Presentation of Two New Empirical Equations for Point-centered quarter Method for 1 Estimating Trees Density in the Forest

6 Background and objectives: The point-centered quarter(PCQ) method is one of the distance 7 sampling methods. Previously, researchers such as Cottam and Curtis (1954), Pollard(1971), 8 and Haidari et al . (2008) introduced three equations to the estimation of plant density using 9 the above method. The objective of this research includes developing two new formula for the 10 estimation of tree density with the PCQ method,which is not biased toward the tree distribution 11 pattern. 12 Materials and methods: In this study, 40 circular sample plots (1000 m 2 as the real state) and 13 PCQ method were measured via a systematic random sampling design (100 m × 100 m) in the 14 educational research forest at Razi University in Dalahoo Mountain in Kermanshah province. 15 Later, through the mentioned formulas, forest stand density was calculated. Then, the obtained 16 density with different formulas of the PCQ method with the circular plot in the spatial pattern 17 of various types (uniform, random, and cluster) was compared in terms of accuracy and 18 precision. 19 Results: The results showed that two new empirical equations for estimating the density of 20 trees in forest stand were more appropriate than the previous equations in terms of accuracy 21 and precision. the equation used for the sample plot methods. Finally, it is suggested to use the new equations for other forests and also other vegetation, such as the grasslands and


Introduction 32
Density is one of the most remarkable vegetation traits (Bonham, 2013). Sampling methods 33 with plot-based and plot-less (distance methods) are used to estimate the density of the trees. 34 The main objective of sampling is to develop an accurate and precise survey of plant 35 communities' characteristics in ecological studies (Borges Silva et al. 2017). Distance 36 sampling methods have been used to measure plant density since the 1950s (Bonham, 2013). 37 Most distance sampling methods have more than one empirical formula. 38 The development of non-39 dimensions and fixed shapes is aimed at increasing inventory speed, reducingsampling time 40 and thus keeping running costs low and achieving correct accuracy (Namiranian, 2010).Spati 41 al patterns are influenced by vegetation density estimation using distance sampling methods. 42 While the density estimation by distance methods is not biased if plants and animals have a 43 random distribution pattern, it will be biased if the plants and animals have a cluster pattern. 44 Therefore, the distribution pattern of individuals should be determined using distance methods 45 before estimating population density (Krebs 1989). The bias is dependent on the plan 46 (inventory network, number of points, etc.) or the estimator. When the distance among sample 47 5 Firstly, the number of trees per unit of area, hectare, and variance in the number of trees were 101 calculated for circle samples, and the dot diagram of the number of trees per area unit of the 102 circle samples was drawn. In the next step, the density of trees in the 40 samples was calculated 103 using different equations of the point-centered quarter method (table 1)

Calculation of the tree distribution pattern 109
There were various indices to quantify the distribution of natural populations. In this study, 110 the variance/mean ratio ( x S 2 ) was used to determine the tree distribution pattern in the area 111 because the circle samples were considered as the control (base). If the ratio equals one, the 112 spatial distribution will be random; the ratio greater than one will indicate a clumped 113 distribution pattern; and the ratio less than one will show a uniform distribution pattern 114 (Moghadam, 2001). The reason that the circle sample plot method was considered as the base 115 was primarily that the circle method is one of the common methods used for Zagros forests, 116 and secondly that all the trees of 40 samples recorded through the point-centered quarter 117 method were inside the circle samples. 118

Rest of calculations 119
To examine the effect of the tree distribution pattern on the results obtained from estimating 120 the density of trees through different equations of the point-centered quarter (equations of 121 Cottam and Curtis (1954), Pollard(1971), Haidari et al. 2008 and also the new equations) after 122 drawing the dot diagram for the 40 samples in the circle sample method, one sample that had 123 the highest deviation from the mean data was eliminated. For the remaining 39 samples, firstly, 124 the spatial distribution pattern (variance/mean ratio) and, then, the number of trees per hectare 6 and also the equations of the point-centered quarter method were. The calculation continued 126 until the distribution pattern changed from the clumped pattern (the variance/mean ratio was 127 2.150 for all the 40 samples) to the random pattern (the variance/mean ratio was 1.02 for 30 128 samples) followed by the uniform pattern (the variance/mean ratio was zero for four samples). 129 In short, the calculations in A and B steps were carried out for 40, 39, and 38 samples in order 130 followed by 4 sample plots with zero variance/mean ratio (the uniform distribution pattern).

Tree distribution 138
As shown in Table 2, the trees in the studied area had a clumped distribution pattern because 139 the variance/mean ratio for the 40 circle samples was 2.150. The tree distribution pattern was 140 also determined for 4-39 samples regarding their variance/mean ratio, and the relevant results 141 are shown in Table 2. 142 Number of trees per hectare 143 Table 2 and Figure 4 show the number of trees estimated per hectare using the circle method 144 and different equations of the point-centered quarter method in different tree distribution 145 patterns (with variance/mean ratio of zero, 1, and 2.150 respectively for the uniform, random, 146 and clumped patterns). 147 A. Regarding the number of samples (4-40 samples in Table 2), values obtained from 148 different equations of the point-centered quarter method for different tree distribution 149 patterns were compared to those obtained from the circle method (the control) using 7 paired t-test (Table 3). 151

B. Values obtained from different equations of the point-centered quarter method were 152
compared to those obtained from the circle method (4-40 samples) regarding the 153 Figure 5). 154

Discussions 155
The results (Table 2) showed that the trees of the studied forest followed the clumped 156 distribution pattern. This result conformed to that of the studies conducted in relation to Zagros 157 forests by other researchers, such as Haidari (2006) (clumped, random, and uniform) similar to those obtained in the circle method (the control), 173 but the best formulas seem to be dalahoo1 and dalahoo2.This was well confirmed by the results 174 of the statistical test, namely the paired t-test (Table 3), and calculation of the acceptable 8 accuracy (Figure 4). According to Table 2, the equations that were not highly affected by the 176 changes in the distribution pattern were the dalahoo1 and dalahoo2 equations. Furthermore, 177 according to Southwoodet al. (1999), an equation with ±10 accuracy could be used in research 178 procedures (Southwood& Henderson 2000). Table 2