Analysis of the effect of landscape component classification on landscape diversity index

The landscape diversity index (LDI) is an important level in biodiversity conservation, and its scale dependence has an important role in regional landscape planning and biological conservation. The aim of this study is to analyze in depth the effects of spatial scale changes in the classification of different landscape components on LDI and to explore the thresholds of LDI. The classification of landscape components was accomplished in the ArcMap environment using fusion and merging tools, and the LDI thresholds and scale changes were quantitatively assessed by LDI values. The results show that there are differences in LDI values for different classifications, and the threshold for LDI without considering scale changes can be interpreted as: 0.4215 ≤ LDI ≤ 1.9754. The grain sizes suitable for landscape diversity analysis are 160m and 1280 m, and the effective amplitude range of the I, II and III land type is 9~31 km, while the effective amplitude of three land use types is 20∼31 km, relatively lagging behind. However, when considering amplitude changes, the LDI threshold can be interpreted as 0.3027 ≤ LDI ≤ 2.0947, which is suitable for large-scale regional landscape diversity studies when the grain size is large. In conclusion, the essence of landscape diversity change with scale is caused by changes in the number and area of landscape components, and the threshold analysis should not only take into account the grain size and amplitude, but also consider the landscape background of the study area.


Introduction
In addition to genetic and species diversity, ecosystem and landscape diversity are an important level of biodiversity (Walz 2015).The study of biodiversity itself is scale-dependent.Studies on small scales (microdiversity) include genetic diversity, organizational diversity, etc, studies on medium scales (mesodiversity) include individuals, species, populations and systems, and the main object of studies on large scales (macrolevel) is landscape diversity (Liu et al 2003).Researchers use biodiversity to capture landscape diversity.For example, pollen type diversity is a reliable index for capturing vegetation structure and landscape diversity (Matthias et al 2015).Some scholars have also used arthropod morphological species diversity profiles to quickly assess landscape biodiversity (Hackman et al 2017).Taxonomic diversity of groups has also been used to predict tropical rural landscape diversity (Smith and Mayfield 2015 ).In recent years, landscape diversity has been quantitatively expressed by Shannon diversity index (SHDI) (Lin et al 2020, Gao and Li 2021, Yi and Wang 2021) or Simpson diversity index (SIDI) (Li et al 2008).However, more researchers choose SHDI and rely on the results of fragstats landscape pattern index software for diversity analysis.
Landscape diversity plays an important role in human production and life (Schippers et al 2015).For instance, it has been found that higher landscape diversity mitigates the impact of extreme weather conditions on crop yields.Consequently, the yields of winter wheat, corn and soybean have increased in to varying degrees (Nelson et al 2022).Landscape diversity has an impact on animal richness.Studies have shown that increasing landscape diversity fosters the proliferation, richness and diversity of birds (Ke et al 2018, Zhang et al 2023).At the same time, landscape diversity shapes farmland species diversity and provides guidance for arthropod diversity conservation (Van Schalkwyk et al 2021, Ali et al 2022).For example, increased landscape diversity increases correlates with greater beetle richness, which promotes the growth of predators (Massaloux et al 2020, Raderschall et al 2022, Deppe and Fischer 2023).Moreover, high landscape diversity had a positive effect on the richness of bee species and on successful bumblebee breeding (Carrie et al 2017, Schweiger et al 2022).
To some extent, landscape diversity determines vegetation diversity.Studies have found that in highly dispersed urban areas, the plant diversity of residual vegetation may depend on landscape heterogeneity (Liu et al 2022), and functional diversity may increase with the increase of landscape heterogeneity (Cursach et al 2020).There are differences in plant species diversity in different landscapes.For example, the species richness and β diversity in the calcareous mosaic landscape are higher than those in the siliceous mosaic landscape (Jentsch et al 2012).However, the study of landscape diversity is also dependent on the landscape context, and natural and geographical micro-regions have an important role in the complex analysis of landscape diversity (Brodka et al 2021).For example, in complex landscapes, landscape diversity was not significantly correlated with insect richness, while it was significantly negatively correlated in simple landscape contexts (Rosch et al 2013).It has also been demonstrated that species richness is high in small patches of habitat in remnant grassland semi-natural agricultural landscapes (Lindborg et al 2014).
In addition, the scale-dependent characteristics of landscape diversity are of greater interest to landscape ecology studies (Zubaida et al 2019, Yang et al 2021, Dong et al 2023).Despite the important impact of landscape patterns on plant diversity, there is a scale effect (Fan et al 2017).A study of spatial scale effects on landscape patterns in a typical arid oasis area found that diversity increased with the widening of amplitude in the 1-15 km range (Huang et al 2018).The results show that within a range of less than 5 km, landscape diversity changes irregularly, while beyond 5 km, it fluctuates until the stabilization trend is observed, with the value range of 0.573-0.710 in the rocky desertification landscape of Du'an County, Guangxi Province (Jing and Wang 2015).Moreover, it was observed that the diversity index undergoes a sharp rise when the grain size is greater than 190 m, suggesting a threshold effect where an increase in grain size up to a certain point produces a mutational effect (Hu et al 2020).Some scholars have predicted the changes in the landscape diversity index and found poor predictability regarding scale changes (Wu et al 2002, Sheng et al 2003).Other scholars have suggested diverse patterns of change in the diversity index as grain size increases.For example, it rises and then stabilizes, falls and fluctuates, or shows a power function decrease (Chen et al 2016, Wu et al 2021).Based on the results of previous studies, we it was found that the landscape diversity index incrementally increases under the same grain size and stabilizes in an interval as the grain size increases (figures 1(A), (B)) (Cui et al 2016, Yin 2016, Chang et al 2019, Wang et al 2020, Xu et al 2021).As the amplitude widens, the diversity index gradually rises, but when the scale the amplitude increases reaches a to a certain level, the diversity value gradually decreases and eventually stabilizes (figures 1(C), (D)) (Zhang et al 2011, Jing and Wang 2015, Liu and Liu 2016, Huang et al 2018, Kong et al 2018).These signs suggest potential thresholds for landscape diversity under certain conditions.These patterns await further exploration and explanation.
Currently, the main focus is on the study of landscape diversity changes with spatial scales (mapping) and impacts on biodiversity.However, there is no report on the analysis of landscape diversity scale change and landscape diversity threshold from the perspective of landscape component classification.In this paper, we classify the landscape components based on the land use vector data of Gangu County, Gansu Province, analyzes the changing rules of spatial scale of landscape diversity under different classifications, explore the landscape diversity thresholds, determine the appropriate scale domains, and explain some of the inflection points and anomalies.This study is an important supplement to the study of landscape diversity in landscape ecology, providing a theoretical framework for future regional landscape planning and implementation of biodiversity conservation measures.

