How can the landscape ecological security pattern be quantitatively optimized and effectively evaluated? An integrated analysis with the granularity inverse method and landscape indicators

The optimization of the landscape ecological security pattern aims to construct a suitable ecological environment and promote the harmonious development between humans and nature. The optimization model of the ecological security pattern for the main urban area of Chongqing was constructed with the granularity inverse method, minimum cumulative resistance model, and spatial network analysis method. We used ecological nodes to optimize the landscape ecological security pattern by organically combining the landscape quantity and spatial structure, and analyzed the effectiveness of the optimized pattern. The results were as follows: (1) The optimal granularity for selecting the ecological source in the study area was 500 m. There were 220 ecological sources with a total area of 188691.03 hm2 and a minimum area of 75.15 hm2. (2) The ecological buffer zone, protection and utilization zone, key development zone, coordinated control zone, and restricted development zone accounted for 57.78%, 20.87%, 12.36%, 6.48%, and 2.50%, respectively, of the total area. (3) The construction of the landscape ecological security pattern contained 70 ecological corridors with a total length of 415.89 km. The longest and shortest ecological corridors had lengths of 20.33 km and 1153.23 m, respectively. There were 17 ecological nodes of corridor-resistance and 27 ecological nodes of corridor-corridor. (4) 41 ecological node service areas were constructed, with a total area of approximately 236.0723 hm2, accounting for 0.04% of the total study area, and the largest and smallest ecological node areas were 6.0744 hm2 and 0.0057 hm2, respectively. (5) The optimized result of the landscape ecological security pattern converted 209.1384 hm2 of nonecological land into ecological land.


Introduction
Ecological security refers to the normal operation of the ecosystem in a specific region, the sound development and supply-demand balance of the environment, resources and human security in the ecosystem, and the social situation with human beings as the main body is not threatened by the external factors (Falkmark 2002;Li et al. 2019). It may provide guarantee for the complete ecological function and sustainability of an ecological economic system (Gao et al. 2017) and provide a direction for sustainable natural environment development (Yu 1996;Opdam et al. 2006), which emphasizes the balance between nature and ecology under the premise of human survival. It is difficult to achieve ecological security, which involves all aspects of society, economy, and natural ecology. However, the construction of ecological security patterns focuses on solving specific ecological problems, which is a quantifiable ecological practice method. The construction of ecological security patterns can be applied in urban ecological environment planning through practical applications.
The landscape ecology theory holds that there is a certain potential ecosystem spatial pattern in the landscape (Mayer et al. 2016;Turner 2005). It is composed of key parts of the landscape, and its orientation and spatial relationship are combined to form a landscape ecological security pattern (LESP) (Mo et al. 2017). The landscape ecological pattern reflects the ecological process of the regional landscape and has an important improvement or degradation significance for these processes (Mayer et al. 2016;Nakagoshi 2006, 2008;Opdam et al. 2006). Different landscape ecological patterns have different responses to the improvement or degradation of ecological processes (López et al. 2020).
The LESP provides important information for ecological protection and management. It can reveal the spatial distribution and concentration characteristics of landscape factors. Therefore, LESP studies should not only consider landscape patterns and processes but should also consider the impact of landscape factors reflecting the landscape structure and function on the ecological security (Zhao and Xu 2015).
The LESP is an important way to identify conservation and strengthen connectivity and management effectiveness on a regional scale. According to the feedback of landscape patterns and ecological processes, existing research shows that optimizing LESP is an effective way to support biological species, maintain natural ecological processes, improve regional ecological security, and achieve ecological security Peng et al. 2018a).
With the increasing development of landscape ecological planning research, LESP optimization started in the 1980s, and an independent ideology on the LESP was formed. LESP optimization aims to construct a scientific optimization spatial structure and ecological network with a practical guiding significance for protecting the ecological environment and promoting regional coordinated development. Currently, the graph theory and spatial simulation methods are adopted in the field of LESP optimization to realize its research objectives (Li and Xu 2010;Yu et al. 2018;Monaco et al. 2020).
At present, LESP optimization in many studies has focused on the construction of optimization models and standards. It is commonly accepted that the model of ecological sourceresistancesurface-ecological corridors and nodes Yu 1996)-can construct the LESP (Yu et al. 2017). However, different scholars tend to select different methods for identifying the ecological sources and ecological resistance surfaces. For example, Peng et al. (2018b) used ecosystem services to identify the ecological sources and adopted the circuit theory to model the ecosystem processes in heterogeneous landscapes by calculating the resistance or current and to thusly identify ecological corridors and key ecological nodes. Wang and Pan (2019) extracted ecological sources and corridors at three safety levels to form corresponding ESPs with the source-sink theory of landscape ecology, minimum cumulative resistance model, and geographic information system techniques. Peng et al. (2019) applied the ant colony algorithm and kernel density estimation to identify the range and restoration points of ecological corridors. LESP focuses on the mechanism research of the relationship between landscape structure and function. The research shows that there is a potential LESP, which can achieve stable ecosystem, orderly ecological process, and efficient ecological function.
Optimization standard identification is also highly effective for constructing and simulating LESP; it includes ecosystem services, ecological land, ecological risk, ecological factors, and socioeconomic conditions, in addition to an evaluation indicator and an integrated framework (Xie et al. 2015). However, different scholars tend to select different indicators and quantities, and a single standard is lacking. For example, Chang et al. (2011) attempted to integrate ecological factors and socioeconomic conditions via landscape function modeling and network analysis to establish strategies for ULP design. Sunderland et al. (2017) applied detailed socioecological methodologies in multifunctional landscapes and assessed the subsequent implications for conservation, livelihood, and food security. Ma et al. (2019) calculated the correlation and correlation coefficients between the ecological security and landscape pattern of the study region to provide useful information for ecological regulation and design. The optimization of urban LESP includes the adjustment of urban ecological landscape components, patch number, and spatial layout, so as to achieve the balance among the components, so as to improve the threatened and damaged ecosystem services, stabilize the overall urban ecological environment, improve productivity, and achieve the overall strategic goal of regional sustainable development. The specific requirements for the optimization of urban LESP include the optimization of natural economic social-dependent environment and spatial layout, regional industrial structure, future development direction, and resource utilization chain, so as to meet the basic needs of urban ecological construction.
Despite the rich research on LESP optimization model construction and optimization standard identification, the following two essential aspects have been less commonly studied over the long term: (1) the determination of important thresholds for constructing LESP is wanted (Desmet 2018), especially because the granularity threshold of ecological sources remains unclear and the shape and the scale threshold of ecological nodes are lacking Mõisja et al. 2016;Weber et al. 2006); (2) many studies have constructed corresponding ecological security patterns based on different standards, different ecological protection goals, or different security pattern levels; however, effectiveness and rationality evaluation after LESP optimization is deficient, especially because quantitative evaluation and indicator evaluation are missing (Jim and Chen 2003;Pili et al. 2019).
Urban planning should play a leading role during the process of civilization construction, which should drive urban development, adjust the urban spatial structure, and plan the urban ecological land layout . Chongqing's main urban area is situated in the core strategic area of Chongqing, China, which is in urgent need of scientific and effective planning and guidance. Against this background, our objective is to construct LESP for Chongqing's main urban area considering the granularity threshold of ecological sources and the shape and scale thresholds of ecological nodes. We employ the landscape indicator method to perform a quantitative evaluation to verify the effectiveness and rationality of the optimized LESP to verify the applicability and operability of the optimized LESP. Our research can serve as a valuable reference for promoting a new urbanization development plan for Chongqing, China, and offers important implications for improving landscape sustainability sciences.

