**2. Methodology**

### *2.1. Geomantic Environment*

The geomancy derived from traditional environmental preferences leads to a highly developed cultural synthesis between the social and natural environment to a certain degree and emphasizes finding auspicious site locations with a favorable ecology and aesthetic perception [9]. Its continuing popularity in practice is used to promote harmonizing with ecological equilibrium [45–47]. This theory is useful to study ancient site selection patterns. However, we have to emphasize that we do not utilize the whole complex theoretical system of geomancy but are only concerned with the method of choosing a good environmental layout in relation to mountains and river.

Mountains, which embrace a site (usually with a river flowing through them), have been inspected to identify an enclosed space for living and justify whether they are beneficial for settlement development [48,49]. The optimal position of a mountain group is presented by Shang [50] as in Figure 1. Mountains behind the site stretch from near to far along the central axis. On the left and right sides, the mountains protect the site area. There are still mountains guarding the exit out of the closed space across the river in a certain distance. This spatial arrangemen<sup>t</sup> of mountains can provide a secure and stable environment. Besides that, it also blocks the cold monsoon from the north in winter and gain more warm sunlight in the south. It is conducive to the formation of a warm and humid microclimate. Moreover, the river can be examined to locate a relatively optimum position. A water city is an ideal site location embraced by a river on three sides. This situation is generalized as three kinds of positional relations, as in Figure 2. The inner side of the river bend, which is called the embraced side, is preferred, in contrast to the reserve side [51]. We can conclude that an auspicious water position has grea<sup>t</sup> influence on the residential area for the convenience of water supply and tra ffic [52,53]. It is also beneficial for forming a closed area for defensive purposes and a moderate microclimate in local environments [54,55]. Additionally, in an ideal landscape, forests are routinely considered to be involved in biological diversity, ecosystem service, and spiritual expectations [6,56,57]. Especially in this study, bamboo forest, which covers almost the whole mountainous area, is the main ecological type in the geomantic environment [58,59].

**Figure 1.** Schematic diagram of geomantic analysis. The closed space is circled by mountains and a river under ideal conditions for site selection.

**Figure 2.** Schematic diagram of the auspicious position of a water city. Positions (**<sup>a</sup>**,**b**) represent the place of the river bend with branches converging, while position (**c**) refers to the bay of the river.

In conclusion, the ideal location of the closed space consisting of mountains and a river lies back on a mountain and faces water toward the south [60]. It is the optimal geomantic environment appreciated by ancient peoples [61,62]. This environmental preference is of universal significance for the application of geomantic theory. We aimed to further study the ecological basis of site selection behind this environmental view and the behavior patterns in ancient times.

### *2.2. Edge E*ff*ect*

The regular law of site selection was mostly studied based on the geospatial distribution of archaeological sites [63]. For example, many researchers focused on the slope, aspect, proximity, etc. [64,65]. However, selecting living environments was more complicated for ancient peoples. The edge e ffect was rarely considered by researchers. It is widely believed that the di fferences and interactions of ecological variables in transition zones of two or several di fferent ecosystems may lead to the gradients starting at patch borders and proceeding along the edges [66]. The edge e ffect is a conspicuous consequence of the interactions between ecological units. The shape and size indices of a fragment patch, as well as the population structure, are widely used variables in edge e ffect calculations conducted by quantitative measurement [25,67,68]. In our study, we tried to organize the effective variables to describe the edge intensity in the locations of archaeological sites in the ecological transition zone. Even though we could not access the missing or not preserved sites, we focused on the general analysis of the known archaeological sites.

In the square bu ffer zone that is built with the edge width as its size for an archaeological object, the perimeter of each patch inside represents the actual contact interface used to exchange materials or energy with its neighboring patches. In this study, the fractal dimension index (FRAC) was used to reflect the edge complexity of each patch. In addition, the weights of di fferent ecotypes (W) were defined according to their contributions to the environmental structure and resource utilization in terms of the nature status in ancient times. With the descending importance of forest, water, farmland, bare land, and settlement, the weights were set to 2.00, 1.75, 1.50, 1.25, and 1.00, respectively. To quantify the edge e ffect, the edge intensity was expressed as follows:

$$E = \sum\_{j=1}^{n} \frac{p\_j}{L} \cdot FRAC\_j \cdot W\_{j\prime} \tag{1}$$

where *j* represents one of the independent patches and *n* is the total number of patches in the square bu ffer zone. *E* means the edge intensity in a square bu ffer zone whose total length of the four edges is indicated with *L*, and the perimeter of an independent patch inside is *Pj. Pj*/*L* refers to the relative edge size. *FRACj* and *Wj* are the multiplicative factors of each patch.

Edge e ffects usually show significant variations at di fferent spatial scales [30,69]. They are influenced by the transferring patch number and ecological constitution, as well as the interface size, shape complexity, and the weight of each component patch. Therefore, the scale problem is non-negligible for edge e ffect analysis. In this study, six edge widths of 100, 200, 400, 600, 800, and 1000 meters were selected to evaluate the changes of edge intensity. We aimed to test scale validity for analyzing the environmental preference of ancient sites. What was more important for us was to explain the site selection pattern based on the discrepancy of the edge e ffect in di fferent scales among the archaeological sites in ecological transition zone.

### *2.3. Ecological Network*

The ecological network can be built based on the interactive relationship between ecological patches that serve as network nodes connected by links that indicate the potential exchange of materials and energy between neighboring patches within an organism [35]. In network analysis, we use network properties and centrality measures to reflect the accessibility and the flow of energy, matter, or species to patches where archaeological sites are located. The general network is evaluated with circuitry (α), the node/line ratio (β), and network connectivity (γ), as presented in Table 1. The well-structured network represents the less possibility of ecological changes and the variation of edge e ffect. It can be used to measure the general stability in the geomantic environment of closed space. In fact, the centrality importance contributes more to the specific site selection pattern based on the analysis of every patch in the network.



Note: *e* means the number of connections, *v* means the number of nodes, and *p* is the number of disconnected subgraphs (*p* = 1 in this studied ecological network).

The centrality metrics are popular indices used to describe the importance of local patches in a network, which mostly include the degree, betweenness, and closeness [37,73,74]. In this study, we wanted to assess the comprehensive importance of each patch in the ecosystem. Therefore, the centrality importance (*CI*) index was defined as

$$CI = Be + \mathbb{C}l,\tag{2}$$

where the *Be* (betweenness), characterizing the importance of a patch by the number of times the information passes through the shortest path between two nodes, and *Cl* (closeness), describing the central rank of a patch by measuring the total sum of the minimum distances from the given node to all other nodes, are deemed to have the same importance, with weight coe fficients of 1. The relationship between the locations of ancient cities and high *CI* of a patch was constructed in this study to indicate superior status for getting more resources in network. It may represent one aspect of ancient site selection patterns.