Study area
Gangu County (latitude 34°31′−35°03′N, longitude 104°58′−105°31′E) belongs to China and is located in the south-eastern part of Gansu Province and the north-western part of Tianshui City, with an area of about 1,572.6 km 2 , and is governed by 13 townships and 2 towns (figure 2).The county has a large area of cultivated land, woodland and grassland, accounting for 78% of the total area.The terrain is relatively flat, with an average altitude of 1972 m, and the surface form is mainly mountains, hills and river valleys, with a temperate climate, four distinct seasons, plenty of light, and an annual precipitation of 365.6 mm.The main rivers in the county are Wei River, Sandu River, Gupo River and Xixiao River.Tree resources are relatively abundant, with 107 species of natural forests and commonly used afforestation species in 32 families and 44 genera in the county.The main food crops are winter wheat, corn, sorghum, grain, soybeans and so on.

Data sources
The basic data of this study were obtained from the land use vector data (Grade III land type) of Gangu County.According to the 'Land Use Status Classification Standard GB/T21010-2017', ArcGIS 10.2 software was used to  fuse and merge grade III land type into grade II land type, and continue to fuse and merge on the basis of II to obtain grade I land type.On the basis of I, II and III land type, individual land types were adjusted to obtain three land use types.We obtained grade III (37), II (34), I (13) land type and three land use types (3), respectively (table 1).Each land type was considered as a landscape component, and the area of each landscape component was counted to facilitate the subsequent calculation of diversity values.