Study area
The main urban area of Chongqing is located at 106°12′-106°59′E longitude and 29°7′-30°7′N latitude and covers 5466 km 2 , accounting for 6.6% of the total area of Chongqing. The main urban area of Chongqing encompasses nine administrative districts (i.e., Yuzhong, Jiangbei, Yubei, Shapingba, Nan'an, Jiulongpo, Dadukou, Banan, and Beibei) ( Fig. 1). Among them, Yuzhong District, covering an area of 23.71 km 2 , is the smallest of the nine districts, which hosts the Chongqing municipal government and is the mother city for the economic and cultural development of Chongqing.
The altitude of the main urban area of Chongqing ranges from 140 to 1327 m, with an average altitude of approximately 425 m. The elevation decreases from north to south. The landform is dominated by hills and low mountains. The river system is mainly composed of the Yangtze River and the Jialing River with 22 secondary rivers. The Jialing River and the Yangtze River meet at Chaotianmen Wharf, flowing from west to east through the city, and the confluence of the main body of water divides the main city into three parts. As a typical mountainous city, the main urban area of Chongqing has obvious characteristics of "mountain, water, and city." The mountains on the East and west sides are the natural vegetation greening areas. The semi natural and artificial forests on both sides of the central ridge line of the urban area play a role in conserving the biodiversity of the main urban area. Urban construction land exists and develops in a group spatial pattern. In recent years, due to the long-term inequality and imbalance between urban development and construction and the relationship between human and land, there are increasingly serious ecological and environmental problems in the main urban area of Chongqing, such as the decline of ecosystem services (Zhou et al. 2020), the urgency of ecological carrying capacity, and the enhancement of landscape fragmentation . However, as an important city in the upper reaches of the Yangtze River, it should take on the "upstream responsibility," give priority to ecology, and develop green, so it is urgent to optimize the LESP.

Data source
Four types of data were used in this study (Table 1): (1) Land use data. The land use data came from the Chongqing Key Laboratory of GIS application research, with spatial resolution of 30 m and data time of 2015. The selected first-level classification standard of the various land use types includes six categories: cultivated land, forestland, lawn, water area, urban and rural residential areas, industrial and mining area, and unused land, among which the construction land contains urban land, rural residential area, and other construction land.
(2) Remote sensing data. The remote sensing data mainly relied on the normalized vegetation indicator (NDVI) data of the main urban area of Chongqing. The NDVI data consisted of Terra-MODIS 16-day normalized vegetation indicator synthetic data with a spatial resolution of 250 m, all of which were archived and downloaded from NASA (http://ladsweb. nascom.nasa.gov).
(3) Basic geographic information data. The basic geographic information data mainly included digital elevation models (DEMs), ecological red lines, scenic spots, and high-geological disaster and high-risk areas of water, soil, and water flow. The DEM data used SRTM1 Arc-Second Global data with a spatial resolution of 30 m of 2015, from the Shuttle Radar Topography Mission (SRTM) jointly measured by the National Aeronautics and Space Administration (NASA) and National Imagery and Mapping Agency (NIMA). The corresponding download website is https:// gdex.cr.usgs.gov/gdex/. The data on the ecological red lines, basic farmland areas, risk areas of soil erosion, scenic areas, green land protection areas, and geological disaster-prone areas and other data were obtained from the Chongqing urban and rural master plan (2007-2020) (http://www.cqupb.gov. cn), after registration and vectorization, followed by unification to the geographic coordinate system of GCS_ WGS_1984 and projection coordinate system of WGS_ 1984_Albers, and a geographic database was uniformly established.

