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Background: Most current approaches in forest science and practice require information about structure and growth of individual trees rather than - or in addition to - sum and mean values of growth and yield at forest stand level as provided by classic experimental designs. By inventing the wheel design, Nelder provided the possibility to turn to the individual tree as basic information unit. Such trials provide valuable insights into the dependency of growth on stand density at particular sites. Methods: Here, we present an extension of the original design and evaluation by Nelder. (i) We established Nelder wheels along an environmental gradient through Europe in atlantic climate in Belgium and Germany, Mediterranean climate in Italy, continental climate in Hungary as well as on high land climate in Mexico. Such disjunct Nelder wheels along an environmental gradient can be regarded and analysed as a two-factor design with the factors of site condition and stand density. (ii) We present an advanced statistical approach to evaluate density dependent growth dynamics of trees planted in form of the Nelder design, which considers spatio-temporal autocorrelation. (iii) We prove the usefulness of the methods in improving ecological theory concerning density related productivity, trade-offs between facilitation and competition, and allometric relations between size variables. Results: First evaluations based on remeasured Nelder wheels in oak (Quercus robur L.) show a size growth differentiation during the first observation period. In particular, height growth is accelerated under higher competition indicating facilitation effects. We detect furthermore a high variability in allometric relations. Conclusions: The proposed design, methods, and results are discussed regarding their impact on forest practice, model building, and ecological theory. We conclude that the extended Nelder approach is highly efficient in providing currently lacking individual tree level information. Keywords: Facilitation; Long-term trial; Nelder; Single tree analyses; Space use efficiency; Stress-gradient-hypothesis; Tree allometry; Quercus * Correspondence: enno.uhl@lrz.tum.de School of Life Sciences Weihenstephan, Technische Universitaet Muenchen, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany Full list of author information is available at the end of the article © 2015 Uhl et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Uhl et al. Forest Ecosystems (2015) 2:17 Page 2 of 19 Background to dominate species interactions under high stress The need for single tree information in forest ecosystem levels (as e.g. strong resource limitation) whereas competi- analysis tion is claimed to prevail in the absence of limitation Especially in advanced phases of stand development, (Callaway and Walker 1997; Holmgren et al. 1997). Bene- high local stand density around a tree may cause compe- fits of species mixing are predicted in harsh and neutral, tition for resources, growth reduction of the tree, or but negative effects in favorable environments (Callaway even its dropout resulting in self-thinning on stand level. and Walker 1997). The net effect of facilitation and com- However, high densities may also cause positive effects petition may also vary temporarily, so that species mixing on plant growth. Competitive and facilitative effects may yields higher benefits in low-growth or stress years com- occur simultaneously. Neighbouring plants may compete pared to high-growth years (del Rio et al. 2014). for contested resources, such as light or water, when these Because of their broad range and gradual increase of are not sufficient for all. At the same time they may facili- local densities from the periphery to the centre, Nelder tate each other, e.g. by reducing wind speed and thus low- trials (Nelder 1962, Fig. 1) can contribute to separate be- ering transpiration or by hydraulic redistribution, which tween the positive and negative effects of density. They may improve the neighbour’s water supply. allow identifying the break-even level of density, where The net effect of co-occurring competition and facili- its positive effects turn into negative net effects. tation on growth is of practical interest. Positive density Especially in the early stand development phase, positive effects on weed suppression and stabilization may exceed effects of density such as control of competing weed, negative effects of resource competition, so that finally avoidance of overheating by mutual shading or dilution ef- trees growing in community may outperform their solitar- fect against herbivores may have the upper hand and may ily growing neighbours. decrease from the inner to the outer parts of a Nelder According to the stress-gradient hypothesis, such wheel. In contrast, resource supply of the individual plant trade-offs between competition and facilitation and the may increase from the inner to the outer circle because of resulting net effects vary along ecological gradients. the larger growing area per tree. Our analysis will address The stress-gradient hypothesis (SGH) states facilitation the interaction between these counteracting effects and Fig. 1 Spacing trial design according to Nelder (1962). Plant positions (green dots) are defined by intersection points of concentric circles and radial spokes Uhl et al. Forest Ecosystems (2015) 2:17 Page 3 of 19 quantify the net effect. Any positive effects in the juvenile Because of the changing growing area and decreasing stage are highly relevant for the whole timespan of stand sample size due to aging and self-thinning, more and development due to the long lasting compound interest more difficulties arose in deriving reliable mean tree and effect of early lead. sum values per hectare from Nelder trials. Parallely, trig- The above-mentioned effects are especially important for gered by paradigm changes in forest modelling (Munro an enhanced understanding of the complex-structured and 1974) and forest policy, science and practice turned from mixed species forests. These are increasingly favoured in a stand-focussed view towards an individual tree based practice, as they are widely held to outperform pure stands analysis and management (Grimm 1999; Pretzsch 2009, in providing a broad range of ecosystem functions and ser- pp 291–336;). While the changing growing area problem vices. While homogeneous pure stands can adequately be hampers classic stand level Nelder design evaluations, described by mean and sum values per hectare at stand especially when mid- or long-term observations are dealt level, more complex stands require more complex ap- with, single tree focussed evaluations become utterly proaches reaching down to the individual tree or even useless if this point is not taken into account. It calls for organ level. The transition to more structured and mixed including fine-tuned measures for individual tree’sgrowing forests increases the need for information on individual tree space and competition. From a statistical point of view, growth in dependence on the local environmental condi- spatial and temporal autocorrelation has to be considered tions, as complex stands and their dynamics are perceived in an individual-tree based Nelder-wheel evaluation. Nei- as amosaicofindividualtrees and their interactions. ther are subsequent measurements of a tree statistically in- This paradigm change from a stand level focus to a dependent nor are the measurements of neighbouring single-tree view creates a new interest in Nelder designs, trees. Ignoring both autocorrelation aspects would violate because they allow a very effective analysis of tree dynam- basic assumptions of classic statistical methods and lead ics along an almost continuous spacing gradient. However, to biased results and overestimated significances. the tree-level-view implies new conceptual and statistical Nelder trials were rarely evaluated at individual tree challenges for a meaningful experiment evaluation. level using competition indices so far, as done by Vanclay et