community richness, height, coverage, and 1 spatial distribution mediate grasshopper 2 abundance in the upper reaches of Heihe 3 River ， China

: Species interactions are often context-dependent and complex, such as the 6 grasshopper community and phytoecommunity. The adaption of grasshopper 7 abundance and plant community were determined by topographical heterogeneity. 8 However, it remains vague about how vegetation community, such as coverage, 9 abundance and height, influence the spatial distribution pattern of grasshopper 10 abundance at the altitude gradient. The geostatistical methods were used in natural 11 grassland of the upper reaches of Heihe River to quantify the relationship of spatial 12 correlation. A 5-years investigation shown that 3149 of grasshoppers was collected ， 13 belonging to 3 families, 10 genera, and 13 species. The semivariable function of 14 grasshopper abundance and vegetation community followed a nonlinear model. 15 Meanwhile, horizontal distribution of two communities was a clear flaky and plaque 16 distribution pattern, especially at the altitude gradient. The abundance of grasshoppers 17 is opposite to the height and coverage of vegetation and the overall follow ability of 18 coverage, while the local following is consistent. Such as grasshopper abundance, the 19 above 2750m sample with the opposite trend, the following areas were consistent. The 20 grasshoppers exhibited the varieties on vegetation characters among all directions. On 21 the different habits, the spatial distribution formed uniform trends; meanwhile, on the 22 same, the trends diversified with altitude gradient, formed embedded striped patches 23 structure.


Introduction 29
Environment heterogeneity is the key influence on the dynamics and structure of 30 ecological communities (Aranda and Olivier 2017;Pickett and Cadenasso 1995;31 Turner, et al. 1989;Viviansmith 1997), and reflect changes in functions and processes. 32 Spatial heterogeneity in ecological systems maintains that all interactions between 33 biotic and abiotic factors. All of them arose from the differential responses of 34 organisms to these factors and the organisms themselves (Milne 1991) and the 35 organisms themselves (Huston 1994). The heterogeneity was a complexity and 36 variability in the ecological system (Gustafson 1998;Li and Reynolds 1994;Wagner 37 and Fortin 2005), especially after carved by topographic fragmentation. Quantifying 38 spatial heterogeneity was a practical way to canvass the ecosystem structure 39 and figure out the relationships among the ecological community in space. Therefore, 40 evaluating the effect of topographical heterogeneity is the basis for recognizing the 41 spatial correlation between the grasshopper abundance and vegetation. 42 Grasshopper was widely distributed in the world and an important component of 43 temperate grassland (Branson, et al. 2006;Samways 1993). There was highly 44 sensitive for grasshopper to change in environmental conditions (Samways and 45 Sergeev 1997), such as grazing, fire, and land type conversion. Moreover, it also was 46 the dominant native herbivore (Guo, et al. 2006) and cause extensive damage to 47

Sampling design 123
The study area belongs to the middle of Qilian Mountains, including alpine 124 desert, alpine steppe, and alpine meadow. We selected a non-grazing grassland area to 125 carry out the composition study. During the year of 2009 to 2013 in mid-July, 36 sites 126 were established on the grassland. The sites were located within a 3500 m ×900 m of 127 area, ranged in elevation from 2300m to 2800 m, and were randomly chosen to 128 include a range of grassland types (Fig. 1b)

Sampling preparation and identification 146
Grasshoppers' specimens were stored in 70% ethanol and later dry mounted and 147 sorted to morph-species based on external characters and general appearance. Genus 148 and/or species were identified according to the Insect Mathematic Ecology (Ding 149 1994). The abundance of grasshoppers in each plot was calculated according to 150 mean of three replicates of each plot. A 5 years investigation was shown that 3149 151 grasshoppers were collected, belonging to 3 families, 10 genera, and 13 species.

