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The functioning of complex forest ecosystems is intimately related to their structural properties. Tree mortality is a major driver of forest stand dynamics and therefore plays an important role in the formation of forest structure. Data from the Estonian Network of Forest Research Plots (ENFRP) was used to estimate the mortality probability of silver birch trees (_{5}) as a measure of tree vitality, or the tree relative diameter (_{rel}) as a measure of competition, or both these two variables, were substantially better than any models not including these variables. In addition, any measures of spatial aggregation (

Tree mortality is an important driver of forest stand dynamics as it determines the formation of forest structure (

Tree mortality occurs when tree vigor declines due to intolerance of the tree to the negative influence of stress factors, such as drought and competition. These stress factors can lead to a wide variety of causes of tree mortality. To achieve a better understanding of mortality, numerous attempts to categorize its causes have been reported (

The ability of a tree to withstand stress factors is affected by a multitude of interacting factors such as tree size, tree viability, competition among trees and stand density (

Measurements of tree size can be easily collected (tree diameter and tree height) or computed (tree growth and tree basal area) and to some extent they contain valuable, but not sufficient, information about the probability of tree mortality (

Competition is the next well-documented contributor to tree mortality. Competition for limited resources (such as water, light and nutrients) is a fundamental ecological process, which has strongly modulated the mortality of suppressed trees (

Theoretically, inclusion of the spatial effects in modeling the competitive environment that surrounds an individual tree is expected to improve the prediction ability of mortality (

Regarding the fact that any desired tree species may be absent due to self-thinning in a final regular stand, thinning during the early self-thinning years is an acceptable management tool to control stand quality and supports favorable tree species (

We focused our study on the mortality of silver birch trees (

The main objectives of this study were to: (i) filter the variables that are meaningful for the mortality of silver birch trees; (ii) test these variables in an empirical model for their ability to predict mortality of silver birch trees; and (iii) examine whether thinning practices effectively minimize the rate of tree mortality in managed forests.

Data from the Estonian Network of Forest Research Plots (ENFRP) was used for this study. This network, consisting of 730 permanent plots, was established during the period 1995-2004, and contains the data for all the main forest types in Estonia (

Clear cutting is the predominant management system in Estonia; consequently overstory trees are mostly even-aged. Most stands have been managed to maintain pure stands, though near-natural situations can occur under good forest growth conditions in any stand after some decades without management. The ENFR permanent plots were circular with a radius ranging from 10 to 30 meters. Depending on the stand age and density, they were delineated so that every plot contained at least 100 trees in the overstory. Within each plot the azimuth, the distance from plot center, the diameter at breast height (d), the tree species identity, and any defects of trees were recorded. For every fifth tree, and also for dominant and rare tree species, the tree height and the height to the live crown base were also measured. The measurements were repeated at intervals of five years.

To carry out this study, we selected 422 research plots with three consecutive measurements where silver birch was present. Other plots of the ENFRP network were excluded because either the plots did not include silver birch or at least three measurements taken at five-year intervals were not available. We used the first five-year interval,

Based on the concept of the influence-zone (

A list of selected variables studied for the contribution in tree death is provided in Tab. S1 of

Non-spatial variables are simple functions of stand or tree level measurements. In Tab. S1 of _{ha}), basal area (^{2}/ha), site index (_{100}, m) and stand age (_{ha} and _{100} was used to measure the site productivity, calculated as the average height of a stand at the reference age of 100 years (

For non-spatial tree level measurements the following variables were used: tree diameter at breast height (_{rel}) calculated as the ratio of tree and stand diameters, tree five-year diameter growth (_{5}, cm), tree basal area (^{2}), and the sum of the trees’ basal areas (per plot) larger than the reference tree (^{2 }ha^{-1} - _{rel} shows the dominance of a reference tree related to other trees in the stand. The tree diameter growth rate (_{5}) is a measure of tree vitality often used in mortality models (_{rel.cz} and _{cz}) were calculated only for trees within the influence zone around each reference tree.

