Fig. 1 Schematic diagram of the grazing experiment treatments. Dark
color treatments indicate sampled treatments. The grazing experiment
treatments (each ca. 4.4 ha) were arranged in a randomized complete
block design, which included four grazing intensity treatments with
three repeats at each grazing intensity.
Vegetation sampling
Within each randomized block of different grazing intensities, a
representative sample plot with the same terrain (5 m×5 m) was selected.
The origin of the coordinate in each sample is defined as the upper left
corner of the sample. Within this sample plot, a 1 m×1 m sample frame
was placed 25 times in turn, and the precise spatial position ofS. breviflora and C. songorica in the sample is determined
by the tape. In this fashion we measured the population density ofS. breviflora and C. songorica on 15 August 2019.
Data analysis
The population density of S. breviflora and C. songoricawere tested for homogeneity of variance (P < 0.05), and
they all obeyed normal distribution. A generalized linear model (GLM)
was used to test the effect of grazing intensity on the density ofS. breviflora and C. songorica . A Duncan test (Levene
homogeneity test) was used to identify significant pairwise
relationships among the different grazing treatments. By using several
quadrats, we could also identify how sampling size may have influenced
our results. To that end, we split the sample size of 5 m×5 m into 5
cm×5 cm, 10 cm×10 cm, 20 cm×20 cm, 25 cm×25 cm, 50 cm×50 cm and 100
cm×100 cm. Data was square-root transformed to meet a normal
distribution, and variance analysis was used to compare the density
changes of S. breviflora and C. songorica under different
grazing intensities and across these increasing spatial scales.The
bidirectional GLM method was used to test the effects of grazing
intensity and spatial scale on the density of S. breviflora andC. songorica , and the generalized linear model was used to test
the effect of spatial scale on the density of S. breviflora andC. songorica . In order to analyze the synergistic change of
density with scale of S. breviflora and C. songorica in
different grazing intensities, the scatter diagram of density ofS. breviflora and C. songorica indifferent grazing
intensities was drawn, and the linear fitting (using MS data) was
carried out (r 2 represents the determination
coefficient). The analysis of variance was performed using SAS 9.4 (SAS
Institute Inc.), and a threshold of P < 0.05 level was
used to assay significant relationships. Assembly process and graphics
rendering are completed in Sigmaplot 14.0 (Systat Software, 2011).
To study the inter-specific association of S. breviflora andC. songorica in desert steppe, the plot of 5 m×5 m was regarded
as a plant community in this study. We used the Jaccard index to
evaluate the strength and direction of inter-specific plant
relationships (Guo et al., 2014). The Jaccard index is negatively
correlated with competitiveness, and positively correlated with
affinity. The calculation formula of Jaccard index is:
CJ =j /(a +b +j )
In the formula, CJ is the Jaccard index; j is the number
of small quadrats with S. breviflora and C. songorica ;a is the number of small quadrats with only S. brevifloraand without C. songorica ; b is the number of small
quadrats with only C. songorica and without S. breviflora .
By repeating this analysis across the various spatial scales (ranging
from 5 cm×5 cm to 100 cm×100 cm), we could evaluate if the strength and
direction of these inter-specific relationship was impacted by sampling
size.