Estimation and modeling of spatial autocorrelation 154
Semivariograms was selected to evaluate the spatial variation (E. Rossi,et al. 155 1992; Sciarretta and Trematerra 2014), after analyzing correlation coefficient, 156 covariance (in covariance functions) and variance (in semivariograms). 157 Semivariograms function expresses the variation of two regionalized variables 158 the Semivariograms of sample pairs against the distance between sampling 160 points (Kemp, et al. 1989;Zurbrügg and Frank 2006). The formula is: 161

Spatial trend analysis 169
A trend-surface analysis was set on spatial sampling data to fit a mathematical 170 surface and used to reflect the change of spatial distribution. It can be divided into two 171 parts: the trend surface and the deviation. The trend surface reflects the trend of the 172 spatial data, which is influenced by the whole situation and the wide range of factors 173 (Cane, et al. 2017;E. Rossi, et al. 1992). Each vertical bar in the trend analysis graph 174 represents the value and position of a data point. These points are projected onto an 175 east-west and a north-south orthogonal plane. An optimal fitting line can be obtained 176 through these projection points, which can be made to simulate the trend in a 177 particular direction. If the line is straight, it is indicated that no trend exists. Spatial analysis of grasshopper abundance index (Table 1) showed good model 181 and (67.05% variance attributable to spatial autocorrelation) spatial structure. The 182 spherical model was selected to describe the semivariograms for grasshopper. The 183 parameter " a " in grasshopper was 9.32m (Table 1)

Spatial trends in grasshopper abundance and vegetation community 200
Based on the rule of principle of uniform distribution of projection points on 201 perspective surface of sampling, the aspect of northeast-southwest and 202 northwest-southeast was selected on vegetation and grasshoppers (Fig.2). The 203 altitude is reducing from northwest to southeast. 204 The spatial trend of grasshopper abundance indicated that the direction of 205 northeast-southwest was more intense than in northwest-southeast (Fig. 2a); the 206 graphical representations inhibited an inverted "U" shape distribution. While the 207 trends on northwest-southeast a Step-like transition was reflected. The region with the 208 maximum abundance value was in the altitude of 2530m -2700m (Fig.2b), the 209 0 c grasshopper populations' assumed highly localized distributions on the middle 210

elevation. 211
On the vegetation community, the spatial trend of vegetation height was 212 confirmed in the direction of northeast-southwest, with a gradient across rows (Fig.  213   2b). The spatial trend of the vegetation coverage on northwest-southeast was 214 identified shaped a ladder-like distribution (Fig. 2c); while on the northwest-southeast, 215 the trend was obviously appeared an inverted "U" shape. The vegetation richness 216 spatial trend exhibited a higher tendency in northeast-southwest than 217 northwest-southeast (Fig. 2d), shaping a "U" distribution at northeast-southwest and 218 an inverted "U" on northwest-southeast. Among the spatial distribution on vegetation, 219 the high coverage consisted with lower height; however, the spatial distribution on 220 height was similarity to abundance, centered in the area of middle elevation. 221

The relationship between Grasshopper abundance and Vegetation Community 222
According to the spatial distribution of vegetation community (height, coverage 223 and abundance) and grasshopper richness, the relationship was found. The properties 224 of grasshopper abundance must be affected by vegetation community and sample 225 location (altitude). The effects of sample altitude on grasshopper abundance and 226 vegetation community were shown in Fig.3. Basically, grasshopper abundance 227 decreased with lower vegetation height; that is, most species of grasshoppers 228 preferred to distribute on the low altitude (Fig. 3a). Totally, the spatial pattern on 229 grasshopper abundance and vegetation coverage were distinct; despite of the altitude 230 of 2700m-2750m were similar, such as the samples of 11, 12 and 13 (Fig. 3b). The 231 relationship between grasshopper abundance and vegetation richness was highly 232 depending on altitude; altitude below 2750m, diversity of grasshopper species was 233 similar to vegetation's; while, the distributions were contrary above 2750m (Fig. 3c). 234