Spatial variables in Tab. S1 of _{sb}); (ii) the proportion of other species that are not silver birch (_{ns}); and (iv) the proportion of Scots pine and other deciduous trees (_{T}), for all neighboring trees within the influence zone.

An important issue in stand development is the self-thinning, when an increased density-dependent mortality rate is expected due to high competition among individuals. Traditionally, the allometric relationship between stand density (_{ha}) and diameter (_{ha} -

On the basis of normal growth and yield tables used in Estonia (

where _{lim}/

Finally the thinning variables _{thin} and _{red} were quantified, where _{thin} is the non-spatial measure of the thinning intensity within the plots, and _{red} is the spatial measure of the reduced load of competition within the zone of influence, because of the removal of competitors during any thinning practices.

Mortality is a discrete event that can only take two values (alive or dead), hence logistic functions are widely applied to model probability of tree mortality (

Assuming that

Since the coefficient of determination is not appropriate when discrete variables are modeled (_{w}). The probability that the model was the best with the lowest expected information loss was determined by the smallest value of AIC and the biggest AIC_{w} (

Models were developed and selected as follows. Initially, pairwise models were calculated between mortality and each variable presented in Tab. S1 of _{thin} and _{red}, on mortality probability of silver birch trees was also tested. About 400 models were fitted with all possible combinations of these selected variables with the restriction that no model could simultaneously include variables representing a similar factor (_{w} value greater than zero, were selected.

Finally, the contribution of thinning to the mortality of individual trees was assessed. To this purpose, variables _{thin }and _{red} were separately added to the selected model as new predictors, and the changes to the quality measure of the full statistical model were investigated. For all models, the

Over the 348 selected research plots the five-year mortality rate of silver birch trees was 9.67%,

The results from the pairwise analyses indicated that tree growth (_{5}), tree size (_{rel.cz}, _{cz}), structure (_{5}, _{100}, were also tested, but they did not provide any improvement to the model performance.

The highest ranked logistic models with different combinations of variables are presented in _{w}. The VIF values for all combinations were less than 3.0, indicating a low multicollinearity. Additionally, we tested different transformations of _{rel }and _{5}, and found them inferior to the untransformed variables (data not shown).

_{rel}<0.2) with low survival probability, and also a slight underestimation of the mortality probability of the small proportion of large silver birch trees (

As shown in _{thin} in the best model did not seem to improve its performance. However, a significant improvement was observed when the spatial thinning variable _{red} was included. Thus, thinning practices in silver birch stands demonstrated that there was a negative influence on the probability of tree mortality (see Coeff_{5} in

In this study, the silver birch trees with an increasing diameter growth rate clearly indicated an increment in survival. Recent radial growth has been frequently used as an indicator of tree health and vigor (

While the mortality of small birch trees in young and dense stands increased due to self-thinning (_{rel} appeared superior to capture this trend. By some means, the hierarchical position of trees within the stand is measured by _{rel }and indirectly indicates their competitive status (

The competition-induced mortality is presumed to decline as local tree density decreases, and the overall plot density showed to be related to the strength of competitive effects (_{rel} could have served as a simple index of competition, but it did not take the variation of stand density into account. Therefore, equipping the model with spatial measures that represented the neighborhood properties of reference trees did appear unavoidable. Surprisingly, contrary to our assumption, adding the new calculations of _{cz}) and _{rel }(_{rel.cz}) only for immediate neighbors inside the influence zone diminished the predictive power of the model. This can be explained by the expected increasing uniformity in tree spacing with tree age or size, due to mortality from competition (

Several studies reported that the competition and growth of silver birch trees, and consequently their survival prospects, are strongly related to the identity of neighboring species (

Thinning to different residual densities produces varying effects on tree mortality, depending on the tree species with different characteristics and site conditions (_{red} indicated that the competition imposed by neighboring trees, which were cut during the thinning operation, partially limited the survival of birch trees. As explained before, density-dependent mortality or self-thinning (

The areas included in the Estonian Network of Forest Research Plots (ENFRP) were mostly located in managed forests,