al. (2013) and Tennent (1975). However, to Transition from stand-based to individual tree-based our knowledge autocorrelation effects, especially spatial evaluation of Nelder wheels ones which emerge from the single tree approach, have When applied to forests, so far, Nelder trials were mainly not yet been considered in the context of Nelder trial used for exploring growing stock and productivity in evaluations. With this study, we introduce a method for terms of dendrometrical mean and sum values per hec- evaluating Nelder trials on single tree level that com- tare. Each tree is permanently assigned to a fix growing bines a spatially explicit view on competition with a area defined by the distance to the adjacent circles’ trees spatial autocorrelation concept. Moreover, we apply the and to the trees on the same circle but on the adjacent approach for analyzing the development of individual spokes. Relating the growing stock or growth itself to this oaks in dependence on stand density and site conditions. growing area can provide practically relevant information about the dependency between stand density and product- Research questions ivity and enable, e.g. the derivation of the optimum stand As described above, this paper introduces an evaluation density for growth and yield (Dippel 1982; Spellmann and approach for Nelder trials that avoids problems typically Nagel 1992). arising when the single tree level is of interest. We test If a tree drops out from a Nelder wheel in the course the approach by using several newly established Nelder of stand development, this inevitably changes the grow- wheels with oak species and by focusing on the following ing area of at least its eight nearest neighbours and re- questions: duces the sample size of trees with continuously constant initial spacing and respective growing area 1) How does growth of trees perform by varying (Fig. 1; Kuehne et al. 2013). This is a minor problem growing space and site conditions? when dealing with annual or biennial agricultural crops 2) Does tree allometry change with varying growing for which Nelder originally developed the wheel design. space and site conditions? However, during the 50–100 years lasting observation 3) Does growing space efficiency vary depending on time of wheels stocked with trees, dropouts occur con- growing space and site conditions? tinuously and inevitably. Over time, this hardly leaves any trees in their original spatial constellation, and thus Methods calls the standard evaluation of their stock and growth Set of Nelder trials along an ecological gradient per initial growing area, or even the continuation of the This study makes use of tree and tree growth informa- whole experiment, into question. tion taken from seven Nelder-trials established during Uhl et al. Forest Ecosystems (2015) 2:17 Page 4 of 19 2008 and 2014. Six out of our trial sites are located in dif- outside forests on erstwhile farmland. An area nearly ferent European countries; one was set up in Mexico without standing stock within a natural forest was (Fig. 2, Table 1). Although this study restricts to the three planted in case of PUE656. The trials in Europe cover sites ING650 (Ingolstadt, Germany), GYO651 (Györ, soils from loess or alluvial sediments with good nutri- Hungary), and SAN653 (Sant’Agata, Italy) because only ent supply, thesameistruefor thedeepclaysoilofthe these were measured twice so far, we give a short overview Mexican site. Climate ranges between atlantic (Brussels), of all trial sites here. Each trial comprises two Nelder- subcontinental (Györ), sub Mediterranean (Sant’Agata), wheels in immediate vicinity to each other. Each wheel and subtropical highland conditions (Puebla). Mean tem- covers a growing space gradient from 0.05 m up to peratures at the European sites vary between 8.2 °C 400 m per plant, being equivalent to stand densities of 25 (Ingolstadt) and 13.2 °C (Sant’Agata), while the long-term up to 200,000 plants per hectare. This emulates a range of average at Puebla amounts to 17.1 °C. Mean annual pre- stand densities as found in natural regeneration down to cipitation is lowest at the Györ site (537 mm), highest at solitary growing trees. Brussels (820 mm) and Puebla (900 mm), respectively. Following the concept of Nelder (1962), these settings bear a geometrically incrementation factor of a = 1.413 Measurements and derivation of tree dimensions and and lead to a wheel design with 18 spokes, having a increment values constant angle distance of 20°, and 14 circles including The coordinates of each plant were recorded. Measure- 14 × 18 = 252 plants per wheel. The outermost circle ments of single trees comprise the diameter at root col- serves as buffer for edge effects, and is thus not included lar (d), if existent the diameter at breast height (dbh), into any analysis. Except for the trials GYO651 and diameter at crown base (dcb), tree height (h) and height PUE656 (Puebla, Mexico) we planted the Nelder-wheels of crown base (hcb). Additional crown properties like ra- with Pedunculate oak (Quercus robur L.). At GYO651 dius (cr) in eight cardinal directions and deflection from and PUE656 Sessile oak (Quercus petraea (Mattuschka) stem base were surveyed. By now, no mortality due to Liebl.) and Neatleaf oak (Quercus rugosa Nee.) were competition could be observed. In some cases weed chosen as the typical oak species at those sites (Table 1). mowing caused cutting of trees. These were immediately In every case, local provenances were used. Plant ages at replaced by new trees with similar tree dimensions from the trials’ establishment were one up to three years with a surrounding buffer zone. The buffer zones were estab- heights between 30 and 70 cm. ING650 and BRU655 lished with the same plant material (provenance, assort- were established on clear-cuts within forests and ment) as the wheels themselves. NEC652 and GYO651 on former agriculturally used In analyses, we always refer to diameter at root collar areas within forests. SAN653 and GYO652 were set up (d). Basal area (ba) was calculated from d, plant volume Fig. 2 Locations of our Nelder-trials with oak species in Europe (left) and Mexico (right) Uhl et al. Forest Ecosystems (2015) 2:17 Page 5 of 19 Table 1 Location and growing conditions, plant species, plot establishment and survey dates of the Nelder trials reported in this study Trial Location Longitude(°) Latitude (°) Altitude (m) Soil characteristics Mat (°C) Map (mm) Tree species Year of Tree age at First survey Second survey planting planting (yr) (age) (age) ING650 Ingolstadt (Germany) 11.49 E 48.86 N 460 Loess cover above tertiary 8.2 670 Quercus robur L. 2008 (a) 2 2010 (4) 2012 (6) limestone weathering products GYO651 Györ (Hungary) 17.60 E 47.79 N 110 Alluvial loam 11.1 537 Quercus robur L. 2009 (a) 3 2010 (4) 2013 (7) NEC652 Neckarsulm (Germany) 9.35 E 49.05 N 380 Superficial loam cover with 9.1 760 Quercus robur L. 2010 (a) 1 2013 (4) – temporary water-logged conditions SAN653 Sant’Agata (Italy) 11.10 E 44.46 N 25 Deep alluvial loam 13.2 660 Quercus robur L. 2010 (a) 2 2011 (3) 2012 (4) GYO654 Györ (Hungary) 17.47 E 47.30 N 181 Very deep loess 9.8 570 Quercus petraea 2014 (s) 1 –– (Mattuschka.) Liebl. BRU655 Brussels (Belgium) 4.26 E 50.44 N 130 Deep loess 9.7 820 Quercus robur L. 2012 (a) 2 –– PUE656 Puebla (Mexico) 98.05 W 19.01 N 2350 Deep clay 17.1 900 Quercus rugosa Nee. 2014 (a) 1 –– Mat mean annual temperature, Map mean annual precipitation, N north, E east, W west, a autumn, s spring Uhl et al. Forest Ecosystems (2015) 2:17 Page 6 of 19 v was derived by using the cone formula v ¼ ⋅ba⋅h.We consideration how much growing area is needed to achieve a given growth unit, i.e. it translates the plant also calculated crown length (cl)and crowncross section growth to the unit area and reflects the growth per area (csa)byapplying thesquarerootofthe quadratic qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ area (Zeide 1987; Sterba and Amateis 1998). If we 2 2 mean of the eight radii cr (csa ¼ cr þ cr þ … þ cr =8). NW NE assume growing area as substitute of resource supply, Crown