Vector data is converted to raster data
Different allocation types have produced the difference between the actual area and the landscape area, which affects the grain size response of landscape diversity (Hua et al 2022).There are three main principles of attribute allocation in vector data conversion raster data.As shown in figure 3

Selection of a quantitative landscape diversity index
The landscape diversity index reflects the number of landscape components and the proportion of each component, and is quantified by the Shannon Diversity Index, calculated using the following formula: In the formula, LDI is landscape diversity index; pi is the probability of patch type i appearing in the landscape, which is usually expressed as the proportion of the area of patch type i to the total area of the landscape; and m is the total number of patch types in the landscape.

Setting of spatial scale
The vector data of the current land use map was converted to raster data by ArcGIS 10.2 software using the 'field' encryption method (figure 4).There are three main types of image element assignment for vector data conversion to raster data.The method of amplitude change has implications for the analysis of scale effects.There are two gradients of amplitude settings: circular and square.It is particularly important to choose the appropriate amplitude gradient change according to the topographic features of the study area.In this study, the gradient square amplitude setting was chosen to cover the entire study area, making the amplitude effect study more comprehensive.The geometric center of the study area is determined as the center point, and the increase is 1 km square gradually increasing from inside to outside to establish the square gradient zone (figure 5), the minimum buffer area is 1 km × 1 km, and the maximum buffer area is 31 km × 31 km.In order to explore the effect of changing magnitude on diversity at different grain sizes, raster maps of grain I and III were used as examples in this study.After several experiments, raster maps with grain sizes of 10 m, 40 m, 160 m, 640 m and 2560 m were finally determined for the magnitude change study.

LDI classification
The spatial distribution analysis of landscape diversity is based on grading (Dong et al 2023).This study uses the mean standard deviation method to classify (Levy 1974).The grading spacing is set to 4 levels, which are low value partition, medium-low value partition, medium-high value partition and high value partition (table 2).The visual expression of landscape diversity can be realized by reclassifying landscape components according to grading rules.

Fitting of functions of LDI values with spatial scales
The curves of landscape index variation with granularity were fitted and the correlation was tested with the fit R 2 .R 2 close to 1 indicates that the function fits the landscape index with a high degree of predictability.Partial landscape index variation with granularity can be fitted to more than one function, and we chose the one with the higher fit (i.e., the largest R 2 ).

Simulation of LDI variation with landscape component area
The total area of the landscape and the number of landscape components were kept constant, the area of the landscape components was changed, the LDI values were calculated and plotted to express more intuitively the effect of the change in the area of the landscape components on the size of the LDI values.

Differences in landscape area under different allocation types
The total area of the landscape corresponding to each grain size under the CELL_CENTER, MAXIMUM_AREA, and MAXIMUM_COMBINED_AREA allocation types (figure 6(A)).Among them, CELL_CENTER and MAXIMUM_COMBINED_AREA allocation types of landscape area vary similarly, and both have small differences between 10 m-1280 m.The CELL_CENTER allocation type landscape area fluctuates in the process of increasing grain size, with an overall increasing trend, and is more stable compared to the other two allocation types.The difference between the actual total area and the total landscape area of the three allocation types, with the dashed line in the figure representing a difference of 0 (figure 6(B)).The difference between the actual area under each grain size and the landscape area of different allocation types is obvious.The difference between the CELL_CENTER allocation type and the actual area is minimal, the difference between the two is close to zero at grain sizes less than 640 m, with almost no area loss or increase.Therefore, CELL_CENTER is more suitable for landscape analysis in Gangu County.

