Research Article


Analysis of Individual Tree Competition Effect on Diameter Growth of Silver Birch in Estonia


Kobra Maleki

Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Forest Management, Kreutzwaldi 5, Tartu 51014, Estonia

Andres Kiviste

Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Forest Management, Kreutzwaldi 5, Tartu 51014, Estonia

Henn Korjus

Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Forest Management, Kreutzwaldi 5, Tartu 51014, Estonia



Aim of study: The present study evaluates a set of competition indices including spatially explicit indices combined with different competitor selection approaches and non-spatially explicit competition indices. The aim was to quantify and describe the neighbouring effects on the tree diameter growth of silver birch trees.

Area of study: Region throughout Estonia.

Material and methods: Data from the Estonian Network of Forest Research Plots was used. After quantifying the selected indices, the best non-spatial indices and spatial indices (combined with neighbour selection methods) were separately devised into a growth model as a predictor variable to assess the ability of the diameter growth model before and after adding competition measures. To test the species-specific effect on the competition level, the superior indices were recalculated using Ellenberg’s light indicators and incorporated into the diameter growth model.

Main results: Statistical analyses showed that the diameter growth is a function of neighbourhood interactions and spatial indices were better growth predictors than non-spatial indices. In addition, the best selections of competitive neighbours were acquired based on the influence zone and the competition elimination angle concepts, and using Ellenberg’s light values had no significant improvement in quantifying the competition effects.

Research highlights: Although the best ranking spatial competition measures were superior to the best non-spatial indices, the differences were negligible.

Keywords: Competition indices; zone of influence; stem diameter increment; Betula pendula Roth.

Citation: Maleki, K., Kiviste, A., Korjus, H. (2015). Analysis of Individual Tree Competition Effect on Diameter Growth of Silver Birch in Estonia. Forest Systems, Volume 24, Issue 2, e023, 13 pages.

Received: 12 Feb 14. Accepted: 08 Apr 2015

Copyright © 2015 INIA. This is an open access article distributed under the Creative Commons Attribution License (CC by 3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Funding: This study was supported by the Institutional Research Funding IUT21-04 (B21004MIMK) and Estonian Science Foundation Grant ETF8890.

Competing interests: The authors have declared that no competing interests exist.

Correspondence should be addressed to Kobra Maleki:





Materials and methods

Methods of competitor identification (SM)






Competition among individual trees is a fundamental ecological process that plays a major role in population dynamics, survival, growth and species replacement (Peet & Christensen, 1987). By definition, competition is ‘‘an interaction between the individuals, leading to a reduction in the survival, growth and reproduction of the competing individuals” (Begon et al., 1996). Several case studies have been conducted in ecology and forestry to develop, improve or modify different competition indices (CIs). Such indices quantify the competition level for an individual tree and are classified into two major groups of non-spatially explicit indices (e.g. Biging & Dobbertin (1995) and Schröder & Gadow (1999)) and spatially explicit indices (e.g. Hegyi (1974) and Alemdag (1978)). Non-spatial indices are functions of stand level variables, or of the initial dimensions of the trees, and therefore do not require the trees coordinates. Whenever spatial indices are used to measure the influence of local neighbours on a central tree (the subject tree), the dimensions and the relative location of neighbour trees are required for the computation (Tomé & Burkhart, 1989; Corral Rivas et al., 2005).

For several species and forest conditions, the effectiveness of different CIs on tree diameter or basal area growth has been examined (Munro, 1974; Martin & Ek, 1984; Pukkala & Kolström, 1987; Holmes & Reed, 1991; Contreras et al., 2011). Since several aspects of stand density and neighbour sizes influence the tree growth, non-spatial CIs with simple structures are parsimonious to quantify the competitive status of trees in each stand. On the other hand, as ecology is spatial (Berger & Hildenbrandt, 2000), therefore by increasing the interval distance, the negative interaction of neighbours will decrease and spatial CIs take the explicit description of tree spacing into account. Additionally the identity of neighbouring species is an important factor in the characterization of their competitive effect (Bella, 1971; Zhao et al., 2006). Competition can occur among conspecific individuals, plants of same species, and hetero-specific individuals, plants of different species, termed intraspecific and interspecific competition, respectively. The competition behaviour of different species can be differentiated by using Ellenberg et al.’s system (1991). It is the most widely used indicator species system, which compares the response of different species to edaphic and climatic parameters, such as light, temperature, moisture and nitrogen at a 9-point scale for each.

To investigate the effect of competition on the diameter growth of trees, we focused our study on silver birch (Betula pendula Roth). Silver birch occurs naturallyin northern temperate and boreal forests and it is an essential ecological and commercial broadleaved tree species (Hynynen et al., 2010). As a pioneer tree species (Fischer et al., 2002), birch is light demanding, and if it grows as a dominant tree with low competitive effects of neighbours, in a stand with relatively wide spacing, birch maintains its vitality and vigorous growth (Hynynen et al., 2010). In Estonia, birch is the second most abundant tree species in terms of forest cover (31.2%) and the coverage is expanding (Yearbook of Forest, 2013). A few attempts have been made to study birch growth related to the negative interaction of tree competitive status in stands (Jõgiste, 1998; Prévosto et al., 1999; Andreassen & Tomter, 2003; Damgaard & Weiner, 2008; Kaitaniemi & Lintunen, 2010).