volume cv was calculated by multiplying csa and cl. it subsequently indicates the resource use efficiency Annual rates of increment (i , i , i , i , i , i )wereesti- d h v cl csa cv (Pretzsch 2006, 2014). mated by dividing the final tree size by the time span from In order to quantify the individual plant growth rates planting to last measurement. we used the mean increment of plant dimensions (i , i , d h i , i , i , i ). By using the mean annual increment over v cl csa cv Detecting tree allometry from successive dendrometrical several years we minimize the effects of biotic and abi- measurement otic stressors and stabilize the response variable growth. As the base information for research question 2, we quan- Those individual tree increments were related to the tify the morphological changes of the plants through the growing area of the tree (Pretzsch 2009). The growing periodic allometric slope (synonym: allometric exponent) area was calculated using Voronoi polygons calculated by using the software R (R Core Team 2014) with the ln y − lnðÞ y ln y =y iþ1 i iþ1 i α ¼ ¼ ð1Þ package deldir (Turner 2014). By this method, the lnðÞ x − lnðÞ x lnðÞ x =x iþ1 i iþ1 i available stand area is completely divided between the Here, y and x are different attributes of the same plant, standing trees (Pretzsch 2009, pp 313–314). Tree e.g. height and volume. If i and i + 1 denote subsequent growth characteristics and occupied area provided the times of measurement, then α is valid for the period be- elements for calculating the following efficiency pa- tween the surveys i and i + 1. The calculation above is rameters (eff = growth/area); ef f :heightgrowth, ef f : i i h d most convenient when y , y , x , and x are available i i+1 i i+1 diameter growth, ef f : volume growth, ef f :growthof i i v cl from subsequent measurements as is the case in this crown length, ef f : growth in crown cross section csa study (Pretzsch and Schütze 2005). Suppose, we have area and ef f : growth in crown volume. cv measured heights h and h and volumes v and v at 1 2 1 2 Information about growing space efficiency is relevant the same tree in two successive surveys, and the calcula- for designing resource use efficient production systems tion of α =ln(h /h )/ln(v /v )yields α = 1/4. This h,v 2 1 2 1 h,v (Zeide 2001). It also reflects the trees’ competitive ability would indicate that a volume increase by 1 %, the relative to contested resources and by this an essential aspect of height increase amounts to 0.25 %. In contrast, α =1/2 h,v individual fitness. would constitute a relative increase of 0.50 % per 1 % vol- ume growth, i.e. a greater allocation into height compared with volume (Pretzsch 2010). Re-thinking evaluation methods for Nelder trials From our Nelder plots we use the measurements of Competition index as substitute for resource supply height (h), tree diameter (d), tree volume (v), crown In the course of tree development on the Nelder wheels, length (cl), crown cross section area (csa), and crown competition-caused mortality is inevitable. As mentioned volume (cv), for calculating each tree’s periodic allomet- above, this alters the competitive situation of at least eight ric slopes α , α , α , α , and α . We use tree surrounding trees. Using simply the growing space defined h,v d,v cl,v csa,v cv,v volume in all of the slopes, as for these cases the meta- by a tree’s position on a certain spoke and circle therefore bolic scaling theory (MST) postulates universally valid does obviously not reflect its competitive status correctly values, which can be used as a reference (α =1/4, under such conditions. We therefore include competition h,v α =3/8, α =1/4, α =1/2, and α =3/4; Enquist indices, which quantify the local density around a tree d,v cl,v csa,v cv,v et al. 1998, 2009). In addition, we calculated the allomet- (Biging and Dobbertin 1992, 1995) into the evaluation of ric slope for tree height based on diameter (α =2/3). Nelder designs. Using the term competition index, we fol- h,d low the usual terminology, although a given local density Evaluation of growing space efficiency and spatial constellation around a tree may cause not only While the allometric analysis focussed on the within- competition but also facilitation, simultaneously. Espe- plant and plant-plant interaction in terms of tree morph- cially in the early phase of stand development higher ology, the following analysis relates the growth to the density and higher competition indices may be coupled occupied area. The former approach represents the view with facilitation overcompensating competition. of plant biology and physiology on inner- and inter- We use a local stand density index (SDI ) as defined individual variation of plant size and growth. The fol- below as a distance independent competition index and lowing approach represents the production ecology the Hegyi-index (Hegyi 1974) representing a distance- perspective (growth per unit area), as it takes into dependent type of competition index. Recently, the same Uhl et al. Forest Ecosystems (2015) 2:17 Page 7 of 19 index was chosen by Vanclay et al. (2013) for evaluating Statistical analyses a mixed species Nelder trial. For the subsequent statistical analyses, we suggest gen- For calculating each tree’s competition status we ap- eral additive regression models (GAM, Zuur et al. 2009). plied a search radii having its center on the tree position They provide a convenient way to combine explanatory and whose extension was defined by the mean height of variables with linear and non-linear influence on a goal the 100-tallest trees on the whole wheel multiplied by variable inside the same model. The non-linear relation- the factor 1.25. Each tree inside the search radius was ships are modelled as nonparametric smoothing func- considered a competitor to the tree of interest. tions in this context. As we cannot a priori assume the The SDI normalizes the stem number per hectare to a relations of interest in this study to be linear, this is an mean tree size of 25 cm according to the formula important feature. In addition to non-linearity, Nelder-designs induce −1:605 specific statistical traits on tree level that have to be SDI ¼ N ð2Þ taken into account. First, they inherently carry the dg problem of spatial correlation among subjects. With Herein, N relates to stem numbers per hectare derived other words, dependent on their distance, the mea- from the stem number and circle area corresponding to surements at different plants may not be statistically the search radius. The variable dg reflects the mean independent, violating a standard assumption of classic diameter of all trees within the search radius. The expo- regression analyses. Furthermore, repeated measure- nent −1.605 was chosen according to the stand density ments atthe same plantmust beassumed to be notin- rule (Reineke 1933) portraying a general decline of tree dependent either, which applies when a Nelder trial is number with increasing diameter. remeasured after a certain time interval. For dealing The Hegyi-index takes into account the distance be- with spatial autocorrelation, there exists a broad var- tween the tree of interest and its competing neighbours, iety of readily available spatial variance models (Zuur i.e. the other trees within the search radius, as well as et al. 2009), however, GAMs provide us with a more their size relative to the tree of interest. It is computed convenient option for the purpose of this study. As as Fahrmeir et al. (2009) state, autocorrelation in statis- tical models mostly results from unobserved or unob- d 1 servable explanatory variables. In our context, this DCI ¼ ⋅ ð3Þ d 1 þ DIST might be e.g. microsite or microclimate influences j ij i¼1 varying with the plant positions. Such growth condi- The index i reflects any the central tree j’s n neighbor tions can be expected to be similar at short and more trees within the search radius. DIST represents the different at longer distances, causing spatial autocor- ij distance between the central tree and tree i. d and d relation when not included in