Research methods
The granularity reverse method In ecology, spatial granularity refers to the size of a particle representing the characteristic length, area, or volume (such as a square or cell) represented by the smallest identifiable unit in space (Wu et al. 2002;Wu 2004). The granularity inversion method is derived from the mathematical disproportion method (Wu et al. 2002;Peng et al. 2020), which is a method to determine the best ecological source in the construction of LESP. Firstly, a series of ecological landscape indicators are selected, and then the connectivity of the structure and quantity of ecological landscape components under different granularity levels is simulated and analyzed by setting different granularity levels. The selection of granularity size is critical for the extraction and reflection of information. Then the principal component analysis method is used to determine the optimal ecological landscape component structure. Finally, the original data is regressed to select the ecological source. It is necessary to first assume that there are different ecological source structures in the research area and then determine the existence of unique optimal source structures by inversion. In this study, landscape indicator analysis method was used to calculate the connectivity of these ecological landscape components, and principal component analysis was used to normalize the results. According to the change trend and quality change point reflected by the overall comprehensive score, the spatial structure of the optimal ecological source selection is counterselected to complete the process of ecological source selection. The specific method steps are as follows: firstly, considering the spatial scale, the ecological landscape of Chongqing's main urban area is simulated with different grid sizes in arcgis10.4 software to generate a series of continuous and different ecological landscape component structures; secondly, from the perspective of the integrity and connectivity of the landscape, nine landscape pattern indicators, namely, the number of patch components (NC), patch density (PD), the number of maximum patch components (Max NC), proximity mean distance (PROX_MN), proportion of like adjacencies (PLADJ), connectivity indicator (CONNECT), aggregation indicator (AI), patch cohesion indicator (COHESION), and landscape division indicator (DIVISION), were selected to calculate the landscape component structure at the landscape level. In order to achieve the scale effect and connectivity of landscape pattern, we selected three landscape indices in terms of area, shape, and aggregation to analyze the patches (Jia et al. 2019), as shown in the Table 2. Within the scope of landscape research at a specific time, the change of spatial sequence is the comprehensive result of the interaction between landscape patches. The change of a spatial pattern component often leads to the difference of connectivity and  (Wang and Liu 2020). The spatial pattern of landscape is not determined by the patch measurement of a single pattern, but by the combination of multiple landscape performance. Therefore, the correlation and interaction between landscape measures should be considered, which is defined as the symbolic effect of spatial pattern components on landscape measurement (Peng et al. 2010). The spatial measurement of landscape pattern can only be determined by selecting different landscape indicators to form the optimal landscape components. In FRAGSTATS software, the quantitative analysis of these ecological landscape component structures was carried out, and the indicator values of ecological landscape components under each granularity were obtained. Then, principal component analysis was carried out in SPSS based on landscape pattern indicator, and 21 landscape component structure indicators were calculated. The overall connectivity was scored by principal components, and the optimal landscape component structure was determined according to the scoring results. Finally, the optimal landscape component structure was determined landscape component structure as a reference, return to the original ecological source data to select part of the ecological source (Fig. 2).

Setting of the granularity level of the ecological sources
Ecological land refers to the type of land use that mainly provides ecosystem service functions in regional or urban land areas. Based on the 30-m resolution data of the main urban areas of Chongqing in 2015, this paper selected forestland, lawn, and water area as ecological land, dominated by forest land, accounting for 90.84% of the total ecological land area, followed by water areas, accounting for 8.52%. Chongqing is a special mountainous city, and its main urban area is also a typical mountainous city. This topographic landform is unsuitable for lawn growth and adaptation, accounting for only 0.64% of all landforms. The land use map and ecological map of the main urban area of Chongqing are shown in Fig. 3. Because the landscape structure of ecological land is composed of forest land, lawn, and water area, which are three landscape types under the first-level classification standard of the land use, this paper used the land use data of ecological land to generate landscape component maps with different granularity levels. To ensure the accuracy of subsequent data analysis and ensure its applicability, the principle of granularity setting focused on the range of 50 to 1500 m, and the granularity was increased accordingly at 50-m intervals up to a granularity of 600 m, after which the granularity was increased every 100 m, thereby constructing a total of 21 landscape component maps of the ecological sources at different granularity levels (Fig. 4).
With increasing granularity, the landscape component of the ecological source decreased, and the integrity increased. Because the ecological land in the main urban area of Chongqing runs from north to south and exhibits a relatively uniform strip-like distribution in the east, central, and west areas, the core form of the ecosystem did not change much. However, in the process of increasing the granularity, its ecological advantages of the larger ecological patches were expanded, and the surrounding ecological patches were a ij is the adjacent area of i plaque and central j plaque, h ij is the shortest distance between i plaque and adjacent j plaque.
Reflects the average distance between the edge of the plaque and the center of the plaque.

Area
Proportion of like adjacencies (PLADJ) is the inclusion number of barycenter points of i patch and adjacent j patches; g ik is the inclusion number of barycenter points of patch i and all adjacent k patches.
Refers to the spatial components of the landscape as scattered patches, and the aggregation degree between patches.
Agglomeration Connectivity index (CONNECT) Â 100 C ijk is the connectivity status of patch j and k related to i type patch in the study area, and N i is the number of i type patches.
Reflects the degree of attribute connectivity among landscape components.
Agglomeration Aggregation index (AI) Reflect the spatial aggregation degree of patches of a certain landscape type in the study area.
Agglomeration Patch cohesion index (COHESIO-N) P ij is the perimeter of patch j of landscape i, a ij is the area, and A is the total number of grids.
Represent the natural connectivity of a certain patch type in a region.
i a ij is the area of patch j of landscape i, and A is the total landscape area.
Reflects the degree of landscape segmentation in the region, which refers to the proportion of patch area to the total landscape area.  continuously merged to form a larger patch, while the highly fragmented and smaller ecological patches were gradually eliminated.