The main objective of this study was to investigate the adequacy of different spatial and non-spatial CIs to explain single-tree silver birch diameter growth in Estonia. Further objectives were to find the best competitor selection method for Estonian birch stands and evaluate the differences in competitive ability of different species by employing Ellenberg’s species-specific light indicator values. Specifically, we hypothesized that (i) the CIs contribute to explain diameter increments in silver birch; (ii) spatial indices perform better than non-spatial indices; (iii) selecting the potential competitors based on the concept of the influence zone is superior to variable competition zone radii; and (iv) considering the species-specific competition improves the ability of spatial indices to account for growth variability.

Materials and methodsTop

Study data

The study was carried out in Estonia, which lies on the eastern shores of the Baltic Sea across the Finnish gulf (lat. 57.3°-59.5° N, long. 21.5°-28.1° E). Average temperatures range from 16.3°C to 18.1°C in July and from -3.5°C to -7.6°C in February. Average annual precipitation increases from west to east within a range of 600-700 mm. In this study, data from the Estonian network of forest research plots (ENFRP) was used. ENFRP was established during the period 1995–2004 and covers Estonia entirely (Kiviste & Hordo, 2002). The permanent plots were circular with a radius of 10, 15, 20, 25 or 30 m depending on the stand age and density and as a rule, every plot had at least 100 trees in the overstory. For the current study, we benefit the data from 121 silver birch dominated research plots (where more than 65% of the number of trees were birches) consisting of 16,186 trees with 5-year measurement intervals.

Within each plot the azimuth, the distance from plot centre, the diameter at breast height (d), and the defects of each tree were assessed. For every fifth tree, and for dominant and rare tree species, the tree height and the height to the live crown base were also measured. Since the height records of all trees were required for some calculations, based on the height-diameter model developed by Kiviste et al. (2003), all unmeasured tree heights were estimated.

Species composition of all trees within the studied plots was 67% silver birch, 24% Norway spruce and 9% of several other species (see Table 4). Plots were established in managed and even-aged forests, and if there was a thinning operation in the time period between the plot measurements, they were excluded. Table 1 summarizes main stand variables of study plots and Fig.1 shows the dynamics of average height, basal area, and quadratic mean diameter.

Table 1. Main characterization of the birch dominated permanent plots*

Figure 1. The dynamics of average height (left), basal area (middle), and quadratic mean diameter (right).

Competition indices

The competition for each subject tree was quantified using 18 different CIs, consisting of 7 non-spatial and 11 spatial indices (Table 2). The indices described below were selected from the literature, taking into consideration the available tree variables for this study, and their simplicity to describe the competition situation of a tree, as it is difficult to understand the statistical qualities of an index with the combination of several primary variables (Weiglet & Jolliffe, 2003).

Table 2. The list of competition indices tested to use in the tree diameter growth model*

The first seven indices in Table 2 are non-spatial indices. In a plot, BA-gjCI proposed by Steneker & Jarvis (1963), is the sum of the basal area (g) of the neighbouring trees j for a subject tree i (m2 ha-1); BAL presented by Wykoff et al. (1982) is the sum of the basal area of trees larger than the subject tree (m2 ha-1). Sdr sums up the d of neighbours divided by the subject tree d in the plot (ha-1). The index drg calculates the ratio of the diameter of the subject tree to the quadratic mean diameter of the plot (Hamilton, 1986) and BAr is another form of Sdr that considers g instead d. The index BALr is the ratio of BAL to the cumulative basal area of the plot (Vanclay, 1991) and finally BALMOD (Schröder & Gadow, 1999) modifies BALr by dividing it into the relative spacing index as following:

where S is plot area (m2), N is the number of trees on plot, and HDom is the stand dominant height (m) (mean height of hundred thickest trees per hectare (Assmann, 1970)).

The next three competition indices Sl, SOr and SOdr in Table 2 are so-called influence-zone overlap indices, which assume that a horizontal circle surrounding the subject tree can represent the active competition area, and that competition occurs where neighbouring trees overlap their influence zone with the subject tree’s influence zone. The radius of these circles is thought to be equal to the expected growing space of open-grown trees, and usually is a function of tree size (Corral Rivas et al., 2005).

Finally, the last eight indices in Table 2 are size-ratio spatial CIs. The idea of this type of indices was derived from the hypothesis that competition effect has positive relationship with the size of neighbouring trees and negative relationship with their distance from the subject tree (Tomé & Burkhart, 1989). For spatial indices of Heg (Hegyi, 1974), Almdg (Alemdag, 1978), Sdrl1(Lorimer, 1983), Sdrl2 (Martin & Ek, 1984), and SBAr (Daniels et al., 1986) the diameter at breast height performs as a tree size indicator. SAng1 (Lin, 1974)is the sum of horizontal angles. Since the average elevation angle of the brightest region of the sky over the growth season can be approximated by angle of 45° (Stadt & Lieffers, 2000), the 45° gauge was employed for this index. The index SAng2 sums up the horizontal angles originating from the subject tree centre and spanning the diameter of each competitor (Rouvinen & Kuuluvainen, 1977), and SdrAng calculates the sum of the horizontal angles multiplied by the ratios of the diameter of the competitors and the subject trees (Fig. 2).