the statistical analysis. In i j are the diameters of the neighbor tree i and the central order to cover such effects we introduced a two- tree j. dimensional nonparametric smoothing function g(E, A simple example reveals the relevance of mortality to N) in each of our GAMs, where E and N express the be considered when estimating the growing situation of coordinates of a tree in easting and northing, respect- trees within Nelder wheels. Figure 3 illustrates the usage ively. In the fitted model, g expresses at any tree of different competition indices for an exemplary tree position the summary effect of the unobserved or un- (No. 55) on ING650, wheel 1. The grey area in Fig. 3a observable local influence variables. represents the approximated rectangular growing area as For temporal autocorrelation, classical autoregressive resulting from the chosen Nelder design. The black cir- models like ARMA or ARIMA exist. We, however, sug- cle in Fig. 3b (local stand density index) and Fig. 3c gest incorporating this as a random effect on plant (Hegyi-index) indicates the search radius for identifying level instead, due to the robustness such an approach competing neighbour trees. Finally, in Fig. 3d the grey shows in practice. In such a case, a GAM would be- area points the growing space after mortality of tree come a generalized additive mixed model (GAMM, numbers 37 and 38 calculated by Voronoi polygons. In Zuur et al. 2009). case of using the approximated growing area competi- tion would not change for tree No. 55 if two trees not Applied regression models growing on the same circle as the centre tree have died. The following basic GAM was used for analysing the in- But the distance-independent and the distance-dependent fluence of local stand density/competition on a tree size competition indices are lowered by 11 % and 14 %, re- y (could be h: tree height, d: diameter at root collar, v: spectively, growing space calculated by Voronoi polygons tree volume, cl: crown length, csa: crown cross section would accelerate by 21 %. area, cv: crown volume), (research question 1). Uhl et al. Forest Ecosystems (2015) 2:17 Page 8 of 19 Fig. 3 Schematic excerpt from a Nelder wheel demonstrating different methods of calculating the competitive status of plants. a) growing space (grey area) defined by location on a certain spoke and circle; b) distance-independent competition index: local stand density index (SDI ); c) distance dependent competition index according to Hegyi (1974) and d) growing space calculated by Voronoi polygons (Turner 2014). Large numbers: tree number, small numbers: tree diameter (mm), black circle: search radius for competitors, empty symbols: previously dropped out trees, D : distance from ij centre tree to neighbouring tree y ¼ β þ β ⋅trial þ β ⋅trial þ f ci ; trial which are 1 for the trial they are named after and 0 in the 651i 653i ij 650i ij 0 1 2 1 other cases. The coefficients named β are linear regression þ f ci ; trial þ f ci ; trial þgE ; N þ ε ij 651i ij 653i ij ij ij 2 3 parameters, ci is a competition index, either the local SDI ð4Þ or the Hegyi-index as described above. f , f ,and f are 1 2 3 The indices i and j denominate tree i on trial j. The vari- nonparametric smoothers each one describing the influ- ables trial , trial ,and trial are dummy variables, ence of ci on y for each trial specifically. The smoother g 650 651 653 Uhl et al. Forest Ecosystems (2015) 2:17 Page 9 of 19 takes the position effect into account as explained above, Applying eq. 4 revealed that only for cv the intercept and ε represents i.i.d. errors. If not significant, linear terms varies significantly between the trials (Table 3). For all were excluded and the model was re-fitted after that. The other cases, β and β were removed from the model. 1 2 same approach was used for modelling increments of tree For GYO651 all tested variables depend significantly sizes iy, however, in addition to the previous model, tree from competition, this is not the case for ING650 and size, expressed as tree volume v was additionally included SAN653. Tree heights over competition show a uni- in form of trial-specific nonlinear smoothers. modal optimum curve culminating in ING650 at smaller DCI values and on smaller level (Fig. 5). The iy ¼ β þ βðÞ trial þ βðÞ trial þ f v ; trial 651i 653i ij 650i ij 0 1 2 1 diameter decreases with accelerating tree density (Additional file 1: Figure S1, upper panel). Thus, taller þ f v ; trial þ f v ; trial ij 651i ij 653i 2 3 heights are not reflected in tree volume so far (Additional þ f ci ; trial þ f ci ; trial ij 650i ij 651i 4 5 file 1: Figure S1, lower panel). The same patterns are þ f ci ; trial þgE ; N þ ε ij 653i ij ij ij found for the shape of tree crowns (Additional file 2: ð5Þ Figure S2). Increasing density modulates crown shapes from short but broad to long but narrow profiles. For analysing effects on tree allometry (research In case of iv and icv the tree volume was used as a trial question 2), the same model (eq. 5) was applied. In this overarching effect in eq. 5 as differentiation between case, iy represents the allometric slopes of interest trials showed no significance. The overarching effect was (α , α , α , α , α , α ). Again, the same h,v d,v cl,v csa,v cv,v h,d significant in both cases (Table 4). In ING650 volume model (eq. 5) was used for growing space efficiency as increment accelerated with increasing stand density. But the dependent variables (research question 3). There, oppositely, there was little effect of stand density on vol- iy stands for ef f ; ef f ; ef f ; ef f ; ef f and ef i i i i i ume increment at GYO651 and SAN653, so far, denot- h d v cl csa f , respectively. For all statistical analyses, we used the ing a decreasing trend by increasing density (Additional cv software R (R Core Team 2014), and the R-package file 3: Figure S3, upper panel). It appears that there is a mgcv (Wood 2011) for regression analysis with GAMs. reverse trend between GYO651 and SAN653 concerning the effect of stand density on crown volume increment Results (Additional file 3: Figure S3, lower panel). This means, Growth performance of trees since planting in relation with the findings concerning crown volume Since establishment, the oaks show a high variability in that smaller crowns have a higher crown volume incre- growth. These facts are valid within trials as well as ment in GYO651 but not yet in SAN653. between observed trial locations (Table 2). The range Local site effects may be caused by small-scale vari- between minimum and maximum values of achieved ation of soil properties or in micro climates. They show tree dimensions is substantial. Taking into account that a relevant influence on the development of tree growth; tree size was similar on trial level when planting trees g (E, N) in eq. 4 and 5 is significant for all tested vari- are found with hardly any gain in dimension as well as ables, except for tree volume increment (Tables 3 and 4). trees with extensive expansion in size by the stage of Figure 6 illustrates exemplarily the expression of the the last survey. This tendency is similar on all trial local side effects for ING650, GYO651 and SAN653. plots although the time span of observation differs The darker the colour the more the variable is enhanced. between four (SAN653) and seven years (GYO651). Isolines separate areas with different conditions. The differentiation of tree sizes also varies between trial locations. Here, ING650 shows the least range Tree allometry variation whereas GYO651 and SAN653 are much broader. The single-tree wise calculated allometric exponents Highest increment values (mean and maximum) con- (eq. 1) show a broad variation across the trials (Table 5, cerning diameter, height, volume and crown dimen- Fig. 7). For the exponents α , α , α , and α the h,v d,v cl,v h,d sions are observed in SAN653. mode of their empirical distribution is remarkably near The competition indices show a clear decreasing to the value predicted by the metabolic scaling theory. trend from the inner to the outer circle, as expected In case of α ,and