Idealized landscape diversity threshold prediction
According to Shannon's diversity formula we anticipate that there is a maximum value of LDI in an idealized landscape.Assuming that there are m components in the landscape and the area of each component is equal (i.e., Pi is equal), for m to take the value can be m = 1, 2, 3, 4, 5, 6, 7, 8 KK (for ease of computation we assign m = 1, 5, 10, 15, KK, 500), when m = 1 the corresponding LDI value is 0, indicating that the landscape is homogeneous, and the sensitivity of LDI to changes in the number of landscape components was strong for m less than 50 (figure 7(A)).However, the number of landscape components in a certain landscape is limited, for example, in Gangu County, there are 37, 34, 13, and 3 landscape components for grade I, II, III land type and the three land use types, respectively, and there is a maximum value of the LDI for each classification under the idealized condition (figure 7(B)).Based on this, the vector data were then used as the basis for an in-depth analysis of the LDI values with scale changes, and the actual thresholds were explored.

Factors affecting landscape diversity values and visualization analysis
From the classification system of three land use types, grade I land type, grade II land type and grade III land type, the change of LDI value shows an increasing trend (figure 8).The LDI value (0.4215) of the three land use types is lower than the average value (1.4574), and the LDI value (1.4578) of the grade I land type is basically the same as the average value.It is worth noting that the LDI values of the grade II and III land classification did differ much, being 1.9749 and 1.9754, respectively, which is due to the number and spatial distribution of landscape components are very similar.This suggests that the number of landscape components in a study area is limited, which indicates that there is a threshold for LDI in the determined study area (landscape background).Without     11(A)).From this, it was determined that the appropriate first and second grain size thresholds for the study of landscape diversity in Gangu County are 160 m and 1280 m.Regarding these turning points, we initially judged that the increase in grain size may merge small land patches and reduce the aggregation of different land types, thus changing the number and area of landscape components, which in turn leads to a significant increase or decrease in LDI values.
Curve fitting was performed on the calculated results of the landscape component classification.The results show a good quadratic function fit.Calculate the coordinates of the curve vertex.The vertex coordinates of the three land use types, grade I, II and III land type are (500, 0.4179), (1000, 1.4650), (500, 1.9772) and (500, 1.9777), respectively.In addition, we also found that the curve on the left side of the vertex changes smoothly, and the curve on the right side of the vertex changes steeply.The LDI value corresponding to the 1280 m grain does not fall on the curve, which is due to the rapid increase or decrease of the LDI value corresponding to the  grain size of 2560 m (table 3, figure 11).In general, landscape diversity has a regular pattern with the change of grain size, and the vertex analysis of the curve can pave the way for landscape diversity threshold analysis.

Landscape diversity amplitude change response analysis
The LDI can be divided into three ranges with respect to amplitude: the LDI value decreases between 1 and 2 km, increases between 3 and 9 km, and when the amplitude is greater than 9 km, the LDI value decreases slowly and then tends to stabilize.The LDI values of the three land use types, grade I, II and III land type are the smallest at 2 km, which are 0.3027, 1.2175, 1.3781 and 1.3781 respectively, and the largest LDI values at 9 km, which are 0.5948, 1.5263, 2.0898 and 2.0914 respectively (figures 12(A)-(D)).Differently, the LDI values of the three land use types is more sensitive to changes in amplitude and increase more rapidly in the range of 2-9 km.When it is greater than 9 km, it decreases rapidly to 20 km and stabilizes.Overall, the LDI shows rules of change with amplitude, with differences in LDI values for different grades, such as the effective range of amplitude for grade I, II and III land type is 9-31 km, and the effective range for three land use types is relatively lagging at 20-31 km.
The curve of the response of LDI to amplitude change can be fitted by Logistic function (table 4, figure 12).The results showed that the fitting effect of land grade was better.Among them, the trend of increasing LDI values in 1 km amplitude for grade II and III land types is similar to that of the logistic growth model.It can be inferred that the landscape component of the study area is limited.Therefore, the trend of LDI with amplitude is similar to a logistic growth curve, and LDI stabilizes when the amplitude increases to a certain range.

