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The potential yield of a site is measured by site index, which is defined as the dominant height of a stand at a base age. A site index model for site quality assessment of ^{2}_{adj}), root mean square error (RMSE), bias, coefficient of determination for the prediction (R^{2}_{pr}) and residual plots were used for the choice of the best-fitting model. The best model was ^{2}, where

Site quality assessment is the evaluation of the natural productive capacity of a forest site for a tree species. Site quality assessment is very important in forest management, because a site could support one species excellently while supporting poorly other species. The oldest and most widely used technique for evaluating site quality or productivity is the site index.

Site index is the average total height of dominant and co-dominant trees at a specified reference or base age (

Site index models are essential quantitative tools in forest management (

Oak forests covers 22.6% of the total forested area in Greece (

The aim of this work was to obtain site index curves for site quality assessment of degraded Hungarian oak stands in central Greece to be used in the management of current and future Hungarian oak stands.

The study was conducted in degraded Hungarian oak stands located in an area of approximately 290 ha (of which 260 are forested) in central Greece (38° 53’ N, 22° 03’ E -

In the past, tree branches in some locations of the area were being cut by residents of nearby villages for livestock feeding, while other places were under agricultural cultivation. Nowadays, the main disturbance is grazing; degree of grazing is low to absent, and only in a small part of the area is severe. Silvicultural treatments have not been applied in the area, mainly because of the lack of adequate forest roads in most of the study area.

Thirty-nine plots 10 x 10 m were established randomly in the forested part of the study area, where the degree of grazing is low to absent, and the main canopy trees were considered approximately even-aged (

Little information is available in the scientific literature on site index for degraded Hungarian oak stands in central Greece; thus the first step was the choice of the appropriate base age. As recommended by several authors (

where _{0}, _{1}, _{2} are the regression coefficients to be estimated, and ^{2}_{adj}) and the lowest absolute and relative root mean square error (RMSE) were considered appropriate criteria for the selection of the best model. Examination of the residuals was also carried out for assessing the best models by calculating absolute and relative biases (

where _{i} is the observed height value for the _{i} is the estimated height value,

The predictive performances of the studied models were also evaluated using prediction errors or PRESS (PREdiction Sum of Squares) residuals. These residuals were calculated by omitting each observation in turn from the dataset, fitting the model to the remaining observations, predicting the response without the omitted observation and comparing the prediction with the observed value (

where _{i} is the observed height value and _{i,-i} is the prediction value obtained by omitting the

The accuracy of the predictions obtained with the different candidate equations was assessed by computing the coefficient of determination for the prediction (

The interpretation of this coefficient of determination is similar to that described for other similar coefficient,

Stands were stratified into three site quality classes, with site quality decreasing from class I to III. Using the predicted height growth trend described by the chosen model (guide curve), anamorphic site index curves were fitted to pass through three different site index classes of I to III. This was accomplished by holding the shape parameters constant and varying the asymptote parameter as necessary to achieve the required dominant height when stand age (_{0} = 50 years). This approach has been successfully used in previous studies (

A summary of the height characteristics of the 39 sample trees used for site index modeling are reported in

The parameters and statistics of the regression models considered (^{2}_{adj }and low RMSE and bias. All parameters included in the models were statistically significant, indicating that none of the models was over-parametrized. As expected, residuals did not display any significant departure from the normal distribution (

Simpson’s paradox (known also as the Yule-Simpson effect, the reversal paradox, or the amalgamation paradox) is an apparent paradox in which the results of separate groups seem reversed when the groups are combined (

In our study, the confounder is the site index, and the Simpson’s paradox concerns the total height estimated in contrast to the base age (50 years). Even though models’ parameters are correctly estimated, it seems that the estimated height at the age of 50 is lower than the true height measured at an age below 50, and higher than the true height measured at an age above 50.

Such apparent paradox may also be attributable to a King Kong effect (

The absence of permanent plots necessitated the use of temporary plot data of different ages. This limitation permitted only the use of the guide curve method for the development of site index models. Therefore, it was assumed that the distribution of plots with respect to site quality was the same across all ages (

The guide curve method was used to generate anamorphic site index curves. These curves are a family of lines with constant slope but various intercepts, achieved by holding the shape parameters constant and varying the asymptote parameter to obtain the required dominant height value when stand age (_{0}). The base age of 50 years used for the development of site index curves in the present study seems appropriate, since base age corresponds to the period of completion of rapid growth,

Even though there are more productive sites in adjacent areas, the Hungarian oak stands of the present study are not productive. Tree height growth, even in the best site quality, is very low.