α , the allometric exponent exceeds csa,v cv,v (Fig. 4). SDI and DCI behave similar. However, a sub- the theoretical value by far. There is a negative, almost lin- stantial variation is obvious within circles indicating ear correlation between the allometric exponents of tree differing growing conditions for plants belonging to height and tree diameter (Table 6). This means, volume the same circle. In the following presentation of re- increment is achieved by either height or diameter growth sults, we use DCI as competition index, but regressions resulting in different tree shapes. A higher resource allo- using SDI as independent variable show principally cation into tree height also accelerates the development same results. of the crown length (r = 0.4333). Vice versa, fostering Uhl et al. Forest Ecosystems (2015) 2:17 Page 10 of 19 Table 2 Tree characteristics of the trials ING650, GYO651 and SAN653 from the last survey Trial Year of Tree age d h v cl csa cv i i i i i i d h v cl csa cv last survey 3 2 3 −1 −1 3 −1 −1 2 −1 3 −1 (yr) (mm) (cm) (dm ) (cm) (m)(m ) (mm · yr ) (cm · yr ) (dm ·yr ) (cm · yr )(m ·yr )(m ·yr ) ING650 2012 6 min 4.0 32.0 0.002 0 0 0 1.0 8.0 0 0 0 0 mean 17.8 98.4 0.99 58.9 0.11 0.08 4.4 24.6 0.025 14.73 0.027 0.02 max 38.0 178.0 0.49 143.0 0.66 0.68 9.5 44.5 0.123 35.8 0.165 0.17 GYO651 2013 7 min 5.0 40.0 0.01 17.0 0.0004 0.002 1.3 10.0 0.02 4.3 0.00009 0.0005 mean 26.7 168.9 0.39 125.6 0.31 0.48 6.7 42.2 0.09 31.4 0.079 0.12 max 61.0 360.0 2.80 329.0 3.47 11.41 15.3 90.0 0.70 82.3 0.867 2.85 SAN653 2012 4 min 1.0 2.0 0 1.0 0.0005 0.00004 0.5 1.0 0.000 0.50 0.0003 0.00002 mean 24.3 81.1 0.15 78.9 0.37 0.32 12.2 40.5 0.08 39.5 0.185 0.16 max 58.00 210.0 1.85 205.0 2.72 3.02 29.0 105.0 0.93 102.5 1.360 1.51 d diameter at root collar, h tree height, v tree volume, cl crown length, csa crown cross section area, cv crown volume, i annual increment since planting, 0 indicates values close to zero Uhl et al. Forest Ecosystems (2015) 2:17 Page 11 of 19 Fig. 4 Boxplot showing the variation of cis within the circles of the Nelder wheels for ING650 at last survey. DCI = Hegyi index, SDI = stand density index diameter increment reduces investments into crown summarized by the non-parametric smoother g (E, N) length (r = −04335). At the same time, the allometric showed a significant impact onto their expression (Table 7). slope of crown cross section area is negatively correlated with α but positively correlated with α .Bythis, h,v d,v Space use efficiency crown shape seem to tend to either short but broad Only in case of the efficiencies, concerning tree diam- crowns or long but narrow crowns as already described eter, crown length and crown projection area the inter- above. cept varied between the trials significantly. In all other Again, the linear regression parameters β and β in 1 2 cases, the trial effect was therefore not included into the eq. 5 had no significant effect on the model results and general additive regression model (Table 8). The course were thus removed from the regression. The values for of the smoothers for tree volume (f − f ) and competi- the respective intercept (Table 7) reflect the mean values 1 3 tion (f − f ) in eq. 5 were significant in case of all vari- from Table 5. However, the allometric exponents are 4 6 ables (Table 8), but concerning ef f at ING650 the more or less modified by tree size and by stand density. cv significance is only reached at the p = 0.1 level. The In SAN653 only α is affected by competition. Higher h,d spatial effect depicted by the term g (E, N) appeared to levels of competition push trees to invest more into be significant for the variables ef f ; ef f and ef f . height when growing (Fig. 8) and to reduce the relative i i i h cl cv diameter feed (only significant for ING650) (Additional At the current young ontological stage, the oaks on file 4: Figure S4) and in consequence to a higher α the Nelder-trials showed clearly higher growth efficiency h,d (Additional file 5: Figure S5). Also α rose with accel- at higher stand densities. Available resources are turned cl,v erating competition showing a linear trend (Additional into higher rates of productivity. Figure 9 (lower panels) file 6: Figure S6). α is negatively affected by density depicts the trend for the effect of competition on height csa,v (Additional file 7: Figure S7). Both relationships link to growth efficiency. Increasing density leads to an explicit a reduced α (Additional file 8: Figure S8). Also in case uprating in efficiency. The curves showed an optimum cv,v of the tested allometric exponents by eq. 5, local effects at stand densities that are represented within the inner Table 3 Regression parameters and level of significance for the smoothers for selected tree and crown dimensions according to eq. 4 h d v cl csa cv Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p β 115.0 1.01 *** 22.82 0.18 *** 0.0002 0.00006 *** 87.29 1.01 *** 0.26 0.007 *** −0.17 0.31 β (651) – – –– – – – – –– – – – – – 1.13 0.53 * β (653) – – –– – – – – –– – – – – – 0.26 0.50 f (DCI, 650) *** *** *** f (DCI, 651) *** *** *** *** *** *** f (DCI, 653) *** *** *** *** g(E, N) *** *** *** *** *** ** h tree height, d diameter at root collar, v tree volume, cl crown length, csa crown cross section area, cv crown volume, DCI Hegyi-index, N northing, E easting, p-value < 0.1, * p-value < 0.05, ** p-value < 0.01, *** p-value < 0.001 Uhl et al. Forest Ecosystems (2015) 2:17 Page 12 of 19 Fig. 5 Graphical illustration of the non-linear smoothers f − f from eq. 4 for tree height as the dependent variable. Straight line: estimate, dashed 1 3 lines: 95 % confidence area; DCI = Hegyi-index circles of the trials. On ING650 and SAN653 the max- Discussion imum effect value was reached at lesser competition Turning Nelder-trials into single tree experiments level than in GYO651 (cf. the value of the smoother on The classical evaluation routines for estimating growing y-axis). Space use efficiency was also accelerated with in- space dependent growth and growth efficiency described creasing tree volume (Fig. 9, upper panels). The progres- by Nelder (1962) concern mostly annual or at maximum sion of the curve is taking an asymptotic course bearing biennial plants. Thus, natural mortality hardly occurs comparisons with diminishing marginal utility. The scales during the trials’ lifetime and can be neglected. Having of the y-axis reveal that tree size had a smaller effect level long living tree species under focus within Nelder wheels compared to competition. at least in parts with higher density competition will The described characteristics concerning the effect cause dropouts of plants after a few years. Missing trees trend of density and tree size were valid for all analysed will change the current situation of competition of growth efficiencies. Additional file 9: Figure S9, Additional neighbouring trees and their provision with ground re- file 10: Figure S10, Additional file 11: Figure S11, lated resources and light. Using the growing space of a Additional file 12: Figure S12, Additional file 13: Figure plant as it is defined by its position on a certain circle S13 illustrate the curve progression for the growth effi- might bias the real resource supply, as missing trees do ciencies concerning diameter, tree volume and crown not affect it. Using competition indices instead of the ap- dimensions. proximated growing space better reflects the growing situation in terms of resource supply. In particular, changes of the respective growing situation in time can Table 4 Regression parameters and level of significance for the smoothers for selected increment parameters according to eq. 5 be retraced. By this, the stand related analyses shift into a single tree focussed approach. i i v cv An advantage of Nelder trials is that they embrace by Est. Std. E. p Est. Std. E. P relative small space requirements a broad range of stand β −0.00001 0.000002 *** −0.002 0.001 densities, which can hardly be realised by classical yield β (651) 0.00002 0.000003 *** – experiments. Here, extreme high and low stand densities