Analysis of changes in the grain size and amplitude of landscape diversity
We have analyzed the response of LDI to changes in grain size or amplitude.However, the effect of changing amplitude on diversity at different grain sizes needs to be further explored.The LDI values at 10 m, 40 m and 160 m were found to decrease when the amplitude was 2 km, and the LDI values at 640 m and 2560 m increased.When the amplitude is 8 km and the grain size is 2560 m, the LDI value is the largest, and when the amplitude is greater than 9 km, the LDI value under all grain sizes tend to be stable (figure 13(A)).The overall trend of the   Initial values A1 = 0, A2 = 1, x 0 = 5, p = 3 grain size and amplitude change of grade III land type raster map is consistent with the change rule of the grade I land type.However, the difference is that the LDI value decreases rapidly at an amplitude of 4 km corresponding to a grain size of 2560 m (figure 13(B)).It is worth noting that when the amplitude of grade I and III land type is 1 km, the LDI value under the 2560 m grain is 0, indicating that the landscape component is single.In general, when the amplitude is less than 9 km and the grain size is similar (e.g., 10 m, 40 m and 160 m), the trend of LDI with the amplitude is consistent.When the grain size difference is large, the LDI varies greatly with the amplitude.When the amplitude continues to increase from 9 km, the LDI at 2560 m is the largest, and the LDI value at 640 m is the smallest.
Landscape diversity not only depends on the spatial scale, but also has a significant relationship with the researchers' identification of landscape components in the study area.As shown in figure 14, the LDI value of the three land use types (3 landscape components) with the change of grain size is mainly concentrated in about 0.4, and fluctuates around 0.5 with the change of amplitude.The LDI value of grade I land type (13 landscape components) is mainly distributed around 1.45 with the change of grain size, and is distributed between 1.45 and 1.50 with the change of amplitude.The LDI values of grade II (34 landscape components) and III (37 landscape components) land type are concentrated around 1.95 with the change of grain size.The LDI value changes greatly when the amplitude is 1-9 km, and it is stable at about 2.0 when it is greater than 9 km.On the whole, the LDI of a study area is different in different land classification analysis.The LDI value increases step by step at the same particle size or amplitude.The LDI values of the same land classification do not vary significantly with grain size, and the variation with amplitude is range-bound.For example, it varies greatly in the range of 1 to 9 km and stabilizes after greater than 9 km.Therefore, the analysis of regional landscape diversity should consider both the identified landscape components and the appropriate research scale.

Optimal distribution type selection and spatial expression of landscape diversity
There are three attribute assignment types in converting vector data to raster, and the conversion process of different assignment types produces different degrees of error, which is not considered by some researchers and has an impact on the result determination (Cao et al 2010, Li and Wang 2012, Ren et al 2018).In this paper, by comparing and analyzing the difference between the total area and the actual area of the three distribution types of the converted raster landscape, we found that the central element distribution type is applicable to this study, which is consistent with the results of Hua Lin's study (Hua et al 2022).In addition, with the use of medium-high resolution data (land use vector data), the complexity of the landscape pattern interferes with the judgment of the study results.Rational categorization helps to simplify the graphical representation of landscape diversity (Qiao et al 2021).In this paper, the mean standard deviation method is used to classify.The results show that the LDI classification of the three land use types in Gangu County is mainly high-value areas, grade I land type is mainly medium-high value areas, and grade II and III land type partitions are similar, mainly medium-high values.Therefore, LDI visualization and quantitative expression can be realized by grading to explore the spatial distribution of landscape diversity in different classification.4.2.Scale effects on landscape diversity under different classifications Most researchers have selected two 'narrow distance' steps of equal or unequal spacing for grain size change, with a maximum grain size within 500 m.However, LDI has been observed to be less sensitive to small changes in grain size (Li et al 2008, Chen et al 2017, Xu et al 2021).Therefore, this study uses the 'field' encryption method to explore the rule pattern of diversity change with grain size.Based on the scale effect under different classification systems, it was pointed out that the first and second grain size thresholds most suitable for landscape analysis in Gangu County were 160 m and 1280 m, which are suitable for biodiversity research and spatial planning.The inflection point of 320 m is due to the decreased number of recognized landscape components and the large difference in area, resulting in a rapid decline in the LDI value.Research on scale effect is also affected by the resolution of basic data and the scope of the study.Therefore, changes in LDI were explored by altering the range (amplitude) size of the study area.With a minimum amplitude of 1 km from the geometric center, the LDI exhibited its lowest value.When the amplitude was doubled to 2 km, there was an increase in LDI value.The trend continued as the amplitude increased to 9 times (9 km).The LDI continued to increase before leveling off.At an amplitude of 2 km, only a few captured landscape components are captured (three land use types: grade I, II and III,with 3,12,24 and 24 components,respectively).The proportion of each type is quite different.For example, under II and III classification systems, the proportion of dry land reached 62%, and the proportion of facility agricultural land, hydraulic construction land, special land and highway land were all below 1%.On the contrary, the landscape components gradually increased and became relatively more evenly distributed when the amplitude increased to 9 km.The LDI value stabilized as the amplitude continued to increase.
There are few studies that simultaneously vary the grain size and amplitude to analyze landscape indices, and the existing studies only use moving window size in raster maps at suitable spatial analysis grain to explore the variation rules of landscape indices (Chang et al 2019).In this paper, through many experiments, based on the 10 m raster map, the amplitude changes under 4, 16, 64, 256 times of grain size changes were carried out to explore the scale dependence of diversity.The results suggest that it is more reliable to select a large area to study landscape diversity when the grain size is larger (lower resolution).This is similar to the analysis results of some researchers, which showed that the appropriate grain size for the study of the Manas River Basin is 400-2000 m (Han and Tang 2017), and the 800 m grain size can stably reflect the changing law of landscape index while accurately retaining the information of land cover area in the upper reaches of the Dadu River (Bai et al 2009).

