B. (2017). Spatial 102 complementarity in tree crowns explains overyielding in species mixtures. Nature Ecology & Evolution 2017 1:4, 1(4), 1–7. https://doi.org/10.1038/s41559-016-0063 Zarnoch, S. J., Bechtold, W. A., & Stolte, K. W. (2004). Using crown condition variables as indicators of forest health. https://doi.org/10.1139/X03-277 ANNEX 1 Crown models of the mixture Pinus Sylvestris - Quercus Petraea applied in the mixture Pinus Sylvestris - Quercus Pyrenaica. 103 4. OAK: Crown at Base Height (CBH) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1 + 𝑒(0.77∙𝐷𝐵𝐻 𝑙𝑛𝐵𝐴+0.22∙𝑙𝑛𝐵𝐴−1.52∙𝐵𝐴𝐿𝑡+0.87∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) Table 4. CBH Oak Analysis 2 Residual standard error: 1.029 on 34 degrees of freedom R2 = 40.57473 p-value = 0.5979 SSE = 35.98185 AIC = 115.7656 5. PINE: Crown Projection Area (CPA) 𝐶𝑃𝐴 = 𝑒(0.12·𝐷𝐵𝐻−0.8·𝐵𝐴𝑡−0.002·𝐶𝐼) Table 5. CPA pine analysis 2 Residual standard error: 2.114 on 46 degrees of freedom R2 = 69.67994 p-value = 0.5437 SSE = 205.5402 AIC = 217.3132 6. OAK: Crown Projection Area (CPA) 𝐶𝑃𝐴 = 𝑒(0.15+0.02·𝐷𝐵𝐻+2.46·𝐵𝐴−4.61·𝐵𝐴𝐿+095·𝑅𝑎𝑡𝑖𝑜 𝑛) Table 6. CPA Oak Analysis 2 Residual standard error: 1.843 on 33 degrees of freedom R2= 30.71497 p-value = 0.958 SSE = 112.1433 AIC = 160.9626 7. PINE: Crown Volume (CV) 𝐶𝑉 = 0.01 · 𝑑2ℎ − 21.93 ·𝐵𝐴𝑡+ 0.42 ·𝐶𝐼 Table 7. CV pine analysis 2 Residual standard error: 9.587 on 46 degrees of freedom Multiple R-squared: 0.8755, Adjusted R- squared: 0.8674 R2 = 62.92323 p-value = 0.5593 SSE = 4227.516 AIC = 365.4759 8. OAK: Crown Volume (CV) 𝐶𝑉 = −5.84 ∙ 𝐷𝐵𝐻 + 0.001 · 𝑙𝑛𝐵𝐴𝑡+27.87 · 𝐵𝐴𝐿𝑡−37.49 ∙ 𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿 Table 8. CV Oak Analysis 2 Residual standard error: 6.074 on 33 degrees of freedom Multiple R-squared: 0.3442, Adjusted R- squared: 0.2647 R2 = 34.41954 p-value = 0.2659 SSE = 1217.285 AIC = 251.5774 ANNEX 3 Residuals analyses of the first 5 models with lower AIC that were developed for the mixture Pinus Sylvestris – Quercus Pyrenaica (Analysis 3) 115 Annex 3. RESIDUALS ANALYSES OF THE FIRST 5 MODELS WITH LOWER AIC THAT WERE DEVELOPED FOR THE MIXTURE PINUS SYLVESTRISQUERCUS PYRENAICA (ANALYSIS 3) 1. PINE: Maximum Crown Width Height (MCWH) Model 1 (Radius = 10) 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1+𝑒(0.03∙𝐷𝐵𝐻−0.66∙𝐵𝐴𝑡−0.9∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) Model 2 (Radius 10) 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1+𝑒(0.03∙𝐷𝐵𝐻−0.78∙𝐵𝐴𝑡−0.82∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴) Model 