β (653) 0.00001 0.000003 *** – were often left out. However, these are most important β (v) −0.87 0.006 *** 533.86 30.36 *** in understanding the mechanisms that link resource f (DCI, 650) *** supply and growth behaviour of trees. We presented re- sults using the Hegyi-index as indicator for competition f (DCI, 651) * * likewise used by Vanclay et al. (2013). But we also tested f (DCI, 653) *** *** the local SDI, which is more useful when upscaling stand g(E, N) *** densities to hectare level. .p-value < 0.1, * p-value < 0.05, ** p-value < 0.01, *** p-value < 0.001,v was Our approach, using GAM regression models for used as trial overarching linear effect. Non-linearity and trial separated usage showed no significance single-tree focussed Nelder-wheel evaluations proved to Uhl et al. Forest Ecosystems (2015) 2:17 Page 13 of 19 Fig. 6 Two-dimensional smoother for the spatial effect as included in our GAMs, exemplarily taken from the fitted model after eq. 4 for tree height. The darker the color, the greater is the smoother’s value. E and N are easting and northing values in m. The original nine-digit values were transformed for a more convenient presentation. Thus, the plots do not show absolute geographic positions, but the relative positions of the two Nelder-wheels in each trial be robust and revealing. Especially, including unmeasured productivity equals the stand productivity for the given and unmeasurable position effects by a two-dimensional stand density. The productivity is of interest for plant ecol- nonparametric smoother turned out to be straightforward ogy as it reflects how efficient the plant uses the available and easy-to-apply way to avoid undesired autocorrelation resource in terms of growing area for growing (Webster effects in the statistics; it does not require assumptions and Lorimer 2003; Pretzsch and Schütze 2005) and it is of like isotropy and homogeneity of spatial autocorrelation. interest for production economy as it reveals the relation- Furthermore, this approach may also be helpful for identi- ship between stand density and yield (Sterba 1999). fying microsite variations at the study sites. Of special interest is which stand density enables max- imum productivity per unit area. A question that has in- Empirical evidence for testing and further development trigued forestry science from its beginning is whether of ecological theory stand volume production is at a maximum in untreated Relationship between stand density and growth self-thinning stands, or whether silvicultural thinning The Nelder design is suitable for revelation of the can raise it. Until present mainly the two different species-specific relationship between stand density and concepts are discussed: Curtis et al. (1997) and Zeide growth. The ratio between the individual plant growth (2001, 2002) assumed that the density-growth curve is (e.g. periodic mean growth of basal area or volume) asymptotic as maximum growth occurs in untreated and the respective growing area results in tree product- (maximum stocked) stands. Among others, Assmann ivity in terms of growth per year and unit area. Suppose, (1970) and Pretzsch (2005) provided evidence that the the trees represent the mean tree development this density-growth curve can be a unimodal or optimum curve where maximum growth is reached at below- maximum densities. Table 5 Across-trial distribution properties of the single-tree Most of the contradictory findings result from allometric exponents middle-aged stands, while respective studies about the α α α α α α h,v d,v cl,v csa,v cv,v h,d density-growth relationships during the early and espe- N 1299 1298 1284 1248 1260 1159 cially during the initial stand phase are missing. How- Min −0.46 0.08 −1.36 −1.51 −1.40 0.01 ever, these are relevant for understanding the later stand dynamics. In addition, they are relevant for forest Mean 0.22 0.39 0.41 1.43 1.85 0.70 practitioner for choosing the most appropriate and Mode 0.24 0.38 0.26 1.22 1.59 0.50 productive initial stand density. Nelder trials pave the Max 0.87 0.73 2.11 4.44 5.34 0.98 way to close this knowledge gap. Results from the first Sd 0.16 0.08 0.42 0.77 0.87 0.46 measurements of the presented Nelder trials support the MST 1/4 3/8 1/4 1/2 3/4 2/3 concept that density-growth relates with an optimum MST metabolic scaling theory curve. Uhl et al. Forest Ecosystems (2015) 2:17 Page 14 of 19 Fig. 7 Selected empirical density curves for the allometric exponents α , α , α and α . The numbers inside the diagrams quantify the h,v d,v cl,v cv,v distributions’ mode Interaction between competition and facilitation in the As the extended Nelder design observes tree growth context of the stress-gradient hypothesis reactions along both a gradient of competition (in terms The presented extended Nelder design may reveal of tree stand area) and a gradient of environmental con- whether facilitation between neighboring trees occur ditions (from mild atlantic climate to temperate, and to rather on poor sites while competition is more relevant rather harsh continental climate) it may contribute to on rich sites, as predicted by the stress-gradient hy- understanding how the balance between facilitation and pothesis, SGH (Callaway and Walker 1997). So far, em- competition is modified by the prevailing site conditions. pirical evidence of this behavior is mostly based on During the first years of observation on our Nelder herbaceous plants growing rather solitarily on sites trials, we observed a different behavior of tree growth providing conditions that are not suitable for trees to dynamics between the trial locations. In ING650 and establish or persist. Extension to forest stands and GYO651, facilitation seems to foster at least height higher densities may contribute to ecological theory growth. Up to now, there is no significant differentiation but also provide valuable knowledge for forest practice. in height by density in SAN653, having best growing The interplay between facilitation and competition on conditions form all three mentioned trials. However, the different sites may affect the choice of the planting time of observation could be here too short to connect density, thinning regime, and stand density regulation this fact with site conditions. Subsequent observation of in view of climate change. various aspects of tree growth (e.g. tree height, volume, Both, living in association or solitary bears pros and biomass, leaf structure) in dependence on both site con- cons in terms of growth. An individual tree may be facil- ditions and stand density may advance the SGH towards itated, e.g. physically by neighbours as they protect applicability to forest ecosystems (Forrester 2013). Thus, against stormbreakage (von Lüpke and Spellmann 1997; the presented Nelder may counteract the present deficit 1999), sun scorch of bark (Assmann 1970), or snow slid- of empirical evidence. ing (Kuoch 1972; Mayer and Ott 1991, pp 194–197). However, neighbourhood is ambivalent as it also means Variability and covariation between allometric relationships competition when there are not sufficient resources for as prerequisite for the individual plants plasticity and all (Connell 1990). The interplay of facilitation and com- competitiveness petition and it’s net effect determine the growth and co- The metabolic scaling theory (MST) provides a promis- existence of trees. ing synthesis for the functioning and structure of plants from organ to ecosystem level (West et al. 1997; Enquist Table 6 Correlation matrix of selected allometric exponents et al. 1998). The mainstay of MST, the scaling between leaf mass, ml, and total plant biomass, mt, is widely held α α α α α h,v d,v cl,v csa,v cv,v 3/4 to follow the 3/4 power scaling rule ml ∝ mt (Niklas α 1 −0.99*** 0.43*** −0.20*** 0.02 h,v 2004; Price et al. 2010). However, allometric scaling α 1 −0.43*** 0.20*** −0.02 d,v appears to be dependent on species (Purves et al. 2007; α 1 −0.05 0.43*** cl,v Pretzsch and Dieler 2012), the species combination in α 1 0.88*** csa,v mixed stands (Dieler and Pretzsch 2013), as well as from α 1 cv,v the