Analysis of landscape diversity thresholds
Collating the results of previous studies reveals that there may be thresholds for landscape diversity (figure 1).We did further verification and the results showed that the threshold of landscape diversity in Gangu County without considering the scale change can be understood as 0.4215 LDI 1.9754.The threshold discussion is related to the number of landscape components, the more landscape components the greater the LDI value (grade III land type > grade II land type > grade I land type > three land use types), which is similar to the conclusions obtained by organizing and analyzing the results of previous studies (table 5) (Xu et al 2007, You et al 2008, Bai et al 2009, Mo et al 2012, Xiao et al 2015, Han and Tang 2017, Zhai et al 2018, Chang et al 2019).For example, Mo identified 18 landscape components with the study area of Yingluo Mangrove, and the LDI values were 2.0224 and 2.0210 at the appropriate grain size of 60 m and 80 m, respectively.There is also a special case, Zhai identified 20 landscape components in the Qinghai Lake Basin, and the LDI value is 1.9351 under the appropriate grain size, which suggests that the landscape diversity is not only related to the number of components in the landscape, but also may be related to the distribution of the components (size, shape, aggregation, etc), which can be explored in depth in the subsequent work.Three landscape components were identified in the three land use types at a amplitude of 2 km, which had the smallest LDI value (0.3027), and 37 landscape components were identified in the grade III land type at a amplitude of 9 km, which had the largest LDI value (2.0947).This indicates that the number of captured landscape components changes during the amplitude increase, and the number of landscape components is the highest when the amplitude increases to a certain degree, corresponding to a relatively large LDI value, which is similar to the results of previous studies (table 6) (Xu et al 2004, Xu et al 2007, Bi and Gao 2012, Liu and Liu 2016, Huang et al 2018, Kong et al 2018, Liu et al 2019, Zhang and Liu 2019, Hu et al 2020, Yang and Liu 2021).However, there are special cases, when we should take into account the distribution status of landscape components.Therefore, the threshold value of landscape diversity in Gangu County in combination with the amplitude analysis can be understood as 0.3027 LDI 2.0947.

Landscape background affects landscape diversity
The landscape background also affects the results of landscape diversity judgments, and the results obtained from selecting different study areas can vary.For example, Hammill produced a set of simulated landscapes to study the relationship between the increase of environmental differences at the landscape level on the impact of diversity indicators and ecosystem functions.The results showed that with the increase of environmental differences at the landscape level, the relationship between diversity indicators and ecosystem functions was strengthened (Hammill et al 2018).Some researchers have also selected 25 landscape systems in islands and studied the effects of management on the diversity and composition of grassland community plants in current and historical landscape background (Schmucki et al 2012).In addition, landscape hotspots in a larger region can be identified by the size of landscape diversity in various natural landscape types or landscape areas.For example, Slovenia has the highest average landscape diversity and is identified as a very diverse place in Europe (Ciglic and Perko 2013).Due to space limitations, this section of the paper on the analysis of landscape diversity in different landscape background is completed in a follow-up.

