Number of species represents the number of tree species in a stand (m).

Index R1 is derived from the number of tree species (m) and the number of trees per hectare (N) according to Margalef (1958):

Index R2 is calculated using the number of tree species (m) and the number of trees per hectare (N) according to Menhinick (1964):

Indices R1 and R2 do not have unique ranges, and cannot be transformed in such a way that their values range from 0 to 1. They can be used in absolute values to compare several simulation periods, or several forest stands (higher values indicate higher tree species richness).

Index lambda is calculated from the basal area proportions of individual tree species (w_i) according to Simpson (1949): 

Entropy H' is calculated from the basal area proportions of individual tree species (w_i) according to Shannon (1948):

while 10 tree species were set as a default for the forest stand rich in tree species (see Hartley measure in the denominator of the formula).

These indices can obtain values in the range from 0 to 1, where 0 stands for the minimum tree species diversity, and 1 represents the maximum value (the second index can exceptionally reach higher values than 1, if there are more than 10 tree species present in the stand with equal proportion; also in this case the value 1 represents optimum condition, and every value above 1 indicates the quality beyond the scope of our idea about the optimum condition).

Index E1 depends on entropy (H') and the number of tree species (m) according to Pielou (1975): 

Index E5 depends on the indices lambda and entropy (H') according to Hill (1973):

These indices can obtain values in the range from 0 to 1, where 0 stands for the minimum tree species diversity, and 1 represents the maximum value. 

Index R is derived from all distances between two nearest neighbours (r_i), number of trees in the plot (N), plot area (p), and the perimeter of the plot (u) according to Clark and Evans (1954):

The range of the index is from 0 to 2.15. The value 0 indicates an aggregated structure, i.e. the trees are aggregated in clusters. The value 1 represents a complete random distribution of trees in the plot area (so called Poisson distribution), while the value 2.15 stands for the regular tree distribution in the plot (in hexagonal spacing).

Paircorrelation function

The paircorrelation function by Stoyan and Stoyan (1992) determines the probability that from the whole set of trees in the plot there exist two trees that are situated from each other at a distance equal to r:

where K'(r) is the derivative of the function K by the variable r. Ripley K-function is defined as a number of trees from the whole set of trees in the simulation plot with the mututal distance shorter than r: 

where I_r is the indicator, which obtains the value 1 if the distance between the trees d_ij is lower than r, otherwise it obtains the value 0; A is the area of the simulation plot, and n is the number of trees. 

In the case, tree distribution in the simulation plot is completely random (following Poisson distribution), the value of the paircorrelation function is equal to 1 for every value of r. It means that the points of the function lie on a straight line, which runs parallel with axis x and intersects axis y in the value 1. The values above 1 represent tree aggregation, while the values below 1 mean that trees are scattered. In order to interpret the paircorrelation function correctly, the function is smoothed by a suitable filter, and corrected for the systematic error from the edge effect (e.g. Ripley or geometrical corrector).  

"Arten Profil" index is calculated using the basal area of i^th tree species in j^th stand layer (p_ij) following Pretzsch (1992): 

The first layer in the stand is composed of the trees with the height above 80% of the maximum height in the stand, the second layer consists of the trees with the height lower than 80% and higher than 50% of the maximum height. The index fluctuates between 0 and 1. Higher index values indicate more diverse vertical structures. If the index exceeds the value 0.9, the stand can be considered to have the structure of the selection forest. 

Diameter differentiation TM_d is related to the ratio between the larger and the smaller diameter of all nearest neighbouring trees in the plot (rd_ij) as defined by Füldner (1995):

Height differentiation TM_h is related to the ratio between the larger and the smaller height of all nearest neighbouring trees in the plot (rd_ij) as defined by Füldner ( 1995):

The index can obtain values from 0 to 1. The values below 0.3, between 0.3 and 0.5, between 0.5 and 0.7, and above 0.7 indicate small, medium, high, and very high differentiation, respectively. 

Total diversity proposed by Jaehne and Dohrenbusch (1997) is calculated using the following relationships:

Total diversity (epsilon) is the aggregation of partial components of diversity: tree species diversity (alfa), diversity of vertical structure (beta), diversity of tree spatial distribution (chí), and diversity of crown differentiation (delta). The input variables are: number of tree species (m), maximum and minimum tree species proportion (Z_max and Z_min), maximum and minimum tree height in the stand (h_max and h_min), maximum and minimum tree spacing (r_max and r_min), minimum height to crown base (KA_min), and minimum and maximum crown diameter (KD_min and KD_max). If the final value is equal to or higher than 9, stand structure is very diverse, the values from 8 to 8.9 indicate a diverse structure, index values in the range from 6 to 7.9 mean an uneven structure, an even structure is indicated by the values between 4 and 5.9, and the values below 4 represent a monotonous structure.