Principal component analysis to determine the best ecological component
Principal component analysis (PCA) is a multivariate statistical analysis method. Its principle is to select less variables with high importance (retaining original features) from multiple variables through linear transformation or rotation (Liu and Shen 2007;Johnson and Wichern 1998). The principle of determining the best ecological component using PCA method is to determine the optimal landscape structure affecting the landscape pattern by principal component analysis (Pan and Liu 2015). Through the determination and analysis of the contribution rate of landscape indicators such as connectivity, it is found that the ecological source structure with the highest comprehensive score exists, and the only optimal ecological source is determined by counter evidence Su et al. 2016). According to the ecological components of the grain size, the best ecological source structure was selected. The core idea of PCA can be expressed as follows: if there are n random variables, they can be expressed as x 1 , x 2 , ..., x n . After standardized processing, the linear combination is carried out according to the data characteristics, and a few new comprehensive variables are obtained to reflect the change characteristics of the data. The formula of comprehensive variable can be expressed as follows: Þ , M i is the weight of the ith known sample point, and m is the number of known sample points. According to the principal component analysis, the results will get the eigenvector and eigenvalue of the principal component. The proportion of the ith eigenvalue in the total number is the contribution rate of the main component M.

Minimum cumulative resistance model
The minimum cumulative resistance (MCR) model refers to the cost of species moving from "source" to "sink"; it was proposed by Knaapen et al. (1992) in 1992 and then applied to the study of two-dimensional spatial expansion of various natural ecological or man-made processes (Evans et al. 2017;Junqueira et al. 2017;Jiang et al. 2019). Because of its simple data structure, good applicability, and convenient visualization results, the MCR model was mostly used to evaluate landscape connectivity, and optimize LESP and urban land use planning (Li et al. 2015). It is one of the best tools to solve the contradictory relation between human and land (construction demand-ecological space).
First of all, we evaluated the ecological resistance, which is the cognition of maintaining ecological sustainability and maintaining integrity under various risks in the ecosystem. Refer to Ye et al.'s (2015) indicator evaluation system for the construction of ecological resistance surface model. Construct the evaluation indicator system of ecological resistance in the main urban area of Chongqing as shown in Table 3, and stipulate the safety level of each constraint factor, i.e., 9, 7, 5, 3, and 1, representing extremely unsafe, unsafe, low safety, medium safety, and high safety, respectively. The smaller the value of the security level, the higher the degree of ecological security and the stronger the ability to resist external interference.
Then, we adopted the minimum cumulative resistance model to calculate the minimum cumulative value of the landscape resistance and applied the minimum cumulative resistance surface to replace the ecological operation one. Based on the comprehensive ecological resistance surface of the main urban area of Chongqing, the cost distance according to the ArcGIS 10.4 Cost Distance Tool was used, and the counterselected ecological source area was set as the source, while the comprehensive ecological resistance surface was set as the cost to obtain the minimum cumulative resistance surface of the landscape ecology of the main urban area of Chongqing. The equation of the minimum cumulative resistance model is as follows: where D ij is the diffusion distance of the species leaving source j through landscape i, R is the resistance of the landscape i, and MCR is the minimum cumulative resistance of the species diffusing from source j to a certain point in space. The function f is unknown but reflects the proportional relationship between the material MCR and variable D ij ? R t . The resistance R t of each landscape to the spread of a species was determined by the base level characteristics of the landscape and the diffusion ability of the species.

Determination of ecological nodes and service area analysis method
The ecological node is the vulnerable part of the ecological network, which is the intersection of the ecological corridor and the maximum ecological resistance path, that is, the most vulnerable part of the ecological corridor, so it needs to focus on the construction (Xia et al. 2017;Wang et al. 2021). Considering that the intersection of different ecological corridors is the key part of material and energy exchange between ecological flows, which is conducive to the connection between ecological sources, the intersection of ecological corridors is also regarded as the ecological node.
A service area is defined as a point centered on a specified point and encompasses all areas reachable to the edge within a certain resistance range. It can represent the shape and size threshold of the ecological node. Using the service area analysis principle in spatial network analysis, considering the spatial location and accessibility of the ecological node network, the polygon range that depends on the network is generated according to the analysis points, which can well express the dependence relationship between the polygon and the network. This idea can better fit the calculation of the shape and size of the ecological node. The analysis shows that the polygon range of the network can better represent the dependence between the polygon and the network. In this study, the service area analysis method was used to calculate the shape and size of ecological nodes in the landscape ecological pattern. The calculation of the extent and shape of the ecological node is mainly based on two points: one is the trend of the ecological corridor, the shape and size of the ecological node should fit well with the ecological corridor. Second, the calculation standard of ecological nodes has a certain scale of areal landscape components, which should have appropriate scale in space. From the geometric characteristics, circles have the best aggregation. Considering that service area analysis constructs a range of polygons based on the center location, this process is similar to the geometric characteristics of circles in calculating the size and shape of ecological nodes in the form of circles.
The steps of calculating the range and shape of the ecological nodes with the service area analysis method in spatial network analysis were as follows: (1) In the process of selecting the inverse of the ecological sources based on the granularity inverse method, the granularity L, i.e., the result of the optimal landscape component structure, was used as a reference standard, which calculated the scale for of ecological nodes.
(2) According to the majority principle, the formation conditions of ecological nodes state that when the scale of the ecological landscape patch is larger than half the granularity, the ecological node exists as a landscape component. The geometric shape of the ecological node had the characteristics of a circle, and the radius calculation equation of the ecological node is shown in Eq. (10). (3) The corridor in the LESP was the operational network in the network analysis. (4) With the ecological node as the analysis center and R as the analysis radius, the specific scope of the ecological node was determined to obtain the shape and scale of the service area of the ecological node.
L is the granularity, which is the result of the optimal landscape component structure, and is the standard for calculating the scale of ecological nodes; R is the analysis radius.

