Competition among individual trees is a fundamental ecological process that plays a major role in population dynamics, survival, growth and species replacement (

For several species and forest conditions, the effectiveness of different

To investigate the effect of competition on the diameter growth of trees, we focused our study on silver birch

The main objective of this study was to investigate the adequacy of different spatial and non-spatial

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 (

Within each plot the azimuth, the distance from plot centre, the diameter at breast height (

Species composition of all trees within the studied plots was 67% silver birch, 24% Norway spruce and 9% of several other species (see

The competition for each subject tree was quantified using 18 different

The first seven indices in _{j}^{2} ha^{-1}); ^{2} ha^{-1}). ^{-1}). The index _{g} calculates the ratio of the diameter of the subject tree to the quadratic mean diameter of the plot (

where ^{2}), _{Dom} is the stand dominant height (m) (mean height of hundred thickest trees per hectare (

The next three competition indices

Finally, the last eight indices in

As well as the mathematical formulation, the value of a competition index depends on the method used to define competitors for the subject tree (

The radius of influence zone was defined as a fraction of the stand’s average height for each plot; _{0.4h} was set equal to 0.4 average height of plot (

Based on

where _{k} is dynamic radius,

The function _{k2}) and three (_{k3}) multiply this distance by two and three, respectively to define _{j ≥ 0.3}_{i} (where _{j} is _{i} is the

The _{1}, _{2} and _{4}tested three basal area factors (^{2 }ha^{-1}, respectively. A tree was considered a competitor if its distance to the subject tree was:

where _{ij} is the distance between the subject tree _{i}is the diameter of the subject tree. The values of

Finally, the

where _{ij} is the distance between the subject tree and the competitor tree, and _{i} is the subject tree height. If the apex of the reversed search-cone is at the crown base height of the subject tree (_{j}) then a neighbouring tree with height _{j} 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 (_{100}, _{80} and _{60}) or at the_{100}, _{80} and _{60}

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_{0.4h} and _{k}) were applicable to quantify the mentioned indices. Moreover, the allometric crown radius model, (developed by

where _{cr} is the crown radius (m), _{1} and _{2}

Preliminary analysis was carried out to pre-select adequate _{d5}) 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 (_{d5} and

Then, we constructed a linear multiple regression model (_{d5} (cm) and some predictor variables that influence diameter growth. In a preliminary assessment,

In order to evaluate the efficiency of the chosen

where _{k} are coefficients to be estimated, _{d5}_{100} is the stand site index.

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

For the recent linear mixed effect model, _{d5} is the dependant variable; _{multiple model} - _{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 (

The relative quality of growth functions, with and without ^{2} (Adjusted^{2}), the root mean square error (_{w}). The probability that model is the best with the lowest expected information loss is illustrated by the smallest value of _{w} (

where _{7} and _{8} are the mean square errors of models 7 and 8, respectively.

Finally, the efficiency of

In _{k3}, _{0.4h} and _{60} demonstrated greater values of Spearman’s _{1}_{2} and _{4}) showed to be an appropriate selection method of competitors. Furthermore, _{ }and

The comparison of the linear mixed effect models and the linear multiple models detected the improvement in linear mixed effect regressions in terms of

^{2}, _{w}, and also _{60} where

The results of analyses for different age groups (^{2} and

Computing the correlation coefficient of tree growth, and determining the efficiency of

Results from comparing different

The results we obtained for non-spatial

While non-spatial _{k} was a multiple of average distance between the trees in the plot and highly affected by stand density. In our study plots, considering

The next superior competition selection approach, _{0.4h}, was simple in practice and in accordance with studies showing that, the optimal influence zone radius strongly depended on the tree’s initial dimensions (_{k3}, the two methods of _{0.4h} and _{60} 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 _{k3}

Despite the fact that the identity of neighbouring species is an important factor in the characterization of their competitive effects (

The overall results of this study provided a better understanding of competition in birch stands. Although spatial

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.