trees’ local competitive constellation (Mäkelä and *p < 0.05, **p < 0.01, ***p < 0.001 Valentine 2006; Duursma et al. 2010). Uhl et al. Forest Ecosystems (2015) 2:17 Page 15 of 19 Table 7 Regression parameters and level of significance for the smoothers for allometric exponents resulting from eq. 5 α α α α α α h,v d,v cl,v csa,v cv,v h,d Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p β 0.22 0.005 *** 0.39 0.003 *** 0.39 0.01 *** 1.43 0.03 *** 1.84 0.03 *** 0.66 0.02 *** β (651) –– – - – – –– –– –– β (653) –– – _ –– . –– –– –– f (v, 650) * ** * f (v, 651) *** *** *** f (v, 653) * * ** . * f (DCI, 650) *** *** . *** * *** f (DCI, 651) *** * *** *** *** f (DCI, 653) *** g(E, N) *** *** *** *** *** ** .p-value < 0.1, * p-value < 0.05, ** p-value < 0.01, *** p-value < 0.001 Fig. 8 Graphical illustration of the non-linear smoothers f − f from eq. 5 for α as the dependent variable. Straight line: estimate, dashed lines: 1 6 h,v 95 % confidence area; v = volume, DCI = Hegyi-index Uhl et al. Forest Ecosystems (2015) 2:17 Page 16 of 19 Table 8 Regression parameters and level of significance for the smoothers for growth efficiencies according to eq. 5 ef f ef f ef f ef f ef f ef f i i iv i icsa icv h d cl Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p Est. Std. E. p β 76.26 2.20 *** 10.20 1.36 *** 0.0001 0.000007 *** 48.26 7.15 *** 0.08 0.03 * 0.10 0.008 *** β (651) –– −2.39 2.10 –– −2.29 11.16 −0.02 0.05 –– β (653) –– 14.40 2.03 *** –– 35.41 10.77 ** 0.12 0.05 * –– f (vol, 650) *** *** * *** * . f (vol, 651) *** *** *** ** *** *** f (vol, 653) * *** * *** *** *** f (DCI, 650) *** *** *** *** *** *** f (DCI, 651) *** *** *** *** *** *** f (DCI, 653) *** *** *** *** *** *** g(E, N) *** . * *** .p-value < 0.1, * p-value < 0.05, ** p-value < 0.01, *** p-value < 0.001 Fig. 9 Graphical illustration of the non-linear smoothers f − f from eq. 5 for ef f as the dependent variable. Straight line: estimate, dashed lines: 1 6 h 95 % confidence area; v = volume, DCI = Hegyi-index Uhl et al. Forest Ecosystems (2015) 2:17 Page 17 of 19 Here, we consider the MST as a first-order relationship Successive surveys will explore the temporal variability for the form development of plants and use it as a refer- of the crown allometry. Additional biomass analysis of ence and starting point. However, we further explored it above and below ground biomass on reserve partial as suggested by Price et al. (2010) based on the Nelder wheels in close vicinity to the main plots will extend the plots in oak. allometric analyses to the root-shoot allometry and The trees in the centre of the Nelder wheels represent deliver total shoot mass, plant mass, and specific wood dense stand and self-thinning conditions, which are density, while present evaluations are based on tree mostly used for allometric analysis. Those trees rather volume as substitute variable. follow in most of their allometry attributes the allometry predicted by MST. With increasing distance from the Conclusions centre and approach to the periphery competition and The presented methods for analysing Nelder trials pave facilitation squeeze or stretch the crown and cause a the way to make the experimental design attractive for broad intra-specific variation in scaling of structure. forest science. The possibility to represent a wide spread Because of the wide range of competitive constellations of stand densities and respectively growing condition on the Nelder plots the structural scaling of the trees within one trial with relative little demand for space showed also a wide intra-specific variation (Fig. 7). improves long-term studies in forest ecology. Single tree Table 6 revealed positive as well as negative correlation based analyses are more and more essential to under- between different scaling exponents of structure, e.g. be- stand the multiform interactions and their possible vari- tween α , α , and α . The assumed stable metabolic h,v csa,v cv,v ation with growing conditions between trees in complex scaling and revealed variable scaling of crown structure ecosystems. Thus, Nelder trials help to strengthen the are not necessarily a contradiction. It is rather this vari- development of ecological theory and provide simultan- ability of the crown, which provides a plastic holding eously relevant results for forest management. The structure for the leaf organs and enables the plant to investigation of Nelder trial is not restricted to issues keep close to the 3/4 power leaf mass-plant biomass concerning growth dynamics. Aspects of e.g. above and trajectory. below ground biodiversity and CO balancing of ecosys- We demonstrate this thought by the scaling rela- tems can be linked to stand dynamics at different stand tions between tree volume, v, and the crown charac- densities. teristics crown length, cl, and crown cross section α α ðÞ cl;v ðÞ csa;v area, csa,( cl∝v ; csa∝v ). As crown volume is Additional files the product of crown length and crown cross section α þα ðÞ cl;v csa;v Additional file 1: Figure S1. Graphical illustration of the non-linear area (cv = cl *csa), this results in cv∝v and smoothers f − f from eq. 4 for tree diameter (upper panel) and tree shows that α = α + α . 1 3 cv,v cl,v csa,v volume (lower panel) as the dependent variable. Straight line: estimate, MST assumes common scaling relationships for dashed lines: 95 % confidence area; DCI = Hegyi-index. allometric ideal plants, e. g. α =1/4, α =1/2, and cl,v csa,v Additional file 2: Figure S2. Graphical illustration of the non-linear as basic assumption according to West et al. (2009) smoothers f − f from eq. 4 for crown length (upper panel), crown cross 1 3 section area (middle panel), and crown volume (lower panel) as the α = 3/4. Insertion of the general scaling exponents cv,v dependent variable. Straight line: estimate, dashed lines: 95 % confidence for an allometric ideal plant into α = α + α cv,v cl,v csa,v area; DCI = Hegyi-index. yields α = (1/4 + 1/2) = 3/4. However, α =3/4 cv,v cv,v Additional file 3: Figure S3. Graphical illustration of the non-linear could also result from diverging components, e. g. smoothers f − f from eq. 4 for tree volume increment (upper panel), 1 3 and crown volume increment (lower panel) as the dependent variable. α = (1/8 + 5/8) = 3/4. In the latter case, there is a cv,v Straight line: estimate, dashed lines: 95 % confidence area; DCI = Hegyi-index. trade-off between both scaling exponents. Crown Additional file 4: Figure S4. Graphical illustration of the non-linear width might increase on the expense of crown length, smoothers f − f from eq. 5 for α as the dependent variable. Straight 1 6 d,v but the combination of both keeps the scaling of the line: estimate, dashed lines: 95 % confidence area; v = volume, DCI = Hegyi-index. crown volume rather stable. Additional file 5: Figure S5. Graphical illustration of the non-linear According to that, morphological variability is even a re- smoothers f − f from eq. 5 for α as the dependent variable. Straight 1 6 h,d quirement for holding trees on a rather stable leaf mass- line: estimate, dashed lines: 95 % confidence area; v = volume, plant mass or root mass-plant mass trajectory even under DCI = Hegyi-index. variable or changing environmental conditions. We found Additional file 6: Figure S6. Graphical illustration of the non-linear smoothers f − f from eq. 5 for α as the dependent variable. Straight 1 6 cl,v an intra-specific correlation between the structural scaling line: estimate, dashed lines: 95 % confidence area; v = volume, exponents which does not keep α constant at 3/4 but cv,v DCI = Hegyi-index. stabilizes it in a quite narrow corridor around 3/4. In view Additional file 7: Figure S7. Graphical illustration of the non-linear of this variability, scaling of the allometric ideal plant may smoothers f − f from eq. 5 for α as the dependent variable. Straight 1 6 csa,v line: estimate, dashed lines: 95 % confidence area; v = volume, be of benefit when using it as reference but is somewhat DCI = Hegyi-index. of a phantom when trying to find it. Uhl et al. Forest Ecosystems (2015) 2:17 Page 18 of 19 