# Verification of the Scots Pine (_Pinus sylvestris_ L.) Crown Length Model
## 4 Discussion
This is justified because it eliminates not only errors resulting from the measurement, but also random variables affecting the shape of a single tree crown. Furthermore, in the model under scrutiny, we hypothesize a density index for the stand, hypothesizing this to be constant for all trees within the experimental plot. The model can be used to calculate the crown length of a single tree, provided it grows at the same density as the calculated average density for the stand. Such a situation under natural conditions will only apply to a small number of individual trees. The model is, therefore, not dedicated to the calculation of a single crown, as this would generate too much error (in some cases, up to 29%) (Figure 6a). In principle, the different authors [55; 56; 57] claim that crown length can be predicted on the basis of standard variables measured in forest management. However, it is believed very difficult to accurately calculate crown length using basic measurements of trees, i.e., diameter at breast height, height, basal area, and stand age, without calibration at the stand level [57]. The tested crown length model showed that the measurements normally performed in forest inventories (\(DBH\), \(H\)) together with \(DI\) are sufficient to calculate crown lengths of pine stands. [PERSON]'s rank correlation coefficient between \(DBH\) and the calculated \(CL_{cal}\) model is high at \(R=0.955\) (\(p<0.05\)), which underlines the relationship between the trunk size and its crown. A strong correlation can also be observed between \(H\) and \(CL_{cal}\) (\(R=0.967\); \(p<0.05\)). This confirms that the predictors used to build the model are adequate and the model construction is correct. It should be noted that these two parameters, \(DBH\) and \(H\), yield a very strong correlation for both individual trees (Figure 4) and stands (Figure 5). The third predictor used in the model, \(DI\), showed a negative correlation with the crown length. The inclusion of \(DI\) in the crown length model seems crucial. In monospecific stands, crown density is reduced by accelerated self-thinning, crown shyness, and biotic or abiotic damage [58; 59]. This predictor plays a key role in younger stands, when there is strong competition among the trees. This results in an initial reduction in size, including of the crown, while the trees separate from the community at a later stage [60]. This is in line with [PERSON] conclusion [61]. [PERSON]'s rank correlation coefficient of \(R=-0.887\) (Table 4) indicates a significant negative correlation: the higher the density, the shorter the crown. This statement is consistent with the assumption that in single-species stands of _Pinus sylvestris_ of the first and second age class (up to 40 years), the length of the crown mainly depends on density. This regularity has been noted by other authors [62, 63] and is reflected in the original survival and ingrowth models for _Pinus sylvestris_ and _Pinus pinaster_[64]. This study revealed several issues that need to be addressed in future works. First of all, the sample size must be larger and include data from forest stands growing in other habitat types and in different climatic conditions. Second, the age of stands should be extended to include younger (up to 20 years old) and older stands (over 40 years old), which should allow one to check and possibly adjust the model to the age of trees. Finally, density can be a useful variable for developing submodels and even better matching.