Supplementary
Finally, it is necessary to add two points: (1) In this study, the relationship between grain size and LDI is close to the quadratic expression by 'field' encryption, and the relationship between amplitude and LDI is close to the logistic curve by using the geometric center as the starting point and a 1 km rectangular outward envelope, both of which may be contingent and need to be supported by a large number of experiments later on.Therefore, this paper does not focus on this discussion.(2) The LDI value calculated by the prepared tiff file directly imported into fragstats software is different from the LDI value calculated by the borrowed formula in excle software,

Conclusion
This study focuses on analyzing the rule of change of landscape diversity under the classification of landscape components.It was found that there are obvious differences in landscape diversity between different classifications, and that there exists a threshold value for landscape diversity in the case of the study area, and the analysis of the threshold value should take into account both grain size and amplitude.

Figure 1 .
Figure 1.Landscape diversity index changes with scale.

Figure 2 .
Figure 2. Geographical location of the study area.
: (1) Central factor allocation (CELL _ CENTER): The face element 'a' located at the center of the raster cell determines the attributes of the image element.(2) Maximum area allocation (MAXIMUM_AREA): The single element 'b' with the largest area in the raster cell determines the attributes of the image.(3) Maximum consolidated area allocation (MAXIMUM_COMBINED_AREA): When multiple elements with the same attributes are combined in a raster cell, the element 'c' with the largest area determines the value of the image element.
According to the allocation type, the grid data with grain size of 10 m × 10 m, 20 m × 20 m, 40 m × 40 m, 80 m × 80 m, 160 m × 160 m, 320 m × 320 m, 640 m × 640 m, 1280 m × 1280 m and 2560 m × 2560 m are converted to select the best allocation type.

Figure 3 .
Figure 3.The principle of distribution of attributes of center, maximum area, and maximum combined area.

Figure 6 .
Figure 6.Difference of actual landscape area and landscape area of different grain under the allocation types.

Figure 7 .
Figure 7. Variation of LDI maxima with the number of landscape components.

Figure 8 .
Figure 8. Changes of landscape diversity index different grades.

3. 4 .
Response analysis of spatial scale changes in landscape diversity 3.4.1.Response analysis of grain change of landscape diversity.LDI varies regularly with grain size.The LDI is essentially stable at grain sizes from 10 to 160 m.For the grade I, II and III land type 320 m is a turning point, and in the grain size from 1280 to 2560 m continue to increase the LDI value decreases sharply (figures 11(B)-(D)).For three land use type 640 m is a turning point, and the LDI increases sharply when the grain size increases from 1280 to 2560 m (figure

Figure 9 .
Figure 9. Simulation of LDI variation with landscape component area.

Figure 10 .
Figure 10.Spatial distribution of LDI at different grades.

Figure 11 .Figure 12 .
Figure 11.Variation characteristics of LDI of different grades with grain size.

Figure 13 .
Figure 13.Variation curves of landscape diversity indices at different spatial scales.

Figure 14 .
Figure 14.Scale variation of LDI of different grades.

Table 1 .
Land use status classification in Gangu County.

Table 2 .
Landscape diversity index classification.
LDI: landscape diversity index, M: mean, SD: standard deviation.The mean value of different landscape components in the study area was 0.0910, and the standard deviation was 0.0367.

Table 4 .
Mathematical model of LDI variation with amplitude.

Table 5 .
Statistics of LDI values under appropriate granularity in different study areas.

Table 6 .
LDI statistics under effective amplitude in different study areas.fragstats software has limitations in the identification of components in complex landscapes.It is more accurate to calculate the LDI results based on the statistical area of the attribute table. because