Fuzzy neartude of grasshoppers' abundance and grassland community 235
According to the uncertainty and dynamics of the community in nature, the fuzzy 236 negritude similarity was used to analyze the intensity and structure of spatial The grasshopper habitat selection was prior on vegetation, relied the altitude as 242 well ( Table 2). The correlations between grasshopper and vegetation were complex. 243 The grasshopper abundance and vegetation richness were positive correlation with 244 high fuzzy nearness value (F=0.68) ( grasshopper spatial pattern probability reliance on altitude, such as a small fuzzy 250 nearness value 0.32 presented in positive correlations (Table 2). 251

252
Spatial heterogeneity was a key point to influence the patterns and changing the 253 relationship on spatial space (Huang, et al. 2017b;Kemp, et al. 1989;Laws and Joern 254 2017). It was a big challenge to predict that the heterogeneity of grasshopper patches 255 is critical factors that influenced by foraging selectivity and habitat heterogeneity. On 256 the research, the results showed that grasshopper species were good at selecting a 257 micro-environment to habitat. The semivariable function of grasshopper abundance 258 and vegetation community was a nonlinear model in geo-statistics; the curves meant 259 that the spatial distribution pattern was aggregated on ecology (Wang, et al. 2010;260 Zhong, et al. 2014). The grasshopper abundance typically produces special 261 heterogeneity with larger range and nuggets than vegetation community (except the 262 range of vegetation coverage in model). The range values were likely to be undetected 263 spatial distance smaller than the 1.5m. Based on the spatial pattern, the grasshopper 264 habitat selection was prior on vegetation community. Heterogeneity on grasshopper 265 distribution was directly influenced by herbivore foraging decisions (Wiggins, et al. 266 2006;Zhu, et al. 2015), probability determined by the topography of Qilan mountains 267 (Li, et al. 2011;Li, et al. 2013;Zhao, et al. 2012), micro-climate and soil condition. 268 The result confirmed that horizontal distribution of two communities presented a flaky 269 and plaque distribution pattern, with obvious heterosexual structure (Huang, et al. 270 2017b;Yan and Chen 1998;Zhao, et al. 2012;Zhao, et al. 2009). 271 The exploratory analysis of ecological community data revealed that the trends 272 were variable in a different method. According to the traditional biostatistics, correlation between grasshopper abundance and plant height presented negative, 274 while the positive correlation exhibited in grasshopper abundance and plant coverage 275 (Zhou, et al. 2011). However, on geostatistics, the relationships between two 276 communities were much more complex, the altitude influenced distribution. Such as 277 altitudinal support a positive relationship between two communities in total, but does 278 exist at every stage of elevation. The result testified that alpine grasshoppers were an 279 important adaptation to the mountain environment (Vandyke, et al. 2009;Wachter 280 1995). to the influence of the altitude, the community was an appearance in the specific area, 286 such as the altitude from 2500m-2700m was the species richness area (Fig.1b, Fig.3). 287 Furthermore, the plant was not only food resources, but also habitat environment for 288 grasshopper. The zone of 2500m-2700m, a transition zone between desert steppe and 289 mountain steppe, with good coverage and richness of plant, was high grasshopper 290 abundance. Lower height provided a wide view to defend predators, good 291 transmittance to keep warm, high coverage and richness to compensate for 292 grasshopper herbivore. Most of species prefer forest or jungles, most lived in dry, 293 hard soil and open habitats with low vegetation height. Yet, the alpine meadow 294 grassland and mountain shrubby-grassland lay above 2750m, with moisture, 295 impermeability, and compactification soil, resulting massive layer of grass felt (Li, et 296 al. 2011;Zhao, et al. 2012). It was difficult for grasshoppers to spawn in soil or keep 297 eggs dry, forming a plaque heterogeneity structure between vegetation and 298 grasshopper with different elevation gradients. 299 The spatial distribution trend reflected that the spatial heterogeneity of vegetation 300 communities and grasshopper appeared evident multiformity in different directions. 301 The trend of grasshopper abundance on the direction of northeast-southwest was more 302 intense than in northwest-southeast. In vegetation communities, the strong trend of the 303 distribution between height and abundance was consistent in northeast-southwest, 304 while the coverage was on northwest-southeast. The results showed that the weather 305 and season took an important part in determining the abundance of grasshopper