3 (Radius 7.5) 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1+𝑒(0.03∙𝐷𝐵𝐻−1.06∙𝐵𝐴𝑡−0.95∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) Model 4 (Radius 10) 𝑀𝐶𝑊𝐻 = 𝑇𝐻 1+𝑒(0.02∙𝐷𝐵𝐻−0.31∙𝑙𝑛𝐵𝐴𝑡−1.38∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) 3. PINE: Crown at Base Height (CBH)) Model 1 (Radius = 5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(12.09∙𝐷𝐵𝐻/𝑙𝑛𝐵𝐴−0.85∙𝑙𝑛𝐵𝐴−0.94∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴) Model 2 (Radius = 5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(11.44∙𝐷𝐵𝐻−0.77∙𝑙𝑛𝐵𝐴−0.90∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 3 (Radius = 7.5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−78.55∙𝐷𝐵𝐻+2.82∙𝐵𝐴+2.22∙𝐵𝐴𝐿𝑝−0.53∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 4 (Radius = 5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(11.15∙𝐷𝐵𝐻−0.69∙𝑙𝑛𝐵𝐴−0.69∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) Model 5 (Radius = 10) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−44.57∙𝐷𝐵𝐻+1.91∙𝐵𝐴+1.12∙𝐵𝐴𝐿𝑝−0.6∙𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝐿) 4. OAK: Crown at Base Height (CBH) Model 1 (Radius = 7.5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−0.05∙𝐶.𝐼.+0.53∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 2 (Radius = 7.5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−0.06∙𝐶.𝐼.+0.53∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 3 (Radius = 10) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−1.01∙𝐵𝐴𝐿𝑡+0.42∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 4 (Radius = 10) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−1.16∙𝐵𝐴𝐿𝑝+0.46∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 5 (Radius = 7.5) 𝐶𝐵𝐻 = 𝑀𝐶𝑊𝐻 1+𝑒(−1.44∙𝐵𝐴𝐿𝑡+0.33∙𝑅𝑎𝑡𝑖𝑜 𝑛) Model 2 (Radius = 7.5) 𝐶𝑃𝐴 = 𝑒(0.24·𝑇𝐻−0.16·𝐶.𝐼.) Model 3 (Radius = 5) 𝐶𝑃𝐴 = 𝑒(0.23·𝑇𝐻−0.22·𝐶.𝐼.) Model 4 (Radius = 10) 𝐶𝑃𝐴 = 𝑒(0.25·𝑇𝐻−0.13·𝐶.𝐼.) Model 5 (Radius = 10) 𝐶𝑃𝐴 = 𝑒(0.26·𝑇𝐻+0.43·𝑙𝑛𝐵𝐴𝑡−3.43·𝐵𝐴𝐿𝑝) 7. PINE: Crown Volume (CV) Model 1 (Radius = 5) 𝐶𝑉 =17.75 + 0.01 · 𝑑2ℎ − 152.77 ·𝐵𝐴𝑡+105.53 · 𝐵𝐴𝐿𝑝−22.15 ∙ 𝑅𝑎𝑡𝑖𝑜 𝑛𝑝 Model 2 (Radius = 5) 𝐶𝑉 =24.08 + 0.01 · 𝑑2ℎ − 143.08 ·𝐵𝐴𝑡+106.01 · 𝐵𝐴𝐿𝑝−29.36 ∙ 𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝑝 Model 3 (Radius = 5) 𝐶𝑉 = 0.01 · 𝑑2ℎ − 131.45 ·𝐵𝐴𝑡+99.12 · 𝐵𝐴𝐿𝑡− 5.66 ∙ 𝑅𝑎𝑡𝑖𝑜 𝑛𝑝 Model 4 (Radius = 5) 𝐶𝑉 = 0.01 · 𝑑2ℎ − 117.28 ·𝐵𝐴𝑡+79.82 · 𝐵𝐴𝐿𝑡 Model 5 (Radius = 10) 𝐶𝑉 = 0.01 · 𝑑2ℎ − 30.78 ·𝐵𝐴𝑡+24.43 · 𝐵𝐴𝐿𝑝 8. OAK: Crown Volume (CV) Model 1 (Radius = 10) 𝐶𝑉 = 1.61 ∙𝑇𝐻 +10.71 · 𝑙𝑛𝐵𝐴𝑡−43.49 · 𝐵𝐴𝐿𝑝+18.01 ∙ 𝑅𝑎𝑡𝑖𝑜 𝐵𝐴𝑝