Additionally, one might expect that building the mortality model to include soil descriptors and climate variables will also improve its performances. In this study, mortality was assessed over periods of five years as the exact year of tree death was unknown. Thus, it was difficult to connect extreme events, such as very cold temperatures or hot summers, which can usually cause high tree mortality. Regarding the costly assessment of annual tree mortality and soil analysis around individual trees for large data sets, a dendrochronological analysis seems to be a more effective method for climate studies (

Natural mortality of individual trees is a stochastic and irregular phenomenon for which we attempted to find the most relevant explanatory variables. Although a number of known and unknown factors affecting tree mortality makes its modeling complicated, the fitted models used in this study did produce results that satisfactorily explained mortality of Estonian silver birch trees. Five-year diameter growth, relative diameter, species proportion, and aggregation were the most appropriate explanatory variables in our mortality models. In order to maintain high survival probabilities, forest management plans and practices should pay a special attention to growth performances of trees, species compositions, tree density and forest stand structure. Furthermore, the reduction of stand density would provide more growing space for light-demanding birch trees, as demonstrated by the reduced mortality predicted by our model when thinning was included as predictor. However, root and stem damage caused by heavy machinery used for thinning operations, and the higher wind exposure of trees after thinning should also be considered. Finally, based on our results, silver birch trees should preferably be managed in mixed stands where they occur along with other tree species, and attempts should be made to minimize the clumping (

Measurement of the Estonian Network of Forest Research Plots has been supported by Estonian Environmental Investment Center. This study was also supported by the Estonian Research Council (ETF8890, IUT21-04).

^{nd}International Conference on Forest Measurements and Quantitative Methods and Management & The 2004 Southern Mensurationists Meeting” (Cieszewski CJ, Strub M eds). Hot Springs (AR, USA) 15-18 Jun 2004. Warnell School of Forestry and Natural Resources, University of Georgia, GA, USA, pp. 74-94.

(a) The distribution of study plots throughout Estonia, and (b) the proportion of three major tree species within the study plots.

(a) Distribution of plots by number of reference trees within the studied plots; (b) relationship between the radius of the influence zone and the average number of neighbors within the reference trees’ influence zones; (c) relationship between the five-year diameter growth and relative diameter in reference tree data set; (d) relationship between quadratic mean diameter and relative sparsity, where plot relative sparsity was calculated as limiting sparsity relative to stand sparsity: _{lim} /

Predicted mortality probability of the most important predictors of the tree mortality (solid lines) with 95% confidence (dashed lines) in pairwise relationship between mortality and predictor variables. b1 (black lines) and b2 (red lines) refer to variables _{rel }and _{rel.cz}, while e1 (black lines) and e2 (red lines) refer to the variables _{cz}, respectively.

The predicted mortality probabilities of the best logistic model against observed mortality. The dashed line represents the ideal probability estimation and the solid line shows how the model fits observed mortality probabilities.

Mortality rate of silver birch trees depending on silver birch proportion.

Proportion of birchin influence zone (%) | Number ofreference trees | Numberof plots | Mortality tosurvival rate | Mortalityrate (%) |
---|---|---|---|---|

81-100 | 864 | 39 | 0.20 | 16.67 |

61-80 | 1606 | 88 | 0.13 | 11.27 |

41-60 | 1526 | 138 | 0.08 | 7.55 |

21-40 | 1274 | 173 | 0.08 | 7.53 |

0- 20 | 739 | 246 | 0.06 | 6.09 |

Mortality probability analyses of silver birch using different spatial and non-spatial variables. id_{5} is the five-year diameter growth of reference trees (cm); dbh is the diameter of reference tree at breast height (cm); d_{rel }and d_{rel.cz} are the relative dbh of reference trees for each plot and zone of influence, respectively; G is the total basal area of trees within the plot (m^{2}ha^{-1}); BAL and BAL_{cz} are the sum of basal area of trees larger than the reference tree within the plot and the influence zone, respectively (m^{2}ha^{-1}); CI is the Hegyi’s competition measure of neighbouring trees inside the zone of influence; agg is the aggregation measure of trees inside the zone of influence and sp is the proportion of other species than silver birch within the influence zone. AIC, ΔAIC, AUC and loglik are the statistical measures of the models. TPR and TNR are the sensitivity and specificity of the models, respectively.