Collecting data for a longer period of time from permanent sample plots may allow site index curves to be validated. Indeed, a good knowledge of growth and yield is necessary for sound forest management plans, especially silvicultural decision-making processes such as time of first and subsequent thinnings. The site index curves developed in this study may be useful in quantifying Hungarian oak growth and yield on various low productivity site conditions. Site index curves may also help as a guide in making thinning decisions for stands of species in analogous low productivity conditions. Among the various methods used to determine the time of first and subsequent thinnings, the dominant height approach is preferred because it reflects site effect more than other methods (

As for Simpson’s paradox, it has been mentioned in several forestry researches (

In our study, Simpson’s paradox can be a key to understanding the apparent inconsistency between height growth rate per tree and the performance of stand level statistics. Measurements of per tree growth rates over time, when used as a whole for site index curve fitting, may give misleading estimates. Actually, foresters must always recognize the effect that each felled tree may have on the forest level growth. Interpretation of our site index curves development, with the awareness of Simpson’s paradox, indicates that results from one region should not be extrapolated to another one too far apart on the basis of equations or graphs showing height growth rate by age class. Analysis of growth data for large areas can be risky, considering that the tree-stand interaction over time is quite composite.

From the analysis of degraded

We would like to thank the Bodossaki Foundation for the financial support of A. Stampoulidis. We also want to thank the Forest Service of Spercheiada (Greece) for their kind cooperation.

(A) Location of the study area (red circle). (B) Wider study area (red rectangle) and approximate location of the experimental plots (yellow squares).

Residual Q-Q plots for the three regression models considered in this study.

Comparison of the observed dominant height-age data and the predicted values obtained using the model from

Site index curves for Hungarian oak stands constructed using the model of

Summary statistics of the sample trees (dominant trees) used in site index modeling. (SE): standard error of the mean.

Trees | Total height (m) | ||||
---|---|---|---|---|---|

Age (years) | Count | Min | Max | Mean | SE |

35 | 1 | 9.5 | 9.5 | 9.5 | - |

38 | 1 | 7.2 | 7.2 | 7.2 | - |

43 | 1 | 7.5 | 7.5 | 7.5 | - |

47 | 1 | 8.7 | 8.7 | 8.7 | - |

50 | 3 | 9.2 | 10 | 9.5 | 0.252 |

51 | 1 | 7.2 | 7.2 | 7.2 | - |

52 | 1 | 7.7 | 7.7 | 7.7 | - |

54 | 7 | 7.2 | 11.5 | 9.31 | 0.489 |

55 | 1 | 9 | 9 | 9 | - |

57 | 7 | 6.8 | 10.5 | 8.8 | 0.492 |

58 | 3 | 6.5 | 10.5 | 7.97 | 1.272 |

59 | 5 | 7 | 12.5 | 10.86 | 1.002 |

60 | 1 | 10 | 10 | 10 | - |

63 | 1 | 9.2 | 9.2 | 9.2 | - |

64 | 2 | 10.2 | 10.5 | 10.35 | 0.15 |

66 | 3 | 9.6 | 11.5 | 10.33 | 0.59 |

Estimated parameters and statistics for the three models fitted to temporary plot data for Hungarian oak stands.

Model | Coeff. | Parameter estimates | ^{2} _{adj} |
RMSE | RMSE% | bias | bias% | ^{2} _{pr} |
---|---|---|---|---|---|---|---|---|

1 | _{0} |
-0.231 | 0.799 | 1.414 | 26.093 | -2.94E-13 | -5.43E-12 | 0.799 |

_{1} |
0.251 | |||||||

_{2} |
-0.001 | |||||||

2 | _{0} |
0.919 | 0.788 | 1.451 | 26.784 | 1.77E-12 | 3.27E-11 | 0.788 |

_{1} |
0.161 | |||||||

_{2} |
-1.404 | |||||||

3 | _{0} |
-3.656 | 0.700 | 1.727 | 31.874 | 1.32E-12 | 2.43E-11 | 0.700 |

_{1} |
2.949 |