Evaluation indicator establishment after optimization
Through the calculation of landscape pattern indicator, the results of LESP of Chongqing main urban area after optimization were evaluated. In this study, the indicator of patch type level indicator and landscape level indicator were selected for quantitative analysis; the indicator of patch type level includes patch area ratio (P), patch density (PD), maximum patch indicator (LPI), landscape shape indicator (LSI), and fractal dimension (FRAC); the indicator of landscape type level includes Shannon diversity indicator (SHDI), Shannon evenness indicator (SHEI), and landscape connectivity indicator (CONTAG).

Determination of the best ecological source
The results of different granularities of ecological land The landscape indicator calculation results for the 21 groups of different granularities of ecological land are listed in Table 5.
According to the results, a statistical scatter plot of the single-landscape indicator was generated, as shown in Fig.  5. It can be intuitively observed that under the singlelandscape indicator, the landscape indicator value changes with increasing granularity.
NC decreased sharply from more than 4000 m to less than 1000 m when the granularity increased to 300 m and then gradually decreased to less than 250 landscape components from 300 to 1500 m, and 300 m was the qualitative change point for NC. The change trend of PD was similar to that of the landscape components, and 300 m was also the qualitative change point, while PD first decreased sharply before this point and then slowly thereafter. The overall density decreased from nearly 2 to nearly 0. Max NC generally exhibited a fluctuating upward trend, reaching its highest value at a granularity of 500 m, and Max NC approached 80. The trend of PROX_MN was similar to that of NC and PD, and 300 m again represented the qualitative change point, and the overall value decreased from more than 6000 to close to 0. The proportion of like adjacencies generally exhibited a uniform downward trend, from less than 90% to approximately 45%, but the qualitative change point was still 300 m. The connectivity indicator exhibited a fluctuating upward trend before 600 m, reached a peak of approximately 0.6, decreased abruptly thereafter, and became randomized after 800 m. The cohesion indicator generally exhibited a fluctuating decrease trend, which was basically divided into two segments before and after the qualitative change point. The qualitative change point was 500 m, and the overall cohesion value decreased from less than 1 to approximately 94%. The DIVISION indicator exhibited a W-shaped fluctuation trend in the middle section and reached its lowest value at 550 m. The trend of the aggregation indicator was similar to the trend of PLADJ and is not described again.
The results of principal component analysis to determine the best ecological component According to the above single landscape indicator, we calculated the comprehensive score of landscape component structure of ecological source areas under each granularity (Fig. 6), so as to select the optimal landscape component structure and provide reference for scientific and objective selection of ecological source areas.
The overall trend of the score was as follows: with increasing granularity to 450 m, the comprehensive score sharply decreased and there was a qualitative change point at 500 m. The comprehensive score increased slightly and then slowly and steadily decreased thereafter to its lowest value. As the granularity continued to increase, small ecological patches were gradually eliminated and became merged, which enhanced the stability of the landscape component structure and decreased fragmentation.
The granularity level of 500 m was the qualitative change point in the landscape component structure, and its integrity was the best, while the left and right sides of this point exhibited a downward trend in the comprehensive score, indicating the optimal landscape component structure of the ecological source. Finally, 500 m was adopted as the optimal granularity to determine the ecological sources.
At a granularity of 500 m, the corresponding number of ecological patch components was 568, which indicated that there are 568 ecological sources in the main urban area of Chongqing with a decisive role in the ecosystem process.
Based on the optimal ecological patch components and sorting according to the size of the ecological patch area, the ecological area of the smallest ecological patch (No. 568) was the smallest ecological source of the research area. Therefore, the ecological source area should be larger than 75 hm 2 , and the ecological patches with corresponding areas larger than 75 hm 2 should be chosen as the ecological sources of the main urban area of Chongqing. We extracted the raster data of the landscape ecological component structure at a granularity of 500 m into ArcGIS10.4, and the ecological patches were converted into ecological source areas with conversion and  intersection tools, eventually establishing the optimal ecological source structure of the main urban area of Chongqing. According to the spatial distribution of the ecological sources, a total of 220 ecological sources were identified, as shown in Fig. 7.
The number of ecological sources in the main urban area of Chongqing was large and there were large-scale differences. The number of ecological sources was 220, with a total area of 188691.03 hm 2 . Among them, the largest ecological source area covered 24257.07 hm 2 , accounting for approximately 12.86% of the total ecological source area. It is located in the northern part of the main urban area of Chongqing and is part of the forest land area connecting Zhongliang Mountain and Longwangdong Mountain. The source area often plays a leading role in maintaining regional ecological security and ecological processes. Ecological source areas should be protected and constructed, and enhanced measures such as buffer zones should be adopted to promote their ecological services. The smallest ecological source area covered 75.15 hm 2 , accounting for approximately 0.04% of the total ecological source area. It is a small-scale ecological patch that may impose a major impact on the ecosystem of the main urban area of Chongqing. The scale of the subsequent constructed new ecological sources should be considered.