Variables | AIC | ΔAIC | AUC | TPR | TNR | loglik |
---|---|---|---|---|---|---|

_{5}, _{rel}, sp, agg |
2583.64 | 0.00 | 0.819 | 0.828 | 0.856 | -1285.8 |

_{5}, _{rel}, sp |
2590.37 | 6.73 | 0.819 | 0.833 | 0.853 | -1290.18 |

_{5}, _{rel}, agg |
2593.54 | 9.90 | 0.820 | 0.812 | 0.866 | -1291.77 |

_{5}, _{rel.cz}, sp |
2593.82 | 10.18 | 0.818 | 0.816 | 0.861 | -1291.91 |

_{5}, _{rel.cz}, sp, agg |
2596.56 | 12.92 | 0.818 | 0.818 | 0.862 | -1294.78 |

_{5}, _{rel}, dbh |
2600.86 | 17.22 | 0.820 | 0.816 | 0.862 | -1295.43 |

_{5}, _{rel.cz}, agg |
2601.25 | 17.61 | 0.817 | 0.809 | 0.864 | -1295.63 |

_{5}, _{rel} |
2603.11 | 19.47 | 0.820 | 0.833 | 0.854 | -1297.55 |

_{5}, _{rel}, |
2605.08 | 21.44 | 0.820 | 0.831 | 0.854 | -1297.54 |

_{5}, _{rel.cz}, dbh |
2605.17 | 21.53 | 0.818 | 0.831 | 0.851 | -1297.58 |

_{5}, _{rel.cz}, |
2617.09 | 33.45 | 0.818 | 0.809 | 0.860 | -1303.55 |

_{5}, dbh, |
2619.02 | 35.38 | 0.818 | 0.833 | 0.855 | -1304.51 |

_{5}, dbh, |
2619.27 | 35.63 | 0.818 | 0.821 | 0.858 | -1304.63 |

_{5}, dbh, agg |
2625.64 | 42.00 | 0.818 | 0.833 | 0.852 | -1307.82 |

_{5}, dbh, _{cz} |
2629.66 | 46.02 | 0.817 | 0.819 | 0.859 | -1309.83 |

_{5}, dbh, |
2633.34 | 49.70 | 0.818 | 0.824 | 0.859 | -1312.67 |

The best combinations of variables predicting silver birch mortality when thinning is included as predictor in the model used. (_{5}): five-year diameter growth of tree (cm); (_{rel}): relative _{red}): Hegyi’s competition measure of thinned trees inside the zone of influence; (_{thin}): thinning intensity of the plot; (_{w} are the statistical measures of models. AUC, TPR and FPR are area under curve, true positive rate and false positive rate of dead trees, respectively. Coeff_{i} are coefficients of the models. TPR and TNR are the sensitivity and specificity of the models, respectively.

Variables | ΔAIC | AIC_{w} |
AUC | TPR | TNR | Intercept | Coeff_{1} |
Coeff_{2} |
Coeff_{3} |
Coeff_{4} |
Coeff_{5} |
---|---|---|---|---|---|---|---|---|---|---|---|

_{5}, _{rel}, _{red} |
0.00 | 0.655 | 0.819 | 0.833 | 0.856 | 2.324 | -1.977 | -3.263 | -1.1053 | -1.008 | -0.195 |

_{5}, _{rel}, |
2.49 | 0.189 | 0.819 | 0.828 | 0.856 | 2.327 | -1.985 | -3.232 | -1.103 | -1.054 | - |

_{5}, _{rel}, _{thin} |
2.86 | 0.157 | 0.819 | 0.811 | 0.863 | 2.303 | -1.981 | -3.262 | -1.098 | -0.993 | -1.273 |

Tab. S1 - List of variables used to study silver birch mortality.