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diameter (dˉg) of the stand represents the tree with the mean basal area (Laar and Akça 2007). The mean stand height (hˉg) was calculated as the heights of the mean basal area tree on each sampling plot. The dominant height of stand (h100) was calculated as the arithmetic mean of the 100 tallest trees per hectare (Kalıpsız, 1984; Kahriman et al., 2018). The number of trees per hectare (N) was calculated by multiplying the number of trees with a stem diameter of > 4 cm in the sample plots by the hectare conversion coefficient. The basal area of the stand (BA) was calculated by adding the basal area of each tree in the sample plot and converting to hectares. Double-entry tree volume equations developed by Kahriman et al. (2016b) were used to estimate sample plot volume (V). Stand volume was determined by converting the sum of individual tree volumes calculated using the double-entry tree volume equations to hectares. The double-entry tree volume (R2adj = 0.992, RMSE= 0.041 m3, and Cf= 1.009) and the dynamic model SI (R2adj = 0.984) from Kahriman et al. (2016b) are provided below.
The double-entry tree volume equation of Calabrian pine was given in Eq.1:
The model structure of the Hossfeld equation obtained by autoregressive modeling can be expressed as:
Where; h is the dominant tree height on the sample plot, t is the age and t0 is the standard age (a.k.a. base age) which is generally used as at 25 and 50 age for fast growing trees, and at 100 age for slow growing trees (Kalıpsız, 1984; Vanclay, 1994; Laar and Akça, 2007; Pretzcsh, 2009). In this study, the standard age was chosen at 60-year for Calabrian pine. The site index of a plot whose dominant height and stand age were determined can be calculated directly for a desired standard age using these equations (Kitikidou et al., 2012; Kahriman et al., 2018; Suliman et al., 2021).
This GADA model had a root mean square error (RMSE) of 0.8013 m, an Akaike’s information criterion difference (AICd) value of 0, and a Durbin-Watson test (DW) value of 2.0099. The fact that the Durbin-Watson value of the model was very close to 2 (DW: 2.0099) indicates that using autoregressive analysis greatly reduced the serial correlation. The developed Hossfeld dynamic site index model successfully modeled age-top height relationships with the S type, polymorphism, multiple asymptotes, and base-age invariable to expected growth principles.
The stand volume and yield parameters such as number of trees per hectare (N), basal area (G), stand volume (V), quadratic mean diameter (), and mean height () of the main stand were predicted using regression equations as a function of stand age (t), site index and stand density. Elements of the remaining trees were predicted using appropriate regression equations generated using variables such as stand age (t), site index (SI) and stand density (sd) and the independent variables derived from these variables using the SPSS statistical software program (SPSS 19.0 Inc., 2010) with forward, backward, and stepwise selection modes. The models that were statistically significant (p <0.05) and those had the highest adjusted coefficient of determination (R2adj), the lowest root-mean-square error (RMSE) and that also complied with the biological laws were selected.
Adjusted Coefficient of Determination
Root-Mean-Square Error
Where; Vi and represent calculated and predicted stand volume, and N and p represent sample size and number of variables used in the model respectively.
The removed stand volume and the yield elements are needed to determine the total stand volume yield since the total stand volume is equal to the sum of the standing timber volume at a given age and the volume removed up to that age (Vanclay, 1994; Pretzsch, 2009). In this study, the volume elements of removed stand were calculated using data on dying or dead trees in the stand. Also the number of trees removed was calculated using the difference between the number of trees in successive age intervals within the same site index and density class (Kalıpsız, 1984).
In addition, the volume of total yield and the percentage of intermediate yield to volume of total yield were computed, along with the current annual volume increment (CAI) and increment percentage. The mean annual increment (MAI) of standing timber and overall yield values were calculated in addition to volume and yield volume elements related to standing timber and removed trees (Vanclay, 1994; Pretzsch, 2009; Kahriman et al., 2016a).
The relationships of quadratic mean diameter (dˉg), mean height (hˉg), number of trees per hectare (N), basal area (G) and volume (V) with stand age (t), site index (SI), and stand