Optimization of the landscape ecological security pattern
Single-factor and comprehensive evaluation of the ecological resistance Based on the spatial data of the ecological resistance in the study area (Table 3), single-element distribution maps of the ecological resistance were generated in five aspects, i.e., Fig. 7 Ecological sources of the main urban area in Chongqing terrain slope, vegetation cover, land cover, ecological sensitivity, and ecological importance, as shown in Fig. 8.
The ecological safety of the ecological source areas was comprehensively evaluated by combining GIS spatially weighted superposition analysis technology and the comprehensive indicator method. According to the indicator weights in Table 4, the raster calculator was applied to analyze the resistance value of the ecological resistance factors in the five categories, and the comprehensive ecological resistance surface of the main urban area of Chongqing was obtained. The comprehensive ecological resistance surface is shown in Fig.  9a.
The minimum cumulative resistance surface of the landscape ecology of the main urban area of Chongqing is shown in Fig. 9b.
The area with a low resistance value was the ecological source and its periphery. As the distance from the ecological source increased, the minimum cumulative resistance value of the landscape ecology gradually increased, and the resistance value reached its maximum in the most well-developed regions of the main city.
The minimum cumulative consumption distance surface of the landscape ecology was divided into five grades according to the natural fracture method (Fig. 10), namely, an extremely low-resistance zone, a low-resistance zone, a moderateresistance zone, a high-resistance zone, and an extremely high-resistance zone.
The ecological buffer zone is the extremely low-resistance zone, covering an area of 313073.46 hm 2 , accounting for 57.78% of the total area. The conservation and utilization zone is the relatively low-resistance zone, covering an area of 113099.13 hm 2 , accounting for 20.87% of the total area. The key development zone is the moderate-resistance zone, covering an area of 66953.88 hm 2 , accounting for 12.36% of the total area. The coordinated control zone is the relatively high-resistance zone, covering an area of 35 101.26 hm 2 , accounting for 6.48% of the total area, while the restricted development area, the area with the extremely high resistance, covers an area of 13569.84 hm 2 , accounting for 2.50% of the total area. In this paper, the minimum cumulative resistance surface was adopted as the cost surface operating the ecological flow, utilizing the idea of hydrological analysis to identify the ecological corridors (Beier and Noss 1998). First, we filled the depressions, calculated the flow direction across depressionfree, and calculated the cumulative confluence amount. Then, we repeatedly adjusted the threshold, thereby extracting portions of the confluence greater than 1500 to obtain a series of operations just like the river network and determined the valley region and performed vectorization and smoothing. Finally, the least-resistance path in terms of the ecological flow in the study area was obtained, and the path connecting the various ecological sources is the ecological corridor.
Generally, there was certain distance between the various ecological sources in the regional space, which should be connected by the ecological corridor. The ecological nodes occurred at the most vulnerable links of the ecological corridor, namely, the intersection of the ecological corridor and the path with the highest ecological resistance. Similarly, with the minimum cumulative consumption resistance surface as the cost surface of the ecological flow operation, the ridge line on the ecological operation surface was determined with the use of the hydrologic analysis module, and the ridge line location is the position with the highest resistance to the ecological process. The ecological corridor was superimposed on the ridge line, and the corresponding ecological node was determined according to the intersection of the ridge line and the ecological corridor. Hence, the corridor-resistance ecological node was thus generated, and the intersection of the corridor itself was considered the corridor-corridor ecological node. The LESP of the main urban area of Chongqing is shown in Fig.  11.
The LESP of the main urban area of Chongqing reveals that there were 220 patches in the ecological source area, with a total area of 188691.03 hm 2 . The largest ecological source covered an area of 24257.07 hm 2 , accounting for 12.86% of the total ecological source area. It was located in the northernmost part of the main urban area of Chongqing and was part of the forest land. The total number of ecological corridors was 70, and the total length was 415.89 km. The longest corridor was 20.33 km, accounting for 4.89% of the total length, which was the junction of Zhongliang Mountain and Longwangdong Mountain in the northern section of Chongqing's main urban area. The length of the shortest corridor was 1153.23 m, is the area of a certain landscape patch type, and A is the total area of the whole landscape.

0-100
The smaller the P, the less A' type patches in the landscape.

Maximum patch index (LPI)
LPI ¼ max a 1 ð ð ;a2;⋯;anÞ AÞÂ100 a 1 , a 2 ... a n are the area of a certain type of landscape patch, and A is the total area of the overall landscape.

1-100
The index represents the influence degree of the largest patch type in a type of landscape Landscape shape index (LSI) E is the sum of the perimeter of all patches in a landscape, and A' is the total area of the landscape.
The larger the LSI, the more irregular the shape of landscape patches.
Fractal dimension (FRAC) À Á P is the perimeter of a certain patch type in a landscape, A' is the total area of the patch type.
The index represents the complexity of plaque shape.
Landscape type level includes Shannon diversity index (SHDI) Þ p i is the area ratio of the ith ecological land to all ecological land.
The index can be used to measure the complexity of ecological land landscape system and characterize landscape heterogeneity. The higher the value is, the more types of landscape patches and the higher the diversity are.
Shannon evenness index (SHEI) p i is the area ratio of the ith ecological land to all ecological land, and m is the number of ecological land types.

0-1
The index indicates whether the landscape system of ecological land is dominated by one or a few dominant patch types.
Landscape connectivity index (CONTAG) a is the total number of a certain patch type, p ij is the probability of two randomly selected adjacent grids, which belong to type i and type j respectively.

0-100
The higher the value, the better the connectivity of patches. accounting for approximately 0.28% of the total length. There were 17 plateau ecological nodes, namely, the ecological nodes of corridor-resistance, and 27 network strategic nodes, namely, the ecological nodes of corridor-corridor (Table 5).

