# Implications for Paleontological Heritage Conservation:
## 3 Results
### Spatial Distribution Characteristics of Fossil Sites
#### 3.1.2 Type of Spatial Distribution  
The nearest neighbor index can be applied to measure the nearest neighbor distance, which is the spatial distribution of point elements. According to Equations (1) and (2) of the average nearest neighbor index, clustered, uniform, and random distribution are the three types of spatial distribution of point elements. According to the calculation in ArcGIS 10.8.1, the theoretical nearest distance of fossil sites in Shandong Province is 15,789.1443 m, the actual average nearest distance is 10,137.2620 m, the nearest neighbor index \(R=0.642040\), and \(Z=-7.897529\), calculated by the Z test (Table 1). A negative Z-score indicates statistical significance in spatial autocorrelation analysis; \(R<1\) means a clustered distribution. Therefore, there is a noticeable clustering in the geographical distribution of fossil sites in Shandong Province. The \(p\)-value of 0.00 indicates that the probability of randomly forming a clustered pattern is less than 5%. The imbalance index can study the degree of equilibrium in the distribution of point-shaped elements in different regions. The \(S\)-value of the imbalance index of fossil sites \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Observed Mean** & **Expected Mean** & **Nearest Neighbor** & **Z-Score** & \(p\)**-Value** \\
**Distance/m** & **Distance/m** & **Index** & & \\ \hline
10,137.2620 & 15,789.1443 & 0.642040 & \(-7.897529\) & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the average nearest neighbor index of fossil sites in Shandong Province. in Shandong is 0.5880 according to Equation (3) using ArcGIS10.8.1, indicating that the distribution of fossil sites in Shandong Province is unbalanced (Table 2). Table 2 shows that the four prefecture-level administrative units of Linyi, Zibo, Weifang, and Jinan collectively accounted for 63.1579% of the total number of fossil sites in Shandong Province. Compared to the above four administrative units, there were fewer fossil sites in others. After calculating the geographic concentration index of the fossil sites of the prefecture-level cities in Shandong Province from Equation (4) in EXCEL 2021, \(G=35.5616\) and \(G_{0}=25\) (Table 3). The \(G\)-value shows that \(G>G_{0}\), thus indicating that the fossil sites in Shandong Province present a cohesive distribution. Based on the average calculation of all 133 fossil sites in Shandong and 16 prefecture-level administrative units, each should contain a minimum of 8.3125 (the integer is nine) fossil sites (Table 3). However, 12 prefecture-level administrative units do not match the average value of Shandong Province. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**S/N**} & \multicolumn{2}{c}{**Prefecture-Level**} & \multirow{2}{*}{**Number of Museums**} & \multirow{2}{*}{\(\mathbf{Y_{i}/\%}\)} & \multicolumn{2}{c}{\(\mathbf{Y_{i}\)** Cumulative**}} \\  & & & & & **Percentage/\%** & \\ \hline
1 & Linyi & 27 & 20.3008 & 20.3008 & \\
2 & Zibo & 22 & 16.5414 & 36.8421 & \\
3 & Weifang & 18 & 13.5338 & 50.3759 & \\
4 & Jinan & 17 & 12.7820 & 63.1579 & \\
5 & Taian & 11 & 8.2707 & 71.4286 & \\
6 & Qingdao & 10 & 7.5188 & 78.9474 & \\
7 & Yantai & 9 & 6.7669 & 85.7143 & \\
8 & Rizhao & 6 & 4.5113 & 90.2256 & \\
9 & Zazohuang & 6 & 4.5113 & 94.7368 & \\
10 & Jining & 6 & 4.5113 & 99.2481 & \\
11 & Binzhou & 1 & 0.7519 & 100 & \\
12 & Dezhou & 0 & 0 & 100 & \\
13 & Dongying & 0 & 0 & 100 & \\
14 & Heze & 0 & 0 & 100 & \\
15 & Liaocheng & 0 & 0 & 100 & \\
16 & Weihai & 0 & 0 & 100 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of imbalance index of fossil sites of the prefecture-level administrative units in Shandong Province.