Biging GS, Dobbertin M (1992) A comparison of distance-dependent competition Additional file 8: Figure S8. Graphical illustration of the non-linear measures for height and basal area growth of individual conifer trees. For Sci smoothers f − f from eq. 5 for α as the dependent variable. Straight 1 6 cv,v 38(3):695–720 line: estimate, dashed lines: 95 % confidence area; v = volume, Biging GS, Dobbertin M (1995) Evaluation of competition indices in individual DCI = Hegyi-index. tree growth models. For Sci 41(2):360–377 Additional file 9: Figure S9. Graphical illustration of the non-linear Callaway RM, Walker LR (1997) Competition and facilitation: a synthetic approach smoothers f − f from eq. 5 for ef f as the dependent variable. Straight 1 6 i to interactions in plant communities. Ecology 78(7):1958–1965 line: estimate, dashed lines: 95 % confidence area; v = volume, Connell JH (1990) Apparent versus “real” competition in plants. In: Grace JB, DCI = Hegyi-index. Tilman D (eds) Perspectives on plant competition. Academic press, INC., Additional file 10: Figure S10. Graphical illustration of the non-linear Harcourt Brace Jovanovich, Publishers, San Diego smoothers f − f from eq. 5 for ef f as the dependent variable. Straight R Core Team (2014) R: A language and environment for statistical computing. R 1 6 i line: estimate, dashed lines: 95 % confidence area; v = volume, Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/. DCI = Hegyi-index. Accessed 15 Oct 2014 Curtis RO, Marshall DD, Bell JF (1997) LOGS. A pioneering example of silvicultural Additional file 11: Figure S11. Graphical illustration of the non-linear research in coast Douglas-fir. J For 95(7):19–25 smoothers f − f from eq. 5 for ef f as the dependent variable. Straight 1 6 i cl del Rio M, Schütze G, Pretzsch H (2014) Temporal variation of competition and line: estimate, dashed lines: 95 % confidence area; v = volume, facilitation in mixed species forests in Central Europe. Plant Biol 16(1):166–176 DCI = Hegyi-index. Dieler J, Pretzsch H (2013) Morphological plasticity of European beech (Fagus Additional file 12: Figure S12. Graphical illustration of the non-linear sylvatica L.) in pure and mixed-species stands. For Ecol Manage 295:97–108 smoothers f − f from eq. 5 for ef f as the dependent variable. Straight 1 6 i csa Dippel M (1982) Auswertung eines Nelder-Pflanzverbandsversuches mit Kiefer im line: estimate, dashed lines: 95 % confidence area; v = volume, Forstamt Walsrode. AFJZ 153:137–154 DCI = Hegyi-index. Duursma RA, Mäkelä A, Reid DEB, Jokela EJ, Porté AJ, Roberts SD (2010) Self-shading Additional file 13: Figure S13. Graphical illustration of the non-linear affects allometric scaling in trees. Funct Ecol 24:723–730 smoothers f − f from eq. 5 for ef f as the dependent variable. Straight 1 6 i cv Enquist BJ, Brown JH, West GB (1998) Allometric scaling of plant energetics and line: estimate, dashed lines: 95 % confidence area; v = volume, population density. Nature 395:163–165 DCI = Hegyi-index. Enquist BJ, West GB, Brown JH (2009) Extensions and evaluations of a general quantitative theory of forest structure and dynamics. Proc Natl Acad Sci U S A 106:7046–7051 Competing interests Fahrmeir L, Kneib T, Lang S (2009) Regression. Modelle, Methoden und The authors declare that they have no competing interests. Anwendungen. Springer, Heidelberg Forrester DI (2013) The spatial and temporal dynamics of species interactions in Authors’ contributions mixed-species forests: From pattern to process. For Ecol Manage EU developed the trial design, analysed and interpreted the data, and wrote 312:282–292 the manuscript. PB designed the statistical methods and wrote the Grimm V (1999) Ten years of individual-based modeling in ecology: what have manuscript. MU collected data, cross checked the data and supported we learned and what could we learn in the future. Ecol Model 115:129–148 analyses. MH developed analysis routines, and proof read the manuscript. TH Hegyi F (1974) A simulation model for managing Jack-pine stands. In: FRIES J (ed) implemented trials in Hungary, collected data and proof read the Growth models for tree and stand simulation. Royal College of Forest, manuscript. FL and JG supported the strategy of analyses and wrote the Stockholm, Sweden, pp 74–90 manuscript. LS implemented the Nelder trials in situ, maintains the plots and Holmgren M, Scheffer M, Huston MA (1997) The interplay of facilitation and collected data. GT supported the strategy of analyses and wrote the competition in plant communities. Ecology 78(7):1966–1975 manuscript. MV implemented the trials in Italy, collected data and proof read Kuehne C, Kublin E, Pyttel P, Bauhus J (2013) Growth and form of Quercus robur the manuscript. HP initiated the trial series and the manuscript, interpreted and Fraxinus excelsior respond distinctly different to initial growing space: the results and wrote the manuscript. All authors read and approved the results from 24-year-old Nelder experiments. J For Res 24(1):1–14 final manuscript. Kuoch R (1972) Zur Struktur und Behandlung von subalpinen Fichtenwäldern. Schweiz Z Forstwes 123:77–89 Acknowledgements Mäkelä A, Valentine H (2006) Crown ratio influences allometric scaling in trees. We thank AUDI AG, Automobili Lamborghini S.P.A., AUDI HUNGARIA MOTOR Ecology 87:2967–2972 Kft. and AUDI BBRUSSELS for supporting the establishment of the Nelder trial Mayer H, Ott E (1991) Gebirgswaldbau Schutzwaldpflege. Gustav Fischer Verlag, series. We also thank AUDI Stiftung für Umwelt for funding the project Stuttgart, New York “Biodiversity, productivity, and C-sequestration of oak stands” (No. 5102150). Munro DD (1974) Forest growth models – a prognosis. In: Fries J (ed) Growth We further wish to thank the Bavarian State Ministry for Nutrition, Agriculture and models for tree and stand simulation. Royal College of Forestry, Stockholm, Forestry for permanent support of the project W 07 “Long-term experimental Sweden, pp 7–21, Research Notes No. 30 plots for forest growth and yield research” (7831-23953-2014). The included trials Nelder JA (1962) New kinds of systematic designs for spacing experiments. are located on areas under responsibility of different forest administrations. We are Biometrics 18(3):283–307 deeply grateful to the respective sponsoring forest administrations. Thanks are also Niklas KJ (2004) Plant allometry: is there a grand unifying theory? Biol Rev due to Ulrich Kern for the graphical artwork and two anonymous reviewers for 79:871–889 their thoroughly criticism. Pretzsch H (2005) Stand density and growth of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.). Evidence from long-term Author details experimental plots. Eur J For Res 124:193–205 School of Life Sciences Weihenstephan, Technische Universitaet Muenchen, Pretzsch H (2006) Von der Standfächeneffizienz der Bäume zur Dichte-Zuwachs- Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany. University of West Beziehung des Bestandes. Beitrag zur Integration von Baum- und Hungary, Faculty of Forestry, Ady E. u. 5, Sopron 9400, Hungary. Faculty of Bestandesebene, Allgemeine Forst- und Jagdzeitung 177(10):188–199 Science and Technology, Freie Universität Bozen, Universitaetsplatz 5, Pretzsch H (2009) Forest dynamics, growth and yield, from measurement to Bolzano 39100, Italy. model. Springer, Berlin, Heidelberg Pretzsch H (2010) Re-evaluation of allometry: state-of-the-art and perspective Received: 27 December 2014 Accepted: 13 May 2015 regarding individuals and stands of woody plants. In: Lüttge U, Beyschlag W, Büdel B, Francis D (eds) Progress in Botany, vol 71, Springer. 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For Sci 48:743–754 Zuur A, Leno EN, Walker N, Saveliev AA, Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, Heidelberg Submit your manuscript to a journal and beneﬁ t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the ﬁ eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com
"Forest Ecosystems" – Springer Journals
Published: Dec 1, 2015
Keywords: Ecology; Ecosystems; Forestry
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