The results of ecological node optimization
The optimal landscape component structure corresponded to a granularity of 500 m, and the radius of the ecological node suitable for the main urban area of Chongqing was calculated with Eq. (10) as 200 m. With the use of service area analysis as part of spatial network analysis, the detailed shape and size of each ecological node were calculated according to the above steps (Fig. 12).
When ecological nodes occurred close to each other, there were overlapping service area, and they were merged into one. The ecological nodes constituted 41 service areas with a total area of approximately 236.0723 hm 2 , accounting for 0.04% of the main urban area of Chongqing. Among these nodes, the largest ecological node area was 6.0744 hm 2 , and the smallest ecological node area was 0.0057 hm 2 .
The patches of nonecological land at the ecological nodes were converted into patches of ecological land, and the target landscape types of ecological node construction were forest land, lawn, and water area. The principle of landscape conversion was based on the principle of proximity and the principle of optimal cost. The land type conversion results of the ecological service area in the main urban area of Chongqing are summarized in Table 6. After optimization of the landscape pattern, the landscape type distribution map of the main urban area of Chongqing was generated, as shown in Fig. 13. According to Table 3 and Fig. 13, we could see the range of ecological nodes and the statistical results of landscape transformation. Among them, 14 cultivated land patches were converted into forest land, with a total area of 77.85 hm 2 ; 3 cultivated land patches were converted into water area, with a total area of 12.22 hm 2 ; and 21 construction land patches were converted into forest land, with a total area of 105.57 hm2. A total of 3 construction land patches were converted into water area, with a total area of 13.51 hm 2 . All the land use patches converted into ecological land patches were 209.14 hm 2 .
The area of construction land converted to forest land is the largest, accounting for 50.48% of the total converted area. This is due to the spatial distribution of land use in the main urban area of Chongqing, the largest number and scale of forest land in the ecological land, the greatest possibility of nonecological land and forest land patches in the service area becoming the closest relationship, and the principle of optimal conversion cost. The optimized landscape pattern of the main urban area of Chongqing in 2015 was as follows: forest area accounts for 38.03%, lawn area accounts for 0.27%, water body accounts for 3.57%, farmland area accounts for 20.16%, unused land area accounts for 0.01%, and cultivated land area accounts for 37.97% (Table 7).

Effectiveness evaluation of landscape ecological security pattern optimization
The raster data of the land use types in the main urban areas of Chongqing after optimization and the raster data of the ecological land of Chongqing were imported into Fragstats4.2 software to calculate the above landscape indicators. The results are listed in Table 7 and 8.
According to the landscape indicator calculation results of the ecological land before and after LESP optimization of the main urban areas of Chongqing, it is concluded that before and after LESP optimization, the proportion of the forest land patch area was the highest, covering 90.8423% and 90.8395% of the total area, respectively, and the proportion of the lawn patch area was the lowest, mainly based on the type of forest land patch, which was roughly the same as the landscape pattern in Chongqing. Compared with the data before optimization, the proportions of the forest land and lawn areas decreased slightly, while that of the water area increased slightly after optimization, but not significantly. PD of the forest land and water area increased, while PD of the lawn area remained unchanged. LPI decreased slightly, and FRAC of the forest land area increased, whereas the lawn area did not change, but the value for the water area decreased. In terms of SHDI, SHEI, and CONTAG, the connectivity of landscape pattern of ecological land decreased insignificantly after optimization. Overall, the overall patch density of ecological land became better after optimization, although the overall value did not change much, it also indicated that the overall landscape structure of ecological land was less fragmented after optimization.
Based on the calculation results of the landscape indicator based on land use and LESP optimization in the study area, it is found that after LESP optimization, the percentage of forest land and water area had increased, while the lawn area percentage did not change. PD of the farmland area increased considerably, that of the lawn area remained unchanged, and that of the forest land and water area decreased and increased slightly, respectively. LPI remained basically constant, and the LSI indicator slightly increased. In terms of FRAC, that of the forest land area increased, that of the lawn area remained the same, and that of the water area decreased, which was consistent with the changes in ecological land. Regarding SHDI, SHEI, and CONTAG, all values decreased slightly. In general, the overall numerical change in the land use landscape indicator was larger than that in the ecological land after optimization, and the land use ratio of the ecological land had clearly increased, indicating that optimization was effective and could provide a reference for actual applications.

Comparison of different landscape ecological security pattern
The construction of LESP is the foundation of regional ecological sustainable development, which plays a guiding role in spatial planning and orderly expansion of land use, and comes true the corresponding protection of important ecological source areas supporting regional environment. In the past researches, researchers conducted different degrees of reconstruction (Wang and Pan 2019), assessment and optimization (Yu et al. 2018) on ecological source areas, ecological corridor (Hepcan and Özkan 2011), ecological nodes, and network structure for different planning purposes. The main methods included MCR model, and least-cost path models (Klar et al. 2012) to assess the importance of ecosystem services (Peng et al. 2018a(Peng et al. , 2019Fu et al. 2020), coefficient of sensitivity (Gurrutxaga et al. 2011), and ecological risk . Patch aggregation and landscape connectivity  were used to build ecological network (Aminzadeh and Khansefid 2010), at the same time, integrating the fragmented landscape ecology in order to reshape and optimize the regional ecological security pattern. The structure results are different for different research contents, research purposes, and research objects. Table 9 summed up the research results Fig. 13 Land use of the main urban area in Chongqing after landscape security pattern optimization of different international scholars on the construction and optimization of ecological landscape, and the research methods are also different. We reviewed the relevant research on LESP over the last 10 years, and concluded the study areas, research framework, and research results. We found that there are no studies done to further optimize the reconstructed ecological pattern nodes, evaluate the effectiveness of the optimized ecological pattern from the perspective of landscape heterogeneity, and plan the overall layout of regional landscape from the perspective of land use. The granularity inverse method was used in this study, and the best ecological landscape component structure of Chongqing urban area is selected by combining granularity and connectivity, which can provide an objective reference for the selection of other ecological sources. This method has more theoretical basis and objectivity than the traditional methods, and the principal component analysis method effectively avoided the subjectivity in the research. In this study, the optimal threshold of the optimal ecological node was determined, and the nearest neighbor principle and the optimal cost principle were adopted to provide a detailed practical basis for the accurate calculation of its shape and scale (Table 9).