Figure 2. Schematic of the horizontal angles originating from the subject tree centre and spanning the diameter (at breast height) of each competitor tree within the competition zone used to calculate indices Sang2 & SdrAng; *dx is the diameter at breast height (cm), lx is the distance between the subject tree and its competitors (m).

Methods of competitor identification (SM)Top

As well as the mathematical formulation, the value of a competition index depends on the method used to define competitors for the subject tree (Bigging & Dobbertin, 1992). Among different proposed methods to choose the potential competitors, we tested four approaches. The first two approaches, approaches 1 and 2, were based on the concept of an influence-zone that assumes an imaginary circle whose centre is constituted by the subject tree (Staebler, 1951) and trees inside this circle are competitors. The last two approaches, approaches 3 and 4, identified competitors based on variable competition zone radii, often weighted by dimensions of the subject tree and its neighbours (Daniels, 1976; Ford & Diggle, 1981):

  1. The radius of influence zone was defined as a fraction of the stand’s average height for each plot; CZR0.4h was set equal to 0.4 average height of plot (Sims et al., 2009).
  2. Based on Lee & Gadow (1997) the influence zone radius was calculated using the following equations:

    where CZRk is dynamic radius, N is the number of trees per hectare, and k is a constant number.
    The function calculates average distance between the neighbours. The values of k equal to two (CZRk2) and three (CZRk3) multiply this distance by two and three, respectively to define CZR. Within the influence zone, trees were considered to be active competitors if dj ≥ 0.3di (where dj is d of competitor and di is the d of subject tree) and they were beyond the crown projection of other competing trees, considering a competition elimination angle of 30˚ (CEA=30˚).
  3. The Bitterlich method (1952) was used to identify the competitors in variable plot radii samplings. BAF1, BAF2 and BAF4tested three basal area factors (BAF) equal to 1, 2 and 4 m2 ha-1, respectively. A tree was considered a competitor if its distance to the subject tree was:
    where lij is the distance between the subject tree i and the neighbouring tree j and diis the diameter of the subject tree. The values of BAF equal to 1, 2 and 4 correspond to the opening angles of β =1.15˚, 1.62˚ and 2.30˚, respectively. Therefore, when the BAF values and boundary angles increase, fewer trees meet the criteria for being considered as competitors (Lorimer, 1983; Tomé & Burkhart, 1989).
  4. Finally, the reserved search-conemethod (Pretzsch, 2009) or angular height method (Richards et al., 2008) applied height angle from the base of the subject tree to identify the competing neighbours. For a search-cone opening angle β,set up at the stem base of the subject tree, competitors are neighbouring trees whose heights are greater than a critical distance, determined as the following:

    where lij is the distance between the subject tree and the competitor tree, and hi is the subject tree height. If the apex of the reversed search-cone is at the crown base height of the subject tree (cbhj) then a neighbouring tree with height hj is a competitor when:

    We tested the opening angle β equal to 100˚, 80˚, and 60˚, respectively where the apex was set up either at the stem base (SCH100, SCH80 and SCH60) or at thecrown base height (SCHCr100, SCHCr80 and SCHCr60).

In all the above-mentioned methods, in order to avoid the interference from the competitive effects of non-measured trees beyond the plot borders, we computed CIs only for interior trees on each plot where the neighbours’ information was available for them. After determining the competitors, we calculated the spatially explicit CIs for each subject tree. Four spatially explicit CIs (Sl, SOr, SOdr, and Sdrl1) were based on the influence zone concept and only the first two approaches of competitor selection (CZR0.4h and CZRk) were applicable to quantify the mentioned indices. Moreover, the allometric crown radius model, (developed by Lang et al., 2007) was used to calculate the crown radius that was required for quantifying indices SOr and SOdr as well as fitting the Eqs. (7) and (8):

where Rcr is the crown radius (m), d and h are the diameter at breast height (cm) and the total height of the tree (m) respectively, and a1 and a2are estimation parameters (Table 3).

Table 3. The values of parameters for the used allometric crown model for main tree species

Statistical and comparative analyses of competition indices

Preliminary analysis was carried out to pre-select adequate CI candidates to include in our growth model. As suggested by Pedersen et al. (2013) we applied the Spearman rank correlation (Spearman’s rho) to characterize the relationship between the 5-year tree diameter increment (id5) and the competition indices. The Spearman correlation is able to consider potential nonlinear trends frequently seen in growth and competition studies, besides it is valid for the data size larger than 10 (Siegel, 1956) which was applicable to our data. The existence of a pairwise relationship between id5 and CIs was proved using the t-test. Based on the Spearman rank correlation results, the four best CIs (two non-spatial and two spatial CIs) were selected for further analyses.

Then, we constructed a linear multiple regression model (Wimberly & Bare, 1996; Jõgiste, 2010) between id5 (cm) and some predictor variables that influence diameter growth. In a preliminary assessment, non-linear extra sum of square method (Bates & Watts, 1988) was applied to evaluate the effect of plots on growth. For this purpose, we considered the simple model of diameter growth as a function of tree diameter. In order to differentiate the study plots, we introduced dummy variables to the defined simple model. Then, we compared the two mentioned models using F-test and a significant effect of plots was detected (F=8.56; P<0.0001). Therefore, predictor variables presenting the initial stand status were also included in the growth models (Eqs. (7) and (8)). Additionally, for each combination of selected variables, the variance inflation factors (VIF) were calculated to certify that our multiple models were not influenced by multicollinearity amongst explanatory variables. We only implemented the combination of variables with VIFs<10 (Soares & Tomé, 2001; Corral Rivas et al., 2005). Eventually, the growth model was fitted by improvising some initial stand variables along with the tree variables.

In order to evaluate the efficiency of the chosen CIs to improve the prediction ability of growth function, the numerical value of each of those indices, two non-spatial CIs and two spatial CIs, was independently added to the previous growth function:

where bk are coefficients to be estimated, id5is the 5-year tree diameter increment (cm), d is the subject tree diameter at breast height (cm) that integrates the past competitive interactions (Soares & Tomé, 1999), cr is the ratio between the crown width and the tree height that depicts the vigour of trees of similar size (Schröder et al., 2002). The relative diameter dr is the ratio between the subject tree diameter and the quadratic mean diameter of the stand that represents the dominance of the subject tree in relation to other trees in the stand, RS is the stand relative spacing,and SI100 is the stand site index. Nilson (2005) model was used to estimate the average height of the stands at reference age 100 years (m) and CI is the competition measure for the subject tree. R statistical software version 3.1.2 (R Development Core Team, 2014) was employed to carry out all the required analyses for this research.

Before proceeding with the subsequent analyses, the existence of any correlation among residuals was explored. For this purpose, the growth model was fit using the lme function from the nlme package in R as following:

For the recent linear mixed effect model, id5 is the dependant variable; b is a vector of fixed effects consisting of the same explanatory variables of Eq. (7); u is a vector of random effects including tree, plot, and growth interval (measurements); e is a vector of random errors; X and Z are design matrices relating the 5-year diameter growth to fixed and effect random effects, respectively. The previous and recent models were compared in terms of AIC (Akaike’s Information Criterion) where ΔAIC = AIC multiple model-AIC mixed model. In addition, to ensure that there was not any remaining within-group correlation, the recent model was checked with an auto-regressive structure (AR1). The mixed effect models, those with and without auto-regressive structures, were compared using ANOVA (analysis of variances).

The relative quality of growth functions, with and without CIs, were estimated using R2 (Adjusted-R2), the root mean square error (RMSE, calculated using the rmse function for the model residuals in R), AIC and Akaike weights (AICw). The probability that model is the best with the lowest expected information loss is illustrated by the smallest value of AIC and the biggest AICw (Wagenmakers & Farrell, 2004). Additionally, the performance and the contribution of each CI to the growth model were assessed with the mean square error reduction (MSER).

where MSE7 and MSE8 are the mean square errors of models 7 and 8, respectively.

Finally, the efficiency of CIs in different stand stages and the contribution of different species in the competition load of a subject tree were evaluated. Stand development stages were defined by the age of the silver birch, as the dominant tree species. First, to differentiate the effect of different neighbouring species on competition, tree diameters were weighted differently. For that purpose, tree diameters were multiplied by their corresponding Ellenberg’s species-specific light transmission coefficients (Ellenberg et al., 1991) from one (plants in deep shade) to nine (plants in full light); then, the selected spatial CIswere recalculated using the new weighted diameters. Table 4 provides the Ellenberg’s light values for more frequent tree species in Estonia. Finally, subject trees were divided into three subdivisions of young (<35 years), middle-aged (35-69 years) and old stands (≥70 years). For each age group, the regression analyses for the selected CIs and tree diameter growth were repeated separately.

Table 4. The Ellenberg’s species-specific light coefficients for more frequent tree species in Estonia


In Table 5 the Spearman’s rank correlation coefficients between the tree diameter growth and non-spatial CIs and also the combination of spatially explicit CIs and the competitor selection methods are presented. Table 5 shows that the competitor selecting approaches significantly affect the growth prediction ability of spatial indices and the competition selection methods of CZRk3, CZR0.4h and SCH60 demonstrated greater values of Spearman’s rho, respectively. Among different spatial indices in these three neighbours selecting methods, SdrAng and Heg were well correlated with diameter increment. However, the values of rho for Heg were slightly lower than SdrAng. None of the alternatives of Bitterlich method (BAF1, BAF2 and BAF4) showed to be an appropriate selection method of competitors. Furthermore, BAL and BALMOD as the best non-spatial CIsdid notperform better than the superior spatial indices SdrAngand Heg.The results presented in Table 5 are based on the analyses of 2,742 subject trees that were presented in different neighbours’ selection methods and 18 different non-spatial and spatial CIs are quantified and available for them.

Table 5. The Spearman’s rank correlation coefficients between the 5-year tree diameter increment and competition indices for a sample of 2,742 subject trees presenting in different neighbours’ selection methods

The comparison of the linear mixed effect models and the linear multiple models detected the improvement in linear mixed effect regressions in terms of AIC, but the ANOVA comparison between the mixed effect models, with and without an auto-regressive structure, did not show significant remaining within-group correlation (P-value>0.05). Subsequently, the growth model was fit into linear mixed effect regression (Eq. (9)) with no auto-regressive structure for further analyses in this study. All explanatory variables used for Eq. (7) were considered as mixed effects and proved significant (P-value<0.05), also VIF indicated no problem with multiclollinearity, all values being less than eight. In order to test the contribution of selected CIs, they were devised into the recent growth model.

Table 6 illustrates the statistical measures of mixed effect models, including R2, RMSE, MSER, AIC, AICw, and also DAIC. The indices comparisons were done for different sample size of subject trees based on each neighbour selection method. Generally, the contributions of CIs were significant but not very large in magnitude, and among the CIs added to the model, SdrAng presented the most significant contribution, no matter which competitor selection method was used. After that, Heg was found to be important in efficiency to improve the growth model. Non-spatial CIs of BAL and BALMOD showed less contributions to the growth model than the spatial indices, except for SCH60 where BAL appeared slightly better than Heg CI.

Table 6. Contribution of the competition indices to tree diameter growth model

The results of analyses for different age groups (Table 7) demonstrated that competition had stronger prediction ability in younger stands, and spatially CIs proved to be better than non-spatial ones. As shown in Tables (6) and (7), the Ellenberg’s light values performed a slight improvement for some models in order to describe the species-specific effect. The profiles of the R2 and AIC did not show considerable variation between the two methods of calculating selected spatial CIs, with and without Ellenberg’s values (Table 6.) However, statistical measures for young stands viewed a slight improvement for including species-specific values in competition quantifications (Table 7).

Table 7. Contribution of the competition indices to tree diameter growth in different age groups


Computing the correlation coefficient of tree growth, and determining the efficiency of CIs when added to a tree growth model, have been widely used (Burkhart & Tomé, 2012). In the current study, adding the CIs to the growth model slightly improved the model, which can be partially due to the inclusion of relative dimensions of the trees in model. Relative dimensions measure the hierarchical position of the subject tree within the stand, and indirectly indicate the competitive status of the trees (Burkhart & Tomé, 2012).

Results from comparing different CIs proposed that spatial CIs of SdrAng and Heg were the best indices suitable to quantify the competition status of birch trees, respectively. Several studies (Castagneri et al., 2008; Contreras et al., 2011) have reported that SdrAng can describe a greater proportion of the investigated variation in growth models. Also, Heg demonstrated superior performance to non-spatial CIs in many studies (Alemdag, 1978; Pukkala & Kolström, 1987; Holmes & Reed, 1991; Mailly et al., 2003). The indices of SdrAng and Heg assign greater weight to the closer and bigger competitor trees (Wimberly & Bare, 1996) and it was following along the Cole & Lorimer (1994) hypothesis that noticeable competitive stress occurs by immediate competitors surrounding the subject tree crown.

The results we obtained for non-spatial CIs showed that BAL and BALMOD improved the predictive ability of Eq. (9), although in a smaller amount than when using the CIs of SdrAng or Heg. Some studies including BAL or BALMOD found an improvement (large or modest) in model performance (e.g. Biging & Dobbertin, 1995; Corral Rivas et al., 2005). However, similar to our study, several other studies suggested that spatial measures provided more precise growth prediction (Boivin et al., 2010; Contreras et al., 2011), and to the contrary, many studies did not report any superiority of spatial indices to non-spatial ones (Soares & Tomé, 1999; Stadt et al., 2007; Roberts & Harrington, 2008). The superiority of size-ratio CIs of SdrAng and Heg that used the d as indicator of size was probably because of the actual correlation between the subject tree’s diameter increment and its d (Holmes & Reed, 1991); however, the strength of competitive stress explained by such correlations might be unclear (Brand & Magnussen, 1988; Larocque, 2002).

While non-spatial CIs are simple functions of the stand or a tree’s dimensions, the selection of the neighbours that affect the growth of a subject tree is of crucial importance when calculating spatial indices. Concerning the competitor selection methods, the best results were acquired with those based on the influence zone and competition elimination angle concepts. Several studies showed that the competition status of a tree could potentially vary depending on the radius of influence zone (Pukkala & Kolström, 1987; He & Duncan, 2000; Nanami et al., 2005). The CZRk was a multiple of average distance between the trees in the plot and highly affected by stand density. In our study plots, considering k equal to three and CEA equal to 30° proved to be a good fit to select the adequate number of active competitors. Although some studies (e.g. Alvarez et al. 2003) found better results using a different angle gauge, the angle gauge of 30° provided satisfactory results in some other studies (e.g. Lee & Gadow, 1997; Corral Rivas et al., 2005; Zhang et al., 2009).

The next superior competition selection approach, CZR0.4h, was simple in practice and in accordance with studies showing that, the optimal influence zone radius strongly depended on the tree’s initial dimensions (D’Amato & Puettmann, 2004; Sims et al., 2009). Considering the third suitable competitor selection method, similar to several other studies, the opening angle of 50°-60° performed well (Biging & Dobbertin, 1995; Pretzsch, 2009; Oheimb et al., 2011) where bigger angles (80° and 100° in this study) mainly decreased the merit of the search-cone method used to detect the competitors (Richards et al., 2008). In contrast to the CZRk3, the two methods of CZR0.4h and SCH60 gave more weight to tree height than distance, and since in our study, there was a lack of height measures for all trees, the selecting system of CZRk3was preferable to identify competitors for central trees.

Despite the fact that the identity of neighbouring species is an important factor in the characterization of their competitive effects (Bella, 1971; Zhao et al., 2006; Kaitaniemi & Lintunen, 2010; Bošelá et al., 2013), no significant improvement appeared in recalculating the selected indices using Ellenberg’s light values except for young trees. One possible explanation is that in our study plots about two-thirds of the trees analysed were birch with the same light factors. Consequently, giving weight to different species did not significantly change the values of measured competition. In addition, interspecific competition mainly caused by Norway spruce appeared inferior due to differences in temporal growth patterns and shade-tolerance (Tahvanainen & Forss, 2008; Hynynen et al., 2011). Furthermore, the influence of competition on diameter growth was not strongly impacted by the number of species in the local neighbourhood as suggested by Oheimb et al. (2011). The slight improvement in young stands might be due to the nature of Ellenberg’s light values that refer to the preferences of the early stage of the tree life cycle. During the early stage, when light-demanding birch trees rapidly occupy regeneration areas, Norway spruce tends to appear more shade-tolerant; consequently, weighting them differently in competition measures is justified. Moreover the performance of CIs changed slightly by stand development. In young stands spatial indices performed better while in older stands, non-spatial indices showed superior results. In the early stage, pioneer birches grow quite fast and vigorously (Hynynen et al., 2011), and spatial CIs explain competition effects better in dense young stands, since they account for the short distances between the neighbouring trees, that are competing for resources. In older stands, due to mortality induced by different factors, including competition (Sims et al., 2009), the number of trees decline and non-spatial CIs are adequate for competition studies.

The overall results of this study provided a better understanding of competition in birch stands. Although spatial CIs performed better than non-spatial CIs, the reported differences between the spatial and non-spatial indices are relatively small. The spatial indices require tree attributes and locations, and the recording of such information is expensive and time consuming. Therefore, we suggest applying the spatial indices only when studying the competition in the natural development of young stands, where the stands are usually dense, because these types of indices give more weight to trees that are closer to the subject tree. In the middle-aged and old managed stands, an efficient measure of competition is possible by employing the non-spatial indices that do not require as many field measurements.


We are sincerely grateful and would like to thank our guest professor, Arne Pommerening, who has kindly contributed recommendations and ideas for this research project.


Alemdag IS, 1978. Evaluation of some competition indexes for the prediction of diameter increment in planted white spruce / by I.S. Alemdag. Forest Management Institute, Ottawa, Canada.
Alvarez MF, Barrio M, Gorgoso F, Alvarez JG, 2003. Influencia de la competencia en el crecimiento en sección en Pinus radiata D. Don. Invest Agrar Sist Rec For 12(2): 25–35.
Andreassen K, Tomter SM, 2003. Basal area growth models for individual trees of Norway spruce, Scots pine, birch and other broadleaves in Norway. For Ecol Manag 180: 11-24.
Assmann E, 1970. The Principles of Forest Yield Study, Pergamon Press, Oxford, UK.
Bates DM, Watts DG, 1988. Nonlinear regression analysis and its applications. Wiley, New York.
Begon M, Harper JL, Townsend CR, 1996. Ecology: individuals, populations and communities. Blackwell Science, New York.
Bella IE, 1971. A New Competition Model for Individual Trees. For Sci 17: 364-372.
Berger U, Hildenbrandt H, 2000. A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighbourhood competition of mangrove trees. Ecol Model 132: 287-302.
Biging GS, Dobbertin M, 1992. A Comparison of Distance-Dependent Competition Measures for Height and Basal Area Growth of Individual Conifer Trees. For Sci 38: 695-720.
Biging GS, Dobbertin M, 1995. Evaluation of Competition Indexes in Individual Tree Growth-models. For Sci 41: 360–377.
Bitterlich W, 1952. Die Winkelzählprobe. Forstw Cbl 71: 215–225.
Boivin F, Paquette A, Papaik MJ, Thiffault N, Messier C, 2010. Do position and species identity of neighbours matter in 8-15-year-old post-harvest mesic stands in the boreal mixedwood? For Ecol Manag 260: 1124-1131.
Bošelá M, Petráš R, Šebeň V, Mecko J, Marušák R, 2013. Evaluating competitive interactions between trees in mixed forests in the Western Carpathians: Comparison between long-term experiments and SIBYLA simulations. For Ecol Manag 310, 577-588.
Brand DG, and Magnussen, S. 1988. Asymmetric, two-sided competition in even-aged monocultures of red pine. Can J For Res 18: 901–910.
Burkhart HE, Tomé M, 2012. Modeling Forest Trees and Stands. Springer Netherlands, Dordrecht.
Castagneri D, Vacchiano G, Lingua E, Motta R, 2008. Analysis of intraspecific competition in two subalpine Norway spruce (Picea abies (L.) Kast.) stands in Paneveggio (Trento, Italy). For Ecol Manag 255: 651–659.
Cole WG, Lorimer CG, 1994. Predicting tree growth from crown variables in managed northern hardwood stands. For Ecol Manag 67: 159–175.
Contreras MA, Affleck D, Chung W, 2011. Evaluating tree competition indices as predictors of basal area increment in western Montana forests. For Ecol Manag 262: 1939-1949.
Corral Rivas JJ, Álvarez González JG, Aguirre O, Hernández FJ, 2005. The effect of competition on individual tree basal area growth in mature stands of Pinus cooperi Blanco in Durango (Mexico). Eur J For Res 124: 133–142.
D’Amato AW, Puettmann KJ, 2004. The relative dominance hypothesis explains interaction dynamics in mixed species Alnus rubra/Pseudotsuga menziesii forests. Ecol 92: 450–463.
Damgaard C, Weiner J, 2008. Modeling the growth of individuals in crowded plant populations. Plant Ecol 1: 111-116.
Daniels RF, 1976. Simple competition indices and their correlation with annual loblolly pine tree growth. For. Sd. 22: 454-456.
Daniels RF, Burkhart HE, Clason TR, 1986. A comparison of competition measures for predicting growth of loblolly pine trees. Can J For Res 16: 1230-1237.
Ellenberg H, Weber HE, Düll R, Wirth V, Werner W, Paulissen D, 1991. Zeigerwerte von Pflanzen in Mitteleuropa. Scripta Geobotanica, 18: 1–248.
Fischer A, Lindner M, Abs C, Lasch P, 2002. Vegetation dynamics in central European forest ecosystems (near-natural as well as managed) after storm events. Folia Geobot 37: 17-32.
Ford ED, Diggle PJ, 1981. Competition for Light in a Plant Monoculture Modelled as a Spatial Stochastic Process. Annals of Botany 48: 481-500.
Hamilton DA, 1986. A logistic model of mortality in thinned and unthinned mixed conifer stands of Northern Idaho. For Sci 32(4): 989–1000.
He F, Duncan RP, 2000. Density-dependent effects on tree survival in an old-growth Douglas fir. For Ecol 88: 676–688.
Hegyi F, 1974. A simulation model for managing jackpine stands, In: Fries, J. (Ed.), Proceedings of IUFRO meeting S4.01.04 on Growth models for tree and stand simulation, Royal College of Forestry, Stockholm, Sweden.
Holmes MJ, Reed DD, 1991. Competition indices for mixed species northern hardwoods. For Sci 37: 1338-1349.
Hynynen J, Niemisto P, Vihera-Aarnio A, Brunner A, Hein S, Velling P, 2010. Silviculture of birch (Betula pendula Roth and Betula pubescens Ehrh.) in northern Europe. Forestry 83: 103-119.
Hynynen J, Repola J, Mielikäinen K, 2011. The effects of species mixture on the growth and yield of mid-rotation mixed stands of Scots pine and silver birch. For Ecol Manag 262: 1174-1183.
Jõgiste K, 1998. Productivity of mixed stands of Norway spruce and birch affected by population dynamics: a model analysis. Ecol Model 106: 77-91.
Jõgiste K, 2010. A basal area increment model for Norway spruce in mixed stands in Estonia. Scan J For Res 15: 97–102.
Kaitaniemi P, Lintunen, A. 2010. Neighbor identity and competition influence tree growth in Scots pine, Siberian larch, and silver birch. Annals of For Sci 67: 604.
Kiviste A, Hordo M, 2002. Eesti metsa kasvukäigu püsiproovitükkide võrgustik (Network of permanent forest growth plots in Estonia) Forestry Studies 37: 43-58.
Kiviste A, Nilson A, Hordo M, Merenakk M, 2003. Diameter Distribution Models and Height-Diameter Equations for Estonian Forests. Modelling Forest Systems 169-179.
Lang M, Nilson T, Kuusk A, Kiviste A, Hordo M, 2007. The performance of foliage mass and crown radius models in forming the input of a forest reflectance model: A test on forest growth sample plots and Landsat 7 ETM+ images. Remote Sensing of Environment, 110(4): 445-457.
Larocque GR, 2002. Examining different concepts for the development of a distance-dependent competition model for red pine diameter growth using long-term stand data differing in initial stand density. For Sci 48: 24–34.
Lee WK, Gadow Kv, 1997. Iterative Bestimmung von Konkurrenzbaeume in Pinus densiflora Bestaenden (Iterative selection of competitor trees in Pinus densiflora stands). Allg. For. Jagdztg 168: 41-45.
Lin JY, 1974. Stand growth simulation models for Douglas-fir and western hemlock in the northwestern United States, in: Fries J. (Ed.), Growth Models for Tree and Stand Simulation, Royal Coll. For., Stockholm, Sweden. Pp.  02–118.
Lorimer CG, 1983. Tests of age-independent competition indices for individual trees in natural hardwood stands. For Ecol Manag 6: 343–360.
Mailly D, Turbis S, Pothier D, 2003. Predicting basal area increment in a spatially explicit, individual tree model: a test of competition measures with black spruce. Can J For Res 33: 435-443.
Martin GL, Ek AR, 1984. A Comparison of Competition Measures and Growth Models for Predicting Plantation Red Pine Diameter and Height Growth. For Sci 30: 731-743.
Munro DD, 1974. Forest growth models –a prognosis. in J. Fries (ed.): Growth models for tree and stand simulation. Royal Coll. For., Res. Notes 30, pp. 7-21. Stockholm, Sweden.
Nanami S, Kawaguchi H, Yamakura T, 2005. Sex ratio and gender-dependent neighbouring effects in Podocarpus nagi, a dioecious tree. Plant Ecol 177: 209-222.
Nilson A, 2005. Generalization of height growth as difference equations fit for estimating the site index of stands. Metsanduslikud Uurimused 43: 173-184.
Oheimb vG, Lang AC, Bruelheide H, Forrester DI, Wäsche I, Yu M, Härdtle W, 2011. Individual-tree radial growth in a subtropical broad-leaved forest: The role of local neighbourhood competition, For Ecol Manag 261: 499–507.
Pedersen RØ, Næsset E, Gobakken T, Bollandsås OM, 2013. On the evaluation of competition indices -The problem of overlapping samples. For Ecol Mang 310: 120-133.
Peet RK, Christensen NL, 1987. Competition and tree death. BioScience 37: 586-595.
Pretzsch H, Biber P, Ďurský J, 2002. The single tree-based stand simulator SILVA:construction, application and evaluation. Forest Ecol Manage 162: 3–21.
Pretzsch H, 2009. Forest Dynamics, Growth and Yield. Springer-Verlag Berlin Heidelberg, Germany.
Prévosto B, Coquillard P, Gueugnot J, 1999. Growth models of silver birch (Betula pendula Roth.) on two volcanic mountains in the French Massif Central. Plant Ecol 144: 231-242.
Pukkala T, Kolström T, 1987. Competition indices and the prediction of radial growth in Scots pine Silva Fenn 21: 55-76.
R Development Core Team, 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria.
Richards M, McDonald AJS, Aitkenhead MJ, 2008. Optimisation of competition indices using simulated annealing and artificial neural networks. Ecol Model 214: 375–384.
Roberts SD, Harrington CA, 2008. Individual tree growth response to variable-density thinning in coastal Pacific Northwest forests. For Ecol Manag 255: 2771-2781.
Rouvinen S, Kuuluvainen T, 1997. Structure and asymmetry of tree crowns in relation to local competition in a natural mature Scot pine forest. Can J For Res 27: 890–902.
Schröder J, Gadow Kv, 1999. Testing a new competition index for Maritime pine in north western Spain. Can J For Res 29: 280-283.
Schröder J, Rodriguez R, Vega G, 2002. An age-independent basal area increment model for Maritime pine trees in northwestern Spain. For Ecol Manag 157: 55–64.
Siegel S, 1956. Nonparametric Statistics for the Behavioral Sciences. McCraw-Hill, New York.
Sims A, Kiviste A, Hordo M, Laarmann D, Gadow K v, 2009. Estimating tree survival: a study based on the Estonian Forest Research Plots Network. Annales Botanici Fennici 46: 336-352.
Soares P, Tomé M, 1999. Distance-dependent competition measures for eucalyptus plantations in Portugal. Ann. For. Sci, 56: 307-319.
Soares P, Tomé M, 2001. A tree crown ratio prediction equation for eucalypt plantations. Ann For Sci, 58: 193-202.
Stadt KJ, Lieffers VJ, 2000. MIXLIGHT:A flexible light transmission model for mixed-species forest stands. Agricultur Foest. Meteorol. 102: 235–252.
Stadt KJ, Huston C, Coates KD, Feng ZL, DaleMRT, Lieffers VJ, 2007. Evaluation of competition and light estimation indices for predicting diameter growth in mature boreal mixed forests. Annals of For Sci 64: 477-490.
Staebler GR, 1951. Growth and spacing in an even-aged stand of Douglas-fir. Master’s thesis, University of Michigan, USA.
Steneker GA, Jarvis JM, 1963. A preliminary study to assess competition in a white spruce-trembling aspen stand. For.Chron. 39: 334–336.
Tahvanainen T, Forss E, 2008. Individual tree models for the crown biomass distribution of Scots pine, Norway spruce and birch in Finland. For Ecol Manag 255: 455-467.
Tomé M, Burkhart HE, 1989. Distance-Dependent Competition Measures for Predicting Growth of Individual Trees. For Sci 35: 816-831.
Vanclay JK, 1991. Mortality functions for north Queensland rainforests. J. Tropical For Sci 4: 15–36.
Vitas A, 2011. Seasonal Growth Variations of Pine, Spruce, and Birch Recorded by Band Dendrometers in NE Lithuania. Bal For 17: 197-204.
Wagenmakers E.J, Farrell S, 2004. AIC model selection using Akaike weights. Psychonomic Bulletin & Review, 11, 192-196.
Weigelt A, Jolliffe P, 2003. Indices of plant competition. Ecol J 91: 707–720.
Wimberly MC, Bare BB, 1996. Distance-dependent and distance-independent models of Douglas-fir and western hemlock basal area growth following silvicultural treatment. For Ecol Manag 89: 1–11.
Wykoff WF, Crookston NL, Stage AR, 1982. User’s guide to the Stand PrognosisModel. USDA Forest Service, Gen. Tech. Rep. INT-133.
Yearbook of Forest, 2013. Estonian environment information centre.Tartu [in Estonian].
Zhang C, Zhao X, Gao L, Gadow Kv, 2009. Gender, neighboring competition and habitat effects on the stem growth in dioecious Fraxinus mandshurica trees in a northern temperate forest. Annals of For Sci vc, 66(8): 812-819.
Zhao DH, Borders B, Wilson M, Rathbun SL, 2006. Modeling neighborhood effects on the growth and survival of individual trees in a natural temperate species-rich forest. Ecol Model 196: 90-102.