Research advantages and development proposals
This study constructed the ecological security pattern scientifically and completely, including the scientific screening of ecological source areas, the construction of ecological resistance surface, and the identification of ecological corridors and ecological nodes. Different from the subjectivity and randomness of traditional ecological source selection, we chose methods with different regional applicability based on the granularity reverse method, which could provide reliable basis for ecological construction. In the construction of ecological resistance surface, we avoided the single consideration of the current situation of land use in the previous studies, and selected the ecological indicator factors which had strong correlation with the landscape ecological security process. The ecological resistance surface indicator factor system constructed was scientific, rigorous, and practical. Combined with the special mountain structure in the study area, the identification of ecological corridors and nodes based on the minimum cumulative resistance surface was pertinence and operable; on the other hand, the content of LESP optimization included two parts: landscape quantity and spatial structure optimization. There was no better optimization method to combine them in the present research results. Based on the microscale, this study constructed the ecological node service area, obtained the optimized land use spatial structure from the patch transformation idea of the ecological node service area, and carried on the quantitative analysis of the optimized landscape patch, which reflected this demand better. At the same time, the existing research scope of landscape ecological pattern was mostly large-scale area. Some suggestions are put forward for the future planning of the main urban area of Chongqing: (1) Reserve the ecological source area and ecological corridor to form the regional ecological network, ensure the scale of the ecological source area, and continue the "multi center, group type" urban pattern development.
(2) In the urban boundary development area, we should pay attention to the proportion of ecological land, increase the number and connectivity of green space, coordinate the relationship between urban green space and ecological landscape, and form an environment suitable for production and life. (3) In the built-up area, the land should be reasonably distributed according to the current landscape situation, so as to reduce the fragmentation of ecological landscape types, increase the scale of ecological patches, form a pattern of ecological landscape encircling and infiltrating, and form an ecological livable city development pattern with the ecological source as the green center and the blue-green ecological corridor in series.   This paper defined which should have a high priority to be kept in a natural state as an aim of land use plans. Klar et al. (2012)

Conclusions
In this study, the main elements of LESP of the main urban area of Chongqing, namely ecological source, ecological corridor, and ecological node, were taken as the research object to construct the LESP. On this basis, the optimization of urban landscape ecological pattern was studied and the optimization results were evaluated. In general, the proportion of ecological land increased significantly and the fragmentation of landscape decreased after optimization, which indicated that the optimization was effective and provided rational reference for urban landscape ecological planning: (1) Taking the ecological land in the main urban area of Chongqing as the research object, the ecological landscape types determined by the ecological benefit analysis are selected, and the ecological landscape component structure is generated according to different granularity. The landscape pattern indicator was selected from the perspective of overall connectivity by using the granularity reverse method and principal component analysis, and the landscape component structure of each granularity was analyzed. Finally, the overall landscape component with the best connectivity was obtained by scoring. Five hundred meters was the most suitable reference for the selection of ecological source areas, and has the lowest degree of obstruction to the operation of ecological flow.
(2) By constructing the single factor evaluation indicator system of ecological resistance and constructing the minimum cumulative resistance surface, the minimum cumulative resistance surface of landscape ecology in the main urban area of Chongqing was divided into ecological buffer area, protection and utilization area, key development area, coordinated control area, and restricted development area, accounting for 57.78%, 20.87%, 12.36%, 6.48%, and 2.50% of the total area. (3) Taking the minimum cumulative consumption resistance surface as the cost surface of ecological flow operation, the ecological corridor and ecological node are constructed by using the hydrological analysis. There were 70 ecological corridors in the LESP in the main urban area of Chongqing, with a total length of 415.89km. There were 17 ecological nodes of plateau type, namely corridorresistance, and 27 are network strategic nodes, namely the ecological nodes of corridor-corridor. (4) Based on the analysis method of service area in network analysis, the radius of service area was calculated with reference to the granularity of optimal landscape components, and the shape and scale of service area of ecological node were obtained. The conversion principle of nonecological land in the service area of ecological node was the principle of nearest neighbor and the principle of optimal cost. The ecological nodes form 41 services; the total area was about 236.0723 hm 2 , accounting for 0.04% of the main urban area of Chongqing. From the comparative analysis of landscape indicator, the optimized landscape pattern results could effectively improve the overall connectivity of the ecosystem and reduce the fragmentation degree of patches. The spatial distribution of this ecological key layout was affected by the current situation of land use and topography. It was shown that the spatial distribution of these ecological key layout was more evenly distributed in the central, southern, and northern parted of the overall pattern, and presented a north-south zonal distribution, which showed the lack of planning of the main urban area of Chongqing and the ecological vulnerability as a typical mountain city.
Author contribution G. D. and C. L. designed the study. J. Y. performed the analysis and prepared the manuscript. C. L. and J. Y. assembled input data, implemented the model, and analyzed output data and results. C. L. conducted data collection and preliminary analysis. G. D. and C. L. revised the original manuscript. G. D. and J. Y. validated modeling results and discussed the results and implications. All authors participated in the writing of the manuscript. Availability of data and materials All data are processed by the author, true, and effective, and all data generated or analyzed during this study are included in this article.

Declarations
Ethical approval All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee.
Consent to participate Informed consent was obtained from all individual participants included in the study.
Consent to publish The manuscript is approved by all authors for publication